# The Net Chance of a Longer Survival as a Patient-Oriented Measure of Treatment Benefit in Randomized Clinical Trials

### Abstract

Importance

Time to events, or survival end points, are common end points in randomized clinical trials. They are usually analyzed under the assumption of proportional hazards, and the treatment effect is reported as a hazard ratio, which is neither an intuitive measure nor a meaningful one if the assumption of proportional hazards is not met.

Objective

To demonstrate that a different measure of treatment effect, called the net chance of a longer survival, is a meaningful measure of treatment effect in clinical trials whether or not the assumption of proportional hazards is met.

Design

In this simulation study, the net chance of a longer survival by at least m months, where m months is considered clinically worthwhile and relevant to the patient, was calculated as the probability that a random patient in the treatment group has a longer survival by at least m months than does a random patient in the control group minus the probability of the opposite situation. The net chance of a longer survival is equal to zero if treatment does not differ from control and ranges from –100% if all patients in the control group fare better than all patients in the treatment group up to 100% in the opposite situation. We simulated data sets for realistic trials under various scenarios of proportional and nonproportional survival hazards and plotted the Kaplan-Meier survival curves as well as the net chance of a longer survival as a function of m. Data analysis was performed from August 14 to 18, 2015.

Main Outcomes and Measures

The net chance of a longer survival calculated for values of m ranging from 0 to 40 months.

Results

When hazards are proportional, the net chance of a longer survival approaches zero as m increases. The net chance of a longer survival (Δ) was 13% (95% CI, 6.5%-19.4%; P < .001) when any survival difference was considered clinically relevant (m = 0 months). When survival differences larger than 20 months were considered relevant (m = 20), the net chance of a longer survival was very close to zero (Δ[20] = 0.5%; 95% CI, –0.1% to 1.1%; P = .09). In contrast, when treatment effects are delayed or when some patients are cured by treatment, the net chance of a longer survival benefit remains high and tends to the cure rate. For crossing hazards, the Δ was negative (Δ = –6.9%; 95% CI, –14.0% to –0.5%; P = .047). However when large survival differences were considered (m = 20), the Δ(m) was positive (Δ[20] = 8.9%; 95% CI, 6.7%-11.1%; P < .001).

Conclusions and Relevance

The net chance of a longer survival is useful whether or not the assumption of proportional hazards is met in the analysis of survival end points and may be helpful as a measure of treatment benefit that has direct relevance to patients and health care professionals.