- Email: [email protected]
Expectancies and functional impairment in chronic low back pain
323
Pain, 33 (1988) 323-331 Elsevier PA1 01227
Expectancies and functional impairment in chronic low back pain James R. Council *, David K. Ahem * *, Michael J. Follick * * and Curtis L. Kline * * Department
o~Psyckolo~,
and * * Brown University Program in Medicine,
North Dakota State University, Fargq ND 5810.5 (U.S.A.), The Miriam Hospital, Chronic Pain Research Unit, Prwidence,
RI 02906 (U.S.A.)
(Received 22 June 1987, accepted 25 January 1988)
s-w
Perceived self-efficacy [2] and pain response expectancies [13] were examined as correlates of movement limitations and impaired functioning in a sample of 40 patients with chronic low back pain. Self-efficacy was operationalized as patients’ ratings of their ability to perform movements, while response expectancies were operationahzed as ratings of the degree of pain expected to accompany the movements. Patients predicted their ability to perform 10 simple movements and the degree of pain that would accompany each movement; on a separate occasion, subjects’ actual performance of the movements was assessed. In general, independent predictions of both movement ability and pain correlated significantly with performance of specific movements as rated from videotapes. Total movement scores correlated 0.55 and -0.54, respectively, with total self-efficacy and pain response expectancy ratings. Expectancy ratings were also predictive of average daily pain ratings and questionnaire ratings of physical impairment in everyday life. Multiple regression analyses, in&ding causal modeling, indicated that actual performance was best predicted by self-efficacy ratings, which in turn appeared to be determined by pain response expectancies. Key wordsr Expectancy ratings; Low back pain; Movement scores
Patients with chronic low back pain often display significant motor impairment and other pain behaviors in the absence of sufficient organic pathology to account for their loss of function [9,20]. Several researchers have proposed that avoidance learning may partially account for this discrepancy. According to this hypothesis, patients appropriately avoid excessive motor activity during the acute phase of an injury. This inactivity is negatively reinforced by pain reduction and may result in avoidance behavior that persists after healing [7,11]. A social learning model could also account for impaired motor functions in chronic
Correspondence to: J.R. Council, Dept. of Psychology, North Dakota State University, Fargo, ND 58105, U.S.A.
pain patients - when an indi~du~ expects aversive experiences to result from attempts to perform particular motor behaviors, he or she will avoid those behaviors. Expected negative outcomes could include increased pain and the experience of failure in an important area of need (e.g., physical competence). Bandura [2,3] and Kirsch [13] have both proposed expectancy constructs that may be useful in understanding maladaptive behaviors associated with chronic pain syndromes. Perceiued self-efficacy [2,3], defined as the expectancy of successful perfo~~ce in a problem situation, has been proposed to affect the functional status of chronic pain patients in 2 major ways. First, the performance of actions necessary for meeting treatment goals may be affected b$ people’s judgments of their behavioral and social skills [3,19]. Second, perceived self-efficacy for cognitively coping with pain may determine the
0304-3959/88/$03.50 6 1988 Elsevier Science Publishers B.V. (Biomedical Division)
324
ways in which people deal with situations associated with pain [3,6,17,19]. For example, patients with low self-efficacy for coping with pain might be more likely to avoid behaviors and situations associated with pain or to use pain medication in those situations. Self-efficacy expectancies of patients in rehab~itative therapy for chronic back pain have been assessed as they relate to motor performance (e.g., daily activities, meeting physical therapy exercise quotas) and the ability to cope with pain without medication. Dolce et al. [7] demonstrated that substantial increases in self-efficacy ratings were associated with improved exercise levels. Other studies have shown that self-efficacy expectancies are sig~fic~tly correlated with post-treatment pain ratings, tolerance for physical activities, use of pain medication, and work status 16,161. While generally supporting the construct’s utility, correlations between measures of self-efficacy and the functional status of chronic back pain patients have been low, with more consistent predictions of motor behaviors than variables related to cognitive control of pain. Dolce and coworkers reported that a number of their patients showed no increase in self-efficacy despite meeting exercise quotas during treatment f7], and that posttreatment self-efficacy ratings failed to account for a significant proportion of variance in a regression analysis of follow-up measures [6]. Dolce et al. [6] noted that their self-efficacy measures consisted of general questions (e.g., ‘how able or capable do you feel you are of.. . : daily exercise; coping without pain mentions’), and that greater specificity may have resulted in stronger associations with treatment outcome measures. Although Kores et al. [16] assessed self-efficacy for specific behaviors, a number of possibly unrelated items (e.g., walking, Lifting, coping with pain, engaging in family activities) were combined to yield a total score which may have lacked predictive power. Correlations reported by Dolce et al. ]6] and Kores et al. [16] may also have been weakened by the use of self-report during interviews rather than objective behavioral ratings to collect data on dependent variables. It is likely that stronger relationships between self-efficacy and functional status would be revealed with more specific and
objective measures of expectancies and criterion behaviors. Self-efficacy theory has been applied to the experience of pain by positing cognitive coping skills used by patients to modulate pain perception. An explanation of avoidance behavior that directly addresses pain experience can be derived from Kirsch’s f 13) response expectancy hypothesis. Response expectancies are defined as subjective predictions of responses that occur without volitional control (e.g., pain, emotional reactions. and conversion symptoms). Kirsch [13] proposed that avoidance of particular situations will vary as a function of the subjectively held probability that an aversive non-volitional response (e.g., pain) will be associated with those situations. Thus, according to the response expectancy hypothesis, patients who expect more severe pain to result from a particular behavior will be more hkely to avoid that behavior than patients expecting less pain. In addition to relating directly to the subjective experience of pain, this model is more parsimonious than that based on self-efficacy. Asking a patient to predict his or her ability to cognitively cope with a painful experience implicitly assumes both that the patient can predict pain intensity and that the patient will ‘cope’ (usually in some unspecified manner). Although the role of response expectancies has been established in fear reduction and for the action of placebos in alleviating pain [13.15], the relationship of response expectancies to chronic pain behavior has not yet been explored. This study was designed to investigate perceived self-efficacy and response expectancy as correlates of functional impairment (i.e., movement limitations) associated with chronic low back pain. It was hypothesized that perceived self-efficacy, operationalized as patients’ ratings of their ability to perform movements, would bear a direct relationship to actual performance. Response expectancies for pain, operationaEzed as patient ratings of the degree of pain expected to accompany the movements, were predicted to bear an inverse relationship to performance. Due to their direct relations~p to the experience of pain, response expectancies were hypothesized to bear a stronger relationship to avoidance behaviors (i.e., functional impairment) than self-efficacy expec-
tancies. In order to maximize the specificity of expectancy measures, self-ratings involved simple movements that were diagrammed step by step; performance of the movements corresponding to specific expectancy ratings was later videotaped. This specificity was predicted to result in substantially higher correlations between expectancy and performance than indicated by previous investigations. Finally, social learning theory postulates that self-predictions to novel situations are based on generalized classes of expectancies drawn from everyday life experiences. Thus, although highly specific, the expectancy ratings in this study were also predicted to bear significant correlations with global measures of pain and functional impairment in everyday life.
Method
No pain
Discomfort
Painful
Very painful
lntolernble
1
2
3
4
0
1. Toe touch from standing position.
Win Prediction
_
_
_
-
-
It you did not circle the last picrure. please put a check mifk next to i&e a&x reami belov:
_ Pear of injury
_Plin
- Leek of ability
Fig. 1. Sample MAPPS item. Subjects respond by circling the stick figure corresponding to their predicted ability to perform the movement and indicate predicted pain for each stage of the movement.
Subjects
Subjects were 20 males and 20 females undergoing evaluation at the Miriam Hospital Chronic Pain Treatment Program. Selection criteria included low back pain of greater than 6 months duration, and no indications of spinal disease or other organic pathology requiring (further) surgical intervention. Low back pain was the primary complaint for 36 (90%) of the subjects, with the remaining 4 subjects (10%) complaining of primary neck and shoulder pain. Subjects ranged in age from 20 to 69 years (mean = 42.9 years, S.D. = 11.4) with a mean duration of pain of 45.4 months (S.D. = 27.0 months). Twenty-two subjects (54%) had undergone some form of surgery related to their pain, and of these, 10 reported two or more surgeries. Thirty-four percent were using medication for pain relief at the time of assessment. Independent measure ~ove~nt and pain predi~t~vn scale ~~~PPS~. The MAPPS depicts S successive stages of 10 simple movements. A sample item is presented in Fig. 1, and the 10 movements are listed in Table I. Subjects predicted the extent to which they would be able to perform each movement (i.e., self-efficacy expectancies) by circling one of the pictured stages. Pain levels expected to accompany each
step of the movement (pain response expectancies) were indicated below each pictured stage. Subjects indicated expected pain for all stages of the movement, including those they did not expect to complete. When subjects predicted they could not complete a movement, they indicated whether fear of injury, pain, or lack of ability was the primary reason for their response. MAPPS movement predictions were scored from 1 to 5, with ‘1’ indicating a subject’s prediction that he or she would be unable to perform any stage of the movement, and ‘5’ indicating a prediction of successful performance of the complete movement. Pain response expectancies were also indicated on a l-5 scale (‘no pain’-‘intoIerable’), and were scored by summing over all stages of each movement. Dependent rne~~es Movement ratings. The major dependent measure was a rating of the performance of each movement for which patients had made predictions on the MAPPS. The sequence of movements was videotaped, and the extent of each movement was rated on a l-5 scale that, like the MAPPS movement predictions in Fig. 1, pictured 5 succes-
326
TABLE I CORRELATIONS BETWEEN SELF-EFFICACY, PAIN RESPONSE EXPECTANCIES AND PERFORMANCE IN RELATION TO 10 SPECIFIC MOVEMENT (N = 40) Movement (starting position)
1 Toe touch (standing) 2 Sit-up (lying supine) 3 Right leg raise (lying supine) 4 Left leg raise (lying supine) 5 Right leg raise (lying on side) 6 Left leg raise (lying on side) 7 Right lateral bend (standing) 8 Left lateral bend (standing) 9 Right trunk rotation (standing) 10 Left trunk rotation (standing) * PcO.05;
Response expectancy: pain
Correlation between self-efficacy and response expectancy
0.49 **
-0.41 **
-0.53 ***
0.38 *
-0.49 **
-0.51 ***
0.74 ***
-0.64 ***
-0.75 ***
0.64 ***
-0.66 ***
-0.71 ***
0.51 ***
-0.45 ***
-0.58 ***
0.51 ***
-0.37 *
-0.67 ***
0.40 *
-0.22
-0.63 ***
0.21
-0.23
-0.69 ***
-0.03
- 0.26
-0.49 **
- 0.07
- 0.21
-0.60 ***
Seifefficacy: movement
** PcO.01;
*** P
sive stages of each movement. Inter-rater reliability for movement ratings was 0.84 (Pearson correlation coefficient), based on 2 independent raters and half the sample. Audiovisual
taxonomy
of pain behavior [?I]. This
empirically derived observational rating system was used to score videotapes for behaviors including movement limitations, verbal complaints and limitation statements, non-verbal sounds, and position shifting. These ratings generated a global index of pain behavior that was not afforded by movement ratings alone. Taxonomy data were missing for 1 subject; therefore analyses using this variable are based on a sample of 39 patients.
ment were included described below:
in the analyses. These are
Sickness impact profile (SIP) (41. The SIP is a behaviorally based self-report measure containing 136 statements about health-related dysfunction in 12 areas of activity. The SIP yields scores on 3 major dimensions: physical imp~rment, psychosocial impairment, and ‘other’ (primarily work and recreational) impairment. The 3 dimension scores are combined to form a total impairment score, Higher scores on aIt measures indicate greater impairment. The SIP has been validated as a global measure of disability in chronic low back pain [lo]. Duily activity diary (91. The daily activity diary is a 7-day record kept by patients that includes reports of daily activities, pain levels and pain behaviors. Average daily pain ratings (on scale of ‘0 = no pain’ to ‘10 = worst possible pain’) from the diary were used in this study. Procedure
Subjects completed the MAPPS and other assessment instruments during their initial evaluation for admission to a multidisciplinary chronic pain treatment program. Approximately 1 week after completing the MAPPS, and before entering treatment, each subject was videotaped while he or she performed the 10 movements for which MAPPS expectancy ratings had been made. (The movements are listed in Table I.) Subjects had not known beforehand that their ability to actually perform these movements would be assessed. The videotaping was part of an ongoing validation of the ‘audiovisual taxonomy of pain behavior’ [8] and included a brief interview component that was not included in the present analysis. Patients were informed that videotaping was a routine component of clinical evaluation although the tapes could possibly be used for research purposes. Written consent to be videotaped was obtained from all subjects.
Rt?!dtS Other measures
In addition to the measures described above, global measures of pain and functional impair-
Correlations between MAPPS expectancy measures and actual performance of the correspond-
327 ing movements are presented in Table I. A number of correlations were highly significant; however, correlations involving lateral bending and trunk rotations from a standing position were generally non-significant. The non-significant relationships are possibly an artifact arising from confusion of right vs. left movements, since figures representing these movements were presented to the subjects as mirror images in full frontal view. The lower correlations might also have resulted if subjects were less familiar with these movements than with the others. Correlations between self-efficacy and pain response expectancy for specific movements were all substantial, ranging from -0.49 to -0.75. With the exception of some items likely to have been affected by measurement error, data from Table I indicate consistent relationships between self-efficacy, response expectancy and performance of specific motor behaviors. Table II presents correlations involving total scores summed over the expectancy and movement ratings. Pain behavior was rated from the videotapes using the pain behavior taxonomy [8]. Other variables presented in Table II include average pain ratings from daily activity diaries and SIP impairment scores. The correlation between self-efficacy and pain response expectancy was
- 0.65, indicating that different, although related, constructs were indeed being measured. Self-efficacy and pain response expectancy correlated 0.55 and -0.54, respectively, with overall performance of movements, while self-efficacy was somewhat more strongly related to pain behavior. (If data on lateral bending and trunk rotations are considered artifactual and disregarded, the correlation between self-efficacy and movement performance rises to 0.63, while other correlations do not change appr~iably.) The pain response expectancy ratings from the MAPPS were also related to pain and functional impairment in everyday life, as indicated by significant correlations with the SIP physical impairment score and average pain ratings from the daily activity diary. Self-efficacy was also significantly correlated with average pain ratings, although at a lower level than pain response expectancies. Multiple regression was employed to further explore relationships between the variables presented in Table II. Regressing movement ratings on self-efficacy and pain response expectancy yielded an R2 of 0.36 (F (2, 37) = 10.41, P -c 0.001). Both variables yielded marginally significant univariate F values when the other variable was forced into the equation first (self-efficacy: (F (1, 37) = 4.01, P < 0.053; pain response ex-
TABLE II CORRELATIONS
OF SUMMED EXPECTANCIES, PB
Movement ratings (MR) Paill behavior (PB) Self-efficacy: movement (SEM) Response expect. : pain (REP) Activity diary pain rating (PR) Sickness impact profile (SIP): Physical (SIPph) Psychosocial (SIPpsy) Other (SIPoth) * P
-0.77
SEM
DEPENDENT
MEASURES, AND ADDITIONAL
REP
PR
0.55 ***
-0.54 ***
-0.45
**
-0.62 ***
0.55 ***
-0.40
*
-0.49
**
***
-0.65
***
SIP
0.66 ***
*** P-=0.001.
-0.32
SIPph *
0.21 -0.16
-0.49
**
0.37 * -0.18
VARIABLES (N = 40)
SIPpsy
SIPoth
-0.13
- 0.24
0.05 - 0.04
0.19 -0.24
0.20
0.42 **
0.40 *
0.54 **I*
0.15
0.50 **
0.85 *** -
0.89 *** 0.55 ***
0.80 *** 071*** 0156 +*
- 0.02
0.24
328 TABLE III SUMMARY OF STEPWISE MULTIPLE REGRESSION ANALYSES No other variables met the 0.15 significance level for entry into these models. Univariate Fs indicate variance controlled after adjustment for previously entered effects. -,--__
Variable entered
Partial R2
Model R2
Significance of change in R2 F
Pi
-----
Dependent variable: movement ratings Overall F (3, 36) = 12.38, P c 0.001
1 Self-efficacy: movement 2 SIP: physical 3 SIP: other
0.302 0.154 0.052
0.302 0.456 0.510
16.45 10.44 3.81
OSKH 0.01 0.06
0.382 0.071 0.032
0.382 0.453 0.485
22.87 4.66 2.19
0.001 0.05 0.15
Dependent variable: pain behavior Overall F (3,35) =I 10.99, P -z 0.001 1 Self-efficacy: movement
2 SIP: physical 3 SIP: other
pectancy: F (1, 37) = 3.35, P < 0.076). Table III presents the results of stepwise multiple regressions in which all variables included in Table I were considered. Both movement ratings and pain behavior were used as dependent variables. Results indicate that self-efficacy for movements was the strongest predictor of both variables. The SIP physical impairment and ‘other’ scores were also selected as significant predictors of both dependent variables. Response expectancy as a determinant of perceived self-efficacy The results presented above indicate that when
variance due to self-efficacy was controlled, pain response expectancies added little to the prediction of movement performance. However, expected pain was the primary reason given by patients for the great majority (83%) of their predictions of impair4 movement, while fear of injury and lack of ability accounted for only 12% and 5% of the predictions, respectively. (Of the 400 movement predictions made across subjects, 83% predicted some degree of impairment.) These findings suggested that although self-efficacy expectancies irately determined performance, pain response expectancies may have exerted their influence at an earlier point in a causal sequence. Correlations generally do not permit causal in-
ferences; however, causal modeling [12] may be used to test hypothesized causal relationships among correlational data. Fig. 2 presents an a priori causal model based on a view of efficacy expectancies as intentions to perform pain-generating behaviors; these intentions may be presumed to vary as a function of expected pain. (This model is explained in greater detail in the Discussion.) The model includes variables revealed in preceding analyses as important predictors of impaired movement and pain behavior. A saturated model (all possible paths) was tested; however, for
Fig. 2. Causal model of expectancies and functional impairment (N = 40). SIPph = SIP physical impairment score; PR = average daily pain rating from daily activity diary; REP= response expectancy for pain; SEM = perceived salf-&kacy for movement; MR = movement raw from videotape; PB pain behavior score from videotape. * P c 0.05; l l P -z 0.01; l ** P<0.001.
329
clarity of presentation only the significant paths are included in the diagram. The path coefficients indicate that both pain behavior (PB) and movement ratings (MR) were most strongly influenced by self-efficacy for movements (SEM), which in turn were determined by response expectancies for pain (REP). Pain response expectancies appear to be a function of general levels of pain experience indicated by diary pain ratings (PR). The SIP physical impairment index (SIPph) was also associated with movement ratings, although at a lower level than SEM.
Discussion
This study examined 2 types of expectancy as predictors of impaired performance of movements in patients with chronic low back pain. Predicted level of performance was presumed to reflect perceived self-efficacy [2,3,6,7,16,17] and predicted pain was considered to indicate pain response expectancies [13]. The results revealed that both self-efficacy and pain response expectancies bore substantial correlations with actual performance, and they appeared to account for approximately equal portions of unique variance when considered alone. Both expectancy measures were related to global measures of pain and/or physical impairment, supporting the hypothesis that specific expectancies are based on general life experiences. Further analyses employing stepwise multiple regressions of movement and pain behavior on all independent variables indicated that pain response expectancies contributed negligible predictive power after movement predictions were taken into account. Thus, the prediction that expected pain would be the strongest determinant of functional impairment was not supported. When considered in relation to pain, efficacy expectancies have typically been defined as a person’s perceived ability to cope with pain. However, patients’ self-efficacy predictions may also be interpreted as decisions regarding desirable levels of performance relative to expected outcomes. In other words, a chronic pain patient might predict that he or she will perform movements to the
extent that pain associated with the movements remains at tolerable levels. Kirsch [14] and Teasdale [18] have argued that self-efficacy ratings reflect behavioral intentions, i.e., decisions to act that are mainly functions of expected outcomes (cf., Ajzen and Fishbein [l]). This view is congruent with operational definitions of the construct in the present study and previous research on self-efficacy and pain [e.g., 6,7,16]. An interpretation of efficacy ratings as intentions is supported by the present finding that expected pain was named most often by patients as the major factor influencing their predictions of movement limitations. It is possible that efficacy ratings were better predictors of performance than pain response expectancies because they accounted not only for variance due to expected pain, but also to physical harm expectancies, the major concern influencing 12% of the predictions. On the other hand, the fact that only 5% of predicted limitations were attributed to lack of ability supports the interpretation of movement predictions as intentions rather than ratings of perceived ability. In the present study, response expectancy ratings index an important expected outcome of motor performances, pain. Post-hoc causal modeling was employed to test the hypothesis that self-efficacy expectancies for the performance of movements may be a function of expected pain. A parsimonious interpretation of the results suggests that average daily pain experience determines pain response expectancies for specific movements. Pain response expectancies appear to influence performance and associated pain behavior through their effects on efficacy expectancies. These results are consistent with the model presented above in which pain response expectancies contribute to functional impairment by affecting behavioral intentions. The findings also indicate that pain response expectancies associated with specific movements are based on generalized expectancies drawn from daily experiences and suggest that chronic pain patients have well-established ideas of how much pain they will experience in different situations. Further research is needed to investigate the effects of expected pain on behavioral intentions. This study demonstrated that correlations between expectancy measures and dependent varia-
330
bles in research on chronic pain can be substantial, if the specificity and objectivity of predictions and criterion variables are maximized [cf., 5,141. The graphic presentation of expectancy items was designed to minimize the effects of verbal ability, while allowing patients to indicate expected levels of performance and pain with ease and precision. Comparison of the present results with those of previous studies indicates that the MAPPS format may offer advantages over conventional verbal self-report in research on expectancy and pain. Improvements on previous research methods also included the use of a standard set of criterion behaviors that were performed in a controlled situation, videotaped, and objectively rated. Although this study was conducted to investigate theoretical and measurement issues, some practical implications may be drawn from the results. In general, the findings suggest that patient expectancies of physical impairment and pain bear a substantial relationship to actual performance; thus, a measure like the MAPPS may be useful in clinical assessment. Stepwise multiple regression suggests that expectancies and SIP data may be fruitfully combined in the evaluation of chronic pain patients. For example, patients’ predictions could be used to add specific content to the global impairment indices on the SIP. Results of causal modeling also suggest that decreasing pain response expectancies may diminish functional impairment in pain patients through positive changes in behavioral intentions. Social learning theorists [3,13,19] have suggested that expectancies are major determinants of pain-related behavior and functional impairment in pain patients. Although the present study does not allow strong causal inferences, the results indicate that a major portion of variance in the performance of movements and other indices of functional impairment can be accounted for by self-efficacy and pain response expectancies. Undoubtedly, many clinicians seek to instill positive expectancies in their patients, and previous investigations have demonstrated positive changes in self-efficacy as chronic pain patients progress through behaviorally oriented rehabilitative therapy [6,7,16]. However, the systematic implementation and evaluation of expectancy modification
procedures have not yet been attempted with samples of chronic pain patients. Along with results of previous investigations, the present findings should encourage research on expectancy modification procedures in chronic pain treatment programs.
Acknowledgements
The authors would like to thank Drs. Irving Kirsch, Kevin D. McCaul, and Paul D. Rokke for their helpful comments on an earlier version of this manuscript.
References
1 Ajzen, 1. and Fishbein, M., Understanding Predicting Social Behavior, NJ, 1980. 2
Prentice-Hall,
Attitudes and Engfewood Cliffs.
Bandura. A., Self-efficacy: toward a unifying theory of
behavioral change, Psychol. Rev., 84 (1977) 191-215. 3 Bandura, A., Social Foundations of Thought and Action, Prentice-Hall, Englewood Cliffs, NJ, 1986. 4 Bergner, M., Bobbitt. R. and Pollard, W., The Sickness Impact Profile: validation of a health status measure. Med. Care, 14 (1976) 56-67. 5 Council, J.R., Kirsch, I., Vickery. A.R. and Carlson. D.. ‘Trance’ versus ‘skill’ hypnotic inductions: the effects of credibility, expectancy and experimenter modeling. J. C’onsult. Clin. Psychol., 51 (1983) 432-440. 6 Dolce, J.J., Cracker, M.F. and Dolys, D.M., Prediction of outcome among chronic pain patients, Behav. Res. Ther.. 24 (1986) 313-319. 7 Dolce, J.J., Cracker, M.F., Moletteire, C. and Dolys, D.M.. Exercise quotas. anticipatory concern, and self-efficacy expectancies in chronic pain: a preliminary report. Pam. 24 (1986) 365-372. 8 Follick, M.J., Ahem, D.K. and Aberger, E.W.. Development of an audiovisual taxonomy of pain behavior: reliability and discriminant validity. Hlth Psychol.. 4 (1985) 555-568. 9 Follick, M.J., Ahem, D. and Laser-Wolston. N., Evaluation of a daily activity diary for chronic pain patients. Pain. 19 (1984) 373-382. 10 Follick, M., Smith, T.W. and Ahem. D.K., The Sickness Impact Profile: a global measure of disability in chronic low back pain, Pain, 21 (1985) 67-76. 11 Fordyce. W.E., Shelton, J.L. and Dundore. E.E., The modification of avoidance learning pain behaviors. J. Behav. Med., 5 (1982) 405-415. 12 Kenny, D.A., Correlation and Causality. Wiley. New York. 1979.
331 13 Kirsch, I., Response expectancy as a determinant of experience and behavior, Am. Psychol., 40 (1985) 1189-1202. 14 Kirsch, I., Response expectancy and phobic anxiety: a reply to Wilkins and Bandura, Am. Psychol., 41 (1986) 1391-1393. 15 Kirsch, I., Tennen, H., Wickless, C., Saccone, A. and Cody, S., The role of expectancy in fear reduction, Behav. Ther., 14 (1983) 520-533. 16 Kores, R., Robert, Murphy and Rosenthal, A self-efficacy scale to predict outcome in chronic pain treatment: preliminary results, Paper presented at the meeting of the Society of Behavioral Medicine, New Orleans, 1985.
17 O’Leary, A., Self-efficacy and health, Behav. Res. Ther., 23 (1985) 437-451. 18 Teasdale, J.D., Self-efficacy: toward a unifying theury of behavioral change?, Adv. Behav. Res. Ther., 1 (1978) 211-215. 19 Turk, D., Meichenbaum, D. and Genest, M., Pam and Behavioral Medicine, Guildford, New York. 20 White, A.A. and Gordon, S.L., Synopsis: workshop on idiopathic low-back pain, Spine, 7 (1982) 141-149.
Pain, 33 (1988) 323-331 Elsevier PA1 01227
Expectancies and functional impairment in chronic low back pain James R. Council *, David K. Ahem * *, Michael J. Follick * * and Curtis L. Kline * * Department
o~Psyckolo~,
and * * Brown University Program in Medicine,
North Dakota State University, Fargq ND 5810.5 (U.S.A.), The Miriam Hospital, Chronic Pain Research Unit, Prwidence,
RI 02906 (U.S.A.)
(Received 22 June 1987, accepted 25 January 1988)
s-w
Perceived self-efficacy [2] and pain response expectancies [13] were examined as correlates of movement limitations and impaired functioning in a sample of 40 patients with chronic low back pain. Self-efficacy was operationalized as patients’ ratings of their ability to perform movements, while response expectancies were operationahzed as ratings of the degree of pain expected to accompany the movements. Patients predicted their ability to perform 10 simple movements and the degree of pain that would accompany each movement; on a separate occasion, subjects’ actual performance of the movements was assessed. In general, independent predictions of both movement ability and pain correlated significantly with performance of specific movements as rated from videotapes. Total movement scores correlated 0.55 and -0.54, respectively, with total self-efficacy and pain response expectancy ratings. Expectancy ratings were also predictive of average daily pain ratings and questionnaire ratings of physical impairment in everyday life. Multiple regression analyses, in&ding causal modeling, indicated that actual performance was best predicted by self-efficacy ratings, which in turn appeared to be determined by pain response expectancies. Key wordsr Expectancy ratings; Low back pain; Movement scores
Patients with chronic low back pain often display significant motor impairment and other pain behaviors in the absence of sufficient organic pathology to account for their loss of function [9,20]. Several researchers have proposed that avoidance learning may partially account for this discrepancy. According to this hypothesis, patients appropriately avoid excessive motor activity during the acute phase of an injury. This inactivity is negatively reinforced by pain reduction and may result in avoidance behavior that persists after healing [7,11]. A social learning model could also account for impaired motor functions in chronic
Correspondence to: J.R. Council, Dept. of Psychology, North Dakota State University, Fargo, ND 58105, U.S.A.
pain patients - when an indi~du~ expects aversive experiences to result from attempts to perform particular motor behaviors, he or she will avoid those behaviors. Expected negative outcomes could include increased pain and the experience of failure in an important area of need (e.g., physical competence). Bandura [2,3] and Kirsch [13] have both proposed expectancy constructs that may be useful in understanding maladaptive behaviors associated with chronic pain syndromes. Perceiued self-efficacy [2,3], defined as the expectancy of successful perfo~~ce in a problem situation, has been proposed to affect the functional status of chronic pain patients in 2 major ways. First, the performance of actions necessary for meeting treatment goals may be affected b$ people’s judgments of their behavioral and social skills [3,19]. Second, perceived self-efficacy for cognitively coping with pain may determine the
0304-3959/88/$03.50 6 1988 Elsevier Science Publishers B.V. (Biomedical Division)
324
ways in which people deal with situations associated with pain [3,6,17,19]. For example, patients with low self-efficacy for coping with pain might be more likely to avoid behaviors and situations associated with pain or to use pain medication in those situations. Self-efficacy expectancies of patients in rehab~itative therapy for chronic back pain have been assessed as they relate to motor performance (e.g., daily activities, meeting physical therapy exercise quotas) and the ability to cope with pain without medication. Dolce et al. [7] demonstrated that substantial increases in self-efficacy ratings were associated with improved exercise levels. Other studies have shown that self-efficacy expectancies are sig~fic~tly correlated with post-treatment pain ratings, tolerance for physical activities, use of pain medication, and work status 16,161. While generally supporting the construct’s utility, correlations between measures of self-efficacy and the functional status of chronic back pain patients have been low, with more consistent predictions of motor behaviors than variables related to cognitive control of pain. Dolce and coworkers reported that a number of their patients showed no increase in self-efficacy despite meeting exercise quotas during treatment f7], and that posttreatment self-efficacy ratings failed to account for a significant proportion of variance in a regression analysis of follow-up measures [6]. Dolce et al. [6] noted that their self-efficacy measures consisted of general questions (e.g., ‘how able or capable do you feel you are of.. . : daily exercise; coping without pain mentions’), and that greater specificity may have resulted in stronger associations with treatment outcome measures. Although Kores et al. [16] assessed self-efficacy for specific behaviors, a number of possibly unrelated items (e.g., walking, Lifting, coping with pain, engaging in family activities) were combined to yield a total score which may have lacked predictive power. Correlations reported by Dolce et al. ]6] and Kores et al. [16] may also have been weakened by the use of self-report during interviews rather than objective behavioral ratings to collect data on dependent variables. It is likely that stronger relationships between self-efficacy and functional status would be revealed with more specific and
objective measures of expectancies and criterion behaviors. Self-efficacy theory has been applied to the experience of pain by positing cognitive coping skills used by patients to modulate pain perception. An explanation of avoidance behavior that directly addresses pain experience can be derived from Kirsch’s f 13) response expectancy hypothesis. Response expectancies are defined as subjective predictions of responses that occur without volitional control (e.g., pain, emotional reactions. and conversion symptoms). Kirsch [13] proposed that avoidance of particular situations will vary as a function of the subjectively held probability that an aversive non-volitional response (e.g., pain) will be associated with those situations. Thus, according to the response expectancy hypothesis, patients who expect more severe pain to result from a particular behavior will be more hkely to avoid that behavior than patients expecting less pain. In addition to relating directly to the subjective experience of pain, this model is more parsimonious than that based on self-efficacy. Asking a patient to predict his or her ability to cognitively cope with a painful experience implicitly assumes both that the patient can predict pain intensity and that the patient will ‘cope’ (usually in some unspecified manner). Although the role of response expectancies has been established in fear reduction and for the action of placebos in alleviating pain [13.15], the relationship of response expectancies to chronic pain behavior has not yet been explored. This study was designed to investigate perceived self-efficacy and response expectancy as correlates of functional impairment (i.e., movement limitations) associated with chronic low back pain. It was hypothesized that perceived self-efficacy, operationalized as patients’ ratings of their ability to perform movements, would bear a direct relationship to actual performance. Response expectancies for pain, operationaEzed as patient ratings of the degree of pain expected to accompany the movements, were predicted to bear an inverse relationship to performance. Due to their direct relations~p to the experience of pain, response expectancies were hypothesized to bear a stronger relationship to avoidance behaviors (i.e., functional impairment) than self-efficacy expec-
tancies. In order to maximize the specificity of expectancy measures, self-ratings involved simple movements that were diagrammed step by step; performance of the movements corresponding to specific expectancy ratings was later videotaped. This specificity was predicted to result in substantially higher correlations between expectancy and performance than indicated by previous investigations. Finally, social learning theory postulates that self-predictions to novel situations are based on generalized classes of expectancies drawn from everyday life experiences. Thus, although highly specific, the expectancy ratings in this study were also predicted to bear significant correlations with global measures of pain and functional impairment in everyday life.
Method
No pain
Discomfort
Painful
Very painful
lntolernble
1
2
3
4
0
1. Toe touch from standing position.
Win Prediction
_
_
_
-
-
It you did not circle the last picrure. please put a check mifk next to i&e a&x reami belov:
_ Pear of injury
_Plin
- Leek of ability
Fig. 1. Sample MAPPS item. Subjects respond by circling the stick figure corresponding to their predicted ability to perform the movement and indicate predicted pain for each stage of the movement.
Subjects
Subjects were 20 males and 20 females undergoing evaluation at the Miriam Hospital Chronic Pain Treatment Program. Selection criteria included low back pain of greater than 6 months duration, and no indications of spinal disease or other organic pathology requiring (further) surgical intervention. Low back pain was the primary complaint for 36 (90%) of the subjects, with the remaining 4 subjects (10%) complaining of primary neck and shoulder pain. Subjects ranged in age from 20 to 69 years (mean = 42.9 years, S.D. = 11.4) with a mean duration of pain of 45.4 months (S.D. = 27.0 months). Twenty-two subjects (54%) had undergone some form of surgery related to their pain, and of these, 10 reported two or more surgeries. Thirty-four percent were using medication for pain relief at the time of assessment. Independent measure ~ove~nt and pain predi~t~vn scale ~~~PPS~. The MAPPS depicts S successive stages of 10 simple movements. A sample item is presented in Fig. 1, and the 10 movements are listed in Table I. Subjects predicted the extent to which they would be able to perform each movement (i.e., self-efficacy expectancies) by circling one of the pictured stages. Pain levels expected to accompany each
step of the movement (pain response expectancies) were indicated below each pictured stage. Subjects indicated expected pain for all stages of the movement, including those they did not expect to complete. When subjects predicted they could not complete a movement, they indicated whether fear of injury, pain, or lack of ability was the primary reason for their response. MAPPS movement predictions were scored from 1 to 5, with ‘1’ indicating a subject’s prediction that he or she would be unable to perform any stage of the movement, and ‘5’ indicating a prediction of successful performance of the complete movement. Pain response expectancies were also indicated on a l-5 scale (‘no pain’-‘intoIerable’), and were scored by summing over all stages of each movement. Dependent rne~~es Movement ratings. The major dependent measure was a rating of the performance of each movement for which patients had made predictions on the MAPPS. The sequence of movements was videotaped, and the extent of each movement was rated on a l-5 scale that, like the MAPPS movement predictions in Fig. 1, pictured 5 succes-
326
TABLE I CORRELATIONS BETWEEN SELF-EFFICACY, PAIN RESPONSE EXPECTANCIES AND PERFORMANCE IN RELATION TO 10 SPECIFIC MOVEMENT (N = 40) Movement (starting position)
1 Toe touch (standing) 2 Sit-up (lying supine) 3 Right leg raise (lying supine) 4 Left leg raise (lying supine) 5 Right leg raise (lying on side) 6 Left leg raise (lying on side) 7 Right lateral bend (standing) 8 Left lateral bend (standing) 9 Right trunk rotation (standing) 10 Left trunk rotation (standing) * PcO.05;
Response expectancy: pain
Correlation between self-efficacy and response expectancy
0.49 **
-0.41 **
-0.53 ***
0.38 *
-0.49 **
-0.51 ***
0.74 ***
-0.64 ***
-0.75 ***
0.64 ***
-0.66 ***
-0.71 ***
0.51 ***
-0.45 ***
-0.58 ***
0.51 ***
-0.37 *
-0.67 ***
0.40 *
-0.22
-0.63 ***
0.21
-0.23
-0.69 ***
-0.03
- 0.26
-0.49 **
- 0.07
- 0.21
-0.60 ***
Seifefficacy: movement
** PcO.01;
*** P
sive stages of each movement. Inter-rater reliability for movement ratings was 0.84 (Pearson correlation coefficient), based on 2 independent raters and half the sample. Audiovisual
taxonomy
of pain behavior [?I]. This
empirically derived observational rating system was used to score videotapes for behaviors including movement limitations, verbal complaints and limitation statements, non-verbal sounds, and position shifting. These ratings generated a global index of pain behavior that was not afforded by movement ratings alone. Taxonomy data were missing for 1 subject; therefore analyses using this variable are based on a sample of 39 patients.
ment were included described below:
in the analyses. These are
Sickness impact profile (SIP) (41. The SIP is a behaviorally based self-report measure containing 136 statements about health-related dysfunction in 12 areas of activity. The SIP yields scores on 3 major dimensions: physical imp~rment, psychosocial impairment, and ‘other’ (primarily work and recreational) impairment. The 3 dimension scores are combined to form a total impairment score, Higher scores on aIt measures indicate greater impairment. The SIP has been validated as a global measure of disability in chronic low back pain [lo]. Duily activity diary (91. The daily activity diary is a 7-day record kept by patients that includes reports of daily activities, pain levels and pain behaviors. Average daily pain ratings (on scale of ‘0 = no pain’ to ‘10 = worst possible pain’) from the diary were used in this study. Procedure
Subjects completed the MAPPS and other assessment instruments during their initial evaluation for admission to a multidisciplinary chronic pain treatment program. Approximately 1 week after completing the MAPPS, and before entering treatment, each subject was videotaped while he or she performed the 10 movements for which MAPPS expectancy ratings had been made. (The movements are listed in Table I.) Subjects had not known beforehand that their ability to actually perform these movements would be assessed. The videotaping was part of an ongoing validation of the ‘audiovisual taxonomy of pain behavior’ [8] and included a brief interview component that was not included in the present analysis. Patients were informed that videotaping was a routine component of clinical evaluation although the tapes could possibly be used for research purposes. Written consent to be videotaped was obtained from all subjects.
Rt?!dtS Other measures
In addition to the measures described above, global measures of pain and functional impair-
Correlations between MAPPS expectancy measures and actual performance of the correspond-
327 ing movements are presented in Table I. A number of correlations were highly significant; however, correlations involving lateral bending and trunk rotations from a standing position were generally non-significant. The non-significant relationships are possibly an artifact arising from confusion of right vs. left movements, since figures representing these movements were presented to the subjects as mirror images in full frontal view. The lower correlations might also have resulted if subjects were less familiar with these movements than with the others. Correlations between self-efficacy and pain response expectancy for specific movements were all substantial, ranging from -0.49 to -0.75. With the exception of some items likely to have been affected by measurement error, data from Table I indicate consistent relationships between self-efficacy, response expectancy and performance of specific motor behaviors. Table II presents correlations involving total scores summed over the expectancy and movement ratings. Pain behavior was rated from the videotapes using the pain behavior taxonomy [8]. Other variables presented in Table II include average pain ratings from daily activity diaries and SIP impairment scores. The correlation between self-efficacy and pain response expectancy was
- 0.65, indicating that different, although related, constructs were indeed being measured. Self-efficacy and pain response expectancy correlated 0.55 and -0.54, respectively, with overall performance of movements, while self-efficacy was somewhat more strongly related to pain behavior. (If data on lateral bending and trunk rotations are considered artifactual and disregarded, the correlation between self-efficacy and movement performance rises to 0.63, while other correlations do not change appr~iably.) The pain response expectancy ratings from the MAPPS were also related to pain and functional impairment in everyday life, as indicated by significant correlations with the SIP physical impairment score and average pain ratings from the daily activity diary. Self-efficacy was also significantly correlated with average pain ratings, although at a lower level than pain response expectancies. Multiple regression was employed to further explore relationships between the variables presented in Table II. Regressing movement ratings on self-efficacy and pain response expectancy yielded an R2 of 0.36 (F (2, 37) = 10.41, P -c 0.001). Both variables yielded marginally significant univariate F values when the other variable was forced into the equation first (self-efficacy: (F (1, 37) = 4.01, P < 0.053; pain response ex-
TABLE II CORRELATIONS
OF SUMMED EXPECTANCIES, PB
Movement ratings (MR) Paill behavior (PB) Self-efficacy: movement (SEM) Response expect. : pain (REP) Activity diary pain rating (PR) Sickness impact profile (SIP): Physical (SIPph) Psychosocial (SIPpsy) Other (SIPoth) * P
-0.77
SEM
DEPENDENT
MEASURES, AND ADDITIONAL
REP
PR
0.55 ***
-0.54 ***
-0.45
**
-0.62 ***
0.55 ***
-0.40
*
-0.49
**
***
-0.65
***
SIP
0.66 ***
*** P-=0.001.
-0.32
SIPph *
0.21 -0.16
-0.49
**
0.37 * -0.18
VARIABLES (N = 40)
SIPpsy
SIPoth
-0.13
- 0.24
0.05 - 0.04
0.19 -0.24
0.20
0.42 **
0.40 *
0.54 **I*
0.15
0.50 **
0.85 *** -
0.89 *** 0.55 ***
0.80 *** 071*** 0156 +*
- 0.02
0.24
328 TABLE III SUMMARY OF STEPWISE MULTIPLE REGRESSION ANALYSES No other variables met the 0.15 significance level for entry into these models. Univariate Fs indicate variance controlled after adjustment for previously entered effects. -,--__
Variable entered
Partial R2
Model R2
Significance of change in R2 F
Pi
-----
Dependent variable: movement ratings Overall F (3, 36) = 12.38, P c 0.001
1 Self-efficacy: movement 2 SIP: physical 3 SIP: other
0.302 0.154 0.052
0.302 0.456 0.510
16.45 10.44 3.81
OSKH 0.01 0.06
0.382 0.071 0.032
0.382 0.453 0.485
22.87 4.66 2.19
0.001 0.05 0.15
Dependent variable: pain behavior Overall F (3,35) =I 10.99, P -z 0.001 1 Self-efficacy: movement
2 SIP: physical 3 SIP: other
pectancy: F (1, 37) = 3.35, P < 0.076). Table III presents the results of stepwise multiple regressions in which all variables included in Table I were considered. Both movement ratings and pain behavior were used as dependent variables. Results indicate that self-efficacy for movements was the strongest predictor of both variables. The SIP physical impairment and ‘other’ scores were also selected as significant predictors of both dependent variables. Response expectancy as a determinant of perceived self-efficacy The results presented above indicate that when
variance due to self-efficacy was controlled, pain response expectancies added little to the prediction of movement performance. However, expected pain was the primary reason given by patients for the great majority (83%) of their predictions of impair4 movement, while fear of injury and lack of ability accounted for only 12% and 5% of the predictions, respectively. (Of the 400 movement predictions made across subjects, 83% predicted some degree of impairment.) These findings suggested that although self-efficacy expectancies irately determined performance, pain response expectancies may have exerted their influence at an earlier point in a causal sequence. Correlations generally do not permit causal in-
ferences; however, causal modeling [12] may be used to test hypothesized causal relationships among correlational data. Fig. 2 presents an a priori causal model based on a view of efficacy expectancies as intentions to perform pain-generating behaviors; these intentions may be presumed to vary as a function of expected pain. (This model is explained in greater detail in the Discussion.) The model includes variables revealed in preceding analyses as important predictors of impaired movement and pain behavior. A saturated model (all possible paths) was tested; however, for
Fig. 2. Causal model of expectancies and functional impairment (N = 40). SIPph = SIP physical impairment score; PR = average daily pain rating from daily activity diary; REP= response expectancy for pain; SEM = perceived salf-&kacy for movement; MR = movement raw from videotape; PB pain behavior score from videotape. * P c 0.05; l l P -z 0.01; l ** P<0.001.
329
clarity of presentation only the significant paths are included in the diagram. The path coefficients indicate that both pain behavior (PB) and movement ratings (MR) were most strongly influenced by self-efficacy for movements (SEM), which in turn were determined by response expectancies for pain (REP). Pain response expectancies appear to be a function of general levels of pain experience indicated by diary pain ratings (PR). The SIP physical impairment index (SIPph) was also associated with movement ratings, although at a lower level than SEM.
Discussion
This study examined 2 types of expectancy as predictors of impaired performance of movements in patients with chronic low back pain. Predicted level of performance was presumed to reflect perceived self-efficacy [2,3,6,7,16,17] and predicted pain was considered to indicate pain response expectancies [13]. The results revealed that both self-efficacy and pain response expectancies bore substantial correlations with actual performance, and they appeared to account for approximately equal portions of unique variance when considered alone. Both expectancy measures were related to global measures of pain and/or physical impairment, supporting the hypothesis that specific expectancies are based on general life experiences. Further analyses employing stepwise multiple regressions of movement and pain behavior on all independent variables indicated that pain response expectancies contributed negligible predictive power after movement predictions were taken into account. Thus, the prediction that expected pain would be the strongest determinant of functional impairment was not supported. When considered in relation to pain, efficacy expectancies have typically been defined as a person’s perceived ability to cope with pain. However, patients’ self-efficacy predictions may also be interpreted as decisions regarding desirable levels of performance relative to expected outcomes. In other words, a chronic pain patient might predict that he or she will perform movements to the
extent that pain associated with the movements remains at tolerable levels. Kirsch [14] and Teasdale [18] have argued that self-efficacy ratings reflect behavioral intentions, i.e., decisions to act that are mainly functions of expected outcomes (cf., Ajzen and Fishbein [l]). This view is congruent with operational definitions of the construct in the present study and previous research on self-efficacy and pain [e.g., 6,7,16]. An interpretation of efficacy ratings as intentions is supported by the present finding that expected pain was named most often by patients as the major factor influencing their predictions of movement limitations. It is possible that efficacy ratings were better predictors of performance than pain response expectancies because they accounted not only for variance due to expected pain, but also to physical harm expectancies, the major concern influencing 12% of the predictions. On the other hand, the fact that only 5% of predicted limitations were attributed to lack of ability supports the interpretation of movement predictions as intentions rather than ratings of perceived ability. In the present study, response expectancy ratings index an important expected outcome of motor performances, pain. Post-hoc causal modeling was employed to test the hypothesis that self-efficacy expectancies for the performance of movements may be a function of expected pain. A parsimonious interpretation of the results suggests that average daily pain experience determines pain response expectancies for specific movements. Pain response expectancies appear to influence performance and associated pain behavior through their effects on efficacy expectancies. These results are consistent with the model presented above in which pain response expectancies contribute to functional impairment by affecting behavioral intentions. The findings also indicate that pain response expectancies associated with specific movements are based on generalized expectancies drawn from daily experiences and suggest that chronic pain patients have well-established ideas of how much pain they will experience in different situations. Further research is needed to investigate the effects of expected pain on behavioral intentions. This study demonstrated that correlations between expectancy measures and dependent varia-
330
bles in research on chronic pain can be substantial, if the specificity and objectivity of predictions and criterion variables are maximized [cf., 5,141. The graphic presentation of expectancy items was designed to minimize the effects of verbal ability, while allowing patients to indicate expected levels of performance and pain with ease and precision. Comparison of the present results with those of previous studies indicates that the MAPPS format may offer advantages over conventional verbal self-report in research on expectancy and pain. Improvements on previous research methods also included the use of a standard set of criterion behaviors that were performed in a controlled situation, videotaped, and objectively rated. Although this study was conducted to investigate theoretical and measurement issues, some practical implications may be drawn from the results. In general, the findings suggest that patient expectancies of physical impairment and pain bear a substantial relationship to actual performance; thus, a measure like the MAPPS may be useful in clinical assessment. Stepwise multiple regression suggests that expectancies and SIP data may be fruitfully combined in the evaluation of chronic pain patients. For example, patients’ predictions could be used to add specific content to the global impairment indices on the SIP. Results of causal modeling also suggest that decreasing pain response expectancies may diminish functional impairment in pain patients through positive changes in behavioral intentions. Social learning theorists [3,13,19] have suggested that expectancies are major determinants of pain-related behavior and functional impairment in pain patients. Although the present study does not allow strong causal inferences, the results indicate that a major portion of variance in the performance of movements and other indices of functional impairment can be accounted for by self-efficacy and pain response expectancies. Undoubtedly, many clinicians seek to instill positive expectancies in their patients, and previous investigations have demonstrated positive changes in self-efficacy as chronic pain patients progress through behaviorally oriented rehabilitative therapy [6,7,16]. However, the systematic implementation and evaluation of expectancy modification
procedures have not yet been attempted with samples of chronic pain patients. Along with results of previous investigations, the present findings should encourage research on expectancy modification procedures in chronic pain treatment programs.
Acknowledgements
The authors would like to thank Drs. Irving Kirsch, Kevin D. McCaul, and Paul D. Rokke for their helpful comments on an earlier version of this manuscript.
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