This before and after study is an example of a matched study. In this case the matching arises from the same participant being observed at each time point. Conditional logistic regression provides a robust method to analyse matched studies. It has, perhaps, most frequently been used to analyse case-control studies. The methodology is discussed, in detail, by Breslow and Day.^w1

In our study we wish to compare two scores for each individual, x₁ taken before the intervention and x₂ taken after the intervention. For a yes/no score, yes can be assigned the value 1 and no the value 0. However, in general a score can take any range of values. Conditional logistic regression essentially reduces to modelling the probability that, for an individual with these two scores on the two occasions, x₂ is observed after the intervention rather than before. This probability can be written as exp[B(x₂-x₁)]/{1+ exp[B(x₂-x₁)]}.

The basic data used for the estimation can therefore be seen to be the difference between the scores. The coefficient B, that is to be estimated, can be regarded simply as a linear discriminant coefficient or can be given an odds ratio interpretation that for two observations of x from the same individual that differ by one unit, exp(B) is the relative odds of the larger observation being taken after the intervention versus being taken before. In either case, the larger B, or the odds ratio exp(B), the more likely it is that higher valued scores are seen after the intervention.

1. Breslow NE, Day CE. Statistical methods in cancer research. Vol 1. The analysis of case-control studies. Lyons: International Agency for Research on Cancer, 1980. (IARC Scientific Publications No 32.)