Toxins such as endocrine disruptors have been linked to downstream health effects among the children and even grandchildren of those exposed, motivating recent interest in transgenerational studies. These studies, however, are prone to exhibiting informative cluster size, occurring when the number of offspring is conditionally related to their outcomes, and both marginal (weighted estimating equations) and conditional (joint models of cluster size and outcomes) approaches to inference have been proposed in such settings. When some latent factor affects both cluster size and outcome, however, it stands to reason that extreme doses might lead to clusters of size zero, a problem not yet described in the literature. This talk will examine the impact of such informatively empty clusters on standard analysis methods, and we further propose a joint marginalized modelling approach to validly estimate marginal parameters even in the presence of empty clusters. This work is illustrated via a motivating study of in-utero exposure to diethylstilbestrol on ADHD outcomes among 106,198 children to 47,540 nurses.