I have a binomial outcome (death in clinic vs. survival till release) observational study looking at assessing the effect of one treatment vs. a control. There are about 25 cases of the treatment (which is less than the number of cases in the control). If I consider the rule of thumb that the number of predictors in a logistic regression should be no more than m / 10 = 25/10, I am able to consider 2 predictors. If I use a propensity score, then this allows me to include both the propensity score and the treatment.
However, in the book on Biostatistics for Biomedical Research (Harrell, Slaughter), the suggestion is to model:
Y = treat + log(PS/(1-PS)) + nonlinear functions of log(PS/(1-PS)) + important prognostic variables
In cases where there is not all that much data, is it better to just use the following model?
Y = treat + log(PS/(1-PS))