The effect of risk factor misclassification on the partial population attributable risk

Abstract

The partial population attributable risk (pPAR) is used to quantify the population-level impact of preventive interventions in a multifactorial disease setting. In this paper, we consider the effect of nondifferential risk factor misclassification on the direction and magnitude of bias of pPAR estimands and related quantities. We found that the bias in the uncorrected pPAR depends nonlinearly and nonmonotonically on the sensitivities, specificities, relative risks, and joint prevalence of the exposure of interest and background risk factors, as well as the associations between these factors. The bias in the uncorrected pPAR is most dependent on the sensitivity of the exposure. The magnitude of bias varies over a large range, and in a small region of the parameter space determining the pPAR, the direction of bias is away from the null. In contrast, the crude PAR can only be unbiased or biased towards the null by risk factor misclassification. The semiadjusted PAR is calculated using the formula for the crude PAR but plugs in the multivariate-adjusted relative risk. Because the crude and semiadjusted PARs continue to be used in public health research, we also investigated the magnitude and direction of the bias that may arise when using these formulae instead of the pPAR. These PAR estimators and their uncorrected counterparts were calculated in a study of risk factors for colorectal cancer in the Health Professionals Follow-up Study, where it was found that because of misclassification, the pPAR for low folate intake was overestimated with a relative bias of 48%, when red meat and alcohol intake were treated as misclassified risk factors that are not modified, and when red meat was treated as the modifiable risk factor, the estimated value of the pPAR went from 14% to 60%, further illustrating the extent to which misclassification can bias estimates of the pPAR.

Keywords: attributable risk; bias; measurement error; risk factor misclassification.

FIGURE 1

Effect of varying ϕ_S, the exposure specificity (θ_T = ϕ_T = p_S. = p._T = 0.75, rr_1S = 1.25, rr_2T = 3, rr_S|T = 1.1) [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 2

Effect of varying ϕ_T, the background specificity (ϕ_S = θ_T = p_S. = p._T = 0.75, rr_1S = 1.25, rr_2T = 3, rr_S|T = 1.1) [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 3

Effect of varying p_S. the exposure prevalence (ϕ_S = ϕ_T = θ_T = p._T = 0.75, rr_1S = 1.25, rr_2T = 3, rr_S|T = 1.1) [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 4

Effect of varying p._T, the background factor prevalence (ϕ_S = ϕ_T = θ_T = p_S. = 0.75, rr_1S = 1.25, rr_2T = 3, rr_S|T = 1.1) [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 5

Effect of varying θ_S, exposure sensitivity, holding ϕ_S = ϕ_T = θ_T = p_S. = p._T = 0.75, rr_1S = 1.25, rr_2T = 3, rr_S|T = 1.1

FIGURE 6

Effect of varying ϕ_S, exposure specificity, holding θ_S = ϕ_T = θ_T = p_S. = p._T = 0.75, rr_1S = 1.25, rr_2T = 3, rr_S|T = 1.1

FIGURE 7

Effect of varying θ_T, background factor sensitivity, holding ϕ_S = θ_S = ϕ_T = p_S. = p._T = 0.75, rr_1S = 1.25, rr_2T = 3, rr_S|T = 1.1

FIGURE 8

Effect of varying rr_S|T, association of X_S with X_T, holding ϕ_S = θ_S = ϕ_T = θ_T = p_S. = p._T = 0.75, rr_1S = 1.25, rr_2T = 3

FIGURE 9

Effect of varying p_S., holding ϕ_S = θ_S = ϕ_T = θ_T = p._T = 0.75, rr_1S = 1.25, rr_2T = 3, rr_S|T = 1.1

FIGURE 10

Effect of varying p._T, holding ϕ_S = θ_S = ϕ_T = θ_T = p_S. = 0.75, rr_1S = 1.25, rr_2T = 3, rr_S|T = 1.1