Regina Louie, Syntex Research, Palo Alto, California Alex Y aroshinsky, Syntex Research, Palo Alto, California

Transcription

1 APPLICATION OF RANDOM EFFECTS MODEL FOR CATEGORICAL DATA TO ANTIEMETIC CLINICAL TRIALS IN CANCER PATIENTS Regina Louie, Syntex Research, Palo Alto, California Alex Y aroshinsky, Syntex Research, Palo Alto, California Abstract The random-effects model for categorical response was applied to the simulated data based on a multicenter study of an antiemetic drug in patients with chemotherapy-induced emesis. The response was defined as a proportion of patients with complete control of emesis. This response for active control is relatively high (55-75%) and varies significantly across different patient populations. This fact and a high (up to 95%) anticipated rate of response for the experimental drug led to different treatmentby-site interaction estimates depending on the scale used, as described by DerSimonian and Laird (1986). Three alternative scales can be used to estimate the treatment effect of the experimental drug comparing to the active control: difference in proportions, log relative risk and log odds ratio. Effect size homogeneity across sites is highly desirable to provide an evidence of consistent treatment effect. For this study the effect size was heterogeneous if measured by log odds ratio ("Breslow-Day test) and homogeneous in the difference-inproportions scale. The latter was chosen as a measure of treatment effect in the randomeffects model. Treatment-by-site interaction was estimated for the difference in proportions using the DerSimonian-Laird procedure; confidence limits for treatment differences were obtained. Introduction The purpose of this paper is to describe a SAS based implementation of random-effects model for categorical response by DerSimonian and Laird (I) and to investigate an application of this model to the data based on a multicenter antiemetic clinical trial in cancer patients. Three treatment effect scales (difference in proportions, log relative risk and log odds ratio) will be discussed with respect to the treatment by blocking factor (center or investigator) interaction and treatment effect estimates based on the DerSimonian-Laird procedure. The treatment effect scale, homogeneous across centers, will be chosen and the treatment effect estimate will be produced using random effects model for categorical data. A SAS macro with options to choose the random-effects model estimates or Cochran-Mantel-Haenszel analysis will be discussed. The random-effects models for continuous response are represented in SAS by GLM and MIXED procedures. However, there is no existing SAS procedure based on the random or mixed effects model for categorical response. This model can be useful when categorical' data is being collected in a multicenter clinical trial. Because of different sample sizes and different patient populations each center has a different level of sampling error. An 1096

2 approach based on the random-effects model assumes that the treatment effect can vary across centers and provides a method of weighing the treatment effects based on the within- and between-center variabilities. The latter can be viewed as a treatment-by-center interaction. This interaction, according to P. Armitage (2), can be regarded as a random effect; this effect is random not because of any explicit random sampling of centers, but because it is inexplicable. The randomeffects model allows this interaction to contribute to, and increase, the error of the pooled estimate (2). This approach can be especially useful when treatment effect size is measured in the difference-in-proportions scale where the Breslow-Day test of treatment-by-center interaction associated with the Cochran-Mantel-Haenszel procedure (CMH option in PROC FREQ) cannot be performed. And, as we will see later, if treatment effect homogeneity across centers is desirable, the difference in proportions may become the optimal scale for the primary response variable. The model described in this paper was tested and validated using the simulated data based on an antiemetic clinical trial in cancer patients with chemotherapy induced emesis. It was a multicenter (3 centers), randomized, double-blind and parallel design study of an antiemetic drug with an active comparator. It is assumed that,antiemetic treatment must completely inhibit vomiting (complete response), so that anticipatory vomiting in later chemotherapy will be prevented (3,4). Thus, the proportion of patients with complete response within 24 hours of chemotherapy was chosen as a measure of treatment effect. Methodology Three measures of treatment effect can be used to estimate the treatment difference between experimental drug and active control: difference in proportions, log relative risk and log odds ratio. The effect size homogeneity across centers is highly desirable to provide convincing evidence of consistent treatment effect. According to (1), unless there is no treatment effect at all, constancy of treatment effect in one scale (for example, difference in proportions) often implies variation across centers in another (e.g., log odds ratio). Thus, the wrong choice of scale could imply heterogeneity in treatment effects, which would not exist if a different measure were used. It is likely to happen if there is a wide range in active control rates of complete response or rates of response are close to 1. In antiemetic trials, the response rate for the active control is relatively high and varies significantly across different patient populations. This fact along with high anticipated rate of response for the experimental drug can lead to different treatment-by-center interaction estimates depending on the scale used (1). A treatment effect scale that will imply the lowest variability across centers will be preferable from both statistical and regulatory view points. The methodology based on the random-effects model for categorical data was used to address these problems. A few assumptions were made to estimate the treatment-by-center interaction and pooled treatment effect confidence limits. The described methodology can be used for multicenter clinical trials with two treatment groups, provided the sample size in each center is large comparing to the number of centers. We also assume that the variation in treatment effect across centers is inexplicable 1097

3 and attributable to the different sample sizes and different underlying proportions. Sampling variances are assumed to be known, although we calculate them from the available data (1). To evaluate consistency of treatment effect across centers, a large sample test based on the statistic Q = L, w,(y, - y' w)2 was used, where y, is the treatment effect estimate for i-th center, based on one of the scales mentioned above, y" w = L, w, y, I L, w, is the weighted estimator of overall treatment effect and w, is the inverse of the corrected sampling variance for the i-th center: Here S,2 is within- and 112 is between-center variances. It is assumed in the randomeffects model that treatment effect varies across centers. Thus, the weights w, in Q include correction for the between-center variation. Under the null hypothesis, Q is approximately a X2 statistic with k-l degrees of freedom (k is number of centers). When each center has a large sample size relative to the number of centers, Q may be used to test the hypothesis of no treatment-by-center interaction. The asymptotic standard error of y', is s.e.(y,) = (L, w, )"112. This standard error can be used for estimation of the confidence limits for the weighted treatment effect based on the one of treatment effect scales. The scale suggesting treatment effect homogeneity across centers is preferable. Results and Discussion There were 340 intent-to-treat patients: 170 in the control group and 170 in the experimental drug group. All patients were included in the analysis. The analysis based on the Cochran-Mantel-Haenszel (CMH) procedure with center being the stratification factor and log odds ratio chosen as the treatment effect scale revealed statistically significant treatment effect (odds ratio = 3.9) for the pooled estimate (p<o.ool). However, the Breslow-Day test for homogeneity of the odds ratio across centers produced the p value of 0.03, indicating statistically significant treatment by center interaction. These results are presented in Figure 1 at the end of this section. To estimate the overall (weighted) treatment effect and to account for its variability across centers, the random-effects model was applied to the data. Difference in proportions was chosen as the measure of treatment effect. The DerSimonian-Laird procedure revealed no treatment-by-center interaction (p=o.17). A [mal decision regarding importance of treatment-by-site interaction is usually based on clinical judgement. The overall treatment effect was statistically significant with p=o.ol. The p-value associated with the random-effects model is higher than that from PROC CMH, because the between-centers variation was taken into account, inflating the error of the pooled result. The random-effects model allowed us to take into account the between-center variability of treatment effect and provided a computationally-efficient test for treatmentby-center interaction for the difference-inproportions scale. As we know, the CMH procedure is optimal for testing the treatment effect, assuming a constant odds ratio across centers (1). If unexplained variability of treatment effect across centers exists, this variability can be taken into account using the DerSimonian-Laird procedure based on the random-effects model for categorical response. It is important to note, though, that validity of the CMH procedure does not depend on the homogeneity of treatment 1098

4 effect across centers. Even in the presence of the treatment-by-center interaction the pooled treatment effect estimate based on the CMH procedure can be used as a statistically valid result. However, a treatment effect estimate homogeneous across centers is preferable from the regulatory view point and allows for better interpretation. Figure 1 RESULTS OF COCHRAN -MANTEL-HAENSZEL ANALYSIS LOG ODDS RATIO 24 m J8 J I 0BNTJm1 CJIi:NTEB II 0EN'l' B 8 CENTER Software Random-effects model for categorical data was implemented as a SAS macro with options for all three treatment effect scales. If log odds ratio is chosen as the scale, PROC CMH analysis will be performed and a plot of treatment effect, by center and overall, with confidence limits based on the CMH procedure will be produced. The following is the format of macro call: %catrand (DAT ASET,RESPONSE,ALGOR, ALPHA), where DATASET is the name of the Original SAS data set with four variables: patient ID, center number, treatment group, and binary response. RESPONSE is the name of the response variable, ALGOR is the treatment effect scale chosen from a list of possible values: difference in proportions, log relative risk or log odds ratio, and ALPHA is the two-sided significance level for the test of interaction based on the random-effects model A PROC FORMAT is used to allow for customization of labels for each investigational center on the graph. If algor=diff or RR (difference in proportions and log relative risk, respectively), this macro produces p-value, point estimate and confidence limits for the overall treatment effect in addition to the p value for the treatment-by-center interaction based on the chosen scale. These estimates are based on the random-effects model 1099

5 If algor=cmh, this macro produces the standard SAS output from the PROC FREQ with the CMH option, including the results of the Breslow-Day test of interaction for log odds ratio. For comparison, p-value from DerSimonian-Laird test of interaction is calculated. In addition, a plot similar to Figure I will be produced. Conclusions 1. For antiemetic clinical trials the variability of response in the control group may be very high. In addition, the response rate for the experimental drug is close to I. Under these conditions the 'wrong' choice of scale for treatment effect could imply heterogeneity of treatment effect which would not exist if a different measure were used. References 1. R. DerSimonian, N. Laird. Meta-Analysis in Clinical Trials. Controlled Clinical Trials, 7: (1986). 2. P. Armitage. Some Topics of Current Interest in Clinical Trials. The Canadian Journal of Statistics, v. 20, I, 1-8 (1992). 3. J. G. Gordon, K.M. de Bruijn. Methodology of Antiemetic Trials. Drugs 43 (Suppl. 3), 1-5 (1992). 4. M. Tonato. Ondansetron Plus Dexamethasone: An Effective Combination in High Dose CispJatin Therapy. Eur J Cancer, V.27, Suppl.1, s12-s14 (1991). 2. The DerSimonian-Laird approach based on the random-effects model for categorical data can be used to test the treatment -bycenter interaction and to estimate the confidence limits for the pooled treatment effect. These estimates take into account the between-center variability of treatment effect. 3. A SAS macro implementing the randomeffects model for categorical data with option for one of three treatment effect scales (difference in proportions, log relative risk and log odds ratio) was developed. If difference in proportions or log relative risk is chosen, this macro will produce point estimates and confidence limits for treatment effect based on DerSimonian-Laird approach. If log odds ratio is chosen, this macro will produce treatment effect estimates from PROC CMH including Breslow-Day test. In all three cases, this macro will produce p value for treatment-by-center interaction. 1100