We discuss maximum likelihood methods for analysing binary responses measured at two times, such as in a cross-over design. We construct a 2 x 2 table for each individual with cell probabilities corresponding to the cross-classification of the responses at the two times; the underlying likelihood for each individual is multinomial with four cells. The three dimensional parameter space of the multinomial distribution is completely specified by the two marginal probabilities of success of the 2 x 2 table and an association parameter between the binary responses at the two times. We examine a logistic model for the marginal probabilities of the 2 x 2 table for individual i; the association parameters we consider are either the correlation coefficient, the odds ratio or the relative risk. Simulations show that the parameter estimates for the logistic regression model for the marginal probabilities are not very sensitive to the parameters used to describe the association between the binary responses at the two times. Thus, we suggest choosing the measure of association for ease of interpretation.
[1]
C. Bombardier,et al.
Auranofin therapy and quality of life in patients with rheumatoid arthritis. Results of a multicenter trial.
,
1986,
The American journal of medicine.
[2]
Ralph A. Bradley,et al.
The asymptotic properties of ML estimators when sampling from associated populations
,
1962
.
[3]
K. Mardia,et al.
Some contributions to contingency-type bivariate distributions.
,
1967,
Biometrika.
[4]
D. Rubin.
INFERENCE AND MISSING DATA
,
1975
.
[5]
S. Zeger,et al.
Longitudinal data analysis using generalized linear models
,
1986
.
[6]
G G Koch,et al.
A general methodology for the analysis of experiments with repeated measurement of categorical data.
,
1977,
Biometrics.
[7]
R. Prentice,et al.
Correlated binary regression with covariates specific to each binary observation.
,
1988,
Biometrics.
[8]
Haseman Jk,et al.
Analysis of dichotomous response data from certain toxicological experiments.
,
1979
.