Statistical Inference for the Rate Ratio in a Two-way Contingency Table with an Empty Cell

Statistical Inference for the Rate Ratio in a Two-way Contingency Table with an Empty Cell

Mahmoud Okasha

m.okasha@palnet.com.

Department of Applied Statistics. Faculty of Economics. Al-Azhar University. Gaza. Palestine

Received : 25-01-2005 , Accepted : 28-08-2005

Language: English

Abstract

In many statistical data analyses, the problem of analyzing contingency tables that contain empty cells is commonly encountered in all fields of research. The odds ratio and risk ratio are not applicable in such a case because of an unidentifiablity problem. In the present paper the rate ratio between the second negative response given an initial negative response and the initial negative response in a two-way contingency table with a zero-count in one of the off-diagonal cells is utilized. Hypothesis testing and confidence interval construction for the rate ratio based on the Wald’s test statistic and its logarithmic transformation will be reviewed. Inference based on large sample theory and small-sample on the rate ratio of this case is discussed. The asymptotic performance of the Wald’s test statistic and its logarithmic transformation is examined. By adopting these statistics, full unconditional exact small-sample procedures that have been proposed by Tang and Tang (2002) are discussed. The procedures are modified by utilizing the maximum likelihood estimator of the rate ratio and the conditional likelihood functions. The accuracy of all the methods is empirically assessed. We show that our modified conditional procedures are more reliable than both exact and asymptotic procedures in terms of coverage probability and expected interval width. The methodology is applied to data on family planning in the Gaza Strip and other examples from the literature.

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