Analysis of epidemiologic case—base studies for binary data

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Abstract
Recent developments in statistical methods for epidemiology have revived the application of sampling techniques in the design and analysis of cohort studies. The ‘case — base’ design involves sampling of both the cases and the cohort base of the study. This paper reviews some data‐analytic imperfections of the approaches to risk ratio estimation, and modifies and advances a consistent likelihood‐based procedure — analogous to Miettinen and Nurminen's proposal for a full cohort design — for interval estimation (and also point estimation and significance testing) in the context of binary case—base data. First, the procedure avoids the use of Taylor‐series approximations to derive variance estimators for non‐linear functions of parameters. Second, the asymptotic condition effects a simple computational expression for the chi‐square function of risk ratios that is universally applicable to small samples. The statistical modelling underlying the method allows inferences about risk ratios without the assumption of rare disease either for the general population or for a particular base. The paper also extends the analysis to encompass stratified data. Finally, a numerical evaluation evinced the accurate small‐sample properties of the proposed method.

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