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I am familiar with fixed-effects linear regression models, and have done reading on mixed-effects models.

I am attempting to fit a model based on observational data, where treatments come at varying times and do not exist at all for a majority of subjects.

I am interested in whether or not the treatment has an effect on the trajectory of a subject's response over time. Graphically:

Varying treatment time mixed model

The most relevant analogous model I have found would be the one specified here, specifically Part 3. However, this example does not use R. I have read through all of Bates' lme4 paper, but I am still uncertain how to specify this effect.

An excerpt of my data:

     ID RESPONSE ID.CONST.1 ID.VAR.1 ID.VAR.2 TREATMENT_ACTIVE RESPONSE.TIME
1077415        7         41        0        5            FALSE           314
1077415        8         41        1        6            TRUE            316
1077415        9         41        10       7            TRUE            319
1077688        1         59        0        1            FALSE           313
1079475        1         85        0        1            FALSE           313
1080811        1         24        0        1            FALSE           314
1081156        1        502        0        1            FALSE           314
1082437        1         50        0        0            FALSE           315
1083154        1        257        0        0            FALSE           315
1083154        2        257        0        0            TRUE            316
1083527        1         69        0        0            FALSE           315
1086283        1         31        0        0            FALSE           316
1088810        1        120        2        1            FALSE           317
1090019        1         93        2        1            TRUE            317
1091048        1         27        0        0            FALSE           317
1091114        1         62        0        1            FALSE           317

Each subject (ID) has time-varying measurements (ID.VAR.X), constant measurements (ID.CONST.X), as well as the time of observation (RESPONSE.TIME). TREATMENT_ACTIVE indicates whether or not the treatment is active for a given subject at the corresponding RESPONSE.TIME. Some subjects have a single observation, others have multiple observations, and treatment times are rarely the same between subjects.

I've attempted to fit models as:

lmer(RESPONSE ~ ID.CONST.1 + ID.VAR.1 + ID.VAR.2 + TREATMENT_ACTIVE + RESPONSE.TIME + (1|ID) + (1|RESPONSE.TIME)
lmer(RESPONSE ~ ID.CONST.1 + ID.VAR.1 + ID.VAR.2 + RESPONSE.TIME + (1|ID) + (1+TREATMENT_ACTIVE|RESPONSE.TIME)

However, I'm fairly certain this is misspecified. I am not sure how to specify the random effects to ensure that the TREATMENT_ACTIVE variable is interpreted as I intend. I am interested in testing both an intercept-only model as well as a intercept+slope model for the treatment effect.

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  • $\begingroup$ I apologise for the very brief answer below. I found your question while I was looking for something slightly different. I hope to update the answer with an example very soon. $\endgroup$ – user02814 Oct 18 '15 at 5:47
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It isn't clear from your description whether the intervention occurs at the same time for all individuals, or whether there is a time-dependency in the intervention. In any case, Chapters 5 and 6 of the book, Applied Longitudinal Data Analysis by Singer and Willet would seem to cover exactly what you want. In fact, you almost got to the right place with the link you included! Have a look at the R code for chapteres 5 and 6 at the website for the Singer and Willet book. Also, search for "discontinuous time".

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  • $\begingroup$ Thank you very much. The intervention occurs at different times for various individuals; there is a time-dependency in the intervention. I will read the mentioned book and accept your answer if it is indeed what I'm looking for. Again, thank you very much for reading my long-winded question and answering! $\endgroup$ – David Oct 18 '15 at 7:24

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