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I encountered the following problem: I have a biomarker measured at baseline and the renal function measured at baseline and Follow-up. 2 continuous variables

My question is: does the biomarker predict a decrease in renal function.

Note, the follow-up is different for every patient which makes it ideal if I could also include time to follow-up in the analysis.

Which analysis should I run? Should I perform this with the difference in renal function or account for the baseline variable as a covariate?

Stex
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1 Answers1

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If you regress change on baseline you can invoke serious bias due to mathematical coupling.

But if you don't account for baseline differences you may also get biased results.

You have repeated measures within patients, so measurements within each patient will be more similar than measurements in other patients - that is, you will have correlations within patients which invalidates the assumption of independence in linear regression.

A good approach to this problem is to use a mixed effects model with random intercepts for patients, which will control for the repeated measures and also allow you to model the time to follow up.

renal.function ~ time + biomarker + (1|patientID)

This will estimate a global intercept, that is, renal function when time and biomarker are both zero (so you might consider centering them accross the whole dataset).

It will also estimate a fixed effect for time which will be interpreted as the estimated change in renal.function associated with a 1 unit increase in time, holding biomarker constant; and also a fixed effect for biomarker which will be interpreted as the estimated change in renal.function associated with a 1 unit increase in biomarker, holding time constant.

You might want to extend the model with an interaction between time and biomarker if you think that the biomarker will have a different association with renal function for longer/shorter times to follow up.

Note that this assumes that the baseline biomarker levels are not causally related to time to follow-up. If, for example, patients with low biomarker levels were followed up sooner than those with higher levels, AND time to follow up also affect the follow-up renal function (which I assume it must, otherwise you wouldn't want to include it in the first place), then time to follow-up is a mediator and should not be included in the model

Robert Long
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  • I would like to deeply thank you for your detailed comment as I spent several hours now diving into linear mixed effects models. And tried to compute them in R.

    What is not absolutely clear to me is if with this model I rather estimate the renal.function by time, biomarker and patient and not the change in renal function. My goal is to predict the change based on the biomarker level.

    Also thanks a lot for bringing up mathematical coupling and time as a mediator. I would say time-point of follow-up is not affected by the biomarker (time-points were chosen pretty randomly).

     – Stex Aug 14 '20 at 07:41
  • So you want to estimate the change in renal.function associated with a change in biomarker ? – Robert Long Aug 14 '20 at 07:58
  • no the change in renal.function associated with the single biomarker baseline value. Evaluation as a prediction tool. – Stex Aug 14 '20 at 10:17