A method to test for a recent increase in HIV‐1 seroconversion incidence: Results from the multicenter AIDS cohort study (MACS)

We have formulated the problem of determining whether there has been an upturn in HIV‐1 seroconversion incidence over the first five years of follow‐up in the Multicenter AIDS Cohort Study (MACS) as that of locating the minimum of a quadratic regression or examination of two‐knot piecewise spline models. Under a quadratic model, we propose a method to obtain a direct estimate and a bootstrap estimate for the location of the temporal turning point (local minimum) for HIV‐1 seroconversion incidence and three methods to estimate confidence intervals for the location of the turning point for HIV seroconversion incidence: (1) Wald confidence interval estimate with or without log transformation assuming the asymptotic normality and applying the Delta method; (2) asymmetric confidence intervals using Fieller's Theorem and its modification; and (3) bootstrapping confidence intervals. Inferences for the temporal turning point based on Wald tests for a single regression term in a non‐linear regression model were not reliable compared to inferences based on confidence intervals placed on calendar time. We present results using these different method applied to the MACS data and we obtain power estimates to illustrate the performance of different methods.