Estimating clinical trial hazard functions

Although the analysis of event-based clinical trials commonly relies on assumptions about the underlying hazard functions, in practice it is rare to see estimates of those functions.

I describe conventional and novel methods for estimating the hazard function using discrete and discretized continuous survival models. The conventional approach involves parametric modeling; the novel approach applies Bayesian model averaging to flexible modeling by splines or fractional polynomials. I evaluate the methods in a Monte Carlo study and illustrate them in the analysis of three historical clinical trials.

Although flexible models can capture features of the hazard functions-such as multimodality-that parametric models miss, they are not foolproof. Spline modeling was generally the most reliable, in the sense of yielding good coverage probabilities for the mean and median with modest loss of efficiency. In the examples, the discreteness of the measurements-days, weeks, or months-had little effect on the shape of estimated hazard functions. All three data sets showed some evidence of departure from the proportional hazards assumption, but in only one did a test for proportionality detect this departure.

Flexible parametric models, estimated in the Bayesian model averaging framework, offer a robust approach to recovering the shape of the hazard function. Analyses of three clinical trial databases suggest that visualization of the hazard function can be a valuable adjunct to conventional survival analysis.