- Email: [email protected]
Assessment of menstrual cycle symptoms by trend analysis
Volume 155 Number 2
Our 25% rate of missing patient charts is high, but unfortunately high rates have been observed in other retrospective chart reviews at this institution. The location of the missing hospital records can only be speculated on; they may have been misfiled, removed for zealous investigation, or requested administratively because of recognized adverse outcome; finally, the possibility of removal for the purpose of limiting medicolegal exposure or promoting claims must be considered. Although some patient charts are missing in most clinical settings, rather few authors mention this problem in retrospective studies. This problem will not be overcome by enlarging the sample size of the retrospective study. The only way to manage this problem is to reduce the number of missing charts to a minimum, and it ought to be a requirement that the number of missing charts be given in retrospective observational studies. The recent introduction of computerized data bases makes it seem that the problem of missing records can
Retrospective study of miSSing hospital records
be solved. However, the use of such a data base will not guarantee a perfect solution to this problem because of difficulties inherent in chart coding, data entry, data manipulation, and misinterpretation. Nevertheless, a carefully executed retrospective study can provide important clinical information. REFERENCES I. Hill AB. Principles of medical statistics. London: Oxford.
University Press, 1967. 2. Cranberg L. Do retrospective controls make clinical trials "inherently fallacious"? Br Med J 1979;2: 1265. 3. Hayden GF, Kramer MS, Horwitz Rl. The case control study. A practical review for the clinician . .lAMA 1982; 247:326. 4. Bergsjo P. What is a retrospective study? AM .l OBSTET GYNECOL 1983;146:117. 5. Louis TA, Lavon PW, Bailar .le, Polansky M. Statistics in practice. Crossover and self-controlled designs in clinical research. N Engl J Med 1984;310:24. 6. Richard TA. Does correlation establish cause? N Engl .l Med 1984;310: 1470. 7. Westgren M, Songster G, Paul R. Preterm breech delivery, another retrospective study. Obstet Gynecol (in press).
Assessment of menstrual cycle symptoms by trend analysis A. L. Magos, M.B., B.S., B.Sc., and J. W. W. Studd, M.D. London, England The physical, psychological, and behavioral changes associated with the menstrual cycle can be assessed statistically by time series analysis. One such method, Trigg's technique for trends, has been adapted for the study of prospective symptom ratings used in evaluation of the premenstrual syndrome. Such analysis provides both qualitative and quantitative information concerning menstrual cycle symptomatology. The pattern of symptoms, as denoted by Trigg's tracking Signal, can be identified. The premenstrual syndrome can be defined mathematically in terms of significant symptom trends at specified times in the menstrual cycle. The overall severity of symptoms at any point in the cycle can be gauged by the exponentially smoothed average symptom ratings. A derived statistic. the menstrual cycle ratio, is proposed as a global index of menstrual cycle morbidity which can be easily standardized to allow for comparability of research reports. (AM J OBSTET GVNECOL 1986;155:271-7.)
Key words: Menstrual cycle. prospective symptom ratings. trend analysis Premenstrual syndrome is a common complaint. af~ fecting an estimated 20% to 40% of women during their reproductive years. I Although there is much controversy concerning etiology and treatment, arguably the major confusion arises from a lack of a universally From the PMS Clinic, Department oJ Gynecology, Dulwich Ho.Ipital. This work was supported by a grant Jrom King's Voluntary Research Trust. Receivedfor publication November 21, 1985; revi5ed April 2, 1986; accepted April 7, 1986. Reprint requesiL' A. L. Magos, PMS Clinic. Department oj Gynecology, Dulwich Hospital, London. England.
agreed on definition and diagnostic criteria." In the absence of a biochemical marker for the condition it is generally believed that prospective daily symptom rating is the most sensitive method of distinguishing 11011cyclical problems from those that are essentially only present before menstruation." The evaluation of these subjective psychologic, behavioral, and physical changes is difficult. Numerous methods have been suggested in the literature. ranging from simply the presence or absence of certain common complaints' to the grading of the severity of symptoms by means of scores or linear analogue scales. I N umer271
272
Magos and Studd
August 1986 Am J Obstet Gynecol
Symptom scorQ
3
2.50 Actual
score 2
Smoothed
f'-'
1. 50
Trend
+-
1 4
7
2 1
28
Days of cycle
Fig. 1. Trend analysis of symptoms during a menstrual cycle showing significant trends that fulfill the criteria for the premenstrual syndrome. Symptoms scored on a scale of () to 3 (no symptoms to severe symptoms). Smoothing constant = 0.25. ESA(max) = Maximum exponentially smoothed av· erage. ESA(min) = Minimum exponentially smoothed average. MeR = Menstrual cycle ratio.
Symptom score
2.50
"-
Iv
2
1. 50
Actual
SmoothQd
IV
-
average
Trend
- f::i
0.50
1I 7
~
+-
I~ In~
nnnn 1 4
2
1
2 8
Days of cycle
Fig. 2. Trend analysis of symptoms during a menstrual cycle showing significant trends that do not fulfill the criteria for the premenstrual syndrome. Symptoms scored on a scale of 0 to 3 (no symptoms to severe symptoms). Smoothing constant = 0.25.
ical methods allow for statistical analysis of the measurements, and simple but arbitrary formulas have been proposed," as well as adaptation of more complex mathematical models." The suitability of all these methods for the assessment of menstrual cycle data and for the detection of nonrandom events is uncertain. The specific statistical approach to chronologie data, that is, observations made sequentially in time, is time series analysis. The special features of this method are, first, that the time order of the observations is important; second, that the observations need not be independent of each other; and third, that when successive
observations are dependent, future values can be predicted with a variable degree of accuracy.' Daily symptom ratings appear to be ideally suited to such analysis, since the data are chronologic and dependent (that is, a "bad" day is more likely to be followed by another bad day and vice versa). Several techniques are available depending on the objectives of the analysis. One method of trend analysis, originally described by Brown" and later modified by Trigg" for the detection of long-term changes in the mean and widely used in industrial process control, has already been adapted to monitoring physiologic and pharmologic responses in
Assessment of menstrual cycle symptoms
Volume 155 Number 2
273
S mptom score
3
2.5 0 ,A,ctual
score 2
1.5 o
Iv
1\ ~P
1
Iv
1\
Smoothed average
\ / jv
I
0.5 0
o
i\~
Trend (p<0.05)
,
+-
In
In
1 !il 1 fl
!il
1 4
7
n In 2 1
2 8
O'jYS of eye I e
Fig. 3. Trend analysis of symptoms during a menstrual cycle showing absence of significant trends. Symptoms scored on a scale of 0 to 3 (no symptoms to severe symptoms). Smoothing constant = 0.25.
intensive carelli and to the control of analytical measurements in clinical chemistry. II More recently, and pertinent to the study of menstrual cycle symptomatology, Forrest'" used a modified form of Trigg's technique in a study of the cyclical mood changes associated with the combined contraceptive pill. As the first part of a study into the symptom characteristics of women complaining of premenstrual syndrome, we would like to present the theoretic basis of Trigg's technique for trends and its application in diagnosis and the assessment of menstrually related symptoms. Description of Trigg's technique for trends
For a particular time series of observations x(l), x(2), x(3), x(4), ... , x(n) Trigg's trend analysis" uses the exponentially smoothed average, ESA(n), as predictor of the next observation, x(n + 1). Exponential smoothing involves taking geometrically weighted sums of the past observations so that greatest weight is placed on the most recent observation ESA(n) = sc . x(n) + sc(l - sc) . x(n - 1) + sc(l - sc)" . x(n - 2) + ... where the smoothing constant, sc, has a range of 0 to 1. The above calculation can be simplified to ESA(n)
=
sc . x(n) + (1 - sc) . ESA(n -
1)
Successive observations allow for the calculation of the forecast error, FE(n), that is the difference between the predicted and actual observations: FE(n) = x(n) - ESA(n - 1)
Trigg's technique uses the exponentially smoothed forecast error, SFE(n), as an index of the degree of change in the observations SFE(n) = sc . FE(n)
+
(1 - sc) . SFE(n - 1)
and the exponentially smoothed absolute forecast error, called the mean absolute deviation, MAD(n), as an index of the degree of random variation in the data MAD(n) = sc' IFE(n)1
+ (1
- sc) . MAD(n - 1)
Trigg's tracking signal, TS, is then defined as the ratio TS(n) = SFE(n)/MAD(n) When observations are relatively constant, the expected and observed values are similar, and both the forecast errors and the tracking signals will fluctuate around zero. With random observations all parameters will also fluctuate randomly above and below zero. However, when the observations consistently change in one direction, the smoothed forecast errors will become increasingly negative (observations becoming smaller) or positive (observations becoming larger), and the tracking signal will approach the theoretical minimum (- 1) or maximum ( + 1), respectively. At these two extremes of the tracking signal, it is certain that there has been a significant decrease or increase in the average value of the parameter measured. With tracking signals between the two extremes, the degree of significance of the tracking signal is a function of the smoothing constant. Batty'" showed that (1) the smoothed forecast errors are generally normally distributed irrespective of the distribution of the observations; (2) the local estimate of the mean absolute deviation is both relatively constant and approximates to the true mean absolute deviation, at least when the
274
Magos and Studd
August 1986 Am J Obstet Gynecol
TrackIng slgnai
PMS trends
o Non-PMS trends
No trends
957. confldencQ
-0. 60 ~~~~~~~""_
11m) ts
-0.00
_,L-__ ____________ ______ ~
~
,
4
~~
2 ,
______________ 2 8
Days of cycle
Fig. 4. Daily Trigg's tracking signals during a menstrual cycle for the different symptom trends. Smoothing constant = 0.25.
smoothing constant is small (sc < 0.1); and (3) the tracking signal is then also normally distributed about zero with a variance that is dependent on the variance of the smoothed forecast errors. Based on this relationship, Batty'" was able to calculate theoretic (sc < 0.1) and simulated (sc > 0.1) confidence limits for the tracking signal for various values of the smoothing constant.
Application of Trigg's technique for the assessment of symptoms Prospective daily symptom ratings form a time series that can be analyzed both qualitatively and quantitatively by Trigg's technique for trends; any psychometric tool fulfilling these criteria can be analyzed, examples ranging from extensive symptom lists such as Moos' menstrual distress questionnaire" to simpler visual analogue scales dealing with major symptoms only.' The tracking signals provide information concerning the pattern of symptoms during the menstrual cycle and allow for the detection of statistically significant changes (that is, trends) in symptomatology in terms of timing, direction, and duration. Conversely the exponentially smoothed averages are an index of the overall magnitude of symptoms at any point in the menstrual cycle which take account of previous symptomatology. Such information can be utilized for the diagnosis of premenstrual syndrome and in the global assessment of the severity of symptoms. Qualitative assessment of symptoms and diagnosis of premenstrual syndrome. Premenstrual syndrome can be considered as a condition associated with "distressing physical, psychological and behavioral symptoms, not caused by organic disease, which regularly recur during the same phase of each menstrual (ovar-
ian) cycle, and which significantly regress or disappear during the remainder of the cycle."" Although such a definition is useful, it is subject to important ambiguities of interpretation. This is particularly so with reference to what is considered (I) distressing as well as (2) fluctuating in phase with the menstrual cycle. Whereas the severity of symptoms cannot be anything but subjective, making a quantitative threshold for the degree of "distress" not only inappropriate but of questionable practical value, Trigg's technique does allow for the objective evaluation of the timing of symptoms during the menstrual cycle by determining the pattern of statistically significant symptom trends. Thus if positive trends are equivalent to worsening symptoms (symptom scores increasing) and negative trends to improving symptoms (symptom scores decreasing), premenstrual syndrome could be defined as a condition associated during the menstrual cycle with (I) distress, (2) significant (p < 0.05) positive symptom trends at some time during the 14 days before menstruation and at no other time in the cycle, and (3) significant (p < 0.05) negative symptom trends at some time after the onset of menstruation and at no time after the presence of significant positive trends. A typical example of this particular pattern of symptom trends is shown in Fig. 1. Alternative trend patterns include those in which significant symptom trends do not fulfill the above definition (for example, Fig. 2) and symptom ratings which do not result in any significant trends during the menstrual cycle (for example, Fig. 3). Trigg's tracking signals for the same data are plotted in Fig. 4, showing when in the cycle the upper and lower 95% confidence limits are exceeded, which gives rise to significant positive and negative trends, respectively.
Assessment of menstrual cycle symptoms 275
Volume 155 Number 2
Table I. Trend pattern of symptoms during a menstrual cycle with different smoothing constants Smoothing constant Day of cycle 1
Symptom rating*
22 23 24 25
2.6 2.4 1.6 1.6 1.2 1.8 2.2 1.4 1.0 0.4 0.8 0.6 0.8 0.0 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.2 0.0 0.8
26
1.0
27
0.6
2 3 4
5 6 7 8 9 10 11 12 13 14 15 16
17 18 19 20 21
28
1.0
29
2.2 2.4 2.0 2.4
30 31
32
0.05
+ +
+
I
0.1
+
+
+
I
0.15
I
0.2
I
0.25
I
0.3
1 0.35 1 0.4 1 0.45
I
0.5
+
+ +
+ + + +
+ + + + +
+ + + + + + +
+ + + + + + +
+ + + + + + + +
+ +
+
+ + + + +
+ + + +
+, Significant positive trend. -, Significant negative trend. *Symptoms scored on a scale of 0 to 3 (no symptoms to severe symptoms).
It is evident from the description of Trigg's technique that the important variable in the analysis is the smoothing constant, since it modulates the calculation of the smoothed averages and the tracking signals as well as the statistical interpretation of the latter. Exponential smoothing is analogous to the calculation of a moving average, and the smoothing constant is directly related to the number of observations (N) in an equivalent moving average":
sc = 2/(N + 1) From the above relationship it is apparent that a small smoothing constant is equivalent to a large number of observations in the moving average, while a large constant is conceptually similar to a small number of observations. Therefore, small or large smoothing constants is the analysis provide information about longterm and short-term trends, respectively. The choice of the smoothing constant depends on the properties of the time series and is commonly between 0.1 and 0.3. 7 With assumption that an average menstrual cycle consists of approximately 28 consecutive ratings and
with consideration of typical plots of symptom scores one would expect in premenstrual syndrome (for example, Fig. I), the use of a smoothing constant of 0.25, equivalent to a moving average of seven observations (days) is reasonable (Chatfield, personal communication). It is the smoothing constant that is typically associated with the maximum sum of smoothed errors squared (ISP) for this type of data and therefore can be considered the most sensitive to symptom changes. As can be seen from the trend analysis of the same set of data with use of various smoothing constants (Table I), the precise value of the constant is generally not critical. This is further highlighted if symptom trends. in this case during the first 7 days. are ignored to allow for equilibration of the exponentially smoothed averages during that time and thereby to reduce the chance of type II error in the analysis. Quantitative assessment of symptoms-the menstrual cycle ratio. Each individual, exponentially smoothed average is a function of the most recent as well as the previous daily symptom ratings and so represents a global index of the severity of symptoms up
276
Magos and Studd
August 1986 Am J Obstet Gynecol
schemes and methods of assessment by expressing each element of the ratio as a proportion of the theoretic maximum daily score. Such a transformation gives a standardized menstrual cycle ratio (SMCR) which, provided identical smoothing constants are employed in the analysis (for example, 0.25), would allow comparisons to be made between research reports in terms of patient characteristics and response to therapy. In the example given in Fig. 1 above, where the symptoms were originally rated on a scoring of scheme of 0 to 3 (0, no symptom, to 3, severe symptoms), the MCR can be standardized by dividing both components by three, the theoretical maximum daily rating, giving: SMCR = 0.58/0.03
Conclusions
Fig. 5. Flow chart of Trigg's trend analysis for senes of observations x(l), x(2), x(3), ...... , x(i). FE = Forecast error. SFE = Smoothed forecast error. MAD = Mean absolute deviation. TS = Tracking signal. ESA = Exponentially smoothed average.
to that time in the menstrual cycle. This property of the smoothed averages can be utilized to describe the overall degree of complaining up to any specified point of a particular menstrual cycle (for example, midcycle or premenstrual day). Furthermore, the maximum, ESA(max), and minimum, ESA(min), exponentially smoothed averages within a cycle can be used in a menstrual cycle ratio (MCR): MCR = ESA(max)/ESA(min) where ESA(max) represents peak and ESA(min) baseline symptomatology. This ratio can be used as a quantitative index of menstrual cycle symptoms both for individuals and groups of patients. Thus, in classical premenstrual syndrome one would expect ESA(max) to be high and ESA(min) to be low, whereas with premenstrual exacerbation of chronic symptoms, ESA (min) would also be relatively high. As an example, the MCR for the daily symptoms depicted in Fig. 1 is: MCR = 1.74/0.08 The MCR can also be standardized for different scoring
Trend analysis appears to be a rational and valid statistical approach to the prospective assessment of the symptoms associated with the menstrual cycle. It can be used to (I) identify and classify symptom patterns, (2) provide a mathematical definition of premenstrual syndrome in terms of significant symptom trends at definable times in the cycle, (3) quantify symptoms, and (4) give a global index of menstrual cycle morbidity as expressed by the menstrual cycle ratio. While the complexity of the mathematics of the technique makes it unsuitable for use outside specialized clinics, trend analysis may have a wider role in gynecology for the study of other cyclical phenomena, such as endocrine and metabolic changes, for which daily measurements are possible. We would like to thank Dr. A. R. W. Forrest for help with the implementation of a computer program to perform Trigg's trend analysis. A listing of the program in BBC BASIC suitable for the BBC-B computer running ZSO CP/M is available from us.
REFERENCES I. Reid RL, Yen SSC. Premenstrual syndrome. A\l./ OBSTET GY~ECOL 1981; 139:85-104. 2. Magos AL, Studd./WW. The premenstrual syndrome. In: Studd JWW, ed. Progress in obstetrics and gynaecology. vol 4. Edinburgh: Churchill Livingstone, 1984:334-50. 3. Robinson K, Huntington KM, Wallace MG. Treatment of the premenstrual syndrome. Br ./ Obstet Gynaecol 1977;84:784-8. 4. O'Brien PMS, Craven D, Selby C, et al. Treatment of premenstrual syndrome by spironolactone. Br ./ Obstet GynaecoI1979;86:142-7. 5. Muse KN, Cetel NS, Futterman LA, et al. The premenstrual syndrome: effects of 'medical ovariectomy.' N Engl J Med 1984;311:1345-9. 6. Sampson GA,Jenner FA. Studies of daily recordings from the Moos menstrual distress questionnaire. Br J Psychiatry 1977; 130:265-71. 7. Chatfield C. The analysis of time series: an introduction. London: Chapman and Hall, 1984. 8. Brown RG. Smoothing, forecasting and prediction of discrete time series. Englewood Cliffs, New Jersey: PrenticeHall, 1962.
Assessment of menstrual cycle symptoms
Volume 155 Number 2
9. Trigg DW. Monitoring a forecasting system. Oper Res Q 1964;15:271-4. 10. Hope CE, Lewis CD, Perry JR, et al. Computed trend analysis in automated patient monitoring systems. Br J Anaesth 1973;45:440-9. II. Cembrowski GS, Westgard JO, Eggert AA, et al. Trend detection in control data: optimization and interpretation of Trigg's technique for trend analysis. Clin Chern 1975;21: 1396-405. 12. Forrest ARW. Cyclical variations in mood in normal women taking oral contraceptives. Br Med J 1979;4: 1403. 13. Batty M. Monitoring an exponential smoothing forecasting system. Oper Res Q 1969;20:319-25. 14. Moos RH. The development of a menstrual distress questionnaire. Psychosom Med 1968;30:853-67.
Appendix A flow chart for Trigg's technique for trends is shown in Fig. 5. At the start of the analysis of a series of data
by Trigg's technique for trends, certain parameters have to be initialized. For the purposes of this study investigating daily symptoms ratings during a menstrual cycle, the following initial settings were used: Smoothing constant Smoothed forecast error Mean absolute deviation Exponentially smoothed average
sc SFE(O) MAD(O) ESA(O)
0.25 0.0 SQR([2/pil . [Series SD]) Series mean
For each member of the time series, the forecast error (FE), smoothed forecast error (SFE), tracking signal (TS) and significance level are calculated. The above variables are updated together with the exponentially smoothed average (ESA) before analysis of the next member of the sequence.
Trend analysis of the symptoms of 150 women with a history of the premenstrual syndrome A. L. Magos, M.B., B.S., B.Se., M. Brineat, Ph.D., and 1.
w. W. Studd, M.D.
London, England The daily symptom records of 150 untreated women with a convincing history of the premenstrual syndrome were investigated qualitatively and quantitatively by means of time series analysis in the form of Trigg's technique for trends. Symptoms were monitored with use of a modified menstrual distress questionnaire. Analysis showed that, depending on the symptom cluster, 60.7% to 85.3% of the women showed symptom trends consistent with the syndrome, 14.0% to 35.3% had trends not typical of the syndrome, and in 0% to 5.3% of records significant trends were absent. Since over 80% of the women were found to have premenstrual syndrome trends for three or more of the six symptom clusters studied, including 32% who showed this trend pattern for all symptoms, a retrospective history of premenstrual syndrome is likely to be confirmed on prospective assessment for at least some symptoms. Quantitatively women who fulfilled the diagnostic criteria for premenstrual syndrome differed from those who did not by exhibiting significantly greater exacerbation of symptoms premenstrually and lesser morbidity postmenstrually. While water retention, negative affect, and pain were the three symptom clusters associated with the most severe ratings, the majority of women suffered from a mixture of physical, psychological, and behavioral complaints, and it was not possible to subdivide the study group by the type of symptoms. (AM J OBSTET GVNECOL 1986;155:277-82.)
Key words: Premenstrual syndrome, diagnosis, trend analysis There is now considerable objective evidence that most if not all the body systems undergo changes in parallel with the ovarian cycle.' Subjective evidence is also available for these changes, since numerous symp-
From the PMS Clinic, Department of Gynecology, Dulwiclt Hospital. This work was supported b.V a grant from King's Voluntary Research Trust. RI'Cl';Vl'd for puhlimfion Novpmher 21, 1985; revised April 2, 1986; accepted April 7, 1986. Reprint requests: A. L. Magos, PMS Clinic, Department of Gvnecology, Dulwich Hospital, London, England.
toms have been reported as regularly fluctuating with the menstrual cycle (Moos RH, Baker K. Literature review and summary of the premenstrual tension syndrome. Unpublished research report, Stanford University, 1965), and these symptoms are experienced to a variable degree by the majority of women during their fertile years.' When severe, this collection of symptoms constitutes the premenstrual syndrome.' Perhaps because of greater public awareness, an increasing number of women seek help for such premenstrual complaints. In the absence of specific bio-
277
Our 25% rate of missing patient charts is high, but unfortunately high rates have been observed in other retrospective chart reviews at this institution. The location of the missing hospital records can only be speculated on; they may have been misfiled, removed for zealous investigation, or requested administratively because of recognized adverse outcome; finally, the possibility of removal for the purpose of limiting medicolegal exposure or promoting claims must be considered. Although some patient charts are missing in most clinical settings, rather few authors mention this problem in retrospective studies. This problem will not be overcome by enlarging the sample size of the retrospective study. The only way to manage this problem is to reduce the number of missing charts to a minimum, and it ought to be a requirement that the number of missing charts be given in retrospective observational studies. The recent introduction of computerized data bases makes it seem that the problem of missing records can
Retrospective study of miSSing hospital records
be solved. However, the use of such a data base will not guarantee a perfect solution to this problem because of difficulties inherent in chart coding, data entry, data manipulation, and misinterpretation. Nevertheless, a carefully executed retrospective study can provide important clinical information. REFERENCES I. Hill AB. Principles of medical statistics. London: Oxford.
University Press, 1967. 2. Cranberg L. Do retrospective controls make clinical trials "inherently fallacious"? Br Med J 1979;2: 1265. 3. Hayden GF, Kramer MS, Horwitz Rl. The case control study. A practical review for the clinician . .lAMA 1982; 247:326. 4. Bergsjo P. What is a retrospective study? AM .l OBSTET GYNECOL 1983;146:117. 5. Louis TA, Lavon PW, Bailar .le, Polansky M. Statistics in practice. Crossover and self-controlled designs in clinical research. N Engl J Med 1984;310:24. 6. Richard TA. Does correlation establish cause? N Engl .l Med 1984;310: 1470. 7. Westgren M, Songster G, Paul R. Preterm breech delivery, another retrospective study. Obstet Gynecol (in press).
Assessment of menstrual cycle symptoms by trend analysis A. L. Magos, M.B., B.S., B.Sc., and J. W. W. Studd, M.D. London, England The physical, psychological, and behavioral changes associated with the menstrual cycle can be assessed statistically by time series analysis. One such method, Trigg's technique for trends, has been adapted for the study of prospective symptom ratings used in evaluation of the premenstrual syndrome. Such analysis provides both qualitative and quantitative information concerning menstrual cycle symptomatology. The pattern of symptoms, as denoted by Trigg's tracking Signal, can be identified. The premenstrual syndrome can be defined mathematically in terms of significant symptom trends at specified times in the menstrual cycle. The overall severity of symptoms at any point in the cycle can be gauged by the exponentially smoothed average symptom ratings. A derived statistic. the menstrual cycle ratio, is proposed as a global index of menstrual cycle morbidity which can be easily standardized to allow for comparability of research reports. (AM J OBSTET GVNECOL 1986;155:271-7.)
Key words: Menstrual cycle. prospective symptom ratings. trend analysis Premenstrual syndrome is a common complaint. af~ fecting an estimated 20% to 40% of women during their reproductive years. I Although there is much controversy concerning etiology and treatment, arguably the major confusion arises from a lack of a universally From the PMS Clinic, Department oJ Gynecology, Dulwich Ho.Ipital. This work was supported by a grant Jrom King's Voluntary Research Trust. Receivedfor publication November 21, 1985; revi5ed April 2, 1986; accepted April 7, 1986. Reprint requesiL' A. L. Magos, PMS Clinic. Department oj Gynecology, Dulwich Hospital, London. England.
agreed on definition and diagnostic criteria." In the absence of a biochemical marker for the condition it is generally believed that prospective daily symptom rating is the most sensitive method of distinguishing 11011cyclical problems from those that are essentially only present before menstruation." The evaluation of these subjective psychologic, behavioral, and physical changes is difficult. Numerous methods have been suggested in the literature. ranging from simply the presence or absence of certain common complaints' to the grading of the severity of symptoms by means of scores or linear analogue scales. I N umer271
272
Magos and Studd
August 1986 Am J Obstet Gynecol
Symptom scorQ
3
2.50 Actual
score 2
Smoothed
f'-'
1. 50
Trend
+-
1 4
7
2 1
28
Days of cycle
Fig. 1. Trend analysis of symptoms during a menstrual cycle showing significant trends that fulfill the criteria for the premenstrual syndrome. Symptoms scored on a scale of () to 3 (no symptoms to severe symptoms). Smoothing constant = 0.25. ESA(max) = Maximum exponentially smoothed av· erage. ESA(min) = Minimum exponentially smoothed average. MeR = Menstrual cycle ratio.
Symptom score
2.50
"-
Iv
2
1. 50
Actual
SmoothQd
IV
-
average
Trend
- f::i
0.50
1I 7
~
+-
I~ In~
nnnn 1 4
2
1
2 8
Days of cycle
Fig. 2. Trend analysis of symptoms during a menstrual cycle showing significant trends that do not fulfill the criteria for the premenstrual syndrome. Symptoms scored on a scale of 0 to 3 (no symptoms to severe symptoms). Smoothing constant = 0.25.
ical methods allow for statistical analysis of the measurements, and simple but arbitrary formulas have been proposed," as well as adaptation of more complex mathematical models." The suitability of all these methods for the assessment of menstrual cycle data and for the detection of nonrandom events is uncertain. The specific statistical approach to chronologie data, that is, observations made sequentially in time, is time series analysis. The special features of this method are, first, that the time order of the observations is important; second, that the observations need not be independent of each other; and third, that when successive
observations are dependent, future values can be predicted with a variable degree of accuracy.' Daily symptom ratings appear to be ideally suited to such analysis, since the data are chronologic and dependent (that is, a "bad" day is more likely to be followed by another bad day and vice versa). Several techniques are available depending on the objectives of the analysis. One method of trend analysis, originally described by Brown" and later modified by Trigg" for the detection of long-term changes in the mean and widely used in industrial process control, has already been adapted to monitoring physiologic and pharmologic responses in
Assessment of menstrual cycle symptoms
Volume 155 Number 2
273
S mptom score
3
2.5 0 ,A,ctual
score 2
1.5 o
Iv
1\ ~P
1
Iv
1\
Smoothed average
\ / jv
I
0.5 0
o
i\~
Trend (p<0.05)
,
+-
In
In
1 !il 1 fl
!il
1 4
7
n In 2 1
2 8
O'jYS of eye I e
Fig. 3. Trend analysis of symptoms during a menstrual cycle showing absence of significant trends. Symptoms scored on a scale of 0 to 3 (no symptoms to severe symptoms). Smoothing constant = 0.25.
intensive carelli and to the control of analytical measurements in clinical chemistry. II More recently, and pertinent to the study of menstrual cycle symptomatology, Forrest'" used a modified form of Trigg's technique in a study of the cyclical mood changes associated with the combined contraceptive pill. As the first part of a study into the symptom characteristics of women complaining of premenstrual syndrome, we would like to present the theoretic basis of Trigg's technique for trends and its application in diagnosis and the assessment of menstrually related symptoms. Description of Trigg's technique for trends
For a particular time series of observations x(l), x(2), x(3), x(4), ... , x(n) Trigg's trend analysis" uses the exponentially smoothed average, ESA(n), as predictor of the next observation, x(n + 1). Exponential smoothing involves taking geometrically weighted sums of the past observations so that greatest weight is placed on the most recent observation ESA(n) = sc . x(n) + sc(l - sc) . x(n - 1) + sc(l - sc)" . x(n - 2) + ... where the smoothing constant, sc, has a range of 0 to 1. The above calculation can be simplified to ESA(n)
=
sc . x(n) + (1 - sc) . ESA(n -
1)
Successive observations allow for the calculation of the forecast error, FE(n), that is the difference between the predicted and actual observations: FE(n) = x(n) - ESA(n - 1)
Trigg's technique uses the exponentially smoothed forecast error, SFE(n), as an index of the degree of change in the observations SFE(n) = sc . FE(n)
+
(1 - sc) . SFE(n - 1)
and the exponentially smoothed absolute forecast error, called the mean absolute deviation, MAD(n), as an index of the degree of random variation in the data MAD(n) = sc' IFE(n)1
+ (1
- sc) . MAD(n - 1)
Trigg's tracking signal, TS, is then defined as the ratio TS(n) = SFE(n)/MAD(n) When observations are relatively constant, the expected and observed values are similar, and both the forecast errors and the tracking signals will fluctuate around zero. With random observations all parameters will also fluctuate randomly above and below zero. However, when the observations consistently change in one direction, the smoothed forecast errors will become increasingly negative (observations becoming smaller) or positive (observations becoming larger), and the tracking signal will approach the theoretical minimum (- 1) or maximum ( + 1), respectively. At these two extremes of the tracking signal, it is certain that there has been a significant decrease or increase in the average value of the parameter measured. With tracking signals between the two extremes, the degree of significance of the tracking signal is a function of the smoothing constant. Batty'" showed that (1) the smoothed forecast errors are generally normally distributed irrespective of the distribution of the observations; (2) the local estimate of the mean absolute deviation is both relatively constant and approximates to the true mean absolute deviation, at least when the
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August 1986 Am J Obstet Gynecol
TrackIng slgnai
PMS trends
o Non-PMS trends
No trends
957. confldencQ
-0. 60 ~~~~~~~""_
11m) ts
-0.00
_,L-__ ____________ ______ ~
~
,
4
~~
2 ,
______________ 2 8
Days of cycle
Fig. 4. Daily Trigg's tracking signals during a menstrual cycle for the different symptom trends. Smoothing constant = 0.25.
smoothing constant is small (sc < 0.1); and (3) the tracking signal is then also normally distributed about zero with a variance that is dependent on the variance of the smoothed forecast errors. Based on this relationship, Batty'" was able to calculate theoretic (sc < 0.1) and simulated (sc > 0.1) confidence limits for the tracking signal for various values of the smoothing constant.
Application of Trigg's technique for the assessment of symptoms Prospective daily symptom ratings form a time series that can be analyzed both qualitatively and quantitatively by Trigg's technique for trends; any psychometric tool fulfilling these criteria can be analyzed, examples ranging from extensive symptom lists such as Moos' menstrual distress questionnaire" to simpler visual analogue scales dealing with major symptoms only.' The tracking signals provide information concerning the pattern of symptoms during the menstrual cycle and allow for the detection of statistically significant changes (that is, trends) in symptomatology in terms of timing, direction, and duration. Conversely the exponentially smoothed averages are an index of the overall magnitude of symptoms at any point in the menstrual cycle which take account of previous symptomatology. Such information can be utilized for the diagnosis of premenstrual syndrome and in the global assessment of the severity of symptoms. Qualitative assessment of symptoms and diagnosis of premenstrual syndrome. Premenstrual syndrome can be considered as a condition associated with "distressing physical, psychological and behavioral symptoms, not caused by organic disease, which regularly recur during the same phase of each menstrual (ovar-
ian) cycle, and which significantly regress or disappear during the remainder of the cycle."" Although such a definition is useful, it is subject to important ambiguities of interpretation. This is particularly so with reference to what is considered (I) distressing as well as (2) fluctuating in phase with the menstrual cycle. Whereas the severity of symptoms cannot be anything but subjective, making a quantitative threshold for the degree of "distress" not only inappropriate but of questionable practical value, Trigg's technique does allow for the objective evaluation of the timing of symptoms during the menstrual cycle by determining the pattern of statistically significant symptom trends. Thus if positive trends are equivalent to worsening symptoms (symptom scores increasing) and negative trends to improving symptoms (symptom scores decreasing), premenstrual syndrome could be defined as a condition associated during the menstrual cycle with (I) distress, (2) significant (p < 0.05) positive symptom trends at some time during the 14 days before menstruation and at no other time in the cycle, and (3) significant (p < 0.05) negative symptom trends at some time after the onset of menstruation and at no time after the presence of significant positive trends. A typical example of this particular pattern of symptom trends is shown in Fig. 1. Alternative trend patterns include those in which significant symptom trends do not fulfill the above definition (for example, Fig. 2) and symptom ratings which do not result in any significant trends during the menstrual cycle (for example, Fig. 3). Trigg's tracking signals for the same data are plotted in Fig. 4, showing when in the cycle the upper and lower 95% confidence limits are exceeded, which gives rise to significant positive and negative trends, respectively.
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Table I. Trend pattern of symptoms during a menstrual cycle with different smoothing constants Smoothing constant Day of cycle 1
Symptom rating*
22 23 24 25
2.6 2.4 1.6 1.6 1.2 1.8 2.2 1.4 1.0 0.4 0.8 0.6 0.8 0.0 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.2 0.0 0.8
26
1.0
27
0.6
2 3 4
5 6 7 8 9 10 11 12 13 14 15 16
17 18 19 20 21
28
1.0
29
2.2 2.4 2.0 2.4
30 31
32
0.05
+ +
+
I
0.1
+
+
+
I
0.15
I
0.2
I
0.25
I
0.3
1 0.35 1 0.4 1 0.45
I
0.5
+
+ +
+ + + +
+ + + + +
+ + + + + + +
+ + + + + + +
+ + + + + + + +
+ +
+
+ + + + +
+ + + +
+, Significant positive trend. -, Significant negative trend. *Symptoms scored on a scale of 0 to 3 (no symptoms to severe symptoms).
It is evident from the description of Trigg's technique that the important variable in the analysis is the smoothing constant, since it modulates the calculation of the smoothed averages and the tracking signals as well as the statistical interpretation of the latter. Exponential smoothing is analogous to the calculation of a moving average, and the smoothing constant is directly related to the number of observations (N) in an equivalent moving average":
sc = 2/(N + 1) From the above relationship it is apparent that a small smoothing constant is equivalent to a large number of observations in the moving average, while a large constant is conceptually similar to a small number of observations. Therefore, small or large smoothing constants is the analysis provide information about longterm and short-term trends, respectively. The choice of the smoothing constant depends on the properties of the time series and is commonly between 0.1 and 0.3. 7 With assumption that an average menstrual cycle consists of approximately 28 consecutive ratings and
with consideration of typical plots of symptom scores one would expect in premenstrual syndrome (for example, Fig. I), the use of a smoothing constant of 0.25, equivalent to a moving average of seven observations (days) is reasonable (Chatfield, personal communication). It is the smoothing constant that is typically associated with the maximum sum of smoothed errors squared (ISP) for this type of data and therefore can be considered the most sensitive to symptom changes. As can be seen from the trend analysis of the same set of data with use of various smoothing constants (Table I), the precise value of the constant is generally not critical. This is further highlighted if symptom trends. in this case during the first 7 days. are ignored to allow for equilibration of the exponentially smoothed averages during that time and thereby to reduce the chance of type II error in the analysis. Quantitative assessment of symptoms-the menstrual cycle ratio. Each individual, exponentially smoothed average is a function of the most recent as well as the previous daily symptom ratings and so represents a global index of the severity of symptoms up
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schemes and methods of assessment by expressing each element of the ratio as a proportion of the theoretic maximum daily score. Such a transformation gives a standardized menstrual cycle ratio (SMCR) which, provided identical smoothing constants are employed in the analysis (for example, 0.25), would allow comparisons to be made between research reports in terms of patient characteristics and response to therapy. In the example given in Fig. 1 above, where the symptoms were originally rated on a scoring of scheme of 0 to 3 (0, no symptom, to 3, severe symptoms), the MCR can be standardized by dividing both components by three, the theoretical maximum daily rating, giving: SMCR = 0.58/0.03
Conclusions
Fig. 5. Flow chart of Trigg's trend analysis for senes of observations x(l), x(2), x(3), ...... , x(i). FE = Forecast error. SFE = Smoothed forecast error. MAD = Mean absolute deviation. TS = Tracking signal. ESA = Exponentially smoothed average.
to that time in the menstrual cycle. This property of the smoothed averages can be utilized to describe the overall degree of complaining up to any specified point of a particular menstrual cycle (for example, midcycle or premenstrual day). Furthermore, the maximum, ESA(max), and minimum, ESA(min), exponentially smoothed averages within a cycle can be used in a menstrual cycle ratio (MCR): MCR = ESA(max)/ESA(min) where ESA(max) represents peak and ESA(min) baseline symptomatology. This ratio can be used as a quantitative index of menstrual cycle symptoms both for individuals and groups of patients. Thus, in classical premenstrual syndrome one would expect ESA(max) to be high and ESA(min) to be low, whereas with premenstrual exacerbation of chronic symptoms, ESA (min) would also be relatively high. As an example, the MCR for the daily symptoms depicted in Fig. 1 is: MCR = 1.74/0.08 The MCR can also be standardized for different scoring
Trend analysis appears to be a rational and valid statistical approach to the prospective assessment of the symptoms associated with the menstrual cycle. It can be used to (I) identify and classify symptom patterns, (2) provide a mathematical definition of premenstrual syndrome in terms of significant symptom trends at definable times in the cycle, (3) quantify symptoms, and (4) give a global index of menstrual cycle morbidity as expressed by the menstrual cycle ratio. While the complexity of the mathematics of the technique makes it unsuitable for use outside specialized clinics, trend analysis may have a wider role in gynecology for the study of other cyclical phenomena, such as endocrine and metabolic changes, for which daily measurements are possible. We would like to thank Dr. A. R. W. Forrest for help with the implementation of a computer program to perform Trigg's trend analysis. A listing of the program in BBC BASIC suitable for the BBC-B computer running ZSO CP/M is available from us.
REFERENCES I. Reid RL, Yen SSC. Premenstrual syndrome. A\l./ OBSTET GY~ECOL 1981; 139:85-104. 2. Magos AL, Studd./WW. The premenstrual syndrome. In: Studd JWW, ed. Progress in obstetrics and gynaecology. vol 4. Edinburgh: Churchill Livingstone, 1984:334-50. 3. Robinson K, Huntington KM, Wallace MG. Treatment of the premenstrual syndrome. Br ./ Obstet Gynaecol 1977;84:784-8. 4. O'Brien PMS, Craven D, Selby C, et al. Treatment of premenstrual syndrome by spironolactone. Br ./ Obstet GynaecoI1979;86:142-7. 5. Muse KN, Cetel NS, Futterman LA, et al. The premenstrual syndrome: effects of 'medical ovariectomy.' N Engl J Med 1984;311:1345-9. 6. Sampson GA,Jenner FA. Studies of daily recordings from the Moos menstrual distress questionnaire. Br J Psychiatry 1977; 130:265-71. 7. Chatfield C. The analysis of time series: an introduction. London: Chapman and Hall, 1984. 8. Brown RG. Smoothing, forecasting and prediction of discrete time series. Englewood Cliffs, New Jersey: PrenticeHall, 1962.
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9. Trigg DW. Monitoring a forecasting system. Oper Res Q 1964;15:271-4. 10. Hope CE, Lewis CD, Perry JR, et al. Computed trend analysis in automated patient monitoring systems. Br J Anaesth 1973;45:440-9. II. Cembrowski GS, Westgard JO, Eggert AA, et al. Trend detection in control data: optimization and interpretation of Trigg's technique for trend analysis. Clin Chern 1975;21: 1396-405. 12. Forrest ARW. Cyclical variations in mood in normal women taking oral contraceptives. Br Med J 1979;4: 1403. 13. Batty M. Monitoring an exponential smoothing forecasting system. Oper Res Q 1969;20:319-25. 14. Moos RH. The development of a menstrual distress questionnaire. Psychosom Med 1968;30:853-67.
Appendix A flow chart for Trigg's technique for trends is shown in Fig. 5. At the start of the analysis of a series of data
by Trigg's technique for trends, certain parameters have to be initialized. For the purposes of this study investigating daily symptoms ratings during a menstrual cycle, the following initial settings were used: Smoothing constant Smoothed forecast error Mean absolute deviation Exponentially smoothed average
sc SFE(O) MAD(O) ESA(O)
0.25 0.0 SQR([2/pil . [Series SD]) Series mean
For each member of the time series, the forecast error (FE), smoothed forecast error (SFE), tracking signal (TS) and significance level are calculated. The above variables are updated together with the exponentially smoothed average (ESA) before analysis of the next member of the sequence.
Trend analysis of the symptoms of 150 women with a history of the premenstrual syndrome A. L. Magos, M.B., B.S., B.Se., M. Brineat, Ph.D., and 1.
w. W. Studd, M.D.
London, England The daily symptom records of 150 untreated women with a convincing history of the premenstrual syndrome were investigated qualitatively and quantitatively by means of time series analysis in the form of Trigg's technique for trends. Symptoms were monitored with use of a modified menstrual distress questionnaire. Analysis showed that, depending on the symptom cluster, 60.7% to 85.3% of the women showed symptom trends consistent with the syndrome, 14.0% to 35.3% had trends not typical of the syndrome, and in 0% to 5.3% of records significant trends were absent. Since over 80% of the women were found to have premenstrual syndrome trends for three or more of the six symptom clusters studied, including 32% who showed this trend pattern for all symptoms, a retrospective history of premenstrual syndrome is likely to be confirmed on prospective assessment for at least some symptoms. Quantitatively women who fulfilled the diagnostic criteria for premenstrual syndrome differed from those who did not by exhibiting significantly greater exacerbation of symptoms premenstrually and lesser morbidity postmenstrually. While water retention, negative affect, and pain were the three symptom clusters associated with the most severe ratings, the majority of women suffered from a mixture of physical, psychological, and behavioral complaints, and it was not possible to subdivide the study group by the type of symptoms. (AM J OBSTET GVNECOL 1986;155:277-82.)
Key words: Premenstrual syndrome, diagnosis, trend analysis There is now considerable objective evidence that most if not all the body systems undergo changes in parallel with the ovarian cycle.' Subjective evidence is also available for these changes, since numerous symp-
From the PMS Clinic, Department of Gynecology, Dulwiclt Hospital. This work was supported b.V a grant from King's Voluntary Research Trust. RI'Cl';Vl'd for puhlimfion Novpmher 21, 1985; revised April 2, 1986; accepted April 7, 1986. Reprint requests: A. L. Magos, PMS Clinic, Department of Gvnecology, Dulwich Hospital, London, England.
toms have been reported as regularly fluctuating with the menstrual cycle (Moos RH, Baker K. Literature review and summary of the premenstrual tension syndrome. Unpublished research report, Stanford University, 1965), and these symptoms are experienced to a variable degree by the majority of women during their fertile years.' When severe, this collection of symptoms constitutes the premenstrual syndrome.' Perhaps because of greater public awareness, an increasing number of women seek help for such premenstrual complaints. In the absence of specific bio-
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