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

Background: Relative hazard is a central measure of association in randomized clinical trials. Relative time (RT) is a competing measure that is rarely used. Purpose: We describe a simple area-based nonparametric estimator of RT and illustrate its use in the Acyclovir Prevention Trial. Methods: 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 Q₁(p) and Q₀(p) with integration over 0 to p, where p = min(p₁, p₀). Confidence limits (CL) are provided by bootstrap. Results: 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. Limitations: An analytical variance estimator for the proposed RT is lacking. Also, more examples and more extensive simulations are warranted. Conclusions: 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.