Likelihood-based methods for estimating the association between a health outcome and left- or interval-censored longitudinal exposure data

Abstract

The Michigan Female Health Study (MFHS) conducted research focusing on reproductive health outcomes among women exposed to polybrominated biphenyls (PBBs). In the work presented here, the available longitudinal serum PBB exposure measurements are used to obtain predictions of PBB exposure for specific time points of interest via random effects models. In a two-stage approach, a prediction of the PBB exposure is obtained and then used in a second-stage health outcome model. This paper illustrates how a unified approach, which links the exposure and outcome in a joint model, provides an efficient adjustment for covariate measurement error. We compare the use of empirical Bayes predictions in the two-stage approach with results from a joint modeling approach, with and without an adjustment for left- and interval-censored data. The unified approach with the adjustment for left- and interval-censored data resulted in little bias and near-nominal confidence interval coverage in both the logistic and linear model setting.

Figure 1

Plot of means of θ̂₁ against sample size from 500 simulations.

Figure 2

Weighted p–p plots (a) random intercept deviations (a_i) and (b) random slope deviations (b_i). Vertical axis: expected (Ф(Ẑ_(i))) Horizontal axis: weighted observed (F̂(Ẑ_(i))), where Ẑ_(i) refers to the standardized estimates of the random effects.

Figure 3

Plot of the posterior predicted means, $Y_i^{*}$, for 109 women. Estimates of $Y_i^{*}$ using IC adjusted method (horizontal axis) versus the midpoint method (vertical axis).