Power and Sample Size Calculations for Clinical Trials of Myofascial Pain of Jaw Muscles T.T.T. DAO, G.J. LAVIGNE', J.S. FEINE, R. TANGUAY, and J.P. LUND FacultJ de mddecine dentaire Canada H3C 3J7
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Centre de recherche
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sciences neurologiques, Universitej de Montreal, C.P. 6128, Succ. A, Montreal, PQ,
When a clinical trial is planned, the approximate number of subjects needed for significant differences between/among groups to be detected must be estimated. Sample-size calculations provide the investigator with this information. This paper discusses the choice of outcome measures and describes the steps used to estimate the numbers of subjects necessary for a study that compares treatments for patients with chronic myofascial pain of jaw muscles. Within- and betweensubject variances were estimated for the chosen variables, the subjects' pain ratings on visual analogue scales. Sample sizes were then calculated for theoretical differences between groups by pre-treatment means and overall standard deviations (Cohen, 1977). The results of this analysis can be used by other researchers when planning studies involving these types of patients. J Dent Res 70(2):118-122, February, 1991
Introduction. Clinical trials are usually designed to assess, with a minimum risk of bias or error, whether a treatment causes a significant difference in outcome when compared with other therapies or control conditions. One of the major determinants of the probability of detecting differences is sample size (Lachin, 1981; Friedman et al., 1985; Spriet and Simon, 1985). Unfortunately, the number of subjects necessary for a study is rarely estimated; instead, the size of the study sample (n) is usually determined by the number of subjects available to the investigators. If n happens to be too small, the statistical power may be insufficient for real differences between treatments to be confirmed (Altman, 1980; Reed and Slaichert, 1981; Young et al., 1983). This was emphasized by Freiman et al. (1978) in a review of 71 published randomized controlled trials. They reported that, because of an insufficient number of patients enrolled, "sixty-seven of the trials had a greater than 10% risk of missing a true 25% therapeutic improvement, and with the same risk, 50% of the trials could have missed a 50% improvement". At the other extreme, if n is too large, patients may be unnecessarily exposed to experimental treatments. In some studies, such as those using potentially toxic drugs or involving patients suffering cancer-related pain, this may be unethical (Schneiderman, 1964; Altman, 1980; Medical Research Council of Canada, 1987). Even if the patient is not exposed to any risk, energy and expense are wasted in needless measurements. Sample-size estimation can also reveal that, for a particular outcome variable, a proposed research design is Received for publication November 2, 1989 Accepted for publication October 29, 1990 Based on a thesis submitted by T.T.T. Dao as a requirement for the MSc degree in neuroscience This research was supported by the Canadian Medical Research Council and the Fonds de la recherche en santd du Quebec. 'To whom correspondence and reprint requests should be addressed 118
not feasible because the n required for detection of the expected difference between groups is too high (Hulley and Cummings, 1988). When the approximate size of a study population cannot be estimated from data gathered from previous controlled trials, a pilot study should be done to estimate the variance and the appropriate n. The size of the trial can then be decided by balancing statistical considerations (more specifically, the power of the test) against ethical considerations and practical factors, such as limitation on time, expense, and availability of patients (Gore, 1981). Despite the importance of sample-size estimation in the planning of a clinical trial, this step is neglected in most of the studies evaluating the efficacy of treatments for chronic myofascial pain of jaw muscles. This condition has also been listed as a subgroup of temporomandibular disorders, and it is reported that approximately 5% of the population is in need of treatment (Rugh and Solberg, 1985). However, no data are presently available that can be used to estimate the sample size for clinical studies of this condition. In a recent paper, Rubinoff et al. (1987) wrote that their "inability to show a significant difference in treatment outcome between the group that received an occluding splint and the group that received a nonoccluding splint" was probably due to the small study sample size (n = 28). Analysis of their data showed that a significant difference in maximal opening could have been detected with 400 subjects and in muscle palpation category scores with a sample size of over 60 subjects. This conclusion emphasizes that the sample sizes needed for various outcome measures can be very different. In this paper, we will discuss the choice of appropriate outcome measures for the evaluation of treatments for chronic myofascial pain of jaw muscles. We will also discuss which criteria should be used to determine the degree of difference sought between treatments, and how variations in this difference will affect the size of the sample. Finally, using these proposed measures, we will provide estimates of the variance within our population of patients, as well as power curves for calculating sample size. This will provide other investigators with the information necessary in planning the sizes of their sample populations for future studies. A short report of this work has previously been presented (Dao et al., 1989).
Materials and methods. Population. -Subjects chosen for this study were referred to the University Research Clinic by local dentists. They presented with the signs and symptoms of myofascial pain of jaw muscles as defined by Bell (1982), accepted by the American Dental Association (Griffiths, 1983), and corresponding to those described by the American Academy of Craniomandibular Disorders (McNeill, 1990). All were French-speaking Canadians, men and women from 15 to 45 years of age, who gave informed consent to procedures approved by the University Human Subjects Ethics Committee. Design. -Data derived from a randomized, blinded, paral-
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lel, controlled, ongoing study were used for these calculations. Groups were counterbalanced and subjects randomly allocated to one of the three groups: treatment, active control, and passive control. Measurements. -At each of seven sessions over a period of ten weeks, the subjects (21) rated the sensory (intensity) and affective (unpleasantness) dimensions of their pain on visual analogue scales (VAS). Data collection and analysis were completed under blind conditions. Statistics for sample-size estimation. -The sample-size estimation consisted of seven steps, following procedures suggested by Cohen (1977): (1) The calculations were first done with an (x value of 0.05 and a P value of 0.20. An oa of 0.05 represents a 5% probability of finding a difference between groups when none exists (type I error). When ,B is fixed at 0.20, the probability of finding no difference when one does exist is 20% (type II error). (2) Sample-size calculations were based on the patients' pain reports recorded on VAS (Price et al., 1983; Duncan et al., 1989). The means of the VAS pain intensity and unpleasantness ratings were calculated from pre-treatment scores. (3) The Interactive Generalized Least Squares procedure (IGLS) was used (Goldstein, 1979, 1987) to estimate the between- and within-subject variances of the post-treatment period because it allows the post-treatment variance to be adjusted for both the pre-treatment variance and for the linear changes in the measurements over time, while taking into account the possible differences in baseline between the groups. It also estimates the two levels of variance (between- and withinsubject) encountered in the hierarchical structure of the study design. The overall (pre- and post-treatment) standard deviation (C) of the preliminary sample was then calculated by the formula: C
= Va2Within subject + &2Between subject
(4) In the fourth step, a series of hypothetical differences between groups was determined. The differences (8) were defined as percentages (15%, 30%, 45%, 60%, and 80%) of the mean pre-treatment pain intensity and unpleasantness VAS ratings calculated in step #2. (5) The corresponding relative size index "f" (relative variance ratio), as defined by Cohen (1977), was calculated with the following formula: f= 8
\/i172k
where f = relative size index, 8 = standardized difference from the mean pre-treatment value calculated in step #4, and k = number of groups. (6) Tables of "f" values (Cohen, 1977) were then consulted for first approximation of the "group size" (n). The choice of table depends on the ax value and the number of groups, while the appropriate row and column depend upon the power of the test (1 - P) and the "f" value, respectively. (7) Since the measurements were repeated over time and are interdependent, a multilevel model (Goldstein, 1987) was used to estimate the intra-subject (or intra-class) correlation (r1cc). In multilevel models, the relative variation for each different level is separated. Thus, when patients and times are analyzed within a two-level model, an intra-subject correlation is carried out from measurements made at different times in the same subject. The intra-subject correlation (rlcc) was estimated from the
119
variances calculated in the third step and was used to adjust the group size obtained in step #6 (Goldstein, 1979), n (1 - rCC2) n* where n = group size (step #6) n* = adjusted group size &=Between subjects ICC = o-2Between subjects + o2Within subjects The total study size (n') was simply the "n*k", where k = 3. Finally, a series of power curves was generated for the two variables for differences of 30%, 45%, 60%, and 80% of the baseline mean values, with a values of 0.05 and 0.01, by the computer program "Design" (Systat, Version 1.0, Systat, Inc., Evanston, IL). Results. The mean pre-treatment pain intensity and unpleasantness VAS ratings were, respectively, 30.6 mm and 33.8 mm. These values, together with the between- and within-subject variances and the overall standard deviations, are given in Table 1. Table 2 contains the values of differences (8) corresponding to 15%, 30%, 45%, 60%, and 80% of the mean pre-treatment pain intensity and unpleasantness ratings. The values for intensity and unpleasantness range from 4.6 to 24.5 mm and from 5.1 to 27.0 mm, respectively. The relative size index "f" for each ar was calculated. These are shown in Tables 3A (intensity) and 3B (unpleasantness). Sample-size tables were then consulted to estimate the number of subjects required per group for each value of "f" (Tables 3A and 3B). For example, in order to detect a 8 of 15% in pain intensity between control and treatment groups, 322 subjects would be needed per group, while the detection of a 8 of 60% requires only 21 subjects (Table 3A). These numbers were then adjusted to take into account the estimated intrasubject correlation (rIcc). This resulted in a considerable reduction in the group sizes for pain intensity, because rtcc = TABLE 1 PRE-TREATMENT MEANS, POST-TREATMENT VARIANCES, AND OVERALL STANDARD DEVIATIONS FOR VAS PAIN INTENSITY AND UNPLEASANTNESS Post-treatment Subject Variance Mean Overall Pre-Tx Variable Within Between S.D. Intensity 30.6 mm 197.1 162.0 19.0 33.8 mm Unpleasantness 208.2 38.8 15.7
TABLE 2 VALUES OF VAS PAIN INTENSITY AND UNPLEASANTNESS RATINGS* THAT CORRESPOND TO PROJECTED DIFFERENCES BETWEEN TREATMENT GROUPS
Intensity Unpleasantness 4.6mm 5.1mm 9.2 mm 10.1 mm 13.5 mm 15.2 mm 18.3 mm 20.3 mm 24.5 mm 27.0 mm 8Projected differences between the means of treatment and control groups. *These were calculated from the VAS pre-treatment mean scores. 15% 30% 45% 60% 80%
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TABLE 3A STUDY POPULATION BASED ON RATINGS OF PAIN INTENSITY Differences Relative Study Tx/Control Size Index Size Group Size n* a f n n' 15% 0.10 322 242 726 0.20 81 30% 61 183 45% 0.30 36 81 27 0.40 60% 21 16 48 80% 0.52 13 10 30 8: Projected % differences between treatment and control groups. n: Unadjusted group size. n*: Adjusted group size, n': Total study size = 3n*.
0.50; for example, in order to detect 8 values of 15% or 60%, 242 or 16 subjects per group could be needed. However, the intra-subject correlation for pain unpleasantness was small (ricc = 0.16), and it had little effect on the adjusted sample sizes (Table 3B). For example, n* was only slightly less than n for 8 values of 15% and 30%, and was identical for the other 8 values. The relationships between the power of the test (1 - f3) and total sample size for pain intensity and unpleasantness at two levels of a (0.05 and 0.01) are shown in Figs. A-D. Corrected sample sizes for the intra-subject correlation can be easily computed by multiplying the tabulated sample size by (1 - rCC2) where r1cc is the intra-subject correlation (rIcc = 0.50 for intensity and 0.16 for unpleasantness).
Discussion. As described in the "Introduction" and illustrated in the "Results" sections, the size of a sample population is dependent on the chosen outcome measure and on the magnitude of the differences to be sought between the groups. The choice of outcome measures.-A major source of systematic error frequently encountered in studies of myofascial pain of jaw muscles is the use of questionable outcome measures. A valid outcome measure must accurately represent the phenomena being studied and must be capable of reflecting real changes in the condition. Although most clinicians rely on patients' reports of pain relief in order to evaluate treatment effects, we have found that this measure is predisposed to subject bias. When patients assess their pain relief, they have to compare post-treatment with pre-treatment pain; thus, the validity of this measure depends upon a patient's ability to remember the initial pain accurately. In our preliminary analysis, we found that there was a systematic error in the memory of pain. Patients remembered their initial pain as being significantly greater than that reported at the first visit (Feine et al., 1989). These results are supported by similar findings in other groups of chronic pain patients (Linton and Melin, 1982; Linton and Gotestam, 1983; Jamison et al., 1989). Dental researchers have often used measurements of the "dysfunctions" associated with this condition as outcome variables-for example, by recording joint sounds, patterns of jaw movement, or electromyographic (EMG) activity of the masticatory muscles (Shields et al., 1978; Van Willigen, 1979; Cooper and Rabuzzi, 1984; Jankelson and Pulley, 1984; M1l1er et al., 1984; Harkins et al., 1988). However, because the sensitivity and specificity of these tests have been shown to be low (Widmer et al., 1990; Mohl et al., 1990a, b), their use in the assessment of treatment cannot be supported. Furthermore, it is probable that the "dysfunction" frequently observed in conjunction with this disorder is actually a secondary
J Dent Res February 1991 TABLE 3B STUDY POPULATION BASED ON RATINGS OF PAIN UNPLEASANTNESS Differences Relative Study Size Index Tx/Control Size Group Size n* f n 8 n' 15% 0.13 191 561 187 0.26 48 47 30% 141 21 0.39 21 45% 63 13 60% 0.53 13 39 80% 0.70 8 8 24 8: Projected % differences between treatment and control groups. n: Unadjusted group size. n*: Adjusted group size. n': Total study size = 3n*.
change in muscle activity resulting from pain (Lund et al., 1989). Moreover, as well as being the symptom of most concern to the patient, pain is also the primary symptom necessary to classify a condition as myofascial pain of jaw muscles (Bell, 1990; McNeill, 1990). For all of these reasons, we chose the patient's rating of actual pain on VAS as the primary measure on which to base treatment effects. VAS are widely used and have been shown to be rapid, easy, and valid methods for measuring both clinical and experimental pain (Woodforde and Merskey, 1972; Ohnhaus and Adler, 1975; Revill et al., 1976; Scott and Huskisson, 1976; Moore et al., 1979; Price et at., 1983). Unfortunately, completion of a VAS scale may be difficult for some subjects (Woodforde and Merskey, 1972; Ohnhaus and Adler, 1975) because no references other than the words at the extremities are given, and because people must imagine their pain in linear terms (Duncan et al., 1989). However, these scales give a more sensitive and accurate representation of pain intensity than the descriptive scales (Ohnhaus and Adler, 1975; Sriwatanakul et al., 1983). VAS have also been reported to be a sensitive measure of pain unpleasantness (Price et al., 1983; Duncan et al., 1989). Consequently, we chose to use VAS to estimate the sample size in this study. Inter-group differences. -One of the most difficult aspects of sample-size planning is the selection of an appropriate difference to be sought between groups. How small a difference is clinically relevant? A statistically significant difference is not necessarily clinically significant. For example, although it may be possible to show that a 5-mm difference in VAS ratings between groups is statistically significant at an a of 0.05 and a P of 0.20 by enrolling 726 (pain intensity) or 561 subjects (pain unpleasantness), there is no point in looking for differences that approximate the error in the method. In an acute pain experiment, Ekblom and Hansson (1988) suggested that a change of ± 5 mm in VAS ratings for pain intensity (corresponding to 15% in our study) was interpreted by subjects as being insignificant. On the other hand, the chance of finding very large effects of treatment-for example, an 80% difference-is slight and unrealistic. The degree of difference to be sought should normally be realistic for clinical application. Other experimental factors should also be taken into consideration. For example, the placebo effect can be expected to be very important in a study like this (Greene and Laskin, 1983). In addition, the fluctuant nature of the symptoms and the high rate of spontaneous remission characteristic of myofascial pain of jaw muscles states lead to a rate of improvement of about 26% in non-treated patients (Clark et al., 1988). A more clinically relevant difference can be derived from the results obtained in the Clark study, which demonstrated that the degree of improvement with an active splint was close to 60%.
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Figs. A-D-These graphs depict the relationship between the power of the test and the total sample size for the two variables: pain intensity (A and B) and pain unpleasantness (C and D) for four levels of intergroup differences and two levels of a. The method for adjusting this sample size for the intra-subject correlation (rIcc) is given in the "Results" section.
Using an inter-group difference of 60% in our study, a total of 48 patients will be needed to meet sample-size estimates when pain intensity ratings are used as the primary outcome measure (or 39 when pain unpleasantness is used). The samplesize estimate in this case was set at a power of 0.80. This conventional value is arbitrary (Rothman, 1986); nevertheless, it is generally considered to be the minimal acceptable level of power (Cohen, 1977). If stricter criteria are applied, the sample-size estimations increase accordingly. For example, analysis of our data indicates that at power levels of 0.85 and 0.90, 57 and 87 subjects, respectively, will be needed (based on an a of 0.05, ratings of pain intensity, and a 60% difference between groups). The power curves that were generated show that if one wishes to reduce the likelihood of a type I error to 0.01, the number of subjects for each power level will approximately double. In an ideal clinical trial, one makes every attempt to detect the smallest clinically significant change with a minimum risk of error using the minimum number of subjects. However, this "ideal" situation is far from that most often encountered. As already mentioned, the smaller the difference sought, the larger the sample size required for a given power. This in turn implies greater demands in terms of time, energy, and expense for both the patients and the researchers. Furthermore, the size of
a pool of patients with this disorder who are available for a study in a given time period and a particular place is often limited. Noncompliance may create an additional burden, because it necessitates recruiting even more subjects than originally anticipated. For all of these reasons, it may be difficult to meet statistical criteria; if this is the case, the researcher may decide either to abandon the study or to re-design it. Sample-size estimation and power analyses provide the clinical researcher with an indication of the minimum sample size necessary to meet pre-determined types I and II errors. The information that we have provided should help in the planning of future studies of myofascial pain of jaw muscles.
Acknowledgments. The authors thank A. Charbonneau, P. Duquette, P. Biron, A.-M. Desgagne, J. Gravel, and G. Boyer for their contributions to this study. REFERENCES ALTMAN, D.G. (1980): Statistics and Ethics in Medical Research. III. How Large a Sample?, Br Med J 281:1336-1338. BELL, W.D. (1982): Classification of TM Disorders. In: The Pres-
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et
Centre de recherche
en
sciences neurologiques, Universitej de Montreal, C.P. 6128, Succ. A, Montreal, PQ,
When a clinical trial is planned, the approximate number of subjects needed for significant differences between/among groups to be detected must be estimated. Sample-size calculations provide the investigator with this information. This paper discusses the choice of outcome measures and describes the steps used to estimate the numbers of subjects necessary for a study that compares treatments for patients with chronic myofascial pain of jaw muscles. Within- and betweensubject variances were estimated for the chosen variables, the subjects' pain ratings on visual analogue scales. Sample sizes were then calculated for theoretical differences between groups by pre-treatment means and overall standard deviations (Cohen, 1977). The results of this analysis can be used by other researchers when planning studies involving these types of patients. J Dent Res 70(2):118-122, February, 1991
Introduction. Clinical trials are usually designed to assess, with a minimum risk of bias or error, whether a treatment causes a significant difference in outcome when compared with other therapies or control conditions. One of the major determinants of the probability of detecting differences is sample size (Lachin, 1981; Friedman et al., 1985; Spriet and Simon, 1985). Unfortunately, the number of subjects necessary for a study is rarely estimated; instead, the size of the study sample (n) is usually determined by the number of subjects available to the investigators. If n happens to be too small, the statistical power may be insufficient for real differences between treatments to be confirmed (Altman, 1980; Reed and Slaichert, 1981; Young et al., 1983). This was emphasized by Freiman et al. (1978) in a review of 71 published randomized controlled trials. They reported that, because of an insufficient number of patients enrolled, "sixty-seven of the trials had a greater than 10% risk of missing a true 25% therapeutic improvement, and with the same risk, 50% of the trials could have missed a 50% improvement". At the other extreme, if n is too large, patients may be unnecessarily exposed to experimental treatments. In some studies, such as those using potentially toxic drugs or involving patients suffering cancer-related pain, this may be unethical (Schneiderman, 1964; Altman, 1980; Medical Research Council of Canada, 1987). Even if the patient is not exposed to any risk, energy and expense are wasted in needless measurements. Sample-size estimation can also reveal that, for a particular outcome variable, a proposed research design is Received for publication November 2, 1989 Accepted for publication October 29, 1990 Based on a thesis submitted by T.T.T. Dao as a requirement for the MSc degree in neuroscience This research was supported by the Canadian Medical Research Council and the Fonds de la recherche en santd du Quebec. 'To whom correspondence and reprint requests should be addressed 118
not feasible because the n required for detection of the expected difference between groups is too high (Hulley and Cummings, 1988). When the approximate size of a study population cannot be estimated from data gathered from previous controlled trials, a pilot study should be done to estimate the variance and the appropriate n. The size of the trial can then be decided by balancing statistical considerations (more specifically, the power of the test) against ethical considerations and practical factors, such as limitation on time, expense, and availability of patients (Gore, 1981). Despite the importance of sample-size estimation in the planning of a clinical trial, this step is neglected in most of the studies evaluating the efficacy of treatments for chronic myofascial pain of jaw muscles. This condition has also been listed as a subgroup of temporomandibular disorders, and it is reported that approximately 5% of the population is in need of treatment (Rugh and Solberg, 1985). However, no data are presently available that can be used to estimate the sample size for clinical studies of this condition. In a recent paper, Rubinoff et al. (1987) wrote that their "inability to show a significant difference in treatment outcome between the group that received an occluding splint and the group that received a nonoccluding splint" was probably due to the small study sample size (n = 28). Analysis of their data showed that a significant difference in maximal opening could have been detected with 400 subjects and in muscle palpation category scores with a sample size of over 60 subjects. This conclusion emphasizes that the sample sizes needed for various outcome measures can be very different. In this paper, we will discuss the choice of appropriate outcome measures for the evaluation of treatments for chronic myofascial pain of jaw muscles. We will also discuss which criteria should be used to determine the degree of difference sought between treatments, and how variations in this difference will affect the size of the sample. Finally, using these proposed measures, we will provide estimates of the variance within our population of patients, as well as power curves for calculating sample size. This will provide other investigators with the information necessary in planning the sizes of their sample populations for future studies. A short report of this work has previously been presented (Dao et al., 1989).
Materials and methods. Population. -Subjects chosen for this study were referred to the University Research Clinic by local dentists. They presented with the signs and symptoms of myofascial pain of jaw muscles as defined by Bell (1982), accepted by the American Dental Association (Griffiths, 1983), and corresponding to those described by the American Academy of Craniomandibular Disorders (McNeill, 1990). All were French-speaking Canadians, men and women from 15 to 45 years of age, who gave informed consent to procedures approved by the University Human Subjects Ethics Committee. Design. -Data derived from a randomized, blinded, paral-
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SAMPLE SIZE IN CHRONIC FACIAL PAIN TRIALS
lel, controlled, ongoing study were used for these calculations. Groups were counterbalanced and subjects randomly allocated to one of the three groups: treatment, active control, and passive control. Measurements. -At each of seven sessions over a period of ten weeks, the subjects (21) rated the sensory (intensity) and affective (unpleasantness) dimensions of their pain on visual analogue scales (VAS). Data collection and analysis were completed under blind conditions. Statistics for sample-size estimation. -The sample-size estimation consisted of seven steps, following procedures suggested by Cohen (1977): (1) The calculations were first done with an (x value of 0.05 and a P value of 0.20. An oa of 0.05 represents a 5% probability of finding a difference between groups when none exists (type I error). When ,B is fixed at 0.20, the probability of finding no difference when one does exist is 20% (type II error). (2) Sample-size calculations were based on the patients' pain reports recorded on VAS (Price et al., 1983; Duncan et al., 1989). The means of the VAS pain intensity and unpleasantness ratings were calculated from pre-treatment scores. (3) The Interactive Generalized Least Squares procedure (IGLS) was used (Goldstein, 1979, 1987) to estimate the between- and within-subject variances of the post-treatment period because it allows the post-treatment variance to be adjusted for both the pre-treatment variance and for the linear changes in the measurements over time, while taking into account the possible differences in baseline between the groups. It also estimates the two levels of variance (between- and withinsubject) encountered in the hierarchical structure of the study design. The overall (pre- and post-treatment) standard deviation (C) of the preliminary sample was then calculated by the formula: C
= Va2Within subject + &2Between subject
(4) In the fourth step, a series of hypothetical differences between groups was determined. The differences (8) were defined as percentages (15%, 30%, 45%, 60%, and 80%) of the mean pre-treatment pain intensity and unpleasantness VAS ratings calculated in step #2. (5) The corresponding relative size index "f" (relative variance ratio), as defined by Cohen (1977), was calculated with the following formula: f= 8
\/i172k
where f = relative size index, 8 = standardized difference from the mean pre-treatment value calculated in step #4, and k = number of groups. (6) Tables of "f" values (Cohen, 1977) were then consulted for first approximation of the "group size" (n). The choice of table depends on the ax value and the number of groups, while the appropriate row and column depend upon the power of the test (1 - P) and the "f" value, respectively. (7) Since the measurements were repeated over time and are interdependent, a multilevel model (Goldstein, 1987) was used to estimate the intra-subject (or intra-class) correlation (r1cc). In multilevel models, the relative variation for each different level is separated. Thus, when patients and times are analyzed within a two-level model, an intra-subject correlation is carried out from measurements made at different times in the same subject. The intra-subject correlation (rlcc) was estimated from the
119
variances calculated in the third step and was used to adjust the group size obtained in step #6 (Goldstein, 1979), n (1 - rCC2) n* where n = group size (step #6) n* = adjusted group size &=Between subjects ICC = o-2Between subjects + o2Within subjects The total study size (n') was simply the "n*k", where k = 3. Finally, a series of power curves was generated for the two variables for differences of 30%, 45%, 60%, and 80% of the baseline mean values, with a values of 0.05 and 0.01, by the computer program "Design" (Systat, Version 1.0, Systat, Inc., Evanston, IL). Results. The mean pre-treatment pain intensity and unpleasantness VAS ratings were, respectively, 30.6 mm and 33.8 mm. These values, together with the between- and within-subject variances and the overall standard deviations, are given in Table 1. Table 2 contains the values of differences (8) corresponding to 15%, 30%, 45%, 60%, and 80% of the mean pre-treatment pain intensity and unpleasantness ratings. The values for intensity and unpleasantness range from 4.6 to 24.5 mm and from 5.1 to 27.0 mm, respectively. The relative size index "f" for each ar was calculated. These are shown in Tables 3A (intensity) and 3B (unpleasantness). Sample-size tables were then consulted to estimate the number of subjects required per group for each value of "f" (Tables 3A and 3B). For example, in order to detect a 8 of 15% in pain intensity between control and treatment groups, 322 subjects would be needed per group, while the detection of a 8 of 60% requires only 21 subjects (Table 3A). These numbers were then adjusted to take into account the estimated intrasubject correlation (rIcc). This resulted in a considerable reduction in the group sizes for pain intensity, because rtcc = TABLE 1 PRE-TREATMENT MEANS, POST-TREATMENT VARIANCES, AND OVERALL STANDARD DEVIATIONS FOR VAS PAIN INTENSITY AND UNPLEASANTNESS Post-treatment Subject Variance Mean Overall Pre-Tx Variable Within Between S.D. Intensity 30.6 mm 197.1 162.0 19.0 33.8 mm Unpleasantness 208.2 38.8 15.7
TABLE 2 VALUES OF VAS PAIN INTENSITY AND UNPLEASANTNESS RATINGS* THAT CORRESPOND TO PROJECTED DIFFERENCES BETWEEN TREATMENT GROUPS
Intensity Unpleasantness 4.6mm 5.1mm 9.2 mm 10.1 mm 13.5 mm 15.2 mm 18.3 mm 20.3 mm 24.5 mm 27.0 mm 8Projected differences between the means of treatment and control groups. *These were calculated from the VAS pre-treatment mean scores. 15% 30% 45% 60% 80%
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TABLE 3A STUDY POPULATION BASED ON RATINGS OF PAIN INTENSITY Differences Relative Study Tx/Control Size Index Size Group Size n* a f n n' 15% 0.10 322 242 726 0.20 81 30% 61 183 45% 0.30 36 81 27 0.40 60% 21 16 48 80% 0.52 13 10 30 8: Projected % differences between treatment and control groups. n: Unadjusted group size. n*: Adjusted group size, n': Total study size = 3n*.
0.50; for example, in order to detect 8 values of 15% or 60%, 242 or 16 subjects per group could be needed. However, the intra-subject correlation for pain unpleasantness was small (ricc = 0.16), and it had little effect on the adjusted sample sizes (Table 3B). For example, n* was only slightly less than n for 8 values of 15% and 30%, and was identical for the other 8 values. The relationships between the power of the test (1 - f3) and total sample size for pain intensity and unpleasantness at two levels of a (0.05 and 0.01) are shown in Figs. A-D. Corrected sample sizes for the intra-subject correlation can be easily computed by multiplying the tabulated sample size by (1 - rCC2) where r1cc is the intra-subject correlation (rIcc = 0.50 for intensity and 0.16 for unpleasantness).
Discussion. As described in the "Introduction" and illustrated in the "Results" sections, the size of a sample population is dependent on the chosen outcome measure and on the magnitude of the differences to be sought between the groups. The choice of outcome measures.-A major source of systematic error frequently encountered in studies of myofascial pain of jaw muscles is the use of questionable outcome measures. A valid outcome measure must accurately represent the phenomena being studied and must be capable of reflecting real changes in the condition. Although most clinicians rely on patients' reports of pain relief in order to evaluate treatment effects, we have found that this measure is predisposed to subject bias. When patients assess their pain relief, they have to compare post-treatment with pre-treatment pain; thus, the validity of this measure depends upon a patient's ability to remember the initial pain accurately. In our preliminary analysis, we found that there was a systematic error in the memory of pain. Patients remembered their initial pain as being significantly greater than that reported at the first visit (Feine et al., 1989). These results are supported by similar findings in other groups of chronic pain patients (Linton and Melin, 1982; Linton and Gotestam, 1983; Jamison et al., 1989). Dental researchers have often used measurements of the "dysfunctions" associated with this condition as outcome variables-for example, by recording joint sounds, patterns of jaw movement, or electromyographic (EMG) activity of the masticatory muscles (Shields et al., 1978; Van Willigen, 1979; Cooper and Rabuzzi, 1984; Jankelson and Pulley, 1984; M1l1er et al., 1984; Harkins et al., 1988). However, because the sensitivity and specificity of these tests have been shown to be low (Widmer et al., 1990; Mohl et al., 1990a, b), their use in the assessment of treatment cannot be supported. Furthermore, it is probable that the "dysfunction" frequently observed in conjunction with this disorder is actually a secondary
J Dent Res February 1991 TABLE 3B STUDY POPULATION BASED ON RATINGS OF PAIN UNPLEASANTNESS Differences Relative Study Size Index Tx/Control Size Group Size n* f n 8 n' 15% 0.13 191 561 187 0.26 48 47 30% 141 21 0.39 21 45% 63 13 60% 0.53 13 39 80% 0.70 8 8 24 8: Projected % differences between treatment and control groups. n: Unadjusted group size. n*: Adjusted group size. n': Total study size = 3n*.
change in muscle activity resulting from pain (Lund et al., 1989). Moreover, as well as being the symptom of most concern to the patient, pain is also the primary symptom necessary to classify a condition as myofascial pain of jaw muscles (Bell, 1990; McNeill, 1990). For all of these reasons, we chose the patient's rating of actual pain on VAS as the primary measure on which to base treatment effects. VAS are widely used and have been shown to be rapid, easy, and valid methods for measuring both clinical and experimental pain (Woodforde and Merskey, 1972; Ohnhaus and Adler, 1975; Revill et al., 1976; Scott and Huskisson, 1976; Moore et al., 1979; Price et at., 1983). Unfortunately, completion of a VAS scale may be difficult for some subjects (Woodforde and Merskey, 1972; Ohnhaus and Adler, 1975) because no references other than the words at the extremities are given, and because people must imagine their pain in linear terms (Duncan et al., 1989). However, these scales give a more sensitive and accurate representation of pain intensity than the descriptive scales (Ohnhaus and Adler, 1975; Sriwatanakul et al., 1983). VAS have also been reported to be a sensitive measure of pain unpleasantness (Price et al., 1983; Duncan et al., 1989). Consequently, we chose to use VAS to estimate the sample size in this study. Inter-group differences. -One of the most difficult aspects of sample-size planning is the selection of an appropriate difference to be sought between groups. How small a difference is clinically relevant? A statistically significant difference is not necessarily clinically significant. For example, although it may be possible to show that a 5-mm difference in VAS ratings between groups is statistically significant at an a of 0.05 and a P of 0.20 by enrolling 726 (pain intensity) or 561 subjects (pain unpleasantness), there is no point in looking for differences that approximate the error in the method. In an acute pain experiment, Ekblom and Hansson (1988) suggested that a change of ± 5 mm in VAS ratings for pain intensity (corresponding to 15% in our study) was interpreted by subjects as being insignificant. On the other hand, the chance of finding very large effects of treatment-for example, an 80% difference-is slight and unrealistic. The degree of difference to be sought should normally be realistic for clinical application. Other experimental factors should also be taken into consideration. For example, the placebo effect can be expected to be very important in a study like this (Greene and Laskin, 1983). In addition, the fluctuant nature of the symptoms and the high rate of spontaneous remission characteristic of myofascial pain of jaw muscles states lead to a rate of improvement of about 26% in non-treated patients (Clark et al., 1988). A more clinically relevant difference can be derived from the results obtained in the Clark study, which demonstrated that the degree of improvement with an active splint was close to 60%.
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SAMPLE SIZE IN CHRONIC FACIAL PAIN TRIALS
Vol. 70 No. 2
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Figs. A-D-These graphs depict the relationship between the power of the test and the total sample size for the two variables: pain intensity (A and B) and pain unpleasantness (C and D) for four levels of intergroup differences and two levels of a. The method for adjusting this sample size for the intra-subject correlation (rIcc) is given in the "Results" section.
Using an inter-group difference of 60% in our study, a total of 48 patients will be needed to meet sample-size estimates when pain intensity ratings are used as the primary outcome measure (or 39 when pain unpleasantness is used). The samplesize estimate in this case was set at a power of 0.80. This conventional value is arbitrary (Rothman, 1986); nevertheless, it is generally considered to be the minimal acceptable level of power (Cohen, 1977). If stricter criteria are applied, the sample-size estimations increase accordingly. For example, analysis of our data indicates that at power levels of 0.85 and 0.90, 57 and 87 subjects, respectively, will be needed (based on an a of 0.05, ratings of pain intensity, and a 60% difference between groups). The power curves that were generated show that if one wishes to reduce the likelihood of a type I error to 0.01, the number of subjects for each power level will approximately double. In an ideal clinical trial, one makes every attempt to detect the smallest clinically significant change with a minimum risk of error using the minimum number of subjects. However, this "ideal" situation is far from that most often encountered. As already mentioned, the smaller the difference sought, the larger the sample size required for a given power. This in turn implies greater demands in terms of time, energy, and expense for both the patients and the researchers. Furthermore, the size of
a pool of patients with this disorder who are available for a study in a given time period and a particular place is often limited. Noncompliance may create an additional burden, because it necessitates recruiting even more subjects than originally anticipated. For all of these reasons, it may be difficult to meet statistical criteria; if this is the case, the researcher may decide either to abandon the study or to re-design it. Sample-size estimation and power analyses provide the clinical researcher with an indication of the minimum sample size necessary to meet pre-determined types I and II errors. The information that we have provided should help in the planning of future studies of myofascial pain of jaw muscles.
Acknowledgments. The authors thank A. Charbonneau, P. Duquette, P. Biron, A.-M. Desgagne, J. Gravel, and G. Boyer for their contributions to this study. REFERENCES ALTMAN, D.G. (1980): Statistics and Ethics in Medical Research. III. How Large a Sample?, Br Med J 281:1336-1338. BELL, W.D. (1982): Classification of TM Disorders. In: The Pres-
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