Pharmacokinetics for multilevel data in STATA. pkcollapse?

[Gianfranco Di Gennaro]

Dar all,

thanks in advance.

I am studying 5 doses of a drug (ranging from 0 to 5, with 0 as the reference dose).
Each dose is administered to 8 different rats (there is no washout, the rat is sacrificed at the last timepoint), and I measure ta clinical outcome (seizure lenght) at various timepoints (0 30 60 90 120 150 180 210).
I am interested in understanding if the AUC differs among the different doses, with a possible significance test compared to dose 0 (reference).
I know this is not properly a Pharmacokinetics study. I need AUC to have an "overall" measure of efficacy.
I have seen that the "pkcollapse" command does not account for the multilevel structure of these data (dose, id).
Do you know of any other STATA tool for this type of evaluation?

Please see below how my dataset appears.

* Example generated by -dataex-. For more info, type help dataex
clear
input byte id int time double lenght byte dose
 1   0     80 0
 1  30 84.007 0
 1  60 85.878 0
 1  90  82.15 0
 1 120   85.2 0
 1 150     85 0
 1 180  88.92 0
 1 210     91 0
 2   0   80.3 0
 2  30  79.01 0
 2  60  83.92 0
 2  90  83.12 0
 2 120 87.056 0
 2 150   83.4 0
 2 180 89.856 0
 2 210     95 0
 3   0 82.357 0
 3  30 81.109 0
 3  60 83.834 0
 3  90 81.134 0
 3 120 87.058 0
 3 150   83.1 0
 3 180 89.858 0
 3 210     92 0
 4   0 79.789 0
 4  30     81 0
 4  60  84.89 0
 4  90 82.102 0
 4 120  88.02 0
 4 150     88 0
 4 180 90.802 0
 4 210     89 0
 5   0   77.9 0
 5  30     82 0
 5  60 83.129 0
 5  90 83.129 0
 5 120 83.029 0
 5 150     83 0
 5 180 91.929 0
 5 210     93 0
 6   0 79.535 0
 6  30 81.009 0
 6  60  82.85 0
 6  90  82.15 0
 6 120 89.169 0
 6 150     85 0
 6 180   88.3 0
 6 210     91 0
 7   0 79.356 0
 7  30   80.1 0
 7  60  84.16 0
 7  90  84.16 0
 7 120 87.089 0
 7 150     84 0
 7 180 87.989 0
 7 210     90 0
 8   0 78.355 0
 8  30 80.356 0
 8  60  81.16 0
 8  90  80.16 0
 8 120 90.167 0
 8 150     92 0
 8 180 86.967 0
 8 210     98 0
 9   0     80 1
 9  30 80.068 1
 9  60  82.52 1
 9  90  81.89 1
 9 120     84 1
 9 150 89.543 1
 9 180 93.818 1
 9 210     94 1
10   0     82 1
10  30 80.478 1
10  60 85.756 1
10  90 83.756 1
10 120  81.34 1
10 150 86.278 1
10 180 94.856 1
10 210     95 1
11   0     82 1
11  30 86.245 1
11  60 87.858 1
11  90 87.977 1
11 120 85.256 1
11 150  83.05 1
11 180 89.858 1
11 210     92 1
12   0     78 1
12  30 81.556 1
12  60 83.402 1
12  90 81.802 1
12 120 83.456 1
12 150 89.078 1
12 180 93.902 1
12 210     95 1
13   0     82 1
13  30  88.04 1
13  60 88.529 1
13  90 83.929 1
end

Thanks again.
Gianfranco

[Joseph Coveney]

I am interested in understanding if the AUC differs among the different doses, with a possible significance test compared to dose 0 (reference).

Maybe try something along the following lines?

bysort id (time): integ lenght time, double generate(auc) trapezoid
anova auc dose if time == 210

[Gianfranco Di Gennaro]

Thank you very much Joseph Coveney .
It works perfectly.

[Gianfranco Di Gennaro]

Dear Joseph Coveney I forgot to ask you for some information.
I know it's not specifically related to STATA, so I apologize in advance if I bother you.
In this case, what is the unit of measurement for AUC? I imagine that since it's an area, it should be a length (time) squared? Thank you in any case.

[Leonardo Guizzetti]

In this context, AUC is the measure of total drug exposure over time and is approximated by the discrete integral of drug dose over time, so its units are (drug dose unit) times (time unit).

[Joseph Coveney]

I measure ta clinical outcome (seizure lenght) at various timepoints (0 30 60 90 120 150 180 210).

. . . what is the unit of measurement for AUC? I imagine that since it's an area, it should be a length (time) squared?

It would be time × time (or time ⋅ time) in units of what was used to measure seizure length × units of time used for the intervals at which the outcome was measured. It would be qualified as AUC_0–210 in the body of the report and in its tables and graphs.

[Nicholas Thomford]

Dear all,

thanks in advance.

I am studying ART-ACT interaction in the same doses but blood samples collected over 5 time points (0-48 hours).

I am interested in understanding how the AUC differs among those who took ART only, ACT only and ART-ACT combined.
I need AUC to have an "overall" measure of efficacy.
I have been trying the "pksumm" command but it keeps giving me this error message "follow-up times are different for each patient" r(459)
Do you know of any other STATA tool for this type of evaluation? Can anyone assist me with what i am doing wrong with the time and how to over come that challenge

Please see below how my dataset appears.

ID	TIME	LUM-BI (ng/ml)
8	0	8.11
8	2	8.11
8	12	3798
8	24	400
8	48
9	0	61.5
9	2	8285
9	12	3490
9	24
9	48
16	0	8.11
16	2	8.11
16	12	914
16	24	3978
16	48	320
19	0	8.11
19	2	8.11
19	12	2497
19	24	935
19	48
20	0	17.5
20	2	16.3
20	12	12940
20	24	8004
20	48	652
21	0	8.11
21	2	8.11
21	12	2126
21	24	4212
21	48	621
22	0	13.6
22	2	11.3
22	12	1259
22	24
22	48
23	0	8.11
23	2	8.11
23	12	337
23	24	1319
23	48	64.9
24	0	8.11
24	2	30.7
24	12	2181
24	24	433
24	48	1623
26	0	8.11
26	2	2016
26	12	1918
26	24	955
26	48	8.11
27	0	1774
27	2	1729
27	12	1727
27	24	1216
27	48	551
28	0	26.6
28	2	25.7
28	12	684
28	24	516
28	48	199
30	0	8.11
30	2
30	12	4569
30	24	9794
30	48	1888
31	0	8.11
31	2	9.72
31	12	4547
31	24	11003
31	48	918
32	0	8.11
32	2	8.11
32	12	1152
32	24	5059
32	48	482
34	0	8.11
34	2	8.11
34	12	995
34	24	3493
34	48	343
35	0	1944
35	2	1972
35	12	3030
35	24	1657
35	48	1896
49	0	26.3
49	2	26.7
49	12
49	24	3247
49	48	3416
50	0	10.2
50	2	16
50	12	5776
50	24	1768
50	48	1455
52	0	162
52	2	181
52	12	1847
52	24	1007
52	48
53	0	8.11
53	2	8.11
53	12	9571
53	24
53	48
54	0	8.11
54	2	8.11
54	12	1420
54	24	806
54	48	74.8
55	0	933
55	2	609
55	12	6865
55	24	3205
55	48	370
56	0	1013
56	2	920
56	12	4196
56	24	11216
56	48	359
58	0	8.11
58	2	8.11
58	12	6022
58	24	12775
58	48	919
59	0	8.11
59	2	515
59	12	869
59	24	64
59	48
60	0	8.11
60	2	8.11
60	12	25.9
60	24
60	48
61	0	8.11
61	2	8.11
61	12	3199
61	24
61	48
62	0	8.11
62	2	8.11
62	12	1243
62	24	183
62	48
63	0	37.4
63	2	981
63	12	1053
63	24	3229
63	48	154
64	0	40.85
64	2	32
64	12	308
64	24	251
64	48	153
65	0	158
65	2
65	12	2796
65	24	1697
65	48	317
66	0	8.11
66	2	8.11
66	12	7073
66	24	2645
66	48	689
67	0	8.11
67	2	10.4
67	12	4458
67	24	841
67	48	302
68	0	8.11
68	2	8.11
68	12	1869
68	24	3609
68	48	351
69	0	57
69	2	72.8
69	12	3564
69	24	1473
69	48	647
70	0	11.6
70	2	7.9
70	12	1904
70	24	1082
70	48	207
87	0	73.2
87	2	3836
87	12	3907
87	24	703
87	48
109	0	8.11
109	2	8.11
109	12	1401
109	24	541
109	48	196
112	0	11.8
112	2	10.7
112	12	3927
112	24	1871
112	48	1585
114	0	101
114	2	84
114	12	3485
114	24	2238
114	48	215
116	0	142
116	2	149
116	12	3811
116	24	5089
116	48	1622
117	0	8.11
117	2	8.11
117	12	2883
117	24	4390
117	48	693
118	0	8.11
118	2	8.11
118	12	2359
118	24	3986
118	48	1617
119	0	179
119	2	159
119	12	1823
119	24	1440
119	48	560
120	0	102
120	2	119
120	12	4591
120	24	5777
120	48	891
123	0	32.7
123	2
123	12	456
123	24	3332
123	48	535
125	0	8.11
125	2	8.11
125	12
125	24	329
125	48	176
126	0	8.11
126	2	8.11
126	12	5060
126	24	1607
126	48	1262
127	0	23.6
127	2
127	12	4502
127	24	1781
127	48	907
128	0	22.8
128	2	1854
128	12	1593
128	24	1368
128	48	496
130	0	55
130	2
130	12	2413
130	24	2882
130	48	1220
131	0	8.11
131	2
131	12	3020
131	24	1564
131	48	583
134	0	45.5
134	2	50
134	12	2118
134	24	2597
134	48	613
135	0	8.11
135	2	121
135	12	2664
135	24	2437
135	48
136	0	119
136	2	8.11
136	12	3930
136	24	877
136	48
137	0	8.11
137	2	8.11
137	12	2969
137	24	5732
137	48	457
139	0	8.11
139	2	8.11
139	12	2989
139	24	5018
139	48	454
140	0	11.4
140	2	11.6
140	12	987
140	24	3507
140	48	354
141	0	8.11
141	2	8.11
141	12	1482
141	24	1846
141	48	381
143	0	57.8
143	2	50.1
143	12	3443
143	24	5785
143	48	1152
144	0	17.9
144	2
144	12	3743
144	24	2547
144	48	550

[Joseph Coveney]

Can anyone assist me with what i am doing wrong with the time and how to over come that challenge

pksumm has an option, notimechk, that would avoid the error message, but I don't recommend that approach.

An alternative would be to fit a mixed-effects model to the concentration values with treatment, time and their interaction as categorical predictors, and then integrate the marginal predictions separately by treatment using the trapezoid rule.

Because the variance of the values varies greatly over time, you would probably want to allow an unstructured residual covariance matrix when fitting the mixed model. (You could also consider taking the logarithm of the concentration values in order to stabilize the variance, and then comparing the areas under the log-concentration curves.)

Your "Please see below how my dataset appears." doesn't show any ACT or ART (whatever they are) treatment variable, but for the pooled data that you do show, the code would be something like the following. (I rename your variables for consistency in case and length, and to comply with Stata's naming rules.)

input int pid byte tim double cnc // ID TIME LUM-BI (ng/ml)
<data redacted for brevity>
end

mixed cnc i.tim || pid: , noconstant residuals(unstructured, t(tim)) ///
    nolrtest nolog
margins , at(tim = (0 2 12 24 48)) post
lincom _b[1._at] + _b[2._at] + (_b[2._at] + _b[3._at]) / 2 * 10 + ///
    (_b[3._at] + _b[4._at]) / 2 * 12 + (_b[4._at] + _b[5._at]) / 2 * 24

The concentration 8.11 ng/ml appears 56 times in your dataset. Is it the limit of quantitation (or detection)? If so, then why is there also a value of 7.9 ng/ml for study participant 70?