The GMBO/PECAN module can be used to binomial probabilities pi for data of the form (yini), where yi is the number of cases and ni the number of trials. Unless otherwise specified the risk (Ri) is described using the odds, that is
and the basic model is the classical log-linear logistic
regression model. However this model can be extended to include
stratification or, since the choice of 
is independent of the
specification of
, any of the more general relative risk
models described earlier. Furthermore, 
can be taken as 
or
.
The key variables in the analysis of binomial data contain the
values of 
and 
. Unless you specify otherwise, it is
assumed that these variables are named cases and trials, respectively. If 
it is no necessary to specify
the number of trials.
As shown by Breslow et al (Breslow, Day et al. 1978) and Prentice and Pyke (Prentice and Pyke 1979), logistic regression can be used to estimate covariate effects on odds ratios and relative risks in case-control studies. Gail et al (Gail, Lubin et al. 1981) developed and Lubin (Lubin 1981) implemented a conditional logistic regression algorithm (PECAN) for the analysis of matched case-control studies. In these studies a case or group of cases is matched to one or more controls (non-cases) with respect to variables such as age or sex. The use of the conditional likelihood is particularly important for matched case control studies in which the number of controls per case is relatively small since in such cases ignoring the matching or estimation of a stratum parameter for each case-control set can result in biased risk estimates (Breslow and Day 1980). The PECAN algorithm is available in the GMBO/PECAN module of Epicure.
The conditional logistic regression is based on a stratified model for the binomial odds that can be written as
with analyses carried out conditional on the number of cases
and controls in the stratum in order to eliminate the dependence of the
likelihood on the stratum parameters. In this model the odds within each stratum
are proportional to the function
. The function is often thought of as an odds
ratio; more precisely, for any two covariate vectors the odds ratio is the ratio
of the.
EPICURE’s GMBO/PECAN module can be used to fit stratified models using either unconditional or conditional likelihood based methods. In analyses of stratified binomial data the conditional likelihood is used for small strata (less than 25 cases and controls, although this threshold can be changed by the user) and the unconditional likelihood is used for larger strata.
Data for unstratified analyses of binomial data may be read from a file of individual records or as a table in which each record contains the number of subjects and number of cases corresponding to a unique set of covariate values. Such a table, which we will call an event-count table, is usually a cross-classification defined by several categorical variables. DATAB can be used to make event-count tables.
For analyses of matched cases-control studies or other stratified binomial data, the data should consist of individual records that contain a variable indicating whether the record describes a case or a control and at least one stratification variable.