Informatively empty clusters with application to multigenerational studies

Abstract

Summary Exposures with multigenerational effects have profound implications for public health, affecting increasingly more people as the exposed population reproduces. Multigenerational studies, however, are susceptible to informative cluster size, occurring when the number of children to a mother (the cluster size) is related to their outcomes, given covariates. A natural question then arises: what if some women bear no children at all? The impact of these potentially informative empty clusters is currently unknown. This article first evaluates the performance of standard methods for informative cluster size when cluster size is permitted to be zero. We find that if the informative cluster size mechanism induces empty clusters, standard methods lead to biased estimates of target parameters. Joint models of outcome and size are capable of valid conditional inference as long as empty clusters are explicitly included in the analysis, but in practice empty clusters regularly go unacknowledged. In contrast, estimating equation approaches necessarily omit empty clusters and therefore yield biased estimates of marginal effects. To resolve this, we propose a joint marginalized approach that readily incorporates empty clusters and even in their absence permits more intuitive interpretations of population-averaged effects than do current methods. Competing methods are compared via simulation and in a study of the impact of in-utero exposure to diethylstilbestrol on the risk of attention-deficit/hyperactivity disorder (ADHD) among 106 198 children to 47 540 nurses from the Nurses Health Study.

The Impact of Early-Life Exposures on Women’s Reproductive Health in Adulthood

“…Pregnancy is increasingly understood in a life course perspective, but rigorous methods for researching this are still difficult. Retrospective studies are subject to recall bias and selective fertility [ 77 ]. Prospective life course studies require a long-term investment of time and money, and information relevant to hypotheses of most interest decades or generations later may not have been measured initially.…”

On The Interplay between Exposure Misclassification and Informative Cluster Size

“…Though we have focused on marginal models, an important corollary is that the observed likelihood correction applies equally to cluster‐specific inference in joint conditional models—in a supplementary simulation, the observed likelihood correction performed similarly for conditional inference (see the on‐line Table H.1). Moreover, observed likelihood for joint models suggests a path forward when clusters may be informatively empty (McGee et al ., 2019).…”

“…One approach to marginal inference is to specify a JMM of outcome and cluster size (McGee et al ., 2019), e.g. where b k ∼MVN(0,Σ), h (·) and g (·) are link functions, is a vector subset of X ki and a diagonal matrix whose elements are a subset of Z k . In particular, the exposure of interest, , appears in both the model for the outcome and the model for cluster size.…”

“…if a shared genetic frailty or toxicity affects both fertility and child development. In such a case, marginal (or population‐average) inference can proceed via joint marginalized models (JMMs) for cluster size and outcome (Seaman et al ., 2014a,b; McGee et al ., 2019) or weighted estimating equations (WEEs) (Williamson et al ., 2003; Benhin et al ., 2005). Cluster‐specific inference proceeds via conditionally specified joint models (Dunson et al ., 2003; Gueorguieva, 2005) or generalized linear mixed models (GLMMs) (Neuhaus and McCulloch, 2011).…”

Smoking During Pregnancy and Risk of Attention-deficit/Hyperactivity Disorder in the Third Generation

“…To account for the potentially informative clustering based on possible effects of smoking on number of children born alive, 18 we calculated odds ratios (ORs) for ADHD related to grandmother smoking using all grandchildren with cluster-weighted generalized estimating equation (CW-GEE) regression models with a logit link, weighted by the inverse of the number of children of each nurse (G1). 19,20…”