The impact of correlated exposures and missing data on multiple informant models used to identify critical exposure windows

Abstract

There has been heightened interest in identifying critical windows of exposure for adverse health outcomes; that is, time points during which exposures have the greatest impact on a person's health. Multiple informant models implemented using generalized estimating equations (MIM GEEs) have been applied to address this research question because they enable statistical comparisons of differences in associations across exposure windows. As interest rises in using MIMs, the feasibility and appropriateness of their application under settings of correlated exposures and partially missing exposure measurements requires further examination. We evaluated the impact of correlation between exposure measurements and missing exposure data on the power and differences in association estimated by the MIM GEE and an inverse probability weighted extension to account for informatively missing exposures. We assessed these operating characteristics under a variety of correlation structures, sample sizes, and missing data mechanisms considering various exposure-outcome scenarios. We showed that applying MIM GEEs maintains higher power when there is a single critical window of exposure and exposure measures are not highly correlated, but may result in low power and bias under other settings. We applied these methods to a study of pregnant women living with HIV to explore differences in association between trimester-specific viral load and infant neurodevelopment.

Keywords: critical windows; exposure timing; generalized estimating equations; inverse probability weights; missing data; multiple informants.

FIGURE 1

Type 1 error rate (associations across trimesters were equal). The green solid line represents a 5% rejection rate (Type 1 error). Both the multiple informant model using generalized estimating equations (MIM GEE) and the multiple informant model using inverse probability-weighted generalized estimating equations (MIM IPW GEE) were analyzed across all correlation structures, sample sizes, and missing data mechanisms. Missing data mechanisms included: no missing exposure data, exposure measures missing completely at random (MCAR), exposures MAR with no correction, and exposures MAR with model correction (IPW)

FIGURE 2

Empirical power analysis under the scenario of different exposure-outcome associations across windows (Scenario 2). The empirical power of the overall test of differences in associations from both the multiple informant model using generalized estimating equations (MIM GEE) and the multiple informant model using inverse probability-weighted generalized estimating equations (MIM IPW GEE) for the second scenario considered, across correlation structures, sample sizes, and missing data mechanisms. These simulations were based on the scenario where exposure measurements had a different association with the outcome across time windows. The conditional association with the outcome was a 1 SD decrease for the first time window, 0.8 SD decrease for the second, and 0.6 SD decrease for the third. Missing data mechanisms included: no missing exposure data, exposure measures missing completely at random (MCAR), exposures MAR with no correction, and exposures MAR with model correction (IPW)

FIGURE 3

Average difference (A) and average squared difference (B) under the scenario of different exposure-outcome associations across windows (Scenario 2). The average difference and average squared difference of the period-specific estimates from both the multiple informant model using generalized estimating equations (MIM GEE) and the multiple informant model using inverse probability-weighted generalized estimating equations (MIM IPW GEE) for the second scenario considered with N = 1500, across correlation structures and missing data mechanisms. These simulations were based on the scenario where exposure measurements had a different association with the outcome across time windows. The conditional association with the outcome was a 1 SD decrease for the first time window, 0.8 SD decrease for the second, and 0.6 SD decrease for the third. Missing data mechanisms included: no missing exposure data, exposure measures missing completely at random (MCAR), exposures MAR with no correction, and exposures MAR with model correction (IPW)

FIGURE 4

Empirical power analysis under the scenario of a single critical window (Scenario 3). The empirical power of the overall test of differences in associations from both the multiple informant model using generalized estimating equations (MIM GEE) and the multiple informant model using inverse probability-weighted generalized estimating equations (MIM IPW GEE) for the third scenario considered, across correlation structures, sample sizes, and missing data mechanisms. These simulations were based on the scenario where a single critical window had an association with the outcome. We simulated this to be a conditional associations of a 0.4 SD decrease in the mean outcome for this critical window. Missing data mechanisms included: no missing exposure data, exposure measures missing completely at random (MCAR), exposures MAR with no correction, and exposures MAR with model correction (IPW)

FIGURE 5

Average difference (A) and average squared difference (B) under the scenario of a single critical window (Scenario 3). The average difference and average squared difference of the period-specific estimates from both the multiple informant model using generalized estimating equations (MIM GEE) and the multiple informant model using inverse probability-weighted generalized estimating equations (MIM IPW GEE) for the third scenario considered with N = 1500, across correlation structures and missing data mechanisms. These simulations were based on the scenario where a single critical window had an association with the outcome. We simulated this to be a conditional association of a 0.4 SD decrease in the mean outcome for this critical window. Missing data mechanisms included: no missing exposure data, exposure measures missing completely at random (MCAR), exposures MAR with no correction, and exposures MAR with model correction (IPW)