Sample Size Requirements for Clinical Trials with Repeated Binary Outcomes
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Sample Size Requirements for Clinical Trials With ReDeated Binarv Outcomes
Chrl PhD Professor, Director of Biostatistjcs, D~~~~~~~~ of Clinical Sciences. University OfTexas
Medical Center, Dallas. Texas
Kay Words Compound symmetry; Dropout; GEE; Independent missing; Monotone missing
Corrrspondtncr Address Chul Ahn. Director of Biostatistics, Department of Clinical Sciences. University ofTexas Southwestern Medical Center, Dallas, Texas 75390 (email: chul.ahn@ utsouthwestern.edu).
Sample size sojlware is readily available for many univariate statistical procedures that invdve one dependentvariableper subject. Howeva power ana!ysis is less availablefor designs with repeated measures, particularfyfor repeated binary outcome variables. Repeated measurement studies usually invdve missing data and serial correlations within each subject. As a consequence, genemlized estimating equation (GEE) models, which do not require complete data for all subjects and which do not depend on the restrictive ‘ m m e t r v assumtAion.” are beine ” increasingly *recommended the evaluation of treatment effects in controlled clinical trials.
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IN T R O D U CTI 0 N In planning a study, it is necessary to determine the number of subjects to be used for the study to achieve sufficient power to detect the hypothesized effect. Although the exact final number that will be used for the analysis will be unknown because of missing information, it is still desirable to determine a target sample size based on the proposed study design. The sample size estimate will allow the estimation of total cost of the proposed study required. Typically, the number of samples is computed to provide a fixed level of power under a specified alternative hypothesis. The alternative hypothesis usually represents a minimal meaningful difference in outcome variables between treatment groups. Power (1- probability of type II error) is an important consideration for several reasons. Low power can cause a true difference in outcome between treatment groups to be rejected. However, too much power may make results statistically significant that are not meaningfully different. The probability of type 1 error (a)of 0.05 and power of 0.80 and 0.90 have been widely used for the sample size estimation in planning a study. Power analysis is readily available for many
GEE has been widely used to examine whether the rates of changes are significanttydifferentbetween groups due to its robustness to misspeciication of the true correlation structure and randomly missing data. We illustrate how the sample size can be estimated in detail through examples and also present the eflect of dropouts in the sample size estimatefor the repeated binary outcomes. In the presence of dropouts, it is suggested to estimate the sample size using the closed form formula provided in this article instead of adjustingthe sample size estimate dividing the sample size estimate obtained under no missing data by the proportions of completm.
univariate statistical procedures that involve one depen
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