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Using the Coefficient of Variation to Detect Sincerity of Effort of Grip Strength
[
S~~~NTIF~C/CL~ICAL~~TI~LES J
Using the Coefficient of Variation to Detect Sincerity of Effort of Grip Strength: A Literature Review Orit Shechtman, PhD, OTRIL
ABSTRACT: Many clinicians use the coefficient of variation (CV) to assess sincerity of effort, without understanding the premise on which it is based or its physiological and mathematical bases. Clinicians who use computerized evaluation systems that calculate the CV may not even be aware of the formula used to derive it. The wide use of the CV in detecting sincerity of effort of grip strength is puzzling, since it lacks empirical support in the literature. This paper examines the physiological rationale for using measures of variability to detect sincerity of effort, the mathematical basis on which the CV is founded, and the reliability and validity of the Cv. The conclusions based on this literature review are that the CV is not an appropriate method for determining Whether an effort is sincere and that CV values may be inflated in injured patients with compromised hand strength. J HAND THER 13:25-32, 2000
Department of Occupational Therapy College of Health Professions University of Florida Gainesville, Florida
espite contradictory research findings and
D lack of strong empirical support, the co-
efficient of variation (CV) is widely used to determine sincerity of effort of grip strength measurements. 1 - 3 Many clinicians judge whether a patient's effort is sincere on the basis of the value of the CV that they derive from a computer output. Therapists who use the CV must understand its premise and the rationale on which it is based. Therapists must also know how the CV is derived and be able to discern whether it is a valid measure of sincerity of effort. The CV is the most common measure of variability used to determine sincerity of effort in isometric strength tests. The formula used to derive the CV is the standard deviation (SD) divided by the average of at least three trials and multiplied by 1004 : CV = (SD/average)
X
100
A greater CV indicates greater variability and smaller consistency. A threshold or cutoff value is usually established for the Cv, above which the effort is considered inconsistent enough to be labeled Correspondence and reprint requests to Orit Shechtman, PhD, OTR/L, Department of Occupational Therapy, College of Health Professions, University of Florida, Gainesville, FL 32610.
submaximal and, therefore, interpreted as insincere. 2,5 This literature review examines the issues surrounding the use of the CV in detecting sincerity of effort. First, a short overview of grip strength and the need for detecting sincerity of effort is provided. Next, the rationale for using measures of variability in detecting sincerity of effort is examined. Finally, the use of the CV to determine sincerity of effort is scrutinized.
GRIP STRENGTH Isometric (static) strength is the amount of muscular force applied by a muscle or group of muscles when it contracts against an immQvable apparatus. The most common and reliable instrument used to evaluate isometric grip strength is the Jamar dynamometer. 6 ,7 Grip strength measured with the Jamar dynamometer is a good indicator of hand function, as suggested by the significant correlations between grip strength and both symptom severity and functional status of the hand. 8 However, grip strength is an objective, reliable, and valid measurement of hand strength only when a patient exerts maximal voluntary effort? Therefore, sincerity of effort can affect the reliability and validity of the test.
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Grip strength measurements are frequently used to estimate physical work capacity, match job requirements to a patient's work capability, determine disability, and assess a patient's ability to return to work after injury.9-11 Furthermore, grip strength measurements are used to determine the extent of worker's compensation awards/ 2- 14 since grip strength is often proportional to the loss of strength in an injured arm. IS It is clear, therefore, that a valid determination of sincerity of effort is essential. Many methods and testing procedures have been developed by researchers to detect sincerity of effort. None of the assessments designed for detecting sincerity of effort has been universally accepted. 1,2,16-31 Assessments such as the five-rung test/ 8- 20 the rapid-exchange grip test/1-24 a combination of multiple grip tests,13 and a combination of these methods 17,25 lack reliability and validity values, norms, and standardized testing protocols. Other assessments have been rejected for being too complex (requiring complicated and expensive equipment, elaborate calculations, or lengthy administration time) and therefore unsuitable for clinical use. These include producing a force-time curve and examining its various characteristics26 -28 and studying the electromyographic nature of maximal and submaximal grip.29,3o Generally, research findings on the effectiveness of the various assessments in detecting sincerity of effort are contradictory.1,2,16-31 Consequently, detecting whether a patient is exerting maximal and sincere effort remains problematic. 17
PHYSIOLOGICAL RATIONALE FOR USING MEASURES OF VARIABILITY TO DETECT SINCERITY OF EFFORT Many of the methods used to detect sincerity of effort are based on measures of variability. * The reason for using measures of variability to determine sincerity of effort stems from the notion that a faked, submaximal exertion shows more variability and less consistency in repeated tests than a maximal voluntary effort.9 Kroemer and Marras 27 refer to the German literature in the 50s and 60s where that premise was presented. On the basis of motor unit recruitment patterns, they developed a model explaining why the variability of repeated grips will be greater in submaximal than in maximal muscular contraction. Motor unit recruitment is achieved by one of three mechanisms. The first is rate coding (speed), which regulates the frequency of firing of motor units. The second is recruitment coding (sequence), which controls the type and the number of contracting motor units. The third is a combination of both. 32 -35 During maximal effort, the muscle is activated by the motor cortex through both maximal *References 3, 11, 12, 15, 17, 26-28, 31.
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frequency of neuronal firing (rate coding) and maximal recruitment of all available motor units (recruitment coding). This generates a synchronous pattern of motor unit firing. Therefore, during maximal effort many motor units are recruited simultaneously.32,33 On the other hand, during submaximal effort both the motor cortex and the cerebellum have to mix and precisely control both submaximal frequency of firing and recruitment of a certain number and a certain type of motor units. 34,35 Repeating any muscular contraction requires afferent (sensory) feedback and efferent (motor) control. A maximal muscular contraction is theoretically easier to replicate because it does not require the proprioceptive feedback necessary to grade and limit contraction. Maximal contraction requires only the simplest motor control, which includes both maximal firing frequency and maximal motor unit recruitment and is independent of rate control. Consequently, a maximal effort represents a "lower-order task.,,26,27 On the other hand, repeating a sub maximal effort, according to the Kroemer and Marras model/7 requires extensive and complex afferent feedback signals to the central nervous system as well as precise recruitment coding and rate coding. This involves continual corrections of the motor signals and represents a "higherorder task," which is more difficult to replicate, takes longer to achieve, and results in greater variability than does repetition of a maximal effort. 26,27 Despite this theory about the consistency of repeated maximal and submaximal efforts, the literature indicates that increased variability between trials may not necessarily indicate malingering or willful deception. Variability is inherently present in repeated measurements-as, for example, in the day-to-day variability between repeated strength trials in healthy subjects. Although Bechtol6 reported a daily variation of 10% or less in grip strength when it was measured at the same time each day, Young et al. 36 showed that mean grip strength fluctuated between 19.2% and 23.7% when measured twice a week for three weeks. Furthermore, some studies indicate that submaximal efforts of certain isometric tasks, such as lumbar extension and elbow, plantar, and hip flexion, can be reproduced consistently.1,2,37,38 Ashford et a1.,12 using the Jamar dynamometer, found no significant differences in variability of grip strength between maximal and submaximal efforts in 22 healthy subjects. Moreover, Robinson et al. 3 suggested that fear, pain, psychological distress, and self-efficacy may increase variability between trials. Indeed, Mitterhauser et al. 17 found that the CV of three grip repetitions was significantly greater in an injured group than in an uninjured group. Therefore, the validity of using variability measures to detect sincerity of effort is questionable despite the theoretical basis for the motor unit recruitment model. Common measures of variability (dispersion) of data include the range, the variance, and the standard deviation, all of which are measures of absolute variability.4 Most measures of variability used to detect sincerity of effort, however, are mea-
sures of relative variability, expressed as a percentage of the mean. Two measures are calculated by dividing a measure of absolute variability by the mean of three or more grip trials: The CV is calculated by dividing the standard deviation by the mean of three strength trials 3,4,1l,31; the other measure is derived by dividing the range (maximum minus minimum) by the mean of three strength trials. 12 The advantage of these measures is their simplicity. They are based on three or more repetitions of any isometric strength effort and are very easy to calculate. Their disadvantage is that they have not been shown to distinguish between maximal and submaximal efforts. 3,12,38
TABLE 1.
THE COEFFICIENT OF VARIATION The Cv, which is based on repeated trials, has been used in conjunction with isometric strength tests of the trunk, legs, and arms 9 ,1l,27,31,37-42 and with grip strength tests?,17 The cutoff value for the CV in the related literature varies greatly and ranges from 10% to 20%.1-3,5 A CV greater than the cutoff values suggests that the effort is inconsistent enough to be labeled submaximal and insincere, The CV values reported in the literature for isometric strength testing of grip, upper extremities, and trunk are shown in Tables 1, 2, and 3, respectively.
Coefficients of Variation (CVs) of Isometric Grip Strength Tests Reported in the Literature
Assessment Tool
Author Mitterhauser et al., 1997'7
NK DIGIT-Grip
Population
Type of Effort
CV(%)
Uninjured subjects
Maximal Sub maximal Maximal
2.8-3.5 13.8-14.5 8.1-8.5
Injured subjects 3
Robinson et al., 1993
Jamar dynamometer
Uninjured subjects
Maximal Submaximal
3.8-4.3 9.3-12.6
Chengalur et al., 199015
Modified Jamar dynamometer with force transducer
Injured men
Sincere Faking Sincere Faking
5.9 8.7 6.9 9.6
Sincere Faking
4.9 16.5
Injured women Smith et al., 198928
TABLE 2.
Modified Jamar dynamometer with force transducer
Uninjured men
Coefficients of Variation (CVs) of Isometric Efforts of Upper Extremity Movements Reported in the Literature
Assessment Tool
Population
Supination
Niemeyer et al., 1989
9
BTE Work Simulator
Uninjured men Uninjured women
8.7-13.8 11.5-16.3
Pronation
Niemeyer et al., 19899
BTE Work Simulator
Uninjured men Uninjured women
8.6-12.1 8.8-14.1
Elbow flexion
Niemeyer et al., 19899
BTE Work Simulator
Uninjured men Uninjured women
9.9-10.4 7.6-11.0
Elbow extension
Niemeyer et al., 19899
BTE Work Simulator
Uninjured men Uninjured women
8.5-10.1 10.3-12.4
Kroemer and Marras, 198027
Dynamometer
Uninjured men Uninjured women
3.9-4.8 3.9-4.6
Bohannon, 198731
Dynamometer
Uninjured women
Movement
TABLE 3. Movement Lifting
Author
Trunk flexion
,,;7.5 (max) 4.3-76.1 (submax)
Coefficients of Variation (CVs) of Isometric Efforts of Various Trunk Movements Reported in the Literature
Assessment Tool
Author
Population
CV(%)
Harber and SooHoo, 198440
Unnamed apparatus
Patients (back pain)
Simonsen, 1995"
ERGOS Work Simulator
Patients (back pain)
6.09-11.95
Unnamed apparatus
Uninjured men Uninjured women
6.0-8.4 7.1-10.0
Unnamed apparatus
General population
4.72
Unnamed apparatus
General population
6.35
Zeh et al., 1986 Trunk extension
CV(%)
42
Biering-Sorensen, 198439 39
Biering-Sorensen 1984
13.2-17.7
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The CV is used by numerous clinicians and is incorporated into many evaluation systems, despite contradictory findings and lack of empirical support. The evaluation systems utilizing the CV include Blankenship (Blankenship Corp., Macon, Georgia), Key (Key Assessment, Minneapolis, Minnesota), Ergos (ErgoScience, Birmingham, Alabama), the BTE Work Simulator (Baltimore Therapeutic Equipment Co., Baltimore, Maryland), and the GreenLeaf (GreenLeaf Medical Technologies, Palo Alto, California).s In these work evaluation systems, the computer calculates the CV, which is then viewed on the computer screen or on a printout. The CV produced by the instrument may be misleading if the clinician does not know the mathematical basis for the computation.
MATHEMATICAL RATIONALE FOR USING THE COEFFICIENT OF VARIATION The CV is a measure of relative variability (dispersion) of data and is widely used with measurements other than those of isometric strength. It is valid to use the CV in only one of the following three conditions. In the first condition, the CV is used as a common measure of risk. 4,43 This is not relevant to grip strength. In the second condition, the CV is used when com~aring dispersion of data that are in different units. 4, Since static grip is measured in only one type of force unit at a time, the use of the CV for this reason is not justified. In the third condition, the CV is used when the magnitude (average) and the variability (standard deviation) of a set of scores increase proportionally.us The use of the CV with grip strength measurements is based on this third condition. In some measurements, such as spirometry and blood concentration of hormones and glucose,46-48 the average and the standard deviation do indeed change proportionally, so it is valid to use the CV to express variability in these measurements. In other words, the CV is used appropriately only when the average and standard deviation tend to change proportionally.4 An example of an appropriate use of the CV is a comparison of the nose lengths of mice and elephants49 (Table 4). Because the nose lengths of the two species are very different (6' and 0.07", respectively), the absolute variability is larger for the longer elephant nose. In other words, the standard deviation of an elephant nose may be 0.5', whereas the standard deviation of a mouse nose may be 0.005". In this situation, the average and the standard deviation change proportionally; that is, the greater the average, the greater the standard deviation. To compare the variability between the two species, the average nose length has to be taken into account. While the absolute variability (standard deviation) is 6" for the elephant nose versus 0.005" for the mouse nose, the relative variation as expressed by the CV is 8.3% for the elephant nose and 7.1% for the mouse nose. Consequently, the CV compares the variability in 28
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nose length more directly by expressing the standard deviation as a percentage of the average. In this situation, the CV is valid. For the CV to be a valid measure of sincerity of grip strength, the third condition has to be met; that is, the average and standard deviation of repeated grip trials must increase proportionally. In other words, the CV would be used appropriately only if people with greater average grip strength exhibited greater variability (standard deviation) than those with lesser average grip strength. Robinson et aP acknowledged this requirement by asserting that "it is expected that larger torque values will also show greater absolute variability." Thus, the CV allows the researcher or clinician to compare the variability of two groups with potentially widely different overall strength. Three studies, however, contradict this assertion. A study by Krombholz so examined the means and standard deviations of different percentages of maximal grip strength in 24 right-handed male university students, using a hand dynamometer manufactured by Martin Inc. The levels of effort were 30%,50%,70%, and 90% of maximal grip strength. Although this study did not examine the CV, the results clearly showed that the standard deviations increased as the percentages of maximal grip, and hence the average strength, decreased. These data show that in submaximal grip strength measurements, the average and the standard deviation do not increase proportionally. The findings by Mitterhauser et al. 17 only partially contradict the assertion that higher mean grip forces also show greater absolute variability. Using multiple linear regression, they found that age and gender were predictors of variability, with male subjects and older subjects showing reduced variabilities. The fact that male subjects are stronger than female subjectsSI but show reduced variabilities l7 indicates that in grip strength measurements the average and standard deviation do not necessarily increase proportionally. In a case study reporting on the examination of three patients before carpal tunnel release surgery and at 6, 13, and 26 weeks after surgery, ShechtmanS2 showed that the means and standard deviations of grip strength measurements did not change proportionally. The measurements for the three patients had similar and at times identical standard deviations despite enormous strength differences. Also, at six weeks after surgery the average strength was the lowest for all patients but the standard deviations remained the same. These three studies show that the means and standard deTABLE 4.
Sample Calculations of Coefficients of Variation (CVs) of the Nose
General formula:
(SD/average) * 100
Elephant nose:
(6" /72") * 100
Mouse nose:
(0.005" /0.07") * 100
NOTE:
SD indicates standard deviation.
= CV
= 8.3% = 7.1%
viations of grip strength do not change proportionally. The problem with using the CV when the average and standard deviation do not change proportionally is that CV values become inflated. The formula for the CV has the standard deviation as the nominator and the average as the denominator. Therefore, for the CV to be greater, either the standard deviation has to be greater or the average has to be smaller. Average grip strength is reduced both during submaximal effort and with hand injury. Consequently, the CV may increase because of the decreased average, not because of a true increase in variability (standard deviation). The fictitious data presented in Table 5 show that when the CV is used to assess sincerity of effort in weaker people, the CV values may be inflated because of the decrease in average strength. The problem of inflated CV values is magnified in patients with hand injuries, whose grip strength is compromised so that their mean grip strength is smaller. In fact, Mitterhauser et aL 17 found that the CV of three grip repetitions was significantly greater in injured than in uninjured subjects. In addition, Bohannon31 found a significant and negative correlation between average strength and the CV of submaximal trials. He stated that, since the CV is a quotient of the standard deviation and the average, it is possible for the CV to be inflated for submaximal efforts because the average strength produced during submaximal efforts is smaller than that produced during maximal efforts. The author cautioned clinicians that decreased strength may bias the CV and advised them to be careful not to make a serious judgment about the patient's sincerity of effort based on the CV alone. Indeed, Shechtman52 showed that, following carpal tunnel release surgery, the CV increased as grip strength decreased, while the standard deviation remained the same. The author concluded that the CV values after surgery were inflated because of compromised hand strength and not because of a true increase in variability. Furthermore, the mathematical requirement for the CV seems to contradict its physiological basis. As mentioned, the mathematical requirement is that the mean and the standard deviation change proportionally.4 In other words, both the mean and the standard deviation of repeated maximal efforts should be greater than those of repeated submaximal efforts. Conversely, according to the physiological principles, the absolute variability (standard deviation) is expected to increase with submaximal effort. 26,27 Thus, the physiological basis calls for the standard deviation to increase with submaximal effort, whereas the mathematical requirement calls for the CV to decrease with submaximal effort. This clash between the physiological and mathematical principles of the CV make its validity questionable. Based on these observations, I hypothesize that larger mean grip forces do not necessarily show greater absolute variability (standard deviation). Grip strength is not a "passive" measure like nose length and blood glucose concentration, which are
TABLE 5.
Sample Calculations of Coefficients of Variation (CVs) of Grip Strength
Measure
Subject 1
Subject 2
Raw data Range Average SD CV
50,52,54 kg 4 kg 52 kg 2 3.8%
10, 12, 14 kg 4 kg 12 kg 2 16.7%
NOTE:
Data are fictitious. SD indicates standard deviation.
not under voluntary control. Grip strength is under voluntary control. It seems logical, then, that the ability of patients to consistently repeat maximal grip strength trials would be independent of the magnitude of their maximal grip strength (torque). For example, for the CV to be used validly, a patient with an average grip strength of 52 kg would have to show greater absolute variability in repeated strength trials than would a weaker person with an average grip strength of 12 kg. I postulate that a stronger person should be able to repeat strength trials with the same absolute variability as a weaker person and that, in the case of grip strength measurements, the average and standard deviation do not tend to change proportionally. Consequently, the CV may not be a valid measure of variability for determining sincerity of effort of grip strength. Absolute variability measures, such as the range and the standard deviation, may be more appropriate measures of variability of grip strength than is the Cv.
VALIDITY OF THE COEFFICIENT OF VARIATION There are three indications that the CV may not be a valid measure of sincerity of effort. The first is the possibility, already discussed, that the CV does not meet its mathematical requirement. The second is that the CV does not seem to be sensitive or specific enough to detect sincerity of effort. The CV is unusual as a descriptive statistic that is used to form a dichotomous measurement (sincere or insincere). The process of determining sincerity of effort using the CV involves forming categories of sincere and insincere, depending on the cutoff value. Therefore, to assess the validity of the Cv, its sensitivity and specificity could be calculated. Sensitivity is a test's ability to provide a positive result when a condition exists (a true positive).4 For the CV of grip strength measurements, sensitivity is expressed as the percentage of people who were considered to exert a submaximal effort and really exerted a submaximal effort. Specificity is the test's ability to provide a negative result when a condition is really absent (a true negative).4 For the CV of grip strength measurements, specificity is expressed as the percentage of people who were considered to exert a maximal effort and really exerted a maximal effort. The sensitivity and specificity of the CV change with its cutoff value (threshold). There are only two studies concerning sincerity of January-March 2000
29
effort of grip strength in which specificity or sensitivity was calculated and discussed. 3,17 Robinson et al./ who assessed the CV of static grip strength using three trials, found that the CV was significantly greater for the submaximal trials, than for the maximal trials. Despite this finding, the authors concluded that the CV cannot be used practically to determine sincerity of effort. The authors based this conclusion on two findings. First, they found that the test-retest correlations of the CV were low, indicating a lack of stability of the Cv. Second, they examined the validity of the CV by calculating its sensitivity. They found that when they used a CV cutoff value of 11 %, 55% of the submaximal efforts (sensitivity, 0.45) were erroneously classified as maximal efforts, and when they used a CV cutoff value of 15%, 69% of the submaximal efforts (sensitivity, 0.31) were erroneously classified as maximal efforts. The low test-retest correlations and the poor sensitivity (too many false negatives) indicated that the CV may not be a valid measure of sincerity of efforts. Studies examining the CV as a measure of sincerity of effort should test both sensitivity and specificity to discern whether the CV is valid. Mitterhauser et al. 17 used a computer-assisted grip strength measurement system to derive the CV from three repeated trials of total hand force. They found that the CV of 116 asymptomatic volunteers was significantly greater for the submaximal effort than for the maximal effort. When specificity and sensitivity were tested, a CV cutoff value of 15% was reported to be very specific but not as sensitive. The specificity was 98%; in other words, only 2% of the subjects who exerted maximal effort were mistakenly classified as exerting submaximal effort. Although sensitivity was not calculated, the data needed to calculate it were easily found. The sensitivity of a CV cutoff value of 15% was 0.74; in other words, 26% of the subjects who exerted submaximal effort were mistakenly classified as exerting maximal effort. The differences in sensitivity of the CV between the two studies (0.31 vs. 0.74?,17 may stem from their different methodologies, including the different instruments used for testing grip strength and the different numbers of subjects, who also differed in their gender composition and average age. Robinson et aP used the hydraulic Jamar dynamometer and tested 29 subjects, whose average age was 25 years and of whom 82% were female. Mitterhauser et al. 17 used a computerized electromechanical device and tested 116 subjects, whose average age was 43 years and of whom 67% were female. The third indication that the CV may not be valid is the lack of empirical support for it in the literature and the fact that studies investigating whether it can detect sincerity of effort have yielded contradictory results. To explain the inconsistent findings, these studies need to be examined more carefully. There are vast differences in methodologies among these studies, including different tasks (lifting, elbow flexion, and grip strength), different 30
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numbers of repeated trials from which the CVs were derived, and different instructions to the subjects (e.g., asking them to feign weakness 3l or specifying the percentage of maximal effort they should exerr,ll,27). Simonsenll showed that CV values of various tasks differ within subjects. He studied the CV of eight different lift tasks in 270 patients with various diagnoses who were referred for functional capacity evaluation. He found no reliable pattern in variability from one task to another and no relationship between the various CVs. The author thus concluded that the CV cannot be used independently as a valid measure of subject effort, particularly among injured subjects. These findings are not surprising, since it makes sense that CV values may be task specific. However, even studies investigating CV values of the same task do not agree. Kroemer and Marras/ 7 who tested the variability of ten repetitions of elbow flexion strength at 100%, 75%, 50%, and 25% of maximal exertion, found no significant differences in the CV values of the various efforts. They concluded that submaximal exertion cannot be detected by a large variability. The authors used a greater number of repetitions than are usually used in the clinic. On the other hand, Bohannon/l who also tested elbow flexion, had different results. He found that the CV of four repetitions was significantly greater for submaximal than for maximal efforts. The contradictory results of these two studies27,3l may stem from the different number of strength trials (four versus ten) and the different instructions to the subjects (Bohannon instructed his subjects to feign weakness, whereas Kroemer and Marras specified the percentage of maximal exertion they should try to achieve). Since CV values may be task specific, scrutinizing studies investigating the CV of tasks other than grip strength may only confound the issue. Only four studies have actually investigated whether the CV can differentiate between maximal and submaximal grip strength efforts. 3 ,lS,17,28 Two of these studies used special equipment (including a force transducer and a computer, which are not readily available in the clinic) to derive a forcetime curve of a single trial of grip strength. ls ,28 In these studies, the CV was based on the average and standard deviation of the curve's plateau. This methodology is very different from the common clinical practice of deriving the CV from the results of repeated strength trials. Therefore, these studies should not be compared with studies based on repeated trials and should not be relied on to justify the use of the CV in clinical situations. Therapists need to be aware of the differences in the two methods of deriving the CV and should not confuse these two entities. In the third study, Mitterhauser et al. 17 tested three groups of injured and uninjured workers and one group of asymptomatic volunteers. The CV was derived from the results of three trials of total hand force. For the asymptomatic volunteers, the CV of the submaximal effort was significantly
higher than that of the maximal effort. The three worker groups comprised 178 preplacement workers, 196 workers with hand injuries, and 55 workers being measured to determine their return-to-work status or impairment rating. Differences between all three groups were significant, with the prep lacement workers showing the smallest CV values (most consistent effort) and the return-to-work workers showing the greatest CV values (least consistent effort). These results indicate that the CV may be a good measure of sincerity of effort. Nevertheless, the CV was not used or recommended for use as a sole predictor of sincerity of effort. The authors combined a few methods to predict sincerity of effort, and the CV was only one factor in their prediction formula. They found that by combining three factors (a stronger ulnar than radial grip strength, a CV greater than 15% in total hand force, and a difference of more than 5% between the CVs of the left and right hands) they could predict submaximal performance with good accuracy. Furthermore, the authors used a computer-assisted grip strength measurement system that is not clinically available. Hence, there is only one study in the literature that empirically examined the ability of the CV derived from three repeated grip trials using the Jamar dynamometer to detect sincerity of effort.3 Robinson et al. found that the CV values of submaximal efforts were significantly greater than those of maximal efforts. However, the authors concluded that the CV was not clinically useful because it was not sensitive enough to detect sincerity of effort; more than 50% of submaximal efforts were erroneously classified as maximal efforts. 3 It is, therefore, perplexing that the CV is widely used to assess sincerity of effort despite the lack of empirical evidence for its validity.
WHY THE COEFFICIENT OF VARIATION IS WIDELY USED Three factors may help explain why clinicians are using the CV to detect sincerity of effort. First, the CV is simple to use, is easy to calculate,1 and is included in many computerized evaluation systems. 5 Second, some studies have shown that the CV differentiates between maximal and submaximal efforts. 3,15,17,28 However, without close examination of their methodologies and results, as discussed, these studies would seem to indicate that the CV does differentiate between sincere and insincere efforts. Third, the CV is based on a standardized test, the static grip test. It is possible that clinicians are not aware of the fact that, although the static grip test meets all the criteria for a standardized test, the CV does not. To elaborate on the third factor, the criteria for a standardized test include reliability and validity values, administrative instructions, equipment criteria, norms, instructions for interpretation, and a bibliography.53 The static grip test has reliability and validity values, norms, equipment criteria for
the Jamar dynamometer, and administrative instructions. 7,5l On the other hand, as Lechner et al. have asserted/ the CV has a questionable reliability, because it varies greatly with the instrumentation, task, and muscle group tested. In addition, the CV has a questionable validity, because of the lack of empirical support in the literature and the contradictory findings regarding its effectiveness in detecting sincerity of effort.1,2,16 Since reliability and validity are the most important components of standardized tests/3 the CV is not and should not be considered a standardized test. Furthermore, the CV has disputable clinical applicability, since it does not seem to be sensitive enough to detect the majority of submaximal efforts. 3 The controversy concerning the use of the CV in assessing sincerity of effort is reflected in three recent review articles. l,2,16 While the author of one article stated that the CV is an objective measure for identifying submaximal effort and that a CV greater than 10% indicates a submaximal effort,16 two articles questioned the effectiveness of the CV as a measure of sincerity of effortY Both of these articles pointed out that the CV lacks empirical support for its predictive validity, that it is unsubstantiated in the literature, and that it therefore should not be used to detect sincerity of effortY Further reasons for not using the CV as a measure of sincerity of effort include its lack of stability over time l,3 and the fact that submaximal efforts can be reproduced consistently?,3
CONCLUSIONS The CV would be used correctly to detect sincerity of effort of grip strength only if grip strength measurements in stronger people were less consistent than those in weaker people. Since that has not been proved, the CV may not be a valid measure of sincerity of effort, especially in injured patients with compromised grip strength. Many clinicians who use the CV without understanding its mathematical basis are not aware that insincere effort is likely to be falsely reported for people with weak grip strength. Therefore, clinicians should not judge a patient's effort as maximal or submaximal, consistent or inconsistent, sincere or insincere, on the basis of the Cv. Research studies with a sufficient sample size are needed to answer the following questions: 1) Do the average and standard deviation of repeated grip strength trials increase proportionally? 2) Are measures of absolute variability such as the standard deviation and range more appropriate for detecting excessive variability in grip strength? 3) Is inconsistency in repeated grip strength trials indicative of insincere effort? These questions should be studied both in injured and uninjured populations. On the basis of the evidence presented in this literature review, I conclude that the CV is not an appropriate method for determining sincerity of effort, especially in patients with compromised hand strength. January-March 2000
31
REFERENCES 1. King PM. Analysis of approaches to detection of sincerity of effort through grip strength measurement. Work. 1998; 10:9-13. 2. Lechner DE, Bradbury SF, Bradley LA. Detecting sincerity of effort: a summary of methods and approaches. Phys Ther. 1998;78:867-88. 3. Robinson ME, Geisser ME, Hanson CS, O'Connor PD. Detecting submaximal efforts in grip strength testing with the coefficient of variation. J Occup Rehabil. 1993;3(1):45-50. 4. Portney LG, Watkins MP. Foundations of clinical research, applications to practice. Norwalk, Conn: Appleton & Lange, 1993. 5. Mueller BA, Adams ED, Isaac CA. Work activities. In: Van Deusen J, Brunt D (ed). Assessment in Occupational Therapy and Physical Therapy. Philadelphia, Pa: WB Saunders, 1997:477-520. 6. Bechtol e. The use of a dynamometer with adjustable handle spacing. J Bone Joint Surg. 1954;36A:820-32. 7. Mathiowetz V, Weber K, Volland G, Kashman N. Reliability and validity of hand strength evaluation. J Hand Surg. 1984; 9A:222-6. 8. Levine DW, Simmons BP, Koris MJ, et al. A self-administered questionnaire for the assessment of severity of symptoms and functional status in carpal tunnel syndrome. J Bone Joint Surg. 1993;75A:1585-92. 9. Niemeyer LO, Matheson LN, Carlton RS. Testing consistency of effort: BTE work simulator. Indust Rehabil Q. 1989; 2:(1):5-13. 10. Schultz-Johnson K. Assessment of upper extremity-injured persons' return to work potential. J Hand Surg. 1987;12A: 950-7. 11. Simonsen Je. Coefficient of variation as a measure of subject effort. Arch Phys Med Rehabil. 1995;76:516-20. 12. Ashford RF, Nagelburg S, Adkins R. Sensitivity of the Jamar dynamometer in detecting submaximal grip effort. J Hand Surg. 1996;21A:402-5. 13. King JW, Berryhill BH. Assessing maximum effort in upperextremity functional testing. Work. 1991;1(3):65-76. 14. Patterson HM. Grip measurements as a part of the preplacement evaluation. Ind Med Surg. 1965;July:555-7. 15. Chengalur SN, Smith GA, Nelson Re. Sadoff AM. Assessing sincerity of effort in maximal grip strength tests. Am J Phys Med Rehabil. 1990;69:148-53. 16. Baker Je. Burden of proof in detection of submaximal effort. Work. 1998;10:63-70. 17. Mitterhauser MD, Muse VL, Dellon AL, Jetzer Te. Detection of submaximal effort with computer-assisted grip strength measurements. J Occup Environ Med. 1997;39:1220-7. 18. Stokes HM. The seriously uninjured hand: weakness of grip. J Occup Med. 1983;25(9):683-4. 19. Niebuhr BR, Marion R. Detecting sincerity of effort when measuring grip strength. Am J Phys Med. 1987;66(1):16-24. 20. Niebuhr BR, Marion R. Voluntary control of submaximal grip strength. Am J Phys Med Rehabil. 1990;69(2):96-101. 21. Czitrom AA, Lister GD. Measurement of grip strength in the diagnosis of wrist pain. J Hand Surg. 1988;13A(1):16-9. 22. Hildreth DH, Breidenbach We. Lister GD, Hodges AD. Detection of submaximal effort by use of the rapid exchange grip. J Hand Surg. 1989;14A:742-5. 23. Joughin K, Gulati P, Mackinnon SE, McCabe S, Murray JF, Griffiths S, Richards R. An evaluation of rapid exchange and simultaneous grip tests. J Hand Surg. 1993;18A:245-52. 24. Lister G. The Hand: Diagnosis and Indications. 2nd ed. New York, NY: Churchill Livingstone, 1984:112. 25. Stokes HM, Landrieu KW, Domangue B, Kunen S. Identification of low-effort patients through dynamometry. J Hand Surg. 1995;20A:1047-56. 26. Gilbert Je. Knowlton RG. Simple method to determine sincerity of effort during a maximal isometric test of grip strength. Am J Phys Med. 1983;62(3):135-44. 27. Kroemer KHE, Marras WS. Towards an objective assessment of the "maximal voluntary contraction" component in routine muscle strength measurements. Eur J Appl Physiol. 1980;45:1-9.
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8. Smith GA, Nelson Re. Sadoff SJ, Sadoff AM. Assessing sincerity of effort in maximal grip strength tests. Am J Phys Med Rehabil. 1989;68(2):73-80. 29. Janda DH, Geiringer SR, Hankin FM, Barry DT. Objective evaluation of grip strength. J Occup Med. 1987;29(7):56971. 30. Neibuhr BR, Marion R, Hasson SM. Electromyographic analysis of effort in grip strength assessment. Electromyogr Clin Neurophysiol. 1993;33:149-56. 31. Bohannon RW. Differentiation of maximal from submaximal static elbow flexor efforts by measurement variability. Am J Phys Med. 1987;66:213-8. 32. Astrand PO, Rodahl K. Textbook of Work Physiology. 2nd ed. New York, NY: McGraw-Hill, 1977. 33. Edgerton VR. Mammalian muscle fiber types and their adaptability. Am Zool. 1978;18:113-25. 34. Milner-Brown HS, Stein RB, Yemm R. The orderly recruitment of human motor units during voluntary isometric contractions. J Physiol. 1973a;230:359-70. 35. Milner-Brown HS, Stein RB, Yemm R. Changes in firing rate of human motor units during linearly changing voluntary contractions. J Physiol. 1973b;230:371-390. 36. Young VL, Pin P, Kraemer BA, Gould RB, Nemergut L, Pellowski M. Fluctuation in grip and pinch strength among normal subjects. J Hand Surg. 1989;14A:125-9. 37. Carlsoo S. With what degree of precision can voluntary static muscle force be repeated? Scand J Rehabil Med. 1986; 18:1-3. 38. Robinson ME, MacMillan M, O'Connor P, Fuller A, Cassisi JE. Reproducibility of maximal versus sub maximal efforts in an isometric lumbar extension mask. J Spinal Disord. 1991;4:444-8. 39. Biering-Sorensen F. Physical measurements as risk indicators for low-back trouble over a one-year period. Spine. 1984;9:106-19. 40. Harber PH, SooHoo K. Static ergonomic strength testing in evaluating occupational back pain. J Occup Med. 1984;26: 877-84. 41. Pao-chun L, Robinson ME, Carlos J, O'Connor P. Detection of submaximal effort in isometric and Isokinetic knee extension tests. J Orthop Sports Phys Ther. 1996;24:19-24. 42. Zeh J, Hansson T, Bigos S, Spengler D, Battie M, Wortley M. Isometric strength testing: recommendations based on a statistical analysis of the procedure. Spine. 1986;11:43-6. 43. Belloit J. Real estate investment. Clarion University Web site. Available at: http://www.clarion.edu/cob_web1/ courses/realest/re471/index. htm. Accessed 1997. 44. Knudsen J. Business statistics syllabus. Creighton University Web site. Available at: http://cobweb.creighton.edu/ Knudsen/DISPERS/tsld009.htm. Accessed Jan 20, 2000. 45. Rozgonyi TG. Statistics for engineers. University of Wollongong Web site. Available at: http://engineering.uow.edu. au/courses/stats/file1586.html. Accessed Jan 20, 2000. 46. Pennock B, Rogers R, McCaffree D. Changes in measured spirometric indices. Chest. 1981;80:97-9. 47. Muggeo M, Verlato G, Bonora E, Zoppini G, Corbellini M, de Marco R. Long-term instability of fasting plasma glucose, a novel predictor of cardiovascular mortality in elderly patients with non-insulin-dependent diabetes mellitus: the Verona diabetes study. Circulation. 1997;96:1750-4. 48. Vestergaard P, Hoeck He. Jakobsen PE, Laurberg P. Reproducibility of growth hormone and cortisol responses to the insulin tolerance test and the short ACTH test in normal adults. Horm Metab Res. 1997;29:106-10. 49. Robinson ME. Fundamentals of functional capacity evaluation [CD-ROM] Orlando, Fla: Intelicus, 1998. 50. Krombholz H. On the association of effort and force of handgrip. Percept Mot Skills. 1985;60:161-2. 51. Mathiowetz V, Kashman N, Volland G, Weber K, Dowe M, Rogers S. Grip and pinch strength: normative data for adults. Arch Phys Med Rehabil. 1985;66:69-72. 52. Shechtman O. Is the coefficient of variation a valid measure for detecting sincerity of effort of grip strength? Work. 1999; 13(2):163-9. 53. Fess EE. The need for reliability and validity in hand assessment instruments. J Hand Surg. 1986;11A:621-3.
S~~~NTIF~C/CL~ICAL~~TI~LES J
Using the Coefficient of Variation to Detect Sincerity of Effort of Grip Strength: A Literature Review Orit Shechtman, PhD, OTRIL
ABSTRACT: Many clinicians use the coefficient of variation (CV) to assess sincerity of effort, without understanding the premise on which it is based or its physiological and mathematical bases. Clinicians who use computerized evaluation systems that calculate the CV may not even be aware of the formula used to derive it. The wide use of the CV in detecting sincerity of effort of grip strength is puzzling, since it lacks empirical support in the literature. This paper examines the physiological rationale for using measures of variability to detect sincerity of effort, the mathematical basis on which the CV is founded, and the reliability and validity of the Cv. The conclusions based on this literature review are that the CV is not an appropriate method for determining Whether an effort is sincere and that CV values may be inflated in injured patients with compromised hand strength. J HAND THER 13:25-32, 2000
Department of Occupational Therapy College of Health Professions University of Florida Gainesville, Florida
espite contradictory research findings and
D lack of strong empirical support, the co-
efficient of variation (CV) is widely used to determine sincerity of effort of grip strength measurements. 1 - 3 Many clinicians judge whether a patient's effort is sincere on the basis of the value of the CV that they derive from a computer output. Therapists who use the CV must understand its premise and the rationale on which it is based. Therapists must also know how the CV is derived and be able to discern whether it is a valid measure of sincerity of effort. The CV is the most common measure of variability used to determine sincerity of effort in isometric strength tests. The formula used to derive the CV is the standard deviation (SD) divided by the average of at least three trials and multiplied by 1004 : CV = (SD/average)
X
100
A greater CV indicates greater variability and smaller consistency. A threshold or cutoff value is usually established for the Cv, above which the effort is considered inconsistent enough to be labeled Correspondence and reprint requests to Orit Shechtman, PhD, OTR/L, Department of Occupational Therapy, College of Health Professions, University of Florida, Gainesville, FL 32610.
submaximal and, therefore, interpreted as insincere. 2,5 This literature review examines the issues surrounding the use of the CV in detecting sincerity of effort. First, a short overview of grip strength and the need for detecting sincerity of effort is provided. Next, the rationale for using measures of variability in detecting sincerity of effort is examined. Finally, the use of the CV to determine sincerity of effort is scrutinized.
GRIP STRENGTH Isometric (static) strength is the amount of muscular force applied by a muscle or group of muscles when it contracts against an immQvable apparatus. The most common and reliable instrument used to evaluate isometric grip strength is the Jamar dynamometer. 6 ,7 Grip strength measured with the Jamar dynamometer is a good indicator of hand function, as suggested by the significant correlations between grip strength and both symptom severity and functional status of the hand. 8 However, grip strength is an objective, reliable, and valid measurement of hand strength only when a patient exerts maximal voluntary effort? Therefore, sincerity of effort can affect the reliability and validity of the test.
January-March 2000
25
Grip strength measurements are frequently used to estimate physical work capacity, match job requirements to a patient's work capability, determine disability, and assess a patient's ability to return to work after injury.9-11 Furthermore, grip strength measurements are used to determine the extent of worker's compensation awards/ 2- 14 since grip strength is often proportional to the loss of strength in an injured arm. IS It is clear, therefore, that a valid determination of sincerity of effort is essential. Many methods and testing procedures have been developed by researchers to detect sincerity of effort. None of the assessments designed for detecting sincerity of effort has been universally accepted. 1,2,16-31 Assessments such as the five-rung test/ 8- 20 the rapid-exchange grip test/1-24 a combination of multiple grip tests,13 and a combination of these methods 17,25 lack reliability and validity values, norms, and standardized testing protocols. Other assessments have been rejected for being too complex (requiring complicated and expensive equipment, elaborate calculations, or lengthy administration time) and therefore unsuitable for clinical use. These include producing a force-time curve and examining its various characteristics26 -28 and studying the electromyographic nature of maximal and submaximal grip.29,3o Generally, research findings on the effectiveness of the various assessments in detecting sincerity of effort are contradictory.1,2,16-31 Consequently, detecting whether a patient is exerting maximal and sincere effort remains problematic. 17
PHYSIOLOGICAL RATIONALE FOR USING MEASURES OF VARIABILITY TO DETECT SINCERITY OF EFFORT Many of the methods used to detect sincerity of effort are based on measures of variability. * The reason for using measures of variability to determine sincerity of effort stems from the notion that a faked, submaximal exertion shows more variability and less consistency in repeated tests than a maximal voluntary effort.9 Kroemer and Marras 27 refer to the German literature in the 50s and 60s where that premise was presented. On the basis of motor unit recruitment patterns, they developed a model explaining why the variability of repeated grips will be greater in submaximal than in maximal muscular contraction. Motor unit recruitment is achieved by one of three mechanisms. The first is rate coding (speed), which regulates the frequency of firing of motor units. The second is recruitment coding (sequence), which controls the type and the number of contracting motor units. The third is a combination of both. 32 -35 During maximal effort, the muscle is activated by the motor cortex through both maximal *References 3, 11, 12, 15, 17, 26-28, 31.
26
JOURNAL OF HAND THERAPY
frequency of neuronal firing (rate coding) and maximal recruitment of all available motor units (recruitment coding). This generates a synchronous pattern of motor unit firing. Therefore, during maximal effort many motor units are recruited simultaneously.32,33 On the other hand, during submaximal effort both the motor cortex and the cerebellum have to mix and precisely control both submaximal frequency of firing and recruitment of a certain number and a certain type of motor units. 34,35 Repeating any muscular contraction requires afferent (sensory) feedback and efferent (motor) control. A maximal muscular contraction is theoretically easier to replicate because it does not require the proprioceptive feedback necessary to grade and limit contraction. Maximal contraction requires only the simplest motor control, which includes both maximal firing frequency and maximal motor unit recruitment and is independent of rate control. Consequently, a maximal effort represents a "lower-order task.,,26,27 On the other hand, repeating a sub maximal effort, according to the Kroemer and Marras model/7 requires extensive and complex afferent feedback signals to the central nervous system as well as precise recruitment coding and rate coding. This involves continual corrections of the motor signals and represents a "higherorder task," which is more difficult to replicate, takes longer to achieve, and results in greater variability than does repetition of a maximal effort. 26,27 Despite this theory about the consistency of repeated maximal and submaximal efforts, the literature indicates that increased variability between trials may not necessarily indicate malingering or willful deception. Variability is inherently present in repeated measurements-as, for example, in the day-to-day variability between repeated strength trials in healthy subjects. Although Bechtol6 reported a daily variation of 10% or less in grip strength when it was measured at the same time each day, Young et al. 36 showed that mean grip strength fluctuated between 19.2% and 23.7% when measured twice a week for three weeks. Furthermore, some studies indicate that submaximal efforts of certain isometric tasks, such as lumbar extension and elbow, plantar, and hip flexion, can be reproduced consistently.1,2,37,38 Ashford et a1.,12 using the Jamar dynamometer, found no significant differences in variability of grip strength between maximal and submaximal efforts in 22 healthy subjects. Moreover, Robinson et al. 3 suggested that fear, pain, psychological distress, and self-efficacy may increase variability between trials. Indeed, Mitterhauser et al. 17 found that the CV of three grip repetitions was significantly greater in an injured group than in an uninjured group. Therefore, the validity of using variability measures to detect sincerity of effort is questionable despite the theoretical basis for the motor unit recruitment model. Common measures of variability (dispersion) of data include the range, the variance, and the standard deviation, all of which are measures of absolute variability.4 Most measures of variability used to detect sincerity of effort, however, are mea-
sures of relative variability, expressed as a percentage of the mean. Two measures are calculated by dividing a measure of absolute variability by the mean of three or more grip trials: The CV is calculated by dividing the standard deviation by the mean of three strength trials 3,4,1l,31; the other measure is derived by dividing the range (maximum minus minimum) by the mean of three strength trials. 12 The advantage of these measures is their simplicity. They are based on three or more repetitions of any isometric strength effort and are very easy to calculate. Their disadvantage is that they have not been shown to distinguish between maximal and submaximal efforts. 3,12,38
TABLE 1.
THE COEFFICIENT OF VARIATION The Cv, which is based on repeated trials, has been used in conjunction with isometric strength tests of the trunk, legs, and arms 9 ,1l,27,31,37-42 and with grip strength tests?,17 The cutoff value for the CV in the related literature varies greatly and ranges from 10% to 20%.1-3,5 A CV greater than the cutoff values suggests that the effort is inconsistent enough to be labeled submaximal and insincere, The CV values reported in the literature for isometric strength testing of grip, upper extremities, and trunk are shown in Tables 1, 2, and 3, respectively.
Coefficients of Variation (CVs) of Isometric Grip Strength Tests Reported in the Literature
Assessment Tool
Author Mitterhauser et al., 1997'7
NK DIGIT-Grip
Population
Type of Effort
CV(%)
Uninjured subjects
Maximal Sub maximal Maximal
2.8-3.5 13.8-14.5 8.1-8.5
Injured subjects 3
Robinson et al., 1993
Jamar dynamometer
Uninjured subjects
Maximal Submaximal
3.8-4.3 9.3-12.6
Chengalur et al., 199015
Modified Jamar dynamometer with force transducer
Injured men
Sincere Faking Sincere Faking
5.9 8.7 6.9 9.6
Sincere Faking
4.9 16.5
Injured women Smith et al., 198928
TABLE 2.
Modified Jamar dynamometer with force transducer
Uninjured men
Coefficients of Variation (CVs) of Isometric Efforts of Upper Extremity Movements Reported in the Literature
Assessment Tool
Population
Supination
Niemeyer et al., 1989
9
BTE Work Simulator
Uninjured men Uninjured women
8.7-13.8 11.5-16.3
Pronation
Niemeyer et al., 19899
BTE Work Simulator
Uninjured men Uninjured women
8.6-12.1 8.8-14.1
Elbow flexion
Niemeyer et al., 19899
BTE Work Simulator
Uninjured men Uninjured women
9.9-10.4 7.6-11.0
Elbow extension
Niemeyer et al., 19899
BTE Work Simulator
Uninjured men Uninjured women
8.5-10.1 10.3-12.4
Kroemer and Marras, 198027
Dynamometer
Uninjured men Uninjured women
3.9-4.8 3.9-4.6
Bohannon, 198731
Dynamometer
Uninjured women
Movement
TABLE 3. Movement Lifting
Author
Trunk flexion
,,;7.5 (max) 4.3-76.1 (submax)
Coefficients of Variation (CVs) of Isometric Efforts of Various Trunk Movements Reported in the Literature
Assessment Tool
Author
Population
CV(%)
Harber and SooHoo, 198440
Unnamed apparatus
Patients (back pain)
Simonsen, 1995"
ERGOS Work Simulator
Patients (back pain)
6.09-11.95
Unnamed apparatus
Uninjured men Uninjured women
6.0-8.4 7.1-10.0
Unnamed apparatus
General population
4.72
Unnamed apparatus
General population
6.35
Zeh et al., 1986 Trunk extension
CV(%)
42
Biering-Sorensen, 198439 39
Biering-Sorensen 1984
13.2-17.7
January-March 2000
27
The CV is used by numerous clinicians and is incorporated into many evaluation systems, despite contradictory findings and lack of empirical support. The evaluation systems utilizing the CV include Blankenship (Blankenship Corp., Macon, Georgia), Key (Key Assessment, Minneapolis, Minnesota), Ergos (ErgoScience, Birmingham, Alabama), the BTE Work Simulator (Baltimore Therapeutic Equipment Co., Baltimore, Maryland), and the GreenLeaf (GreenLeaf Medical Technologies, Palo Alto, California).s In these work evaluation systems, the computer calculates the CV, which is then viewed on the computer screen or on a printout. The CV produced by the instrument may be misleading if the clinician does not know the mathematical basis for the computation.
MATHEMATICAL RATIONALE FOR USING THE COEFFICIENT OF VARIATION The CV is a measure of relative variability (dispersion) of data and is widely used with measurements other than those of isometric strength. It is valid to use the CV in only one of the following three conditions. In the first condition, the CV is used as a common measure of risk. 4,43 This is not relevant to grip strength. In the second condition, the CV is used when com~aring dispersion of data that are in different units. 4, Since static grip is measured in only one type of force unit at a time, the use of the CV for this reason is not justified. In the third condition, the CV is used when the magnitude (average) and the variability (standard deviation) of a set of scores increase proportionally.us The use of the CV with grip strength measurements is based on this third condition. In some measurements, such as spirometry and blood concentration of hormones and glucose,46-48 the average and the standard deviation do indeed change proportionally, so it is valid to use the CV to express variability in these measurements. In other words, the CV is used appropriately only when the average and standard deviation tend to change proportionally.4 An example of an appropriate use of the CV is a comparison of the nose lengths of mice and elephants49 (Table 4). Because the nose lengths of the two species are very different (6' and 0.07", respectively), the absolute variability is larger for the longer elephant nose. In other words, the standard deviation of an elephant nose may be 0.5', whereas the standard deviation of a mouse nose may be 0.005". In this situation, the average and the standard deviation change proportionally; that is, the greater the average, the greater the standard deviation. To compare the variability between the two species, the average nose length has to be taken into account. While the absolute variability (standard deviation) is 6" for the elephant nose versus 0.005" for the mouse nose, the relative variation as expressed by the CV is 8.3% for the elephant nose and 7.1% for the mouse nose. Consequently, the CV compares the variability in 28
JOURNAL OF HAND THERAPY
nose length more directly by expressing the standard deviation as a percentage of the average. In this situation, the CV is valid. For the CV to be a valid measure of sincerity of grip strength, the third condition has to be met; that is, the average and standard deviation of repeated grip trials must increase proportionally. In other words, the CV would be used appropriately only if people with greater average grip strength exhibited greater variability (standard deviation) than those with lesser average grip strength. Robinson et aP acknowledged this requirement by asserting that "it is expected that larger torque values will also show greater absolute variability." Thus, the CV allows the researcher or clinician to compare the variability of two groups with potentially widely different overall strength. Three studies, however, contradict this assertion. A study by Krombholz so examined the means and standard deviations of different percentages of maximal grip strength in 24 right-handed male university students, using a hand dynamometer manufactured by Martin Inc. The levels of effort were 30%,50%,70%, and 90% of maximal grip strength. Although this study did not examine the CV, the results clearly showed that the standard deviations increased as the percentages of maximal grip, and hence the average strength, decreased. These data show that in submaximal grip strength measurements, the average and the standard deviation do not increase proportionally. The findings by Mitterhauser et al. 17 only partially contradict the assertion that higher mean grip forces also show greater absolute variability. Using multiple linear regression, they found that age and gender were predictors of variability, with male subjects and older subjects showing reduced variabilities. The fact that male subjects are stronger than female subjectsSI but show reduced variabilities l7 indicates that in grip strength measurements the average and standard deviation do not necessarily increase proportionally. In a case study reporting on the examination of three patients before carpal tunnel release surgery and at 6, 13, and 26 weeks after surgery, ShechtmanS2 showed that the means and standard deviations of grip strength measurements did not change proportionally. The measurements for the three patients had similar and at times identical standard deviations despite enormous strength differences. Also, at six weeks after surgery the average strength was the lowest for all patients but the standard deviations remained the same. These three studies show that the means and standard deTABLE 4.
Sample Calculations of Coefficients of Variation (CVs) of the Nose
General formula:
(SD/average) * 100
Elephant nose:
(6" /72") * 100
Mouse nose:
(0.005" /0.07") * 100
NOTE:
SD indicates standard deviation.
= CV
= 8.3% = 7.1%
viations of grip strength do not change proportionally. The problem with using the CV when the average and standard deviation do not change proportionally is that CV values become inflated. The formula for the CV has the standard deviation as the nominator and the average as the denominator. Therefore, for the CV to be greater, either the standard deviation has to be greater or the average has to be smaller. Average grip strength is reduced both during submaximal effort and with hand injury. Consequently, the CV may increase because of the decreased average, not because of a true increase in variability (standard deviation). The fictitious data presented in Table 5 show that when the CV is used to assess sincerity of effort in weaker people, the CV values may be inflated because of the decrease in average strength. The problem of inflated CV values is magnified in patients with hand injuries, whose grip strength is compromised so that their mean grip strength is smaller. In fact, Mitterhauser et aL 17 found that the CV of three grip repetitions was significantly greater in injured than in uninjured subjects. In addition, Bohannon31 found a significant and negative correlation between average strength and the CV of submaximal trials. He stated that, since the CV is a quotient of the standard deviation and the average, it is possible for the CV to be inflated for submaximal efforts because the average strength produced during submaximal efforts is smaller than that produced during maximal efforts. The author cautioned clinicians that decreased strength may bias the CV and advised them to be careful not to make a serious judgment about the patient's sincerity of effort based on the CV alone. Indeed, Shechtman52 showed that, following carpal tunnel release surgery, the CV increased as grip strength decreased, while the standard deviation remained the same. The author concluded that the CV values after surgery were inflated because of compromised hand strength and not because of a true increase in variability. Furthermore, the mathematical requirement for the CV seems to contradict its physiological basis. As mentioned, the mathematical requirement is that the mean and the standard deviation change proportionally.4 In other words, both the mean and the standard deviation of repeated maximal efforts should be greater than those of repeated submaximal efforts. Conversely, according to the physiological principles, the absolute variability (standard deviation) is expected to increase with submaximal effort. 26,27 Thus, the physiological basis calls for the standard deviation to increase with submaximal effort, whereas the mathematical requirement calls for the CV to decrease with submaximal effort. This clash between the physiological and mathematical principles of the CV make its validity questionable. Based on these observations, I hypothesize that larger mean grip forces do not necessarily show greater absolute variability (standard deviation). Grip strength is not a "passive" measure like nose length and blood glucose concentration, which are
TABLE 5.
Sample Calculations of Coefficients of Variation (CVs) of Grip Strength
Measure
Subject 1
Subject 2
Raw data Range Average SD CV
50,52,54 kg 4 kg 52 kg 2 3.8%
10, 12, 14 kg 4 kg 12 kg 2 16.7%
NOTE:
Data are fictitious. SD indicates standard deviation.
not under voluntary control. Grip strength is under voluntary control. It seems logical, then, that the ability of patients to consistently repeat maximal grip strength trials would be independent of the magnitude of their maximal grip strength (torque). For example, for the CV to be used validly, a patient with an average grip strength of 52 kg would have to show greater absolute variability in repeated strength trials than would a weaker person with an average grip strength of 12 kg. I postulate that a stronger person should be able to repeat strength trials with the same absolute variability as a weaker person and that, in the case of grip strength measurements, the average and standard deviation do not tend to change proportionally. Consequently, the CV may not be a valid measure of variability for determining sincerity of effort of grip strength. Absolute variability measures, such as the range and the standard deviation, may be more appropriate measures of variability of grip strength than is the Cv.
VALIDITY OF THE COEFFICIENT OF VARIATION There are three indications that the CV may not be a valid measure of sincerity of effort. The first is the possibility, already discussed, that the CV does not meet its mathematical requirement. The second is that the CV does not seem to be sensitive or specific enough to detect sincerity of effort. The CV is unusual as a descriptive statistic that is used to form a dichotomous measurement (sincere or insincere). The process of determining sincerity of effort using the CV involves forming categories of sincere and insincere, depending on the cutoff value. Therefore, to assess the validity of the Cv, its sensitivity and specificity could be calculated. Sensitivity is a test's ability to provide a positive result when a condition exists (a true positive).4 For the CV of grip strength measurements, sensitivity is expressed as the percentage of people who were considered to exert a submaximal effort and really exerted a submaximal effort. Specificity is the test's ability to provide a negative result when a condition is really absent (a true negative).4 For the CV of grip strength measurements, specificity is expressed as the percentage of people who were considered to exert a maximal effort and really exerted a maximal effort. The sensitivity and specificity of the CV change with its cutoff value (threshold). There are only two studies concerning sincerity of January-March 2000
29
effort of grip strength in which specificity or sensitivity was calculated and discussed. 3,17 Robinson et al./ who assessed the CV of static grip strength using three trials, found that the CV was significantly greater for the submaximal trials, than for the maximal trials. Despite this finding, the authors concluded that the CV cannot be used practically to determine sincerity of effort. The authors based this conclusion on two findings. First, they found that the test-retest correlations of the CV were low, indicating a lack of stability of the Cv. Second, they examined the validity of the CV by calculating its sensitivity. They found that when they used a CV cutoff value of 11 %, 55% of the submaximal efforts (sensitivity, 0.45) were erroneously classified as maximal efforts, and when they used a CV cutoff value of 15%, 69% of the submaximal efforts (sensitivity, 0.31) were erroneously classified as maximal efforts. The low test-retest correlations and the poor sensitivity (too many false negatives) indicated that the CV may not be a valid measure of sincerity of efforts. Studies examining the CV as a measure of sincerity of effort should test both sensitivity and specificity to discern whether the CV is valid. Mitterhauser et al. 17 used a computer-assisted grip strength measurement system to derive the CV from three repeated trials of total hand force. They found that the CV of 116 asymptomatic volunteers was significantly greater for the submaximal effort than for the maximal effort. When specificity and sensitivity were tested, a CV cutoff value of 15% was reported to be very specific but not as sensitive. The specificity was 98%; in other words, only 2% of the subjects who exerted maximal effort were mistakenly classified as exerting submaximal effort. Although sensitivity was not calculated, the data needed to calculate it were easily found. The sensitivity of a CV cutoff value of 15% was 0.74; in other words, 26% of the subjects who exerted submaximal effort were mistakenly classified as exerting maximal effort. The differences in sensitivity of the CV between the two studies (0.31 vs. 0.74?,17 may stem from their different methodologies, including the different instruments used for testing grip strength and the different numbers of subjects, who also differed in their gender composition and average age. Robinson et aP used the hydraulic Jamar dynamometer and tested 29 subjects, whose average age was 25 years and of whom 82% were female. Mitterhauser et al. 17 used a computerized electromechanical device and tested 116 subjects, whose average age was 43 years and of whom 67% were female. The third indication that the CV may not be valid is the lack of empirical support for it in the literature and the fact that studies investigating whether it can detect sincerity of effort have yielded contradictory results. To explain the inconsistent findings, these studies need to be examined more carefully. There are vast differences in methodologies among these studies, including different tasks (lifting, elbow flexion, and grip strength), different 30
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numbers of repeated trials from which the CVs were derived, and different instructions to the subjects (e.g., asking them to feign weakness 3l or specifying the percentage of maximal effort they should exerr,ll,27). Simonsenll showed that CV values of various tasks differ within subjects. He studied the CV of eight different lift tasks in 270 patients with various diagnoses who were referred for functional capacity evaluation. He found no reliable pattern in variability from one task to another and no relationship between the various CVs. The author thus concluded that the CV cannot be used independently as a valid measure of subject effort, particularly among injured subjects. These findings are not surprising, since it makes sense that CV values may be task specific. However, even studies investigating CV values of the same task do not agree. Kroemer and Marras/ 7 who tested the variability of ten repetitions of elbow flexion strength at 100%, 75%, 50%, and 25% of maximal exertion, found no significant differences in the CV values of the various efforts. They concluded that submaximal exertion cannot be detected by a large variability. The authors used a greater number of repetitions than are usually used in the clinic. On the other hand, Bohannon/l who also tested elbow flexion, had different results. He found that the CV of four repetitions was significantly greater for submaximal than for maximal efforts. The contradictory results of these two studies27,3l may stem from the different number of strength trials (four versus ten) and the different instructions to the subjects (Bohannon instructed his subjects to feign weakness, whereas Kroemer and Marras specified the percentage of maximal exertion they should try to achieve). Since CV values may be task specific, scrutinizing studies investigating the CV of tasks other than grip strength may only confound the issue. Only four studies have actually investigated whether the CV can differentiate between maximal and submaximal grip strength efforts. 3 ,lS,17,28 Two of these studies used special equipment (including a force transducer and a computer, which are not readily available in the clinic) to derive a forcetime curve of a single trial of grip strength. ls ,28 In these studies, the CV was based on the average and standard deviation of the curve's plateau. This methodology is very different from the common clinical practice of deriving the CV from the results of repeated strength trials. Therefore, these studies should not be compared with studies based on repeated trials and should not be relied on to justify the use of the CV in clinical situations. Therapists need to be aware of the differences in the two methods of deriving the CV and should not confuse these two entities. In the third study, Mitterhauser et al. 17 tested three groups of injured and uninjured workers and one group of asymptomatic volunteers. The CV was derived from the results of three trials of total hand force. For the asymptomatic volunteers, the CV of the submaximal effort was significantly
higher than that of the maximal effort. The three worker groups comprised 178 preplacement workers, 196 workers with hand injuries, and 55 workers being measured to determine their return-to-work status or impairment rating. Differences between all three groups were significant, with the prep lacement workers showing the smallest CV values (most consistent effort) and the return-to-work workers showing the greatest CV values (least consistent effort). These results indicate that the CV may be a good measure of sincerity of effort. Nevertheless, the CV was not used or recommended for use as a sole predictor of sincerity of effort. The authors combined a few methods to predict sincerity of effort, and the CV was only one factor in their prediction formula. They found that by combining three factors (a stronger ulnar than radial grip strength, a CV greater than 15% in total hand force, and a difference of more than 5% between the CVs of the left and right hands) they could predict submaximal performance with good accuracy. Furthermore, the authors used a computer-assisted grip strength measurement system that is not clinically available. Hence, there is only one study in the literature that empirically examined the ability of the CV derived from three repeated grip trials using the Jamar dynamometer to detect sincerity of effort.3 Robinson et al. found that the CV values of submaximal efforts were significantly greater than those of maximal efforts. However, the authors concluded that the CV was not clinically useful because it was not sensitive enough to detect sincerity of effort; more than 50% of submaximal efforts were erroneously classified as maximal efforts. 3 It is, therefore, perplexing that the CV is widely used to assess sincerity of effort despite the lack of empirical evidence for its validity.
WHY THE COEFFICIENT OF VARIATION IS WIDELY USED Three factors may help explain why clinicians are using the CV to detect sincerity of effort. First, the CV is simple to use, is easy to calculate,1 and is included in many computerized evaluation systems. 5 Second, some studies have shown that the CV differentiates between maximal and submaximal efforts. 3,15,17,28 However, without close examination of their methodologies and results, as discussed, these studies would seem to indicate that the CV does differentiate between sincere and insincere efforts. Third, the CV is based on a standardized test, the static grip test. It is possible that clinicians are not aware of the fact that, although the static grip test meets all the criteria for a standardized test, the CV does not. To elaborate on the third factor, the criteria for a standardized test include reliability and validity values, administrative instructions, equipment criteria, norms, instructions for interpretation, and a bibliography.53 The static grip test has reliability and validity values, norms, equipment criteria for
the Jamar dynamometer, and administrative instructions. 7,5l On the other hand, as Lechner et al. have asserted/ the CV has a questionable reliability, because it varies greatly with the instrumentation, task, and muscle group tested. In addition, the CV has a questionable validity, because of the lack of empirical support in the literature and the contradictory findings regarding its effectiveness in detecting sincerity of effort.1,2,16 Since reliability and validity are the most important components of standardized tests/3 the CV is not and should not be considered a standardized test. Furthermore, the CV has disputable clinical applicability, since it does not seem to be sensitive enough to detect the majority of submaximal efforts. 3 The controversy concerning the use of the CV in assessing sincerity of effort is reflected in three recent review articles. l,2,16 While the author of one article stated that the CV is an objective measure for identifying submaximal effort and that a CV greater than 10% indicates a submaximal effort,16 two articles questioned the effectiveness of the CV as a measure of sincerity of effortY Both of these articles pointed out that the CV lacks empirical support for its predictive validity, that it is unsubstantiated in the literature, and that it therefore should not be used to detect sincerity of effortY Further reasons for not using the CV as a measure of sincerity of effort include its lack of stability over time l,3 and the fact that submaximal efforts can be reproduced consistently?,3
CONCLUSIONS The CV would be used correctly to detect sincerity of effort of grip strength only if grip strength measurements in stronger people were less consistent than those in weaker people. Since that has not been proved, the CV may not be a valid measure of sincerity of effort, especially in injured patients with compromised grip strength. Many clinicians who use the CV without understanding its mathematical basis are not aware that insincere effort is likely to be falsely reported for people with weak grip strength. Therefore, clinicians should not judge a patient's effort as maximal or submaximal, consistent or inconsistent, sincere or insincere, on the basis of the Cv. Research studies with a sufficient sample size are needed to answer the following questions: 1) Do the average and standard deviation of repeated grip strength trials increase proportionally? 2) Are measures of absolute variability such as the standard deviation and range more appropriate for detecting excessive variability in grip strength? 3) Is inconsistency in repeated grip strength trials indicative of insincere effort? These questions should be studied both in injured and uninjured populations. On the basis of the evidence presented in this literature review, I conclude that the CV is not an appropriate method for determining sincerity of effort, especially in patients with compromised hand strength. January-March 2000
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