Accuracy loss due to selection bias in cohort studies with left truncation

Abstract

Background: Selection is a common problem in paediatric and perinatal epidemiology, and truncation can be thought of as missing person time that can result in selection bias. Left truncation, also known as late or staggered entry, may induce selection bias and/or adversely affect precision. There are two kinds of left truncation: fixed left truncation where the start of follow-up is initiated at a set time, and variable left truncation where follow-up begins at a stochastically varying time-point.

Methods: Using data from a time-to-pregnancy study, augmented by a simulation study, we demonstrate the effects of fixed and variable truncation on estimates of the hazard ratio.

Results: First, fixed or variable non-differential left truncation results in a loss of precision. Fixed or variable differential left truncation results in a bias either towards or away from the null as well as a loss of precision. The extent and direction of this bias is a function of the size and direction of the association between exposure and outcome, and occurs in common scenarios and under a wide range of conditions.

Conclusions: As demonstrated in simulation studies, selection bias due to left truncation could have a serious impact on inferences, especially in the case of fixed or variable differential left truncation. When present in epidemiologic studies, proper accounting for left truncation is just as important as proper accounting for right censoring.

Keywords: Selection bias; fixed left truncation; variable left truncation.

Figure 1.

Graphs of fixed and variable truncation where deaths may occur before the start of follow-up, both differential and non-differential by exposure status. Horizontal lines represent subjects (solid = exposed, dashed = unexposed). Dots represent events. (a) Fixed truncation − non-differential; (b) fixed truncation − differential; (c) variable truncation − non-differential; (d) variable truncation − differential; (e) fixed and variable truncation − non-differential; (f) fixed and variable truncation − differential.

Figure 2.

(a and b) Number of pregnancies and Kaplan-Meier curves for time to pregnancy by smoking status for 586 women followed 12 months^a. ^aAdministratively censored in month 13.

Figure 3.

Pregnancy and l = log[−log(1 − pregnancy)] for fixed non-differential (top) and differential (bottom) truncation at months 0 (no truncation) and 6, the difference of l between non-smokers and smokers (δ = l_non-smoker − l_smoker) for truncation at months 0, 2, 4, and 6.

Figure 4.

Pregnancy and l = log[−log(1 − pregnancy)] for variable non-differential (top) and differential (bottom) truncation with 0% (no truncation) and 40% truncation, the difference of l between non-smokers and smokers (δ = l_non-smoker − l_smoker) for 0%, 10%, 20%, and 40% truncation.