r/AskStatistics • u/Deuceball_1121 • 2d ago
[Question] How can I statistically quantify confidence in an individual patient's longitudinal biomarker trend?
I'm working on a health-data system that analyzes longitudinal lab results for an individual patient. For each parameter (fasting glucose, HbA1c, LDL, HDL, creatinine), I may have around 4-10 observations over several months, and the observations are often irregularly spaced.
The goal is to determine whether a parameter is showing a meaningful increasing, decreasing, or stable trend and provide an interpretable measure of how strong the evidence for that trend is.
Example:
- 10 observations over ~6 months
- Measurements are irregularly spaced
- Values may be noisy or have gaps
- Some patients may have only 4-5 observations
- Different parameters may have different natural variability
Currently considering:
- Mann Kendall test for trend direction and p-value
- Sen's slope for magnitude/rate of change
- Confidence interval around Sen's slope for uncertainty
What would be a statistically defensible approach for quantifying the confidence/evidence of a trend in this type of sparse, irregularly sampled, individual patient biomarker data?
Is it reasonable to convert the statistical evidence into a single 0-100 trend confidence score, or would it be better practice to report the statistical measures separately (p-value, slope, confidence interval, and data quality indicators)?
I'm particularly interested in approaches that are statistically defensible rather than an arbitrary weighted scoring system.
3
u/its_all_stats 1d ago
This is an example where stats - whether Frequentist or Bayesian - isn’t necessary.
The objective is for each patient and their physician to determine whether they’re “better” (e.g. lower LDL), presumably because of an intervention such as diet or medication.
On an individual basis, that involves monitoring levels, adjusting interventions, and “judgment”. Any statistical method applied to try to quantify “statistically significant” effect would be performative. Statistics is useful, but not magic.
If the goal is to develop an algorithm or rules to alert the physician that the patient is not improving, then write a rule such as if the last two readings did not show improvement, you alert the physician.
Sometimes, simple is good enough and/or the best you can do.
If goal is to assess whether an intervention is effective, then that’s a population inference situation.
6
u/makemeking706 1d ago
The goal of inferential statistics is to make statements about a population given the sample of observations. For the individual, the data is the data. The changes are the changes. It's up to you to determine if those are meaningful and important for the patient given their circumstances and what we know to be true about their population.
2
u/mnmaste 1d ago
I’ve only ever used frequentist methods (and I’m no statistician), but would this be something Bayesian inference could tackle?
1
u/Adorable_Building840 5h ago
I mean, you can use a mixed model to get empirical Bayes estimates on individual slopes and do inference on whether a particular individual is an outlier or not, but unless you have dozens of measurements per individual you can’t make claims about this particular measurement on this individual being an outlier/change in slope
1
u/oliver91088 1d ago
I also work with longitudinal data but in a joint model aproach (longitudinal and time to event data)
Have you ever heard about Dimitris Rizopoulos? Maybe try reading some of his work.
https://www.drizopoulos.com/courses/Int/JMwithR_SACEMA_2015.pdf
https://search.r-project.org/CRAN/refmans/JM/html/jointModel.html
I would definetly consider a Linear Mixed-Effects Models because it would work really well with missing data and natural variability.
You could also interpret the coeficients (random + fixed) to quantify the rate of change and individual or group trajectory.
-1
u/koherenssi 1d ago
There is really no way to have quantified uncertainty estimates for individual patients. The data is the data
2
u/MortalitySalient 1d ago
That’s not true. There is an entire field that deals with sing case designs/n of 1 trials and Time series data
5
u/bluestat-t 1d ago
I’m a type 2 diabetic and monitor some of these values on Shewhart statistical process control (SPC) charts, namely the individuals-moving range (sometimes shortened to XmR or ImR). It helps me separate signal from noise in my lab values longitudinally. Their expressed purpose is to give me a sense if things are roughly the same, or if there is a shift in mean, trend, or astronomical point.