Binary data logistic regression

An important feature of the logistic regression method is that although the input modelling data (P0) are binary, the calculated probability (P) is a continuous function. 

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. 

There are also connections between the Cochran—Mantel—Haenszel procedures and logistic regression for binary and ordinal data, but these issues are beyond the scope of this text. 

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. 

Selected characteristics were compared between cases and controls by using test. The analyses of data were performed using the computer software SPSS for Windows version 11.5. Max type 1 error was accept as 0.05. Binary logistic regression was performed to calculate the odds ratios (ORs), and 95% confidence intervals (Cls) to assess the risk of breast cancer. 

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. 

Log-odds ratio. The logarithm of the odds ratio. A transformation very frequently used for modelling binary data. See logistic regression. 

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