Estimating disease attack rates in heterogeneous interacting populations, with applications to HIV vaccine trials
type: Item
instance of: scholarly article
title: Estimating disease attack rates in heterogeneous interacting populations, with applications to HIV vaccine trials
zbMATH Open document ID: 0926.62113
author: David Wick
author: Steven G. Self
published in: The Annals of Statistics
publication date: 1999-11-28T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62P10
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 62M05
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 1029336
zbMATH Keywords: infectious diseases
zbMATH Keywords: interacting processes
zbMATH Keywords: asymptotics of Nelson-Aalen estimators
zbMATH Keywords: counting processes
zbMATH Keywords: vaccine trials
zbMATH Keywords: HIV disease
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1031833667
OpenAlex ID: W2026428803
cites work: Nonparametric inference for a family of counting processes
cites work: Statistical models based on counting processes
cites work: Q4035823
cites work: Q5560061
cites work: Q5574850
cites work: Ordinary differential equations in Banach spaces
cites work: Mathematical methods for hydrodynamic limits
cites work: Generalized Ornstein-Uhlenbeck processes and infinite particle branching Brownian motions
cites work: Q4741623
cites work: Tightness of probabilities on C([0,1];\(S_ p\)) and D([0,1];\(S_ p\))
cites work: Q4169489
cites work: Central limit theorems for local martingales
cites work: Q4272620
DOI: 10.1214/AOS/1031833667
description: scientific article; zbMATH DE number 1029336