I have repeated measures of a serum biomarker in 60 patients. 30 patients had pneumonia and 30 had asthma. Measurements were taken whenever blood was drawn during routine care, not at specific time points (unbalanced data). I have 2-10 measures per person, collected over the space of 1 year of care.
I don't know much about splines, so maybe I am thinking about this in the wrong way. But I want to (1) fit splines to see how the biomarker levels changed over time within each group, and (2) compare the spline of the pneumonia cases to that of the asthma cases to see if they were significantly different. Is that even possible? If so, could anyone cite some procedures used in Stata or SAS?
Have you tried fitting a linear mixed model with SAS Proc Mixed? That's how I usually analyze the type of situation that you described above. For starters, plot the data for 5-10 participants and see whether it appears to follow a line or a polynomial.
If the data appears to be linear, here is some sample SAS code.
Experiment with different covariance structures by using the Type= option on the repeated statement. If a quadratic or polynomial model would better suit your data, add the variables timepointn2, timepointn3, etc. to your dataset and include them in your model. I especially like SAS proc mixed because it produces such nice diagnostic plots.
ods html; ods graphics on;
Proc Mixed Data= AcrossTimeLong Method=REML NOCLPRINT plots(only)=(StudentPanel(conditional box));;
Class ID TreatN;
Model Outcome=TimepointN TreatN TimepointN*TreatN/ Solution Influence(effect=ID Est) ddfm=KR;
Repeated / Type=CS Subject=ID R RCorr;
Run;
ods graphics off; ods html close;
Hope this helps.
Brandy
Thanks Brandy! The relationship is definitely not linear. There seems to be a sort of hump with a tail--low at the start, rising to hit a peak somewhere between 6 weeks and 3 months, then tapering off, with the possibility of another hump occurring at 6 months. Maybe I can divide the time period into blocks and run a separate linear mixed models for each time bock? Would that methodology pass peer review?
You can refer to this article "Functional data analysis in longitudinal settings using smoothing splines W Guo - Statistical methods in medical research, 2004" to get an idea to solve your problem.
Hi Leah,
If your data has a parabola shape, that implies a time^2 term.
I suggest experimenting with 2nd, 3rd, and 4rth degree polynomials. Compare the AIC and BIC values. Choose the model with the lowest AIC and BIC values.
Brandy
Hi Leah,
I would do a graphical representation of both splines functions with their confidence intervals and see whether they overlap or not.
In stata you need to reshape your data into wide marker1 , marker2 etc.. in columns) and use for each group:
mkspline2 marker = varname, cubic nknots(4) displayknots
Then you regress and plot:
regress Outcome marker*
adjustrcspline
Not sure I understood the problem though.
Omar
I analyzed reproductive hormone data from daily 1st-catch urine samples, and used a semi-parametric approach (see attached publication).
After fitting the splines, we calculated their 95% confidence intervals, and the difference between the curves (also w/95% CI). To see plots of these curves, loo at pp. 10-13 of the article.
The semi-parametric approach used a macro developed by Daowen Zhang, based on his work published in:
Zhang D, Lin X, Raz J, Sowers MF. Semiparametric stochastic mixed models for longitudinal data. J Am Stat Assoc. 1998;93:710 –719.
and
Zhang D, Lin X, Sowers MF. Semiparametric regression for periodic
longitudinal hormone data from multiple menstrual cycles. Biometrics.
2000;56:31–39
- Badges
- Science topic
- Similar topics
- Medicine
- Physiology
- Biosignals
- Biomedical Signal Processing
- Statistical Analysis