A weak-signal-assisted procedure for variable selection and statistical inference with an informative subsample

This paper is motivated from an HIV-1 drug resistance study where we encounter three analytical challenges: to analyze data with an informative subsample, to take into account the weak signals, and to detect important signals and also conduct statistical inference. We start with an initial estimation method, which adopts a penalized pairwise conditional likelihood approach for variable selection. This initial estimator incorporates the informative subsample issue. To accounting for the effect of weak signals, we use a key idea of partial ridge regression. We also propose a one-step estimation method for each of the signal coefficients and then construct confidence intervals accordingly. We apply the proposed method to the Stanford HIV-1 drug resistance study and compare the results with existing approaches. We also conduct comprehensive simulation studies to demonstrate the superior performance of our proposed method.