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EDITED I'm performing a clinical analysis where we are measuring health parameters over time. One of these functions is a continuous variable that tracks kidney function (estimated GFR based on creatinine values). For each patient, we have eGFR at various time points, and want to calculate the rate of change (slope). I am interested in the trend over long periods of time (years).

Due to nature of clinical data collection, the sampling over time for each patient was uneven. Usually this results in few data points over long periods when patients are well and eGFR changes are slow and stable, and many data points over short periods while patients are acutely ill and and eGFR can fluctuate considerably. The eGFR during non-acute illness is likely of greater value since it is more representative of the patient's long-term trend.

However, I'm worried that the clustered data will skew the analysis as there will more data points during acute illness over short periods of time, where the eGFR is most volatile (and less likely to represent true kidney function). I'm wondering if there's any technique to "penalize the weight" of these values, so to speak - Something along the lines of a simple moving average, but that doesn't only consider the sequential ordering of data, but also the time periods between sequential points. Maybe performing linear interpolation at regular intervals (e.g. monthly) before smoothing with a simple moving average might address this?

Does this make sense, or are there any alternative techniques I can consider?

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    $\begingroup$ It depends on your model. If you are fitting splines, clustering can affect the fit by affecting where knots are chosen, for instance -- but the solution is not to penalize the clustered value. But in the more usual case of a linear regression, linear in the explanatory variable, this wouldn't make much sense. Please, then, include a little more information about your model in your question. $\endgroup$
    – whuber ♦
    Commented Feb 28, 2022 at 16:10
  • $\begingroup$ I'm more worried that outliers at the extremes of the time range would be leading to problems. For example, GFR estimates might not be made often when patients are doing well but more frequently when they are developing renal failure, maybe more so at late times. Slopes based on such outcome-associated selections of measurement times could be problematic. Please edit your question to include more information about the nature of your data, what determines when GFR is estimated, and the hypothesis you wish to test. $\endgroup$
    – EdM
    Commented Feb 28, 2022 at 18:29
  • $\begingroup$ Thank you both - I am interested in effect of diseases on GFR changes over long periods of time, and am using linear models for this (admittedly the trajectory may not be linear). Patients undergo much more frequent testing during acute illness, during which time their GFRs may vary considerably and become less accurate. Meanwhile, trends during non-acute illness (both preceeding and following), are fewer but span longer periods of time, may be more representative of their long-term trajectory, but may be outwheighed by acute illness readings. Any way to increase their weight? $\endgroup$
    – psm
    Commented Feb 28, 2022 at 21:27
  • $\begingroup$ Please edit the question to include the information you provided in your comment. Comments are easy to overlook and can get deleted. Also, please say more when editing the question about your GFR measurements. Are these true GFR measurements or just the eGFR based on blood creatinine levels? I think that distinction might matter for the answer. $\endgroup$
    – EdM
    Commented Mar 1, 2022 at 15:29
  • $\begingroup$ Thanks @EdM - the question has been edited. I'm wondering whether I can use some form of a moving average for this purpose. $\endgroup$
    – psm
    Commented Mar 2, 2022 at 16:15

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If your interest is in long-term trends in eGFR, you should just omit any measurements made during acute illness. Penalize those values completely, as they are unreliable.

For those unfamiliar with this subject matter, the glomerular filtration rate (GFR) is the rate at which fluid (containing dissolved solutes like the metabolic byproduct creatinine) is filtered from blood into the kidneys. The estimated GFR, eGFR, is an approximation based on the concentration of the creatinine in blood serum. The kidneys tend to excrete all of the creatinine in the fluid they filter. If creatinine production in the body is relatively constant over time, then in the steady state (with creatinine production equal to creatinine excretion) a higher serum creatinine means a lower GFR. The formulas for eGFR combine serum creatinine measurements with age, gender, and race to give estimated GFR values based on values in specific study populations.

The National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK) notes limitations in using eGFR:

When Not to Use the Creatinine-based Estimating Equations: Although the best available tool for estimating kidney function, eGFR derived from the MDRD Study or CKD-EPI equations may not be suitable for all populations. All creatinine-based estimates of kidney function are only useful when renal function is stable. Serum creatinine values obtained while kidney function is changing will not provide accurate estimates of kidney function.

That's particularly true if the acute episodes involve hospitalization, as steady states can't be assumed for either creatinine production or kidney function:

GFR-estimating equations have poorer agreement with measured GFR for ill hospitalized patients...

As much as I hate to recommend discarding data, I'd recommend removing eGFR values obtained during acute episodes or hospitalizations from your evaluation of long-term trends. Those values can't be counted on to represent true GFR.

You might consider displaying those acute-episode values along with smoothed estimates based on non-acute eGFR values, to see how much they disagree.

For evaluating long-term trends over time based on reliable eGFR values, flexible methods like regression splines allow the data to help illustrate potentially nonlinear trends. Adding large numbers of unreliable eGFR values from acute episodes won't improve your analysis, however.

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  • $\begingroup$ Thank you @EdM - I do agree with this solution. the challenge here is that it is difficult to identify for us which values truly account for acute illness based on the data we are allowed to collect. We can only assume that closely spaced values with variable eGFRs represent acute illness, but we are unable to confirm it, and with the number of patients we are dealing with, this would involve much more manpower in reviewing charts than we currently have. This is why I am looking for an alternative solution that doesn’t involve discarding data. $\endgroup$
    – psm
    Commented Mar 2, 2022 at 20:44
  • $\begingroup$ @psm you don't have to confirm that closely spaced values represent acute illness to omit them. The risks of including such values, very likely incorrect, would seem to outweigh advantages of including them, even if some actually are correct. Try defining a local spacing in time of values that you think would represent acute-disease measurements, and use your chart-review capability to check how well that works in a data sample to omit acute-disease measurements. Regression models do allow for case weights, but it's not clear how to weight a measurement that is likely to be frankly erroneous. $\endgroup$
    – EdM
    Commented Mar 2, 2022 at 21:06

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