Ordered logistic regression

Chapter 9.5.1. in Ryan (2008)). In the case that the outcome is ordinal (i.e., good, better, best), another variant called ordered logistic regression is suitable. The logistic regression methods do not require normal distribution of the predictor variables (Tabacknick and Fidell, 1996, p. 575). 

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. 

A retrospective analysis of postoperative renal function in patients undergoing cardiac operations has been conducted to evaluate whether the use of prophylactic intravenous diltiazem, in order to reduce the incidence of ischemia and dysrhythmias, was associated with increased renal dysfunction (10). The incidence of acute renal insufficiency requiring dialysis was 4.4% with diltiazem versus 0.7% in the controls. Logistic regression analysis suggested that the risk of acute renal insufficiency was strongly associated with intravenous diltiazem, age, baseline serum creatinine, the presence of left main coronary disease, and the presence of cerebrovascular disease. 

As an alternative to the classification methods hsted above, logistic regression can be used as a parametric approach. A logistic regression model cannot be used if the number of predictors exceeds the number of observations. In this case, a variable selection needs to be conducted in order to utilize logistic regression. 

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