Effect of cumulative exposure to risk factors in magnetic resonance parameters

[Carlos Real]

Dear all,

I am trying to study the effects of cumulative exposure to cardiovascular risk factors in several cardiovascular magnetic resonance values.

To sum up, I have a cohort with a 4-year follow-up with three assessments (baseline, year 2 and year 4) and the cardiovascular magnetic resonance (CMR) was done in the last follow-up (year 4).

I want to study the effects of cumulative exposure to different risk factors, which are continuous variables (as systolic blood pressure, blood cholesterol, etc...) that were measured in the three follow-ups (0, 2 and 4), in the CMR parameters (which are also continous variables, but only measured in the last follow-up).

I have checked different studies and this forum and I have seen that it is interesting to obtain the area under curve (AUC) of the risk factors in these circumstances. I found different ways to do this:

- In a previous discussion in this forum (incremental area under the curve - Statalist) Clyde Schechter recommended to use the following code to obtain the AUC of several blood glucose assessments:
// TO CALCULATE COMPLETE GLUCOSE AUC integ glucose time, by(id) gen(total_auc) by id (time), sort: replace total_auc = total_auc[_N] But this case was slightly different (the measurements were taken with 30-minute differences between them). - However, I have checked different papers (the most interesting is this one: DOI: 10.1002/sim.1921, link: Using the area under the curve to reduce measurement error in predicting young adult blood pressure from childhood measures - Cook - 2004 - Statistics in Medicine - Wiley Online Library (csinet.es)) In this paper, they used mixed models to predict a curve, and after that they calculated the AUC. What do you think it is the more correct way of doing this with my database? I feel that using mixed models would be better because it would allow me to estimate also missing values, while doing directly the integral would be less accurate. What is the code in Stata to do this with mixed models? Thank you very much in advance. All the help will be much appreciated

[Clyde Schechter]

Thanks for calling my attention to that 2004 paper. I have not seen that method used before. While I think that approach makes sense in the context of their data, I don't think it is workable in yours. The reason is that you have only three time points per individual, and they are the same timepoints for every participant. So there is not enough variation in the time coordinate for you to fit random coefficient quadratic models: there are simply too many parameters and not enough time points.

[Carlos Real]

Dear Clyde,

Thank you very much for your quick responde.

What do you recommend us to do, then? The code you recommended to use in the previous message that I attached (integ)? The only problem with this is the problem with the missing values, right?

[Clyde Schechter]

What do you recommend us to do, then? The code you recommended to use in the previous message that I attached (integ)? The only problem with this is the problem with the missing values, right?

Yes, use the -integ- approach. The missing values only make the difficulties with the random coefficient quadratic model even worse! If you had, say, 10 timepoints, and most people were missing a small number of them, then the random coefficient quadratic model would work nicely. But with three time points you don't have enough information to properly fit the parameters needed, and if some of those are missing, you are in even worse trouble.

[Leonardo Guizzetti]

I think you should consider mixed models for repeated measures, or maybe, linear mixed models equivalent to a linear growth curve. I suggest these for the main reason that Clyde has pointed out, your time dimension is limited and can only (maximally) support a linear trend. Since you posit a cumulative dose may lead to an outcome, it’s reasonable to look at the contrast at 4 years.

From a physical perspective, is there any evidence of a cumulative effect of any kind of magnetic exposure, let alone short durations of non-ionizing emf? I’d be worried about uncontrolled confounding on your biological parameters. I simply wonder what the eventual results may mean.

[Carlos Real]

Thank you very much to both of you for your amazing help! I will do the analysis just how you recommend me to do, If I have any further doubt I will contact you through this line.

Thank you very much,

[Carlos Real]

Dear all,

Thank you very much for your quick responses and sorry for opening this forum again. We were trying to apply all the methods that you recommend us to do and we found some problems.

Summary: we have a cohort with three assessments (baseline, year 2 and year 4) of the INDEPENDENT variable (cardiovascular health score) and one assessment (year 4) of the dependent variables (different quantitative magnetic resonance parameters). Our main objective is to determine the influence of the cumulative effect of cardiovascular health (throughout the full follow-up) in the cardiac resonance parameters assessed only in the last timepoint.

We will apply the AUC method, as recommended by Clyde, but we would also like to include some mixed models for repeated measures (MMRM) as Leonardo Guizzeti told us to do. However, we found some problems to implement the latter.

Thus, our input is something like this (in long format, CVH is the cardiovascular health score):

input int id float time float CVH float Resonance_parameter
1 0 90 .
1 1 60 .
1 2 40 5.6
2 0 50 .
2 1 60 .
2 2 95 4.2
3 0 30 .
3 1 20 .
3 2 10 8.1
4 0 70 .
4 1 20 .
4 2 40 3.4
5 0 90 .
5 1 90 .
5 2 90 2.3
End

And we tried to use MMRM with the following command:

mixed Resonance_parameter CVH i.time || id:

But it is not possible to execute it:

“could not calculate numerical derivatives -- discontinuous region with missing values encountered”
r(430);

It seems that it is not possible to use MMRM if you only have one assessment of the dependent variable, as in our case. Could you confirm this to us? Do you know any other method to perform this analysis?

We are aware that we can use latent growth modelling to assess the effect of the change in the cardiovascular health during the follow-up in the dependent variable (https://www.researchgate.net/post/Wh...-measured-once), but I think this is not what we want to assess.

We would sincerely appreciate any help

Best
Carlos

[Clyde Schechter]

Yes, you will get nowhere with the mixed model approach in this data. This data does not have repeated measures. It has outcome measurement only at the final time point. When you try to run that -mixed- command, as with any Stata estimation command, observations with a missing value for any of the command's variables are omitted from the estimation sample. Consequently, in your estimation sample you have only the observations with time = 2, leaving you with only one observation per person. When there is only one observation per person, there is no way to separately identify an id-level intercept and a residual, and the model fails to converge.

[Carlos Real]

Thank you very much for your answer. Do you recommend us to us any other approach (apart from the -integ- approach)?

Thanks in advance

Carlos

[Clyde Schechter]

You could reshape the data to wide. Each participant would then have a single observation containing the resonance parameter and three CVH variables (one for each of the three time points in the study.) You could then regress the resonance parameter on those three CVH variables. This might enable you to see if there is a distinction among the three time periods as to which one most strongly influences the resonance parameter outcome. But it's a difficult analysis to do because the three CVH variables are probably going to be fairly strongly correlated with each other, and consequently their effects will be confounded with each other. So this analysis will only be useful if you have a very large sample.

[Carlos Real]

Dear Clyde,

Thank you very much for your answers. The point is that the objetive is to know the cumulative effect of the CVH in the three timepoints. The first objective is not to know which visit is more associated with the magnetic resonance parameters. So we want to measure the cumulative effect of the three visits. By the way, our sample size is not big (123 participants).

First, I thought in using the mean of the three assessments as independente variable. Another option is using the AUC, as you suggested. But do you think there are any other methods that could fit in our database. Thank you and sorry for being so insistent.

Best

[Clyde Schechter]

Well, I'm going to answer that question with a question. What is it about the mean and the AUC that you feel is too limited? What are you trying to accomplish that these will not do for you? There are lots of other things one could do, but the mean or the AUC would be the most appropriate way to go if the three time points are thought to have equivalent impacts.

[Carlos Real]

I agree with you Clyde. Thank you very much for your response. Really appreciate it