What are the assumptions of multiple linear regression, multiple logistic regression, and proportional hazards analysis?

As shown in Table 5.1, the assumptions underlying the three multivariable models differ somewhat with respect to what is being modeled, the relationship of multiple independent variables to outcome, the relationship of an interval-independent variable to the outcome, the distribution of the outcome variable, and the variance of the outcome variable. These assumptions are explained in this chapter.

Proportional hazards analysis has two additional assumptions with regard to censored observations and relative hazards over time (referred to as the proportionality assumption). These are dealt with in Sections 5.9 and 10.10, respectively.

What is being modeled in multiple linear regression, multiple logistic regression, and proportional hazards analysis?

In multiple linear regression, as the independent variable increases (or decreases) the mean or expected value of the outcome increases (or decreases) in a linear fashion. Many clinical situations fit this linear assumption.

For example, Figure 5.1 shows the relationship between B12 levels and pneumococcal antibody levels following receipt of pneumococcal vaccination among elderly persons. Each square represents an observation (a person) and their vitamin B12 level (the independent variable), and their antibody titer after vaccine (the dependent variable). Although arbitrary, the convention is to show the independent variable on the x-axis and the dependent variable on the y-axis.