I want to assess the predictive ability of biomarkers in a nested case-control study. The primary analysis with use conditional regression. I’d some questions: 1)Can I determine the AUC, sensitivity and specificity for the biomarkers? I’ve seen it done before using standard logistic regression adjusted for the matching variables to generate the probabilities. 2)I would like to examine prediction of an outcome which wasn’t used for the matching using the full population, should this be done using conditional or standard logistic regression? My understanding is that subgroups should use standard logistic regression.
Conditional logistic regression is not a model that's been widely developed in a lot of software packages, and requiring results for screening diagnostics such as sens/spec from conditional is more problematic. For your first question, yes you could implement a cluster variable to represent each cluster of a case and its controls, and then adjust a regular logistic model by the cluster variable. When time is involved in e.g. clinical trial data, most of the longitudinal regression models allow you to set a cluster id for subjects in order to appropriately determine the regression coefficient standard errors based on within-cluster, i.e., within matched sets, correlation between covariates. You might consider evaluating the model using GEE regression, but without using a time-treatment interaction term. You would be able to specify a logit family link (logistic), Gaussian (normal), Poisson, etc. as well as specify the correlation structure between outcomes within each matched set like exchangeable, autoregressive, independent, unstructured.
So perhaps consider using a panel data approach via longitudinal regression with a logit family link, and specify that e.g. each of the four data records for the first matched set (1 case, 3 controls) has an ID=1, the same covariate values, but the case (first record) has y=1, and records 2-4 have y=0. This will preserve within matches set correlation, but may not get you close to sens/spec and marker AUC, as GEE commonly doesn't output sens/spec/AUC, but you may find a package that does. Many packages allow you to use a cluster variable (i.e, matched set number) in the majority regression models.
So firstly, start looking for software that will allow use of a cluster ID within logistic regression, and then merely set the ID=1 for the first 4 subjects in matched set one. The rest is a variation on a theme. Going back to the need for having a conditional logistic package capable of running screening diagnostics (sens/spec/AUC) may bomb out.
I fully programmed conditional logistic years ago for matched case-control sets, but never developed screening diagnostics for it.
For your second question, yes, employ standard logistic regression.