# How to estimate the effect of treatment duration on survival outcomes

I'm reading the paper "How to estimate the effect of treatment duration on survival outcomes using observational data"(https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6889975/), and it states that:

"Quantifying the effect of treatment duration on survival outcomes is not straightforward because only people who survive for a long time can receive a treatment for a long time. Suppose we want to estimate the effect of statins on the mortality of patients with cancer using a healthcare database.1 A direct comparison of long term users, short term users, and non-users would be biased because long term users have, by definition, survived for a long time. Several methods can be used to tackle this bias, but some do not enable estimation of absolute risks or appropriate adjustment for time varying confounders".

I'm curious about what some of these methods are. Thank you!

In the paper you cite, Hernán explains some methods in detail. The point is that not all such methods are unbiased unless they are combined appropriately.

The 3-step method recommended in the paper, for an observational study with a set of defined intended treatment durations, is:

1. Make copies of all individuals such that each individual has a copy with one of the possible treatment durations. That gets around the problem of not knowing the initial treatment strategies for the individuals.
2. For each row, if the received treatment is known to have deviated from the treatment duration indicated on the row, right-censor the case at the time of the deviation. That step ensures that no data row provides information beyond a potentially observable combination of time, treatment, and outcome in the data.
3. To remove the "selection bias" introduced in the prior step, use a type of inverse probability weighting on the cases: "Informally, uncensored individuals receive a weight equal to the inverse of their probability of being uncensored."

A valid alternative noted in the paper is the "g-formula" method of Robins. See this page for an outline.

This is one example of a general causal modeling approach that asks what would have happened if, hypothetically, each individual might have been cloned to receive each of the treatments in parallel. See "Causal Inference: What If?" by Hernán and Robins for a useful introduction to such approaches.

• Thanks for your answer! @EdM I'm not really asking about the 3-step trial emulation method, which is what this paper is all about, or about the g-formula that's briefly mentioned as an alternative, but the "several methods" mentioned in the introductory paragraph that are probably more "conventional" and unsatisfactory to have led to this new 3-step method being proposed. Or did I misread it? Apr 27 at 16:34
• @purino as I read it, the less-than-satisfactory "several methods" would be those that omit one or more of those steps. This page describes what might be done without the "cloning" of individuals in the first step, which is key. For example, the answer on that page discusses omitting individuals who die before the shortest planned treatment duration, matching or inverse-probability weighting to evaluate counterfactual outcomes, and using time-varying coefficients in addition to time-varying covariates.
– EdM
Apr 27 at 16:51
• I see. This is helpful. Thanks! @EdM Apr 27 at 17:46