Estimating disease attack rates in heterogeneous interacting populations, with applications to HIV vaccine trials
We describe models for infectious disease attack rates outside Aalen's multiplicative class and incorporating heterogeneity and interactions between subjects. Large-sample theory for the Nelson-Aalen estimator is developed, and its relevance examined in a simulation study. Planning for randomized, controlled clinical trials of prophylactic HIV vaccines partly motivated this work. In Section 2 we construct stochastic models of the infection counting process, focusing exclusively on the situation in which contacts are unobservable. Although counting processes in multiplicative models have been widely studied by statisticians, our models are closer to the ``interacting particle processes'' known to probabilists and mathematical physicists. For these processes the large-sample limiting dynamics is typically nontrivial and governed by infinite-dimensional evolution equations. In Section 3 we prove limit theorems for a wide class of random variables related to our infection process, and in Section 4 we apply these to the Nelson-Aalen estimator of attack rates and related variance estimators. A central limit theorem justifies use of conventional Wald-type confidence intervals. In Section 5 we relax certain modeling assumptions and show that nonnormal statistics can dominate the large-sample limit. We also present a small simulation study. Finally, in Section 6 we state our conclusions and discuss directions for further research.
scientific article; zbMATH DE number 1029336