Absolute Risk Reductions and Numbers Needed to Treat Can Be Obtained from Adjusted Survival Models for Time-to-event Outcomes

Objective: Cox proportional hazards regression models are frequently used to determine the association between exposure and time-to-event outcomes in both randomized controlled trials and in observational cohort studies. The resultant hazard ratio is a relative measure of effect that provides limited clinical information.

Study Design And Setting: A method is described for deriving absolute reductions in the risk of an event occurring within a given duration of follow-up time from a Cox regression model. The associated number needed to treat can be derived from this quantity. The method involves determining the probability of the outcome occurring within the specified duration of follow-up if each subject in the cohort was treated and if each subject was untreated, based on the covariates in the regression model. These probabilities are then averaged across the study population to determine the average probability of the occurrence of an event within a specific duration of follow-up in the population if all subjects were treated and if all subjects were untreated.

Results: Risk differences and numbers needed to treat.

Conclusions: Absolute measures of treatment effect can be derived in prospective studies when Cox regression is used to adjust for possible imbalance in prognostically important baseline covariates.