Sparse data are often encountered in many biomedical studies, such as in matched case-control design and familial aggregation analysis. In this paper, we extend the semiparametric proportional likelihood ratio model in Luo and Tsai (2012) to sparse independent data incorporating stratum-specific baseline density functions. In this case, the maximum likelihood estimator is inconsistent as it involves estimating many stratum-specific density functions. To circumvent this problem, we construct weighted pseudolikelihood by a conditioning procedure which eliminates the stratum-specific density functions. We further extend the model and inferential procedure to sparse correlated data. The optimal weights in the pseudolikelihood to retain the maximum statistical efficiency are derived for both sparse independent data and sparse correlated data. The performance of the proposed method is evaluated through simulation studies and a real data example of claims data from the UnitedHealth Group (UHG) Clinical Discovery Database.