A new modeling and inference approach for the Systolic Blood Pressure Intervention Trial outcomes

Clin Trials. 2018 Jun;15(3):305-312. doi: 10.1177/1740774518769865. Epub 2018 Apr 19.


Background/aims In clinical trials with time-to-event outcomes, usually the significance tests and confidence intervals are based on a proportional hazards model. Thus, the temporal pattern of the treatment effect is not directly considered. This could be problematic if the proportional hazards assumption is violated, as such violation could impact both interim and final estimates of the treatment effect. Methods We describe the application of inference procedures developed recently in the literature for time-to-event outcomes when the treatment effect may or may not be time-dependent. The inference procedures are based on a new model which contains the proportional hazards model as a sub-model. The temporal pattern of the treatment effect can then be expressed and displayed. The average hazard ratio is used as the summary measure of the treatment effect. The test of the null hypothesis uses adaptive weights that often lead to improvement in power over the log-rank test. Results Without needing to assume proportional hazards, the new approach yields results consistent with previously published findings in the Systolic Blood Pressure Intervention Trial. It provides a visual display of the time course of the treatment effect. At four of the five scheduled interim looks, the new approach yields smaller p values than the log-rank test. The average hazard ratio and its confidence interval indicates a treatment effect nearly a year earlier than a restricted mean survival time-based approach. Conclusion When the hazards are proportional between the comparison groups, the new methods yield results very close to the traditional approaches. When the proportional hazards assumption is violated, the new methods continue to be applicable and can potentially be more sensitive to departure from the null hypothesis.

Keywords: Adaptively weighted log-rank test; average hazard ratio; non-proportional hazards; time-to-event outcomes.

Publication types

  • Research Support, N.I.H., Extramural

MeSH terms

  • Blood Pressure
  • Clinical Trials as Topic / methods*
  • Humans
  • Hypertension / therapy*
  • Kaplan-Meier Estimate
  • Proportional Hazards Models*
  • Research Design
  • Time Factors
  • Treatment Outcome