We consider nonparametric and semiparametric estimation of a conditional probability curve in the case of group testing data, where the individuals are pooled randomly into groups and only the pooled data are available. We derive a nonparametric weighted estimator that has opti-mality properties accounting for group sizes, and show how to extend it to multivariate settings, including the partially linear model. In the group testing context, it is natural to assume that the probability curve depends on the covariates only through a linear combination of them. Motivated by this condition, we develop a nonparametric estimator based on the single-index model. We study theoretical properties of the proposed estimators and derive data-driven procedures. Practical properties of the methods are demonstrated via real and simulated examples, and our estimators are shown to have smaller median integrated square error than existing competitors.