Bias amplification in the g-computation algorithm for time-varying treatments: a case study of industry payments and prescription of opioid products

BACKGROUND: It is often challenging to determine which variables need to be included in the g-computation algorithm under the time-varying setting. Conditioning on instrumental variables (IVs) is known to introduce greater bias when there is unmeasured confounding in the point-treatment settings, and this is also true for near-IVs which are weakly associated with the outcome not through the treatment. However, it is unknown whether adjusting for (near-)IVs amplifies bias in the g-computation algorithm estimators for time-varying treatments compared to the estimators ignoring such variables. We thus aimed to compare the magnitude of bias by adjusting for (near-)IVs across their different relationships with treatments in the time-varying settings. METHODS: After showing a case study of the association between the receipt of industry payments and physicians’ opioid prescribing rate in the US, we demonstrated Monte Carlo simulation to investigate the extent to which the bias due to unmeasured confounders is amplified by adjusting for (near-)IV across several g-computation algorithms. RESULTS: In our simulation study, adjusting for a perfect IV of time-varying treatments in the g-computation algorithm increased bias due to unmeasured confounding, particularly when the IV had a strong relationship with the treatment. We also found the increase in bias even adjusting for near-IV when such variable had a very weak association with unmeasured confounders between the treatment and the outcome compared to its association with the time-varying treatments. Instead, this bias amplifying feature was not observed (i.e., bias due to unmeasured confounders decreased) by adjusting for near-IV when it had a stronger association with the unmeasured confounders (≥0.1 correlation coefficient in our multivariate normal setting). CONCLUSION: It would be recommended to avoid adjusting for perfect IV in the g-computation algorithm to obtain a less biased estimate of the time-varying treatment effect. On the other hand, it may be recommended to include near-IV in the algorithm unless their association with unmeasured confounders is very weak. These findings would help researchers to consider the magnitude of bias when adjusting for (near-)IVs and select variables in the g-computation algorithm for the time-varying setting when they are aware of the presence of unmeasured confounding. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12874-022-01563-3.