Estimating Incidence Rates from Population-Based Case-Control Studies in the Presence of Nonrespondents

• Published in: Biometrical journal Vol. 44; no. 2; pp. 227 - 239
• Main Authors: Arbogast, Patrick G., Lin, D.Y., Siscovick, David S., Schwartz, Stephen M.
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag Berlin GmbH 01.03.2002; WILEY‐VCH Verlag Berlin GmbH; Wiley-VCH
• Subjects: Absolute risk; Disease incidence; Exact sciences and technology; Horvitz-Thompson estimator; Logistic regression; Mathematics; Missing data; Multivariate analysis; Nonparametric inference; Nonresponses; Parametric inference; Probability and statistics; Sciences and techniques of general use; Statistics; Rank statistic; Parameter estimation; Score test; Non parametric estimation; Probability distribution; Case control study; Multivariate analysis; Asymptotic convergence; Score function; Parametric method; Selection method; Public health; Likelihood function; Asymptotic behavior; Statistical association; Statistical estimation; Logistic model; Variance analysis; Logistic distribution; Statistical regression; Selection problem; Estimating function; Risk rate; Regression model; Asymptotic normality; Weight function; Risk factor; Asymptotic approximation; Response probability; Biased estimation
• ISSN: 0323-3847; 1521-4036
• DOI: 10.1002/1521-4036(200203)44:2<227::AID-BIMJ227>3.0.CO;2-B

In population‐based case‐control studies, it is of great public‐health importance to estimate the disease incidence rates associated with different levels of risk factors. This estimation is complicated by the fact that in such studies the selection probabilities for the cases and controls are unequal. A further complication arises when the subjects who are selected into the study do not participate (i.e. become nonrespondents) and nonrespondents differ systematically from respondents. In this paper, we show how to account for unequal selection probabilities as well as differential nonresponses in the incidence estimation. We use two logistic models, one relating the disease incidence rate to the risk factors, and one modelling the predictors that affect the nonresponse probability. After estimating the regression parameters in the nonresponse model, we estimate the regression parameters in the disease incidence model by a weighted estimating function that weights a respondent's contribution to the likelihood score function by the inverse of the product of his/her selection probability and his/her model‐predicted response probability. The resulting estimators of the regression parameters and the corresponding estimators of the incidence rates are shown to be consistent and asymptotically normal with easily estimated variances. Simulation results demonstrate that the asymptotic approximations are adequate for practical use and that failure to adjust for nonresponses could result in severe biases. An illustration with data from a cardiovascular study that motivated this work is presented.