A Frailty Approach for Survival Analysis with Error-prone Covariate

This paper discovers an inherent relationship between the survival model with covariate measurement error and the frailty model. The discovery motivates our using a frailty-based estimating equation to draw inference for the proportional hazards model with error-prone covariates. Our established framework accommodates general distributional structures for the error-prone covariates, not restricted to a linear additive measurement error model or Gaussian measurement error. When the conditional distribution of the frailty given the surrogate is unknown, it is estimated through a semiparametric copula function. The proposed copula-based approach enables us to fit flexible measurement error models without the curse of dimensionality as in nonparametric approaches, and to be applicable with an external validation study. Large sample properties are derived and finite sample properties are investigated through extensive simulation studies. The methods are applied to a study of physical activity in relation to breast cancer mortality in the Nurses’ Health Study

Causal mediation analysis with a failure time outcome in the presence of exposure measurement error

Causal mediation analysis is widely used in health science research to evaluate the extent to which an intermediate variable explains an observed exposure-outcome relationship. However, the validity of analysis can be compromised when the exposure is measured with error, which is common in health science studies. This article investigates the impact of exposure measurement error on assessing mediation with a failure time outcome, where a Cox proportional hazard model is considered for the outcome. When the outcome is rare with no exposure-mediator interaction, we show that the unadjusted estimators of the natural indirect and direct effects can be biased into either direction, but the unadjusted estimator of the mediation proportion is approximately unbiased as long as measurement error is not large or the mediator-exposure association is not strong. We propose ordinary regression calibration and risk set regression calibration approaches to correct the exposure measurement error-induced bias in estimating mediation effects and to allow for an exposure-mediator interaction in the Cox outcome model. The proposed approaches require a validation study to characterize the measurement error process between the true exposure and its error-prone counterpart. We apply the proposed approaches to the Health Professionals Follow-up study to evaluate extent to which body mass index mediates the effect of vigorous physical activity on the risk of cardiovascular diseases, and assess the finite-sample properties of the proposed estimators via simulations

Pattern and Predictors of Weight Gain During Pregnancy Among HIV-1-Infected Women from Tanzania

Progression of HIV disease is often accompanied by weight loss and wasting. Gestational weight gain is a strong determinant of maternal and neonatal outcomes; however, the pattern and predictors of weight gain during pregnancy among HIV-positive women are unknown. We obtained monthly anthropometric measurements in a cohort of 957 pregnant women from Tanzania who were HIV infected. We estimated the weekly rate of weight gain at various points during the second and third trimesters of pregnancy and computed rate differences between levels of sociodemographic, nutritional, immunologic, and parasitic variables at the first prenatal visit. The change in mid-upper arm circumference (MUAC) from baseline to delivery was also examined. The rate of weight gain decreased progressively during pregnancy. There was an average decline of 1 cm in MUAC between weeks 12 and 38. Lower level of education and helminthic infections at first visit were associated with decreased adjusted rates of weight gain during the third trimester. High baseline MUAC, not contributing to household income, lower serum retinol and selenium concentrations, advanced clinical stage of HIV disease, and malaria infection were related to decreased rates of weight gain during the second trimester. Low baseline CD4 T-cell counts were related to a poorer pattern of weight gain throughout pregnancy. Prevention and treatment of parasitic infections and improvement of nutritional status are likely to enhance the pattern of gestational weight gain among HIV-infected women

Causal Covariate Selection for the Imputation-based Regression Calibration Method for Exposure Measurement Error Bias Correction

In this paper, we identify the criteria for the selection of the minimal and most efficient covariate adjustment sets for the regression calibration method developed by Carroll, Rupert and Stefanski (CRS, 1992), used to correct bias due to continuous exposure measurement error. We utilize directed acyclic graphs to illustrate how subject matter knowledge can aid in the selection of such adjustment sets. Valid measurement error correction requires the collection of data on any (1) common causes of true exposure and outcome and (2) common causes of measurement error and outcome, in both the main study and validation study. For the CRS regression calibration method to be valid, researchers need to minimally adjust for covariate set (1) in both the measurement error model (MEM) and the outcome model and adjust for covariate set (2) at least in the MEM. In practice, we recommend including the minimal covariate adjustment set in both the MEM and the outcome model. In contrast with the regression calibration method developed by Rosner, Spiegelman and Willet, it is valid and more efficient to adjust for correlates of the true exposure or of measurement error that are not risk factors in the MEM only under CRS method. We applied the proposed covariate selection approach to the Health Professional Follow-up Study, examining the effect of fiber intake on cardiovascular incidence. In this study, we demonstrated potential issues with a data-driven approach to building the MEM that is agnostic to the structural assumptions. We extend the originally proposed estimators to settings where effect modification by a covariate is allowed. Finally, we caution against the use of the regression calibration method to calibrate the true nutrition intake using biomarkers.Comment: 11 pages, 4 tables, 3 figures. arXiv admin note: text overlap with arXiv:2212.0079

Design of egocentric network-based studies to estimate causal effects under interference

Many public health interventions are conducted in settings where individuals are connected to one another and the intervention assigned to randomly selected individuals may spill over to other individuals they are connected to. In these spillover settings, the effects of such interventions can be quantified in several ways. The average individual effect measures the intervention effect among those directly treated, while the spillover effect measures the effect among those connected to those directly treated. In addition, the overall effect measures the average intervention effect across the study population, over those directly treated along with those to whom the intervention spills over but who are not directly treated. Here, we develop methods for study design with the aim of estimating individual, spillover, and overall effects. In particular, we consider an egocentric network-based randomized design in which a set of index participants is recruited from the population and randomly assigned to treatment, while data are also collected from their untreated network members. We use the potential outcomes framework to define two clustered regression modeling approaches and clarify the underlying assumptions required to identify and estimate causal effects. We then develop sample size formulas for detecting individual, spillover, and overall effects. We investigate the roles of the intra-class correlation coefficient and the probability of treatment allocation on the required number of egocentric networks with a fixed number of network members for each egocentric network and vice-versa.Comment: 30 pages for main text including figures and tables, 5 figures and 3 table