Cumulative exposure - best way to model it

[Ma Ba]

Hi all,

I've data from a longitudinal study, where for each patient I have several observations, one every time they got exposed. The outcome of interest is leukaemia, and the risk of the patient developing leukaemia increases with accumulated exposure. Once the patient is diagnosed with leukaemia or reaches the end of the follow-up is out of the study.
Initially, I modelled it using Cox proportional hazards for multiple observations, creating a final dummy observation with no dose associated where it is stated if the patient has leukaemia or not at the time of exiting the study. I created also a cumulative exposure variable, where the exposure is added up observation after observation.


Find below an excerpt of the snapshot database:

Idpatient	leuk	age	dose	cum_dose
1	0	2	0,3	0,3
1	0	3	0,6	0,9
1	0	5	0,8	1,7
1	0	7	0,9	2,6
1	0	8	0,4	2,7
1	1	12	.	2,7
2	0	5	0,6	0,6
2	0	7	0,8	1,4
2	0	8	.	1,4
3	0	1	0,1	0.1
3	0	2	0,3	0,4
3	0	3	0,5	0,9
3	0	7	0,8	1,7
3	1	8	.	1,7

An abbreviated version of what I did was:

I snapspanned the data by:
. snapspan Idpatient age leuk, generate(t0_age) replace

the result was:

Idpatient	leuk	t0_age	age	dose	cum_dose
1	0	.	2	.	.
1	0	2	3	0,3	0,3
1	0	3	5	0,6	0,9
1	0	5	7	0,8	1,7
1	0	7	8	0,9	2,6
1	1	8	12	0,4	2,7
2	0	.	5	.	.
2	0	5	7	0,6	0,6
2	0	7	8	0,8	1,4
3	0	.	1	.	.
3	0	1	2	0,1	0.1
3	0	2	3	0,3	0,4
3	0	3	7	0,5	0,9
3	1	7	8	0,8	1,7

and then I stsetted the data by:
. stset age , failure(leuk) id(Idpatient) origin (t0_age)

and run a Cox model with it.
stcox cum_dose

Is the Cox proportional hazard a correct approach for cumulative exposures if we are interested in modelling how the leukaemia hazard proportionally scales by the cumulative dose? I've found lots of examples in the stata guide for different designs but nothing quite like this.

Any help on this will be highly appreciated.

Thank you very much,

Ma

[Clyde Schechter]

I think the Cox proportional hazard model can handle this just as it would any other kind of exposure variable. There is always the question of whether the proportional hazards assumption is reasonable, but, again, this is no different from any other kind of exposure variable. The only concern I have is in the calculation of cumulative exposure itself: those missing values. It seems that once you have a single missing value for dose, from that point on, all of the summed exposures are wrong, biased downward. In effect, you are imputing an exposure of dose = 0 whenever dose is missing. Is that reasonable in your context?

[Ma Ba]

Hi Clyde,
Thanks for answering to this topic. My database has no missing doses at all. The observations that you see with a missing value for the variable dose in the first excerpt of the database are "dummy observations" I created to specify the age at which the patient was diagnosed with leukaemia or the age of the patient at the end of the study if he/she is cancer- free, so these observations don't have any dose associated (there was no exposure).
This was done to adapt the database to the format specified in the description of stset for multiple-records:

(Page 13 of the stata manual http://www.stata.com/manuals13/ststset.pdf)

	patid	t	died	x1	x2
1.	90	100	0	1	0
2.	90	150	1	0	0
3.	91	50	1	1	1
4.	92	100	0	0	0
5.	92	150	0	0	1
6.	92	190	0	0	0
7.	93	100	0	0	0

Regarding the proportionality assumption I will visually check it out with log-log plots and analytically with stphtest once the model is fitted.
Thanks,

Ma