title: Valid statistical inference methods for a case-control study with missing data.
abstract: The main objective of this paper is to derive the valid sampling distribution of the observed counts in a case-control study with missing data under the assumption of missing at random by employing the conditional sampling method and the mechanism augmentation method. The proposed sampling distribution, called the case-control sampling distribution, can be used to calculate the standard errors of the maximum likelihood estimates of parameters via the Fisher information matrix and to generate independent samples for constructing small-sample bootstrap confidence intervals. Theoretical comparisons of the new case-control sampling distribution with two existing sampling distributions exhibit a large difference. Simulations are conducted to investigate the influence of the three different sampling distributions on statistical inferences. One finding is that the conclusion by the Wald test for testing independency under the two existing sampling distributions could be completely different (even contradictory) from the Wald test for testing the equality of the success probabilities in control/case groups under the proposed distribution. A real cervical cancer data set is used to illustrate the proposed statistical methods.
authors.affiliation: 1 Department of Mathematics, South University of Science and Technology of China, Shenzhen City, Guangdong, P. R. China.
authors.forename: Guo-Liang
authors.initials: GL
authors.lastname: Tian
authors.affiliation: 2 Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, P. R. China.
authors.forename: Chi
authors.initials: C
authors.lastname: Zhang
authors.affiliation: 1 Department of Mathematics, South University of Science and Technology of China, Shenzhen City, Guangdong, P. R. China.
authors.forename: Xuejun
authors.initials: X
authors.lastname: Jiang
mesh_terms: D015982:Bias; D016022:Case-Control Studies; D016013:Likelihood Functions; D015233:Models, Statistical; D014798:Vital Statistics
keywords: Bootstrap methods; Wald test; case–control study; missing at random; the mechanism augmentation method