2E-01 - A weighting method to remove bias due to within-subject exposure dependency when the exposure has multiple levels in case-crossover studies: A simulation study

Background: Bias due to within-subject exposure dependency in case-crossover (CCO) studies may occur when the exposure status is dependent between case and control periods (e.g., successive use of a drug) and the standard conditional logistic regression (SCL) is used. We showed that for a binary exposure variable, the Mantel-Haenszel or weighting method can remove this bias (AJE 2023; 192:1701). We extend the study for the multi-level exposure variable.

Objectives: To show the method to remove bias due to within-subject exposure dependency for a multi-level exposure variable in CCO studies.

Methods: We present results from a simulation study assuming one patient has two drugs (drug A and drug B) causing a transient change in risk of an acute-onset disease during the exposure period of 60 days. Every day, after the washout period, 20 patients started (on Day 1) and continued drug A for 40 days, and started drug B on Day 21 and continued it for 40 days. Thus, a patient was exposed to drug A only, drug A and drug B, and drug B only, for the first, middle, and last 20 days, respectively, before being unexposed. The incidence rate of an outcome was 0.00002 per day when unexposed, and rate ratio (RR) =2, 3, and 6 with drug A only, drug B only and, drug A and drug B, respectively. Cases were identified during 200 days under the “steady state”. The time window (TW) for the CCO study varied between 11 and 61 days (1 period = 1 day). The number of control periods (M) varied up to the size of (TW-1). The combination of the exposure status of drug A and drug B is considered as a new variable with 4 exposure levels k=0 (unexposed), 1 (drug A only), 2 (drug B only), and 3 (drug A and drug B). The probability that the exposure level is k at the case period (π_k) is estimated by solving ∑(l≠k) π_k PT_kl/a_k =∑(l≠k) π_lPT_lk/a_l where a_k is the number of cases with the exposure level=k at the case period and PT_kl is the number of control periods with the exposure level=l in a_k cases. Data by 1000 iterations were analyzed by the SCL and the conditional logistic method with the weight w_ik = (π_k/π_0)/n_ik where n_ik is the number of the periods at the k-th exposure level in individual i (BMC Med Res Methodol 2021; 21:214) by the three-variable model (X1 (drug A only), X2 (drug B only), and X3 (drug A and drug B)) and the two-variable model (X (drug A) and Y (drug B)) to estimate odds ratios (ORs).

Results: The SCL was biased while the weighting method was not. For example, for the two-variable model with TW=21 days, ORs were 0.6 to 0.7 for X (true value=2.0) and 6.2 to 12.0 for Y (true value=3.0) by the SCL while ORs were without bias (2.0 for X and 3.0 for Y) by the weighting method.

Conclusions: Unlike the SCL with bias due to within-subject exposure dependency, the proposed weighting method was unbiased in CCO studies when the exposure variable has multiple levels.