Gaining Insight from Flexible Models

Summary

Objectives: We present results from a secondary prevention trial of coronary heart disease (CHD) in the Czech male population from northern Bohemia with the history of myocardial infarction (MI) and high prevalence of metabolic syndrome. We compare several approaches to analyzing survival data from our study in terms of respective model assumptions.

Methods: While both the Cox and Weibull survival regression models assume proportionality of the hazard functions over time, in many instances this assumption appears incompatible with the data at hand. Gray’s implementation of flexible models using penalized splines allows for a more realistic assessment of the covariate effects which may vary over time.

Results: Gray’s model results revealed a steady decline in the age-adjusted intervention effect over time, which remained significant until about 2.7 years of follow-up. This was in contrast with the results obtained from the Cox and Weibull models which suggested an overall risk reduction due to intervention during the total follow-up of 6.7 years. Survival estimates based on the Cox and Gray models are shown for the two treatment groups and selected sample quantiles of the age distribution for illustration.

Conclusions: Gray’s time-varying coefficients model facilitated a more realistic assessment of the intervention effect. Using suitable historical controls with MI history the effect of intervention was found to gradully diminish over time.

Keywords

Coronary heart disease - non-proportional hazards - secondary prevention - survival

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