Hi everyone,
I would need some help with calculating the area under the curve. In my study patients' heart rate was measured at different time points throughout an operation (at the start of the operation, after 1 minute, 5 minutes, 10 minutes, etc.). For my analysis, I would need to calculate the area under the curve before comparing different groups of patients who received different treatments.
My problem is: some patients only have data for the first 2 or 3 time points as it was a short operation, while others have data for all 5 time points as it was a rather long operation.
If I now calculate the area under the curve in spss using the syntax below, I obtain a very large area under the curve for patients who had a long operation, while a rather small area is obtained for patients who only have data for the first time points. I believe it is not correct to compare this data as this has nothing to do with the treatment they received/the group they belonged to, but rather with the length of their operation, right? Is their any way to take into account the number of time points when calculating the area under the curve?
This is the syntax I've been using:
Thank you so much in advance!
SORT CASES BY ID.
CASESTOVARS
/ID=ID
/GROUPBY=VARIABLE.
VECTOR time = T0 to T3.
VECTOR SAT = T0spo2 to T3spo2.
COMPUTE cmax = MAX(T0spo2 to T3spo2).
COMPUTE tmax = $sysmis.
COMPUTE lagSAT = $sysmis.
COMPUTE lagtime = $sysmis.
COMPUTE auc = 0.
LOOP #k = 1 to 3.
DO IF (NOT(MISSING(SAT(#k)))).
IF (NOT(MISSING(lagSAT)))
auc = auc + (time(#k) - lagtime)*(lagSAT + SAT(#k))/2 .
IF (SAT(#k) = cmax and missing(tmax)) tmax = time(#k) .
COMPUTE lagSAT = SAT(#k).
COMPUTE lagtime = time(#k).
END IF.
END LOOP.
EXECUTE.
Wow. There are tons of methods to do this going back at least to Gauss in the early 1800s . I would suggest consulting a numerical analyst or a computational statistician at your university. They should be aware of locally available software and can help you choose a good approach. You can find them in either a mathematics or statistics dept. If all else fails you can look at a book like this:
https://www.amazon.com/Introduction-Scientific-Computing-Computational-Engineering/dp/331930254X/ref=sr_1_16?keywords=Numerical+analysis+in+statistics&qid=1575162066&s=books&sr=1-16
Chapters on interpolation and integration are what you want. I am sure that R and Matlab are packages that can solve this problem but you would likely need help to use them. An excellent statistician that is quite near you should also be able to help. He is described here: https://en.wikipedia.org/wiki/Peter_Rousseeuw
If you contact him please mention my name as I have discussed our work at multiple meetings with him. He, of course, may not remember. Good luck, David Booth
PS you may also find this link helpful. Look at the later posts.
https://www.researchgate.net/post/How_to_calculate_area_under_curve_AUC_in_R
Best wishes, David
Sofie Heirweg Let me better understand your problem. If you are measuring the patients' heart rate (say, hr, beats/min) at different time points, then the area under the curve hr(time) vs time is the total number of beats B(tmax) for the time of operation, from 0 to tmax. The integral B(tmax) from 0 to tmax can easily be calculated using any numerical method, including the one that you presented. The problem, as I see it, is normalization of the number of beats B(tmax) for various durations, tmax. I guess you can do it by dividing the integral, B(tmax) by the duration, giving b(normalized)=B(tmax)/tmax, or by (tmax - tmin), if you integrate not from 0 but from tmin to tmax. This way you would be able to compare different treatment groups for different durations using their normalized total beats / min, b (normalized).
One further thought. Length of operation probably does have something to do with treatment. For example, my recent Aortic valve replacement took longer because I also had an ascending aortic aneurysm as well. Best wishes, David Booth
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