Covariates logistic regression

As we shall see later the data type to a large extent determines the class of statistical tests that we undertake. Commonly for continuous data we use the t-tests and their extensions analysis of variance and analysis of covariance. For binary, categorical and ordinal data we use the class of chi-square tests (Pearson chi-square for categorical data and the Mantel-Haenszel chi-square for ordinal data) and their extension, logistic regression. 

In Chapter 6 we covered methods for adjusted analyses and analysis of covariance in relation to continuous (ANOVA and ANCOVA) and binary and ordinal data (CMH tests and logistic regression). Similar methods exist for survival data. As with these earlier methods, particularly in relation to binary and ordinal data, there are numerous advantages in accounting for such factors in the analysis. If the randomisation has been stratified, then such factors should be incorporated into the analysis in order to preserve the properties of the resultant p-values. 

Arena VC, Sussman NB, Mazumdar S, et al. The utility of structure-activity relationship (SAR) models for prediction and covariate selection in developmental toxicity Comparative analysis of logistic regression and decision tree models. SAR QSAR Environ Res. 2004 15(1) 1-18. 

The theory and techniques described in this chapter focus on the application of logistic regression to binary outcome data and the development of models to describe the relationship between binary endpoints and one or more explanatory variables (covariates). While many software options are available for fitting fixed or mixed effects logistic regression models, this chapter endeavors to illustrate the use of nonlinear mixed effects modeling to analyze binary endpoint data as implemented in the NONMEM software. 

Robinson LD, Jewell NP (1991) Some surprising results about covariate adjustment in logistic regression models. International Statistical Review 58 227-240. 

---