Effects and non‐effects of paired identical observations in comparing proportions with binary matched‐pairs data

Binary matched-pairs data occur commonly in longitudinal studies, such as in cross-over experiments. Many analyses for comparing the matched probabilities of a particular outcome do not utilize pairs having the same outcome for each observation. An example is McNemar's test. Some methodologists find this to be counterintuitive. We review this issue in the context of subject-specific and population-averaged models for binary data, with various link functions. For standard models and inferential methods, pairs with identical outcomes may affect the estimated size of the effect and its standard error, but they have negligible, if any, effect on significance. We also discuss extension of this result to matched sets.

[1]  D. Cox.  Two further applications of a model for binary regression , 1958 .

[2]  R. Tarone,et al.  On summary estimators of relative risk. , 1981, Journal of chronic diseases.

[3]  Alan Agresti,et al.  HIERARCHICAL BAYESIAN ANALYSIS OF BINARY MATCHED PAIRS DATA , 2000 .

[4]  P. M. E. Altham,et al.  The analysis of matched proportions , 1971 .

[5]  P. Holland,et al.  Discrete Multivariate Analysis. , 1976 .

[6]  S. Shapiro.  Collapsing Contingency Tables—A Geometric Approach , 1982 .

[7]  Markku Nurminen,et al.  Asymptotic efficiency of general noniterative estimators of common relative risk , 1981 .

[8]  W. G. Cochran.  The comparison of percentages in matched samples. , 1950, Biometrika.

[9]  Gary G. Koch,et al.  Average Partial Association in Three-way Contingency Tables: a Review and Discussion of Alternative Tests , 1978 .

[10]  M. Lesperance,et al.  Estimation efficiency in a binary mixed-effects model setting , 1996 .

[11]  J. D. Kalbfleisch,et al.  Conditions for consistent estimation in mixed-effects models for binary matched-pairs data† , 1994 .

[12]  Jiahua Chen.  On the conditional and mixture model approaches for matched pairs , 1996 .

[13]  J. Neuhaus.  Estimation efficiency and tests of covariate effects with clustered binary data. , 1993, Biometrics.

[14]  J M Robins,et al.  Estimation of a common effect parameter from sparse follow-up data. , 1985, Biometrics.

[15]  Tue Tjur,et al.  A Connection between Rasch's Item Analysis Model and a Multiplicative Poisson Model , 1982 .

[16]  B. Lindsay,et al.  Semiparametric Estimation in the Rasch Model and Related Exponential Response Models, Including a Simple Latent Class Model for Item Analysis , 1991 .

[17]  M G Kenward,et al.  Modelling binary data from a three-period cross-over trial. , 1987, Statistics in medicine.

[18]  S L Zeger,et al.  On the use of concordant pairs in matched case-control studies. , 1988, Biometrics.

[19]  J. Kalbfleisch,et al.  A Comparison of Cluster-Specific and Population-Averaged Approaches for Analyzing Correlated Binary Data , 1991 .

[20]  Erling B. Andersen,et al.  Discrete Statistical Models with Social Science Applications. , 1980 .

[21]  Robert F. Woolson,et al.  Analysis of categorical incomplete longitudinal data , 1984 .

[22]  W. Haenszel,et al.  Statistical aspects of the analysis of data from retrospective studies of disease. , 1959, Journal of the National Cancer Institute.

[23]  Q. Mcnemar.  Note on the sampling error of the difference between correlated proportions or percentages , 1947, Psychometrika.

[24]  J. Richard Landis,et al.  A Note on the Equivalence of Several Marginal Homogeneity Test Criteria for Categorical Data , 1982 .