TY - JOUR
T1 - Exact Bayesian p-values for a test of independence in a 2 × 2 contingency table with missing data
AU - Lin, Yan
AU - Lipsitz, Stuart R.
AU - Sinha, Debajyoti
AU - Fitzmaurice, Garrett
AU - Lipshultz, Steven
N1 - Funding Information:
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: We are grateful for the support provided by grants MH 054693, NIDA 042847, CA 160679, and CA 06922 from the U.S. National Institutes of Health.
PY - 2018/11/1
Y1 - 2018/11/1
N2 - Altham (Altham PME. Exact Bayesian analysis of a 2 × 2 contingency table, and Fisher’s “exact” significance test. J R Stat Soc B 1969; 31: 261–269) showed that a one-sided p-value from Fisher’s exact test of independence in a 2 × 2 contingency table is equal to the posterior probability of negative association in the 2 × 2 contingency table under a Bayesian analysis using an improper prior. We derive an extension of Fisher’s exact test p-value in the presence of missing data, assuming the missing data mechanism is ignorable (i.e., missing at random or completely at random). Further, we propose Bayesian p-values for a test of independence in a 2 × 2 contingency table with missing data using alternative priors; we also present results from a simulation study exploring the Type I error rate and power of the proposed exact test p-values. An example, using data on the association between blood pressure and a cardiac enzyme, is presented to illustrate the methods.
AB - Altham (Altham PME. Exact Bayesian analysis of a 2 × 2 contingency table, and Fisher’s “exact” significance test. J R Stat Soc B 1969; 31: 261–269) showed that a one-sided p-value from Fisher’s exact test of independence in a 2 × 2 contingency table is equal to the posterior probability of negative association in the 2 × 2 contingency table under a Bayesian analysis using an improper prior. We derive an extension of Fisher’s exact test p-value in the presence of missing data, assuming the missing data mechanism is ignorable (i.e., missing at random or completely at random). Further, we propose Bayesian p-values for a test of independence in a 2 × 2 contingency table with missing data using alternative priors; we also present results from a simulation study exploring the Type I error rate and power of the proposed exact test p-values. An example, using data on the association between blood pressure and a cardiac enzyme, is presented to illustrate the methods.
KW - Dirichlet prior
KW - Fisher’s exact test
KW - missing at random
KW - missing completely at random
KW - quasi-Monte Carlo integration
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U2 - 10.1177/0962280217702538
DO - 10.1177/0962280217702538
M3 - Article
C2 - 28633606
AN - SCOPUS:85043470142
VL - 27
SP - 3411
EP - 3419
JO - Statistical Methods in Medical Research
JF - Statistical Methods in Medical Research
SN - 0962-2802
IS - 11
ER -