## Electronic Journal of Statistics

- Electron. J. Statist.
- Volume 6 (2012), 672-685.

### Effect of a preliminary test of homogeneity of stratum-specific odds ratios on their confidence intervals

Paul Kabaila and Dilshani Tissera

#### Abstract

Consider a case-control study in which the aim is to assess a factor’s effect on disease occurrence. We suppose that this factor is dichotomous. Also suppose that the data consists of two strata, each stratum summarized by a two-by-two table. A commonly-proposed two-stage analysis of this type of data is the following. We carry out a preliminary test of homogeneity of the stratum-specific odds ratios. If the null hypothesis of homogeneity is accepted then we find a confidence interval for the assumed common value (across strata) of the odds ratio. We examine the statistical properties of this two-stage analysis, based on the Woolf method, on confidence intervals constructed for the stratum-specific odds ratios, for large numbers of cases and controls for each stratum. We provide both a Monte Carlo simulation method and an elegant large-sample method for this examination. These methods are applied to obtain numerical results in the context of the large numbers of cases and controls for each stratum that arose in a real-life dataset. In this context, we find that the preliminary test of homogeneity of the stratum-specific odds ratios has a very harmful effect on the coverage probabilities of these confidence intervals.

#### Article information

**Source**

Electron. J. Statist., Volume 6 (2012), 672-685.

**Dates**

First available in Project Euclid: 27 April 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.ejs/1335531218

**Digital Object Identifier**

doi:10.1214/12-EJS688

**Mathematical Reviews number (MathSciNet)**

MR2988424

**Zentralblatt MATH identifier**

1274.62215

**Subjects**

Primary: 62F25: Tolerance and confidence regions

Secondary: 62P10: Applications to biology and medical sciences

**Keywords**

Case-control study coverage probability odds ratio simultaneous confidence intervals test of homogeneity

#### Citation

Kabaila, Paul; Tissera, Dilshani. Effect of a preliminary test of homogeneity of stratum-specific odds ratios on their confidence intervals. Electron. J. Statist. 6 (2012), 672--685. doi:10.1214/12-EJS688. https://projecteuclid.org/euclid.ejs/1335531218