Nonparametric estimator of relative time with application to the Acyclovir Prevention Trial

Abstract

Relative hazard is a central measure of association in randomized clinical trials. Relative time (RT) is a competing measure that is rarely used. We describe a simple area-based nonparametric estimator of RT and illustrate its use in the Acyclovir Prevention Trial. Let Q( x)(p) be the quantile function for the xth treatment group, defined as the time by which p% of the treatment group experience the event, and p( x) be the maximum event proportion observed. Our consistent estimator is defined as the ratio of the integrals of Q(1)(p) and Q(0) (p) with integration over 0 to p, where p =min(p(1), p( 0)). Confidence limits (CL) are provided by bootstrap. A total of 703 immunocompetent adult men and women (54% male, 79% Caucasian, median age 49 years) with a history of ocular herpes simplex virus (HSV) were enrolled in 1992-1996, randomized to acyclovir or placebo, followed for up to 1 year for the 1st episode of ocular HSV, and 170 events were confirmed by a study-certified ophthalmologist using slit-lamp biomicroscopy. The nonparametric RT comparing acyclovir use with nonuse was 2.6 (bootstrap 95% CL: 1.6, 4.2). For comparison, the best-fitting parametric model was the lognormal (RT = 2.5; 95% CL: 1.5, 3.9). In limited simulations, the average proposed estimate of RT was similar to the true RT with a relative root mean squared error of 1.13 compared to a correctly specified parametric (lognormal) model. An analytical variance estimator for the proposed RT is lacking. Also, more examples and more extensive simulations are warranted. Similar to Cox's relative hazard estimator, the proposed RT does not assume the data are generated from a particular distribution. RTs should be more widely used as a measure of association in clinical trials.