Sage Journals: Discover world-class research

Abstract

2times2 contingency tables are frequently obtained from independent binomial sampling. However, when the probabilities of the outcome of interest are small, we may use independent negative binomial sampling in which sampling stops after a predetermined number of the outcome of interest occurs. The obtained 2times2 contingency tables are likely to be unbalanced, and the asymptotic tests could be unreliable. In this article, we develop exact conditional tests for the risk difference, the risk ratio, and the odds ratio in 2 times 2 contingency tables obtained from independent negative binomial sampling. We investigate the exact unconditional powers of the exact tests. The main advantage of exact test is that it is guaranteed to control type I errors under the nominal level unconditionally.

Keywords

Exact unconditional power 2 times 2 contingency table Epidemiology Rare event Vaccine

Get full access to this article

View all access options for this article.

References

Fleiss

Levin

Paik

. Statistical Methods for Rates and Proportions. 3rd ed. Wiley. New York; (2003).

Haldane

JBS

. On a method of estimating frequencies. Biometrika. 1945; 33:222–225.

Kudo

. 2 times 2 tables emerging out of different chance mechanisms. Commun Stat. 1978;A7(10): 977–986.

Lui

. Confidence limits for the population prevalence rate based on the negative binomial distribution. Stat Med. 1995a; 14:1471–1477.

Lui

. Confidence intervals for the risk ratio in cohort studies under inverse sampling. Biometric J. 1995b; 37:965–971.

Lui

. Point estimation of relative risk under inverse sampling. Biometric J. 1996a; 38:669–680.

Lui

. Notes on confidence limits for the odds ratio in case-control studies under inverse sampling. Biometric J. 1996b; 38:221–229.

Lui

. Notes in case-control studies with matched pairs under inverse sampling. Biometric J. 1996; 38:681–693.

Lui

. Conditional maximum likelihood estimate and exact test of the common relative difference in combination of 2 times 2 tables under inverse sampling. Biometric J. 1997; 39:215–225.

10.

Lui

. Tests of homogeneity for the relative difference between strata under inverse sampling. Biometric J. 1998; 40:227–235.

11.

Lui

. Interval estimation of simple difference under independent negative binomial sampling. Biometric J. 1999; 41(l):83–92.

12.

Lui

. Asymptotic conditional test procedures for relative difference under inverse sampling. Biometric J. 2000; 34:335–343.

13.

Lui

. Estimation of rate ratio and relative difference in matched pairs under inverse sampling. Environmetrics 2001; 12:539–546.

14.

Jia

Hwang

. Use of inverse binomial sampling in exact conditional test of relative risk for rare events in clinical trials. ASA Proc Joint Stat Meetings. 2004;578–585.

15.

Lui

. Statistical Estimation of Epidemiological Risk. New York: John Wiley & Sons; 2004.

16.

Agresti

. A survey of exact inference for contingency table. Stat Sci. 1992; 7:131–177.

17.

Mehta

. The exact analysis of contingency tables in medical research. Stat Meth Med Res. 1994; 3:135–156.

18.

Cytel

StatXact, Version 6.0: Software for Exact Non-parametric Statistical Inference With Continuous or Categorical Data. Cambridge, MA: Cytel Software; 2006.

19.

Kang

Kim

. A comparison of the three conditional exact tests in two-way contingency tables using the unconditional exact power. Biometric J. 2004; 46(3):320–330.

20.

Dragalin

Fedorov

Cheuvart

Statistical approaches to establishing vaccine safety. Stat Med. 2002; 21:877–893.

21.

Polman

Barkhof

Sandberg-Wollheim

Linde

Nordle

Nederman

. Treatment with laquinimod reduces development of active MRI lesions in relapsing MS. Neurology. 2005; 64:987–991.

Exact Tests for Epidemiological Risks under Independent Negative Binomial Sampling for Rare Events in Clinical Trials

Abstract

Keywords

Get full access to this article

References