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I want to analyze some survival data. I have measurements of a biomarker (real-valued variable) before a first treatment, after that first treatment, and then after a second treatment (different to the first). I also have patient age and disease stage (ordinal variable) at enrollment. I am particularly interested in how values of the biomarker affect survival. All else being equal, I guess I'd run a Cox analysis.

However, we have reason to believe that treatment efficacy may depend on the value of the biomarker, and that the first treatment may change the biomarker in some patients. For example, if the biomarker is high before treatment, the first treatment may be effective, but may decrease the biomarker, reducing the scope for the the second treatment to be effective.

I could run a Cox analysis, for example using as explanatory variables the raw pre-treatment biomarker and relative changes from this value at the subsequent two time points. However, I've not been able to convince myself that this adequately models the possible temporal dependencies (does it?).

How should I analyze this data? Our sample size is about 45, so I doubt there's scope for a complex model.

Thanks in advance.

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The first thing I would do is plot the data to see if you are right. A "spaghetti plot" could be useful, perhaps divided into part (multiple plates of spaghetti????).

First divide the 45 people into (say) tertiles based on the value of the biomarker at baseline. Then plot time on the x axis, value of the biomarker on the y axis, and color the lines differently for treatment and control. Then take a look.

In the modeling stage, it sounds like you are looking for an interaction of control vs. treatment and level of the biomarker at baseline (and maybe at other times).

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  • $\begingroup$ Thanks, Peter, for your plotting and interaction suggestions. If one quantifies the treatment effect as relative change from baseline, then the interaction between baseline biomarker value and treatment effect is simply equal to the post-treatment biomarker value—which I hadn't thought of before. $\endgroup$
    – Chris
    Commented Jul 7, 2014 at 15:37

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