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Yuan, A., Piao, J., Ning, J. and Qin, J. (2020), Semiparametric isotonic regression modelling and estimation for group testing data. Can J Statistics. https://doi.org/10.1002/cjs.11581
Group testing is a cost-effective sampling strategy to reduce the time and labor in large screening studies. In the group testing procedure, several individual samples are grouped and the pooled samples, instead of each individual sample, are tested for outcome status (e.g., infectious disease status). The cost-effectiveness of group testing does not, however, come without a price. The use of group testing creates challenges for statistical analysis due to the absence of individual responses. There is extensive literature on estimating procedures for group testing, most of which has focused on nonparametric procedures. In many studies that use the group testing procedure, one or several risk factors are also available, and it is of interest to estimate the conditional probability of the response, given such covariate information. We consider semiparametric isotonic regression models for the simultaneous estimation of the conditional probability curve and effects of risk factors, in which a parametric form for combining the risk factors is assumed and the monotonic link function is left unspecified. We develop an expectation-maximization algorithm to overcome the computational challenge and embed the pool-adjacent violators algorithm to facilitate the computation. Although the estimating algorithm involves iterative steps, it is computationally simple and efficient. The conditional expectations in the E-step can be simply obtained with closed forms. In the M-step, the non-specified monotonic function can be estimated easily by using available R function “Isoreg” in the R basic package. We apply the proposed method to data from the National Health and Nutrition Examination Survey for illustration.