American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2017, 5(2), 80-89
DOI: 10.12691/ajams-5-2-6
Open AccessArticle

Methods for Analyzing Binary Repeated Measures: The Small Sample Case

Dharmaratne ADVTT1, and Sooriyarachchi MR1

1Department of Statistics, University of Colombo, Colombo, Sri Lanka

Pub. Date: July 29, 2017

Cite this paper:
Dharmaratne ADVTT and Sooriyarachchi MR. Methods for Analyzing Binary Repeated Measures: The Small Sample Case. American Journal of Applied Mathematics and Statistics. 2017; 5(2):80-89. doi: 10.12691/ajams-5-2-6

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.

Keywords:
Binary Repeated Measures (BRM) small samples Generalized Estimating Equations (GEE) Method Generalized Linear Mixed Model (GLMM) Method simulation

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References:

[1]  Fitzmaurice, G., Davidian, M., Verbeke, G. and Molenberghs, G, Longitudinal Data Analysis, CRC Press, 2008, 3-27.
 
[2]  Fong, Y., Rue, H. and Wakefield, J, “Bayesian inference for generalized linear mixed models,” Biostatistics, 11(3). 397-412. Dec.2009.
 
[3]  Gawarammana, M. B. and Sooriyarachchi, M. R, “Comparison of methods for analyzing binary repeated measures data: A Simulation Based Study (comparison of methods for binary repeated measures),”Communications in Statistics - Simulation and Computation, 46(3). 2103-2120. May.2015.
 
[4]  Lalonde, T. L., Nguyen, A. Q., Yin, J., Irimata, K. and Wilson, J. R, “Modeling Correlated Binary Outcomes with Time-Dependent Covariates,” Journal of Data Science, 11(4). 715-738. Oct .2013.
 
[5]  Liang, K.Y. and Zeger, S. L, “Longitudinal data analysis using generalized linear models,” Biometrika, 73(1). 13-22. Apr.1986.
 
[6]  Locascio, J. J. and Atri, A, “An Overview of Longitudinal Data Analysis Methods for Neurological Research,” Dementia and geriatric cognitive disorders extra, 1(1). 330-357. Oct.2011.
 
[7]  Mahan, V. L, “Clinical Trial Phases,” International Journal of Clinical Medicine, 5(21). 1374-1383. Dec.2014.
 
[8]  Ramezani, N, “Analyzing Correlated Data in SAS®,” in SAS® GLOBAL FORUM 2017, 1251.
 
[9]  SAS Institute Inc, SAS/STAT® 9.2 User's Guide, 2008. [E-book] Available: open e-book.
 
[10]  Sunethra, A. A. and Sooriyarachchi, M. R, “Sandwich Variance Estimation for random effect misspecification in Generalized Linear Mixed Models,” GSTF Journal of Mathematics, Statistics and Operations Research (JMSOR), 3(2). 8-11. Jul.2016.
 
[11]  Szmaragd, C., Clarke, P. and Steele, F, “Subject specific and population average models for binary longitudinal data: a tutorial,” Longitudinal and Life Course Studies, 4(2). 147-165. May 2013.
 
[12]  Wang, M, “Generalized Estimating Equations in Longitudinal Data Analysis: A Review and Recent Developments,” Advances in Statistics, 2014. Dec.2014.