Adjusted Rank Probabilities

[Rischi95]

Hi all,

I am a new user of SAS. I just wonder if someone can help me sort out what kind of analysis should I use to rank the adjusted probabilities. I have tried to use logistic regression proc means, and proc rank but the results were not reliable. This is the condition I am currently facing, I have 25 hospitals in my dataset which each hospital having certain number of patients, making the total 4 millions records in my dataset. The effectiveness of this hospital is measured by how effective the doctor in detecting the TB symptoms as true TB positive. However, in this case there are several factors (5 variables) that influence the level of TB detection. Now, I confuse how to obtain the detection probabilities (with considering the variables) of these hospital and rank it accordingly. 

Thank you 🙂

[Rick_SAS]

It's not clear how many doctors are in each hospital, so let me outline the approach for each doctor. 

If you use all the data and covariates to build a logistic model, you can find, for each patient, the predicted probability, prob_k, that the k_th patient will be correctly diagnosed. 

The i_th doctor saw N_i patients and correctly diagnosed T_i. For the i_th doctor, the EXPECTED number of correct diagnoses is predicted by the model to be E_i = Sum(prob_k), where the sum is over the patients that the i_th doctor treated.  Therefore, you can compare the observed proportion (T_i/N_i) and the expected proportion E_i/N_i.

Thus, you can use all the usual formulas for comparing observed and expected (mean) proportions, or you can use the normal approximation on the scale of the number of observed and expected patients. For example, if a doctor saw 50 patients and correctly diagnosed 30 of them, but the expected value of the model predicts that the average doctor would have correctly diagnosed 40, then this doctor performed worse than expected. You can use the usual statistics to quantify whether a doctor's actual proportion is within a few standard  deviations of the expected proportion, given the patients.