Group testing, through the use of pooling, has proven to be an efficient method of reducing the time and cost associated with screening for a binary characteristic of interest, such as infection status. A topic of key interest in the statistical literature involves the development of regression models that relate individual-level covariates to testing responses observed from pooled specimens. In this article, we propose a general semiparametric framework that allows for the inclusion of multi-dimensional covariates, decoding information, and imperfect testing. The asymptotic properties of our estimators are presented and guidance on finite sample implementation is provided. We illustrate the performance of our methods through simulation and by applying them to chlamydia and gonorrhea data collected by the Nebraska Public Health Laboratory as a part of the Infertility Prevention Project.

We consider testing the equality of two regression functions using two independent samples. Three tests are proposed that are free of the restriction of having the same covariate values or sample sizes for both samples. Asymptotic distributions are given and results from a simulation study are presented that show the superior power properties of these tests over a competing test in a variety of cases, including the testing of hypotheses involving high-frequency curves when the design points for the two samples differ. It is also observed that the tests have good level properties when proper smoothing parameters are selected.

In this paper, we are concerned with the estimation of a proportion based on group testing data where the prevalence of a disease is observed for groups of individuals. Based on the covariates measured on all individuals in every group, we propose a local likelihood estimator of the prevalence probability as a function of the covariate. We show that the proposed estimator has an asymptotic normal distribution. Finite sample performance of the method is exhibited via some simulated examples and a real data analysis.

In this work we propose a method for optimal treatment assignment based on individual covariate information for a patient. For the K treatment ($K\ge 2$ ) scenario, we compare quantities that are suitable surrogates to true conditional probabilities of outcome variable of each treatment dominating outcome variables for all other treatments conditional on patient specific scores constructed from patient-specific covariates. As opposed to methods based on conditional means, our method can be applied for a broad set of models and error structures. Furthermore, the proposed method has very desirable large sample properties. We suggest Single Index Models as appropriate models connecting outcome variables to covariates and our empirical investigations show that correct treatment assignments are highly accurate. The proposed method is also rather robust against departures from a Single Index Model structure. Furthermore, selection of a treatment using the proposed metric appears to incur no losses in terms of the average reward for cases when two treatments are close in terms of this metric. We also conduct a real data analysis to show the applicability of the proposed procedure. This analysis highlights possible gains both in terms of average response and survival time if one were to use the proposed method.