Hazard Ratio in Clinical Trials

Abstract

3Time-to-event curves analyzed by Cox proportional hazards regression are commonly used to describe the outcome of drug studies. This methodology has the advantage of using all available information, including patients who fail to complete the trial, such as in cancer chemotherapy or human immunodeficiency virus antiviral treatment studies. The goal of treatment in such studies may be to prevent the development of a complication, for example, Pneumocystis carinii pneumonia, and to describe the likelihood of this complication's developing in the treatment group compared to the control group. The hazard ratio describes the relative risk of the complication based on comparison of event rates.Hazard ratios have also been used to describe the outcome of therapeutic trials where the question is to what extent treatment can shorten the duration of the illness. However, the hazard ratio, a type of relative risk, does not always accurately portray the degree of abbreviation of the illness that occurred. In these circumstances, time-based parameters available from the time-to-event curve, such as the ratio of the median times of the placebo and drug groups, should be used to describe the magnitude of the benefit to the patient. The difference between hazard-based and time-based measures is analogous to the odds of winning a race and the margin of victory. The hazard ratio is the odds of a patient's healing faster under treatment but does not convey any information about how much faster this event may occur.We have observed that there is substantial confusion among clinicians and clinical investigators about the difference between the hazard ratio and the median ratio. This report presents examples of this confusion, the exact distinction between the two statistics, and proper use of the hazard ratio and median ratio when interpreting the results of clinical trials to patients. COX PROPORTIONAL HAZARDS MODELTime-to-event analysis. Clinical trials commonly record the length of time from study entry to a disease endpoint for a treatment and a control group. These data are commonly depicted with a Kaplan-Meier curve (Fig. 1), from which the median (time at which 50% of cases are resolved) and the mean (average resolution time) can be derived. The groups are compared by a time-to-event analysis (survival analysis) (1, 7). Time-to-event analysis provides a method to include patients who fail to complete the trial or do not reach the study endpoint (censored data) by making comparisons between the number of survivors in each group at multiple points in time. The alternative approach, excluding patients who are lost to follow-up, may introduce considerable bias because the data that these patients generate prior to their exit are important to the power and validity of the study. Time-to-event analysis can also incorporate information about subjects that may change over time (time-dependent covariates). Clinically important differences in the effect of treatment may be obscured if the proportions of survivors or recovered individu...

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