# Continuous Treatment effect to assess the impact of Early vs Late treatment

I have an observational dataset with only treated observations with different ages, but treated at different times for 7 years. Each treatment had different durations; from 2 days to 160 days. The outcome variable is continuous measured at the same point in time for all observations after 7 years elapsed from the time of the 1$^{st}$ treatment. The cofounders were time invariant.

I would like to measure the causal impact of the treatment on my dependent variable. In particular, treatments occurring at an early age, affected the outcome more so than for older subjects.

The Generalized Propensity Score (gspsore in Stata) with the focus on dose-response function is not interesting for me given that I don't care about the impact of the treatment duration, but rather about the early versus late time of treatment administration.

I have tried to consider the early treatments as "treated" and late treatments as "control" groups and run a normal PSM (psmatch2 in Stata), but this definition is blurry given that in the end all subjects were treated.

What will be the most suitable method of testing for differences?

• Look into Marginal Structural Models (MSMs). I think they do exactly what you want. When you've figured out how to use them, check out the CBPS package, which has methods of estimating them. I can't help you any further, though. – Noah Dec 1 '16 at 0:50
• Thank you very much for your answers. The Marginal Structural Models require time changing covariates which I unfortunately don't have. As for the Hirano & Imbens (2004), Imai and van Dyk (2004) they explore the dose-response function, which analyses the intensity of the treatment which is not my interest in this study. I will explore Kennedy et al. (2016). Thank you once again – Joramo Dec 8 '16 at 12:10