Parametric conditional frailty models for recurrent cardiovascular events in the lipid study

Analysis of recurrent event data is frequently needed in clinical and epidemiological studies. An important issue in such analysis is how to account for the dependence of the events in an individual and any unobserved heterogeneity of the event propensity across individuals.

We applied a number of conditional frailty and nonfrailty models in an analysis involving recurrent myocardial infarction events in the Long-Term Intervention with Pravastatin in Ischaemic Disease study. A multiple variable risk prediction model was developed for both males and females.

A Weibull model with a gamma frailty term fitted the data better than other frailty models for each gender. Among nonfrailty models the stratified survival model fitted the data best for each gender. The relative risk estimated by the elapsed time model was close to that estimated by the gap time model. We found that a cholesterol-lowering drug, pravastatin (the intervention being tested in the trial) had significant protective effect against the occurrence of myocardial infarction in men (HR = 0.71, 95% CI 0.60-0.83). However, the treatment effect was not significant in women due to smaller sample size (HR = 0.75, 95% CI 0.51-1.10). There were no significant interactions between the treatment effect and each recurrent MI event (p = 0.24 for men and p = 0.55 for women). The risk of developing an MI event for a male who had an MI event during follow-up was about 3.4 (95% CI 2.6-4.4) times the risk compared with those who did not have an MI event. The corresponding relative risk for a female was about 7.8 (95% CI 4.4-13.6).

The number of female patients was relatively small compared with their male counterparts, which may result in low statistical power to find real differences in the effect of treatment and other potential risk factors.

The conditional frailty model suggested that after accounting for all the risk factors in the model, there was still unmeasured heterogeneity of the risk for myocardial infarction, indicating the effect of subject-specific risk factors. These risk prediction models can be used to classify cardiovascular disease patients into different risk categories and may be useful for the most effective targeting of preventive therapies for cardiovascular disease.