[Hazard ratio estimated from a proportional hazard model including two strongly correlated prognostic factors]

Estimates of hazard ratio from hypothetical survival data were examined, under the condition that the survival is affected by two prognostic factors X1 and X2 with two discrete values (0, 1) which are strongly correlated. Survival curves from the data were assumed to fit an exponential function. As an example, following numbers of subjects were used; 100 cases with X1 = 0 and X2 = 0, 10 cases with X1 = 1 and X2 = 0, 10 cases with X1 = 0 and X2 = 1, and 100 cases with X1 = 1 and X2 = 1. When the hazard ratio of X1 = 1 or X2 = 1 to X1 = 0 and X2 = 0 was 3, univariate analysis gave reasonable estimates around 3. Under the same condition, estimates of hazard ratio from multivariate analysis including the two variables X1 and X2 varied widely, depending on the survivals of 20 cases with X1 = 1 X2 = 0 or X1 = 0 X2 = 1. Probability of having extremely deviated estimates was demonstrated. The result illustrated successfully some points we should take into account when proportional hazard models including strongly correlated variables are applied.