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The analysis of category comparisons of binary response data with the combination of continuous and categorical explanatory variables models. (Thai. English summary) Zbl 1362.62193

Summary: In an analysis of clinical experiment with binary outcome, the analysis is required for treatments or study category comparisons, adjusted for covariate effects. Problems arise with categorical response variables and mixed binary or categorical and continuous covariates. The correct model for such data structures is of the logistic form. In the past, the analyses of such situations have been carried out by linear regression as well as logistic regression methods which were of limitation focused on the predictive ability of the models. In this paper, 1,000 computer simulation experiments for each condition of fixed parameters and sample sizes were generated to study the performance of the analysis of covariance models which were used, especially for category comparisons when applied to a binary response data obeying a logistic model with mixed binary and Gaussian explanatory covariates. The \(F\) and \(t\) statistics, the observed proportion of interests and the true Type I error levels of the analysis of covariance techniques at \(\alpha=0.01\), 0.05 and 0.10 were then analysed. Computer programs for both the simulation and analysis of this article were developed using the Minitab macro language and run by macros in MINITAB release 11. The results of the simulation studies, considered from the average \(F\) and \(t\) statistics, show that for hypothesis testing to detect a classification effects with binary response data and mixed binary and Gaussian covariate, the magnitudes of most \(F\) and \(t\) statistics in the simulation that below the indicated percentile of the \(F(2,\infty)\) and \(t\) distributions, respectively, are mostly satisfied and lead to the true Type I error rate at a minimum of 0.005. In addition, it is found that the true Type I error level depends on the actual parameters or covariate effects, used in the models. Some recommendations are made for studying sample sizes, covariate effects and covariates distributions, in more details, to examine their relationships to the true Type I error rate.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62J12 Generalized linear models (logistic models)

Software:

MINITAB
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