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Analysis of an outcome-dependent enriched sample: hypothesis tests

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  • Christopher Vahl
  • Qing Kang

Abstract

An outcome-dependent sample is generated by a stratified survey design where the stratification depends on the outcome. It is also known as a case–control sample in epidemiological studies and a choice-based sample in econometrical studies. An outcome-dependent enriched sample (ODE) results from combining an outcome-dependent sample with an independently collected random sample. Consider the situation where the conditional probability of a categorical outcome given its covariates follows an explicit model with an unknown parameter whereas the marginal probability of the outcome and its covariates are left unspecified. Profile-likelihood (PL) and weighted-likelihood (WL) methods have been employed to estimate the model parameter from an ODE sample. This article develops the PL- and WL-based families of tests on the model parameter from an ODE sample. Asymptotic properties of their test statistics are derived. The PL likelihood-ratio, Wald and score tests are shown to obey classical inference, i.e. their test statistics are asymptotically equivalent and Chi-squared distributed. In contrast, the WL likelihood-ratio statistic asymptotically has a weighted Chi-squared distribution and is not equivalent to the WL Wald and score statistics. Our theoretical derivation and simulation show that tests based on these new statistics carry nominal type I error and good power. Advantages of ODE sampling together with the implementation of the PL and WL methods are demonstrated in an illustrative example. Copyright Springer-Verlag Berlin Heidelberg 2015

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  • Christopher Vahl & Qing Kang, 2015. "Analysis of an outcome-dependent enriched sample: hypothesis tests," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 387-409, September.
    • Handle: RePEc:spr:stmapp:v:24:y:2015:i:3:p:387-409
    DOI: 10.1007/s10260-014-0285-4
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