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## Exposure-response analysis

Hi All,

I am doing a study in which I examine whether exposure to an agent (metabolite of a certain drug) can predict a longitudinal outcome in that patient. I am looking at patients in a treatment arm from a trial. Each patient may have taken a different quantity (dose) of the underlying drug. They then had a blood test checking for its active metabolite. Different patients will have different numbers of readings, depending on the duration for which they were in the study (dropped out, died, withdrawal etc) and therefore how many visits and subsequent blood tests they had. I want to see how exposure to the drug influences a longitudinal outcome, which itself is time-varying. What would be the best way to analyze this information? Presently, I have added together the total exposure values over however many visits the patient had, and done simple linear regression with the change in the longitudinal variable. I also calculated average exposure for each patient (total exposure/number of visits) and correlated this with the change in the longitudinal outcome (which itself I regressed over the amount of time patients were in the study). However, I feel this is a bit simplistic and am wondering if there is a better statistical method to analyze this question? At the least I feel I probably need to do some analysis with repeated measures. I hope this makes sense. Grateful for any help.

## Re: Exposure-response analysis

One thing that jumps out at me about the summing to get an exposure variable in a longitudinal study is that the shape of the exposure likely will have a profound effect on the response - suppose all the mass for exposure is at time=0 and no other exposure compared to equal exposure at the various time points such that the sum is identical in both cases.  That would almost certainly lead to different responses over time.

I don't know if this would work or not, but you might consider a multimember EFFECT, where the inputs in the EFFECT statement are the current exposure level and lagged values of the exposure level.  Run something that calculates the autoregression to get the number of lags you might need, stopping when the autocorrelation levels out (a sill in a semivariogram).  If there are a lot of time points, you might need to thin them for inputs.  I would start with patients that completed the trial, and then work on developing methods to deal with missing measurements, either at random or due to drop out.

SteveDenham

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