Sage Journals: Discover world-class research

Abstract

Comparison of treatment differences in incidence rates is an important objective of many clinical trials. However, often the proportion is affected by covariates, and the adjustment of the predicted proportion is made using logistic regression. It is desirable to estimate the treatment differences in proportions adjusting for the covariates, similarly to the comparison of adjusted means in analysis of variance. Because of the correlation between the point estimates in the different treatment groups, the standard methods for constructing confidence intervals are inadequate. The problem is more difficult in the binary case, as the comparison is not uniquely defined, and the sampling distribution more difficult to analyze. Four procedures for analyzing the data are presented, which expand upon existing methods and generalize the link function. It is shown that, among the four methods studied, the resampling method based on the exact distribution function yields a coverage rate closest to the nominal.

Keywords

Proportions logistic regression covariates risk difference confidence interval

Get full access to this article

View all access options for this article.

References

Ranganath

Khanna

Paulus

. ACR remission criteria and response criteria. Clin Exp Rehumatol 2006; 24: S14–S21.

Austin

Manca

Zwarenstein

et al.

A substantial and confusing variation exists in handling of baseline covariates in randomized controlled trials: A review of trial published in leading medical journals. J Clin Epidemiol 2010; 63: 142–153.

Chan

Hopewell

et al.

Reporting on covariate adjustment in randomized controlled trials before and after revision of the 2001 CONSORT statement: A literature review. Trials 2010; 11: 59–59.

Moor

van der Laan

. Covariate adjustment in randomized trials with binary outcomes: Targeted maximum likelihood estimation. Stat Med 2009; 28: 39–64.

Robinson

Jewell

. Some surprising results about covariate adjustment in logistic regression models. Int Stat Rev 1991; 58: 227–240.

Garrett

. Therapeutic equivalence: Fallacies and falsification. Stat Med 2003; 22: 741–762.

SAS. SAS/STAT 9.2 user’s guide. 2nd ed. http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_glm_a0000000866.htm (accessed 10 July 2013).

Hummel J and Wiseman S. Non-inferiority studies with binary endpoint: Analysis with adjustment for covariates. In: Presented at PSI/EFSPI annual conference, 20 May 2008, http://ppdesurvey.com/resource_library/presentations/NonInferiorityStudieswithBinaryEndpointPresentation_Hummel.pdf.

Billingsley

. Probability and measure, 3rd ed. New York: John Wiley & Sons, 1995.

10.

Lehmann

. Testing statistical hypotheses, 2nd ed. New York: John Wiley & Sons, 1986, pp. 267–267.

11.

Little RJA. Generalized linear models for cross-classified data from the WFS. World Fertility Survey Technical Bulletins, 1978, Number 5.

12.

Rodriguez G. Generalized linear models, http://data.princeton.edu/wws509/datasets/#cuse (accessed 5 October 2011).

13.

National Institute of Standards and Technology. Engineering statistics handbook, Section 1.3.3.26.11. http://www.itl.nist.gov/div898/handbook/eda/section3/eda33qb.htm (accessed 7 January 2014).

14.

Johnson

Riess

. Numerical analysis, 2nd ed. Reading, MA: Addison-Wesley Publishing Company, 1982.

15.

Venzon

Moolgavkar

. A method for computing profile-likelihood-based confidence intervals. Appl Stat 1988; 37: 87–94.

16.

Thulin M. The cost of using exact confidence intervals for a binomial proportion. arXiv:1303.1288 [math.ST], 2013.

17.

Agresti

. Dealing with discreteness: Making ‘exact’ confidence intervals for proportions, differences of proportions, and odds ratios more exact. Stat Meth Med Res 2003; 12: 3–21.

18.

Fagerland

Lydersen

Laake

. Recommended confidence intervals for two independent binomial proportions. Stat Meth Med Res 2015; 24: 224–254.

19.

Wang

. On construction of the smallest one-sided confidence interval for the difference of two proportions. Ann Stat 2010; 38: 1227–1243.

20.

Wang

. An inductive order construction for the difference of two dependent proportions. Stat Probab Lett 2012; 82: 1623–1628.

21.

Kawasaki

Niyaoka

. A posterior density for the difference between two binomial proportions and the highest posterior density credible interval. J Jpn Stat Soc 2010; 40: 265–275.

22.

Newcombe

. Interval estimation for the difference between independent proportions: Comparison of eleven method. Stat Med 1998; 17: 873–890.

23.

Zou

. A modified Poisson regression approach to prospective studies with binary data. Am J Epidemiol 2004; 159: 702–706.

Confidence interval of difference of proportions in logistic regression in presence of covariates

Abstract

Keywords

Get full access to this article

References