Counting process survival analysis - T1/T2 affects results

[haoduonge]

Hi all,

I posted this question under 'SAS Text and Content Analytics' but suggested it more relevant under here.

I have multiple time varying covariates and unfortunately their time intervals (start, stop) are different, so I split time (start, stop) of one variable into interval (T1, T2) that can be matched/merged with other variables. I run the analyses using data before (table 1) and after splitting time (table 2) and hope to get the same results but I don't.

*Before time split - table 1; HR=0.587(0.074-4.673)

proc phreg data=TABLE1;class treatment (ref=first);

model (start, stop)*outcome(0)=treatment / TIES = EFRON RL;run;

*After time split - table 2; HR=0.378(0.089-1.60)

proc phreg data=TABLE2;class treatment (ref=first);

model (start, stop)*outcome(0)=treatment/ TIES = EFRON RL;run;

I really appreciate if any could have explanations and/or how to adjust it?

Thank you!

Table 1

ID	start	stop	treatment	outcome
1	0	0.0001	0	0
1	0.0001	2.218	1	0
2	0	0.0001	0	0
3	0.0001	2.779	1	0
3	0	2.105	0	0
4	0	5.092	0	0
4	5.092	6.47	1	0
5	0	3.532	0	0
5	3.532	6.494	1	0
6	0	3.603	0	0
6	3.603	6.47	1	0
7	0	2.382	0	1
8	0	0.969	0	1
9	0	0.0001	0	0
9	0.0001	1.18	1	0
10	0	2.642	0	0
11	0	1.254	0	0
12	0	5.07	0	0
13	0	6.494	0	0
14	0	2.661	0	0
15	0	4.279	0	0
16	0	3.671	0	1
17	0	4.66	0	0
17	4.66	6.48	1	0
18	0	6.489	0	0
19	0	2.669	0	0
20	0	4.728	0	0
20	4.728	6.486	1	0
21	0	6.47	0	0
22	0	2.45	0	0
23	0	6.494	0	0
24	0	0.052	0	0
24	0.052	1.41	1	0
25	0	0.0001	0	0
25	0.0001	1.725	1	0
26	0	6.018	0	0
27	0	3.617	0	0
27	3.617	6.453	1	0
28	0	0.0001	0	0
28	0.0001	3.907	1	0
29	0	3.047	0	0
30	0	6.497	0	0
31	0	1.982	0	0
32	0	0.0001	0	0
32	0.0001	1.399	1	0
33	0	0.621	0	0
34	0	2.579	0	0
35	0	6.448	0	0
36	0	5.24	0	0
37	0	4.227	0	0
38	0	1.114	0	1
39	0	4.285	0	1
40	0	1.61	0	1
41	0	3.844	0	1
42	0	2.522	0	1
43	0	1.769	0	1
44	0	3.48	0	1
45	0	0.0001	0	0
45	0.0001	1.667	1	1
46	0	0.0001	0	0
46	0.0001	1.895	1	0

Table 2

ID	start	stop	outcome	treatment	T1	T2
1	0	0.0001	0	0	0	1
1	0.0001	1	0	1	0	1
1	1	2	0	1	1	2
1	2	2.218	0	1	2	2.218
2	0	0.0001	0	0	0	1
2	0.0001	1	0	1	0	1
2	1	2	0	1	1	2
2	2	2.779	0	1	2	2.779
3	0	1	0	0	0	1
3	1	2	0	0	1	2
3	2	2.105	0	0	2	2.105
4	0	1	0	0	0	1
4	1	2	0	0	1	2
4	2	3	0	0	2	3
4	3	4	0	0	3	4
4	4	5	0	0	4	5
4	5	5.092	0	0	5	6
4	5.092	6	0	1	5	6
4	6	6.47	0	1	6	6.47
5	0	1	0	0	0	1
5	1	2	0	0	1	2
5	2	3	0	0	2	3
5	3	3.532	0	0	3	4
5	3.532	4	0	1	3	4
5	4	5	0	1	4	5
5	5	6	0	1	5	6
5	6	6.494	0	1	6	6.494
6	0	1	0	0	0	1
6	1	2	0	0	1	2
6	2	3	0	0	2	3
6	3	3.603	0	0	3	4
6	3.603	4	0	1	3	4
6	4	5	0	1	4	5
6	5	6	0	1	5	6
6	6	6.47	0	1	6	6.47
7	0	1	1	0	0	1
7	1	2	1	0	1	2
7	2	2.382	1	0	2	2.382
8	0	0.969	1	0	0	0.969
9	0	0.0001	0	0	0	1
9	0.0001	1	0	1	0	1
9	1	1.18	0	1	1	1.18
10	0	1	0	0	0	1
10	1	2	0	0	1	2
10	2	2.642	0	0	2	2.642
11	0	1	0	0	0	1
11	1	1.254	0	0	1	1.254
12	0	1	0	0	0	1
12	1	2	0	0	1	2
12	2	3	0	0	2	3
12	3	4	0	0	3	4
12	4	5	0	0	4	5
12	5	5.07	0	0	5	5.07
13	0	1	0	0	0	1
13	1	2	0	0	1	2
13	2	3	0	0	2	3
13	3	4	0	0	3	4
13	4	5	0	0	4	5
13	5	6	0	0	5	6
13	6	6.494	0	0	6	6.494
14	0	1	0	0	0	1
14	1	2	0	0	1	2
14	2	2.661	0	0	2	2.661
15	0	1	0	0	0	1
15	1	2	0	0	1	2
15	2	3	0	0	2	3
15	3	4	0	0	3	4
15	4	4.279	0	0	4	4.279
16	0	1	1	0	0	1
16	1	2	1	0	1	2
16	2	3	1	0	2	3
16	3	3.671	1	0	3	3.671
17	0	1	0	0	0	1
17	1	2	0	0	1	2
17	2	3	0	0	2	3
17	3	4	0	0	3	4
17	4	4.66	0	0	4	5
17	4.66	5	0	1	4	5
17	5	6	0	1	5	6
17	6	6.48	0	1	6	6.48
18	0	1	0	0	0	1
18	1	2	0	0	1	2
18	2	3	0	0	2	3
18	3	4	0	0	3	4
18	4	5	0	0	4	5
18	5	6	0	0	5	6
18	6	6.489	0	0	6	6.489
19	0	1	0	0	0	1
19	1	2	0	0	1	2
19	2	2.669	0	0	2	2.669
20	0	1	0	0	0	1
20	1	2	0	0	1	2
20	2	3	0	0	2	3
20	3	4	0	0	3	4
20	4	4.728	0	0	4	5
20	4.728	5	0	1	4	5
20	5	6	0	1	5	6
20	6	6.486	0	1	6	6.486
21	0	1	0	0	0	1
21	1	2	0	0	1	2
21	2	3	0	0	2	3
21	3	4	0	0	3	4
21	4	5	0	0	4	5
21	5	6	0	0	5	6
21	6	6.47	0	0	6	6.47
22	0	1	0	0	0	1
22	1	2	0	0	1	2
22	2	2.45	0	0	2	2.45
23	0	1	0	0	0	1
23	1	2	0	0	1	2
23	2	3	0	0	2	3
23	3	4	0	0	3	4
23	4	5	0	0	4	5
23	5	6	0	0	5	6
23	6	6.494	0	0	6	6.494
24	0	0.052	0	0	0	1
24	0.052	1	0	1	0	1
24	1	1.41	0	1	1	1.41
25	0	0.0001	0	0	0	1
25	0.0001	1	0	1	0	1
25	1	1.725	0	1	1	1.725
26	0	1	0	0	0	1
26	1	2	0	0	1	2
27	2	3	0	0	2	3
27	3	4	0	0	3	4
27	4	5	0	0	4	5
27	5	6	0	0	5	6
27	6	6.018	0	0	6	6.018
27	0	1	0	0	0	1
27	1	2	0	0	1	2
27	2	3	0	0	2	3
27	3	3.617	0	0	3	4
27	3.617	4	0	1	3	4
27	4	5	0	1	4	5
27	5	6	0	1	5	6
27	6	6.453	0	1	6	6.453
28	0	0.0001	0	0	0	1
28	0.0001	1	0	1	0	1
28	1	2	0	1	1	2
28	2	3	0	1	2	3
28	3	3.907	0	1	3	3.907
29	0	1	0	0	0	1
29	1	2	0	0	1	2
29	2	3	0	0	2	3
29	3	3.047	0	0	3	3.047
30	0	1	0	0	0	1
30	1	2	0	0	1	2
30	2	3	0	0	2	3
30	3	4	0	0	3	4
30	4	5	0	0	4	5
30	5	6	0	0	5	6
30	6	6.497	0	0	6	6.497
31	0	1	0	0	0	1
31	1	1.982	0	0	1	1.982
32	0	0.0001	0	0	0	1
32	0.0001	1	0	1	0	1
32	1	1.399	0	1	1	1.399
33	0	0.621	0	0	0	0.621
34	0	1	0	0	0	1
34	1	2	0	0	1	2
34	2	2.579	0	0	2	2.579
35	0	1	0	0	0	1
35	1	2	0	0	1	2
35	2	3	0	0	2	3
35	3	4	0	0	3	4
35	4	5	0	0	4	5
35	5	6	0	0	5	6
35	6	6.448	0	0	6	6.448
36	0	1	0	0	0	1
36	1	2	0	0	1	2
36	2	3	0	0	2	3
36	3	4	0	0	3	4
36	4	5	0	0	4	5
36	5	5.24	0	0	5	5.24
37	0	1	0	0	0	1
37	1	2	0	0	1	2
37	2	3	0	0	2	3
37	3	4	0	0	3	4
37	4	4.227	0	0	4	4.227
38	0	1	1	0	0	1
38	1	1.114	1	0	1	1.114
39	0	1	1	0	0	1
39	1	2	1	0	1	2
39	2	3	1	0	2	3
39	3	4	1	0	3	4
39	4	4.285	1	0	4	4.285
40	0	1	1	0	0	1
40	1	1.61	1	0	1	1.61
41	0	1	1	0	0	1
41	1	2	1	0	1	2
41	2	3	1	0	2	3
41	3	3.844	1	0	3	3.844
42	0	1	1	0	0	1
42	1	2	1	0	1	2
42	2	2.522	1	0	2	2.522
43	0	1	1	0	0	1
43	1	1.769	1	0	1	1.769
44	0	1	1	0	0	1
44	1	2	1	0	1	2
44	2	3	1	0	2	3
44	3	3.48	1	0	3	3.48
45	0	0.0001	0	0	0	1
45	0.0001	1	1	1	0	1
45	1	1.667	1	1	1	1.667
46	0	0.0001	0	0	0	1
46	0.0001	1	0	1	0	1
46	1	1.895	0	1	1	1.895

[FreelanceReinh · Accepted solution]

Hi @haoduonge,

Thanks for posting extended sample data and the corresponding PROC PHREG results (and code) -- in the appropriate forum for this question.

The reason for the difference in hazard ratios is that you set variable outcome to 1 in many of the newly introduced observations of table 2. The documentation Counting Process Style of Input says (about the start/stop times):

The subject remains at risk during the interval (t₁, t₂], and an event might occur at t₂.

So, for example ID 7 has an event at time 2.382 according to table 1, but three events (at times 1, 2 and 2.382) according to table 2. In total, you introduced 21 additional events, most of them in observations with treatment 0 -- thus making treatment 1 look much better (smaller hazard ratio).

With a modified version of TABLE2, named TABLE2a, I get identical estimates (incl. HR) as with TABLE1:

data table2a;
set table2;
by id;
if ~last.id & outcome=1 then outcome=0;
run;

Of course, you need to decide which version, if any, appropriately reflects the event times in your study.

(I'm going to call "PROC SLEEP" now as it's after midnight in my CEST time zone. Will be back on Saturday.)

[haoduonge]

That is it!

I guess it is too late to say good night as you are about to wake up.

Thank you so much!