Estimating the Incubation Period of AIDS by Comparing Population Infection and Diagnosis Patterns

Abstract

The incidence of AIDS virus infections over time among gay men in San Francisco is nonparametrically estimated from interval-censored data by using an EM algorithm to maximize a roughness-penalized likelihood. Because the distribution of AIDS diagnoses is the convolution of the infection and incubation distributions, the incubation distribution can be estimated by comparing the estimated infection distribution and the observed pattern of diagnoses. This is again accomplished by nonparametrically maximizing a roughness-penalized likelihood using the EM algorithm. The optimal degree of smoothness for the estimates is chosen using external data and subjective assessments of plausibility. Three prospective studies of initially uninfected men produce comparable estimated infection rates and are merged to produce an overall estimate, which shows rates increasing until late 1981 and then falling sharply. The estimated incubation period hazard function is near 0 for two years following infection and then increases until it flattens out at about seven years after infection. Bootstrap simulations are used to gauge the variability of the estimates. The incubation estimate is as accurate as other published estimates. Inclusion of the roughness penalty in the criteria to be optimized greatly reduces the variability of the estimates while also greatly speeding the convergence of the algorithms.

Key Words:

• Smoothing
• Penalized likelihood
• EM algorithm
• Ill-posed problem
• Epidemiology