A Monte Carlo study of three odds ratio estimators and four tests of association in several 2x2 tables when the data are sparse

Abstract

Epidemiologic data are often summarized in the form of several 2x2 tables where it is of interest to estimate the odds ratio for each 2x2 table. More importantly these estimators are often combined into a single estimator and a test statistic for the hypothesis of no association computed. The performance of three such combined odds ratio estimators and four tests of association was studied using Monte Carlo methods. The results of these studies are described in this paper. For the Monte Carlo studies, a constant odds ratio was used with equal numbers of cases and controls. A wide range of odds ratios, probabilities of exposure, number of cases, and number of strata were used. For each of the 1000 Kx2x2 tables used in one simulation, the Mantel-Haenszel (1959), maximum conditional likelihood (Gart, 1971), and weighted least squares (Woolf, 1955) estimators of the odds ratio were computed along with the likelihood-ratio (Bishop et al., 1975), Mantel-Haenszel, Pearson, and weighted least squares tests of association. The results of these studies indicate that the mean squared error of the weighted least squares estimator is usually less than the mean squared Pearson statistic (9), since it may take negative values. It was included in this simulation since it is a statistic produced by some software packages. The LR and MH tests are recommended since they maintain their size near 5% over the range of parameters used in the simulation.

Keywords:

• categorical data
• chi-square tests
• Mantet-Haenszel statistic
• sparse data