Citation:
Abstract:
The Evaluating Public Health Interventions AJPH series offers excellent practical guidance to public health researchers. The eighth part of the series provides a valuable introduction to effect estimations of time-invariant public health interventions. In their commentary Spiegelman and Zhou suggest that, in terms of bias and efficiency, there is no advantage to using modern causal inference methods over classical multivariable modeling. However, this statement is not always true. Most important, both effect modification and collapsibility are critical concepts when assessing the validity of using regression for causal effect estimation.
Suppose that one is interested in the effect of combined radiotherapy and chemotherapy versus chemotherapy only on one-year mortality among patients diagnosed with colorectal cancer. A clinician may ask: how different would the risk of death have been had everyone received dual therapy as compared with if everyone had experienced monotherapy? The causal marginal odds ratio (MOR) offers an answer to this question. Each individual has a pair of potential outcomes: the outcome he or she would have experienced had he or she been exposed to dual treatment (A = 1), denoted Y(1), and the outcome had he or she been unexposed, Y(0). The MOR is defined as
[P(Y(1) = 1)/(1 − P(Y(1) = 1))]/[P(Y(0) = 1)/(1 − P(Y(0) = 1))].
A common approach would be to use logistic regression to model the odds of mortality given the intervention and adjust for confounders (W) such as clinical stage and comorbidities. Note that this regression will provide an estimate of the conditional odds ratio (COR), which is
[P(Y = 1 A = 1,W) / (1 − P(Y = 1 A = 1,W))] / [P(Y = 1 A = 0,W) / (1 − P(Y = 1 A = 0,W))].
The MOR and COR are typically not identical. First, if there is effect modification (e.g., if the effect of dual therapy is different between patients with no comorbidities and those who have hypertension), logistic regression including an interaction term will not provide a marginal effect estimate but only the conditional effect of the interaction term between dual therapy and hypertension. Second, the odds ratio is noncollapsible, which means that the MOR is not necessarily equal to the stratum-specific odds ratio (i.e., the COR). This holds even when a covariate is related to the outcome but not the intervention and is thus not a confounder.
Extended note: Monte Carlo simulations and code supporting the letter can be found at https://github.com/migariane/hetmor
