Methods for Analyzing Binary Repeated Measures: The Small Sample Case

Abstract

Binary repeated measurements occur often in a variety of fields. Particularly in medicine, small samples are used in the early phases (phase I and II) of clinical trials, in bio equivalence studies and in crossover trials where human participation is multitudinous. Hence, it is vital to develop a precise method to analyze binary Repeated Measures Data (RMD) with small sample size which is related to humans and even to animals. As a result, this simulation study was carried out in SAS to examine the performance of the two methods used with general sample sizes; the Generalized Estimating Equations (GEE) method and Generalized Linear Mixed Models (GLMM) towards analysis of binary RMD with small sample size, after adjusting the bias that occurs in small samples. Being motivated by the study of literature, large scale simulations are carried out for each method with the facilitation of PROC GENMOD and PROC GLIMMIX procedures respectively, along with varying options of small sample bias correction methods available in SAS, the Sandwich Variance Estimation (SVE) technique and its variants. Each method with all possible SVE techniques available in SAS were compared and contrasted with respect to the properties; Type I error, power, unbiasedness, consistency, sufficiency, convergence, speed of computation and efficiency. The results obtained from the simulation study depicted that for binary RMD which adhere to AR(1) process, with no missing values and with no covariates, GLMM with SVE techniques FIROEEQ and ROOT perform equally and exceptionally well for a small sample size binary repeated case with respect to all the properties of parameter estimates considered except for sufficiency. However the GEE method with the naive option while being marginal with respect to type I error, performs well in analyzing very small sample sizes and satisfies all the properties including sufficiency.