incremental area under the curve

[Jean Utumatwishima]

Dear team,

I am trying to compare the area under the curve of blood glucose results after the meal. The samples are taken at 0, 30 min, 60 min, 90 min and 120 minutes.

what is the formula to generate the area under the curve above the baseline (The incremental area under the curve).

Is it possible using Stata command?

Thank you.

[Clyde Schechter]

Yes. You need to have the data in long layout, that is each patient has 5 observations in the data set, one each for times 0, 30, 60, 90, and 120 minutes. Let's say the patient is identified by the variable id, and time since the meal is in a variable called time. The glucose measurements are in a variable called glucose. Then you use the -integ- command Here's an example with some made up (and rather unrealistic) data:

* Example generated by -dataex-. To install: ssc install dataex
clear
input int id float time int glucose
 1   0 255
 1  30 218
 1  60 160
 1  90  69
 1 120 150
 2   0  67
 2  30 205
 3   0  92
 3  30 164
 3  60 124
 3  90 155
 4   0 181
 4  30 170
 4  60 163
 4  90 148
 4 120 128
 5   0 138
 5  30 121
 5  60 117
 5  90 136
 5 120 123
 6   0 293
 6  30 315
 6  60 363
 6  90 308
 6 120 225
 7   0 199
 7  30 176
 7  60 135
 7  90 224
 8   0 288
 8  30 208
 8  60  99
 8  90  34
 8 120 152
 9   0  85
 9  30  75
 9  60  84
 9  90  84
 9 120  93
10   0  96
10  30  88
end

//    TO CALCULATE COMPLETE GLUCOSE AUC
integ glucose time, by(id) gen(total_auc)
by id (time), sort: replace total_auc = total_auc[_N]

//    TO CALCULATE AUC FOR INCREMENT ABOVE BASELINE GLUCOSE
by id (time), sort: gen delta_glucose = glucose - glucose[1]
integ delta_glucose time, by(id) gen(incr_auc)
by id (time), sort: replace incr_auc = incr_auc[_N]

[Jean Utumatwishima]

Thank you so much dear Clyde.

I used the commands above after arranging my data the way you showed.

I managed to calculate the total and incremental area under the curve but I found some differences when I tried to validate my answers with the trapezoidal rule.

the delta_glucose that you calculate, does it take into account the entire baseline area under the curve?

For example: 0 85
30 140
60 137
120 120
by above commands: AUC= 15479.849
incr_AUC=5279.849
But with trapezoidal rule: I found:
AUC=15240
incr_AUC=5040

Can you try to help me understand these differences?

Thanks
Jean

[Clyde Schechter]

-integ- by default fits cubic splines when calculating integrals, rather than using the trapezoidal rule. If you want it to use the trapezoidal rule instead, you can get that with the -trapezoid- option. If you do that, the results will match what you calculated. Do read -help integ-.

The trapezoidal rule gives exact results when the function you are trying to integrate is linear or quadratic. But a glucose tolerance curve will not be one of those. It will have a different shape that is probably better approximated with cubic splines. So I would suggest sticking with -integ-'s default here.

I do not understand your question about delta_glucose. By differencing each glucose measurement from the time 0 (i.e. baseline) glucose, you remove from the integration everything below that level, yes. Why do you think it might be otherwise?

[Karthik Balachandran]

I have a similar problem, but with five different diets. How can I calculate the incremental area under the curve for each diet for each person ? Your help will be greatly appreciated. I have attached sample data

* Example generated by -dataex-. For more info, type help dataex
clear
input byte(id diet) int time float glucose
1 1   0  5.222222
1 1  15  8.444445
1 1  30  8.944445
1 1  45  7.944445
1 1  60  8.555555
1 1  90         6
1 1 120       5.5
1 2   0         5
1 2  15  5.777778
1 2  30  7.333333
1 2  45  5.944445
1 2  60       5.5
1 2  90  6.055555
1 2 120  5.444445
1 3   0         5
1 3  15  6.055555
1 3  30  7.055555
1 3  45  6.833333
1 3  60  6.833333
1 3  90         6
1 3 120         5
1 4   0  4.777778
1 4  15         6
1 4  30  4.944445
1 4  45  5.888889
1 4  60  5.388889
1 4  90       4.5
1 4 120 4.4444447
1 5   0 4.4444447
1 5  15 4.6666665
1 5  30  5.611111
1 5  45  5.666667
1 5  60         5
1 5  90  5.166667
1 5 120  4.888889
2 1   0  4.888889
2 1  15  7.222222
2 1  30  7.277778
2 1  45  6.444445
2 1  60  5.833333
2 1  90  5.333333
2 1 120  4.833333
2 2   0 4.7222223
2 2  15  4.944445
2 2  30  5.833333
2 2  45  5.722222
2 2  60 4.7222223
2 2  90  4.833333
2 2 120         5
2 3   0 4.4444447
2 3  15  4.888889
2 3  30  5.777778
2 3  45  5.666667
2 3  60 4.4444447
2 3  90  5.888889
2 3 120  5.111111
2 4   0  3.166667
2 4  15       5.5
2 4  30         6
2 4  45  5.722222
2 4  60       5.5
2 4  90  5.222222
2 4 120  5.111111
2 5   0 4.6666665
2 5  15  4.888889
2 5  30 4.6666665
2 5  45         5
2 5  60  4.777778
2 5  90         5
2 5 120 4.6666665
3 1   0  5.222222
3 1  15  7.555555
3 1  30       9.5
3 1  45 11.333333
3 1  60 10.944445
3 1  90  9.555555
3 1 120  8.222222
3 2   0  5.833333
3 2  15  5.555555
3 2  30  6.222222
3 2  45  6.277778
3 2  60  6.111111
3 2  90  5.555555
3 2 120  4.833333
3 3   0  5.277778
3 3  15  5.611111
3 3  30  6.777778
3 3  45       6.5
3 3  60  6.944445
3 3  90  5.888889
3 3 120  5.555555
3 4   0  5.888889
3 4  15  5.722222
3 4  30  5.944445
3 4  45         6
3 4  60 4.5555553
3 4  90  5.055555
3 4 120  5.111111
3 5   0       5.5
3 5  15  5.333333
end

[Clyde Schechter]

I don't know what you mean by the "incremental" area under the curve. If you want, in each observation, the area under the curve from time 0 for that person and that diet, up to that point in time:

by id diet (time), sort: integ glucose time, gen(auc)

[Karthik Balachandran]

Thank you very much. It worked perfectly.