Random date assignment in comparator study

[Matthew Milano]

I'm using a large electronic health record database to run a cohort study comparing users of drug X with unexposed (non-drug X users). I have the index date (start of follow up) for drug X users and want to assign start dates for follow up at random to the unexposed group by incidence density sampling from the distribution of index dates in the drug X cohort.

I have no idea how to do this.

Sample of drug X cohort:

* Example generated by -dataex-. For more info, type help dataex
clear
input byte ID int dob byte sex str1 drug int(index_date index_year enddate)
 1   547 2 "X" 16755 2005 20583
 2 -1279 2 "X" 18207 2009 21184
 3 -1645 2 "X" 16810 2006 20941
 4 -2010 2 "X" 21031 2017 21184
 5 -2375 2 "X" 19537 2013 19990
 6 -2010 2 "X" 16149 2004 16580
 7 -7854 2 "X" 14628 2000 21184
 8 -2010 2 "X" 18219 2009 18238
 9 -8584 2 "X" 14810 2000 21184
10   912 2 "X" 19885 2014 20039
11   547 2 "X" 17288 2007 21184
12 -7854 2 "X" 15041 2001 19775
13   912 2 "X" 18114 2009 21184
14 -8219 2 "X" 17713 2008 18536
15 -3471 2 "X" 17143 2006 18373
end
format %td dob
format %td index_date
format %td enddate
label values sex sex
label def sex 2 "M", modify

Sample of unexposed cohort:

* Example generated by -dataex-. For more info, type help dataex
clear
input byte ID int dob byte sex int enddate
 1  -4567 2 22585
 2  -4932 2 17055
 3  -1279 2 20947
 4  -7123 2 19508
 5 -11141 2 18478
 6  -8219 2 20396
 7 -11141 2 20947
 8 -10776 2 21678
 9  -8584 2 14768
10 -13698 2 16917
11  -1645 2 20852
12  -8950 2 19674
13  -5297 2 19504
14  -6758 2 20717
15  -8584 2 14976
16  -4567 2 20710
17 -13333 2 19046
18  -4201 2 21141
19   -184 2 18141
20  -6028 2 20264
21  -1279 2 18669
22  -2375 2 22586
23 -12602 2 21490
24   -184 2 15749
25  -6393 2 22586
26  -6758 2 19969
27 -12602 2 16148
28 -14063 2 15813
29  -2375 2 22316
30   -549 2 22586
31  -2375 2 15985
32  -7854 2 20718
33  -1645 2 21132
34   -914 2 19874
35  -1279 2 21338
36  -3471 2 16881
37   -184 2 20816
38 -14063 2 16020
39  -7123 2 20999
40  -7489 2 16544
41  -6028 2 21155
42  -1279 2 22586
43 -11872 2 19814
44  -6758 2 17898
45  -9680 2 20216
46   -184 2 16071
47  -2010 2 22585
48  -4567 2 20216
49  -1279 2 22585
50  -1645 2 20397
end
format %td dob
format %td enddate
label values sex sex2
label def sex2 2 "M", modify

[Carlo Lazzaro]

Matthew:
I would follow this approach:
1) calculating the therapy duration, its mean and standard error in the treated dataset:

. g duration= enddate-index_date

. mean duration

Mean estimation                             Number of obs = 15

--------------------------------------------------------------
             |       Mean   Std. err.     [95% conf. interval]
-------------+------------------------------------------------
    duration |     2588.6   590.8859      1321.276    3855.924
--------------------------------------------------------------

.

2) using what above to fit a a random gamma distribution to therapy duration for unexposed individuals (assuming that therapy duration follows this kind of distribution):

. g distribution=(590.8859^2/2588.6)*invgammap((2588.6^2/590.8859^2),runiform())

[Joseph Coveney]

I . . . want to assign start dates for follow up at random to the unexposed group by incidence density sampling from the distribution of index dates in the drug X cohort.

If I wanted to mimic an empirical distribution, then I would probably use bootstrap-like resampling (that is, with replacement).

You can use bsample for this. There's a little fiddling needed to draw a sample from your exposed group to match the size of your unexposed group: see below for an illustration of one way to accomplish this (begin at the "Begin here" comment).

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿ//ÿseedem
.ÿsetÿseedÿ661633865

.ÿ
.ÿquietlyÿinputÿbyteÿIDÿintÿdobÿbyteÿsexÿstr1ÿdrugÿ///
>ÿÿÿÿÿÿÿÿÿint(index_dateÿindex_yearÿenddate)

.ÿ
.ÿformatÿdobÿ*dateÿ%tdCY-N-D

.ÿ
.ÿlabelÿdefineÿSexesÿ1ÿFÿ2ÿM

.ÿlabelÿvaluesÿsexÿSexes

.ÿ
.ÿtempfileÿexposed

.ÿquietlyÿsaveÿ`exposed'

.ÿ
.ÿdropÿ_allÿ

.ÿquietlyÿinputÿbyteÿIDÿintÿdobÿbyteÿsexÿintÿenddate

.ÿ
.ÿformatÿdobÿ*dateÿ%tdCY-N-D

.ÿ
.ÿlabelÿvaluesÿsexÿSexes

.ÿ
.ÿtempfileÿunexposed

.ÿquietlyÿsaveÿ`unexposed'

.ÿ
.ÿ*
.ÿ*ÿBeginÿhere
.ÿ*
.ÿ//ÿGetÿsampleÿsizeÿofÿunexposedÿpatientÿpopulation
.ÿquietlyÿcount

.ÿlocalÿtarget_Nÿ=ÿr(N)

.ÿ
.ÿ//ÿCreateÿaÿlargeÿdatasetÿofÿrandomlyÿsampledÿexposedÿpatients'ÿfollow-upÿelapsedÿdays
.ÿuseÿ`exposed'

.ÿgenerateÿintÿdeltaÿ=ÿenddateÿ-ÿindex_date

.ÿkeepÿdelta

.ÿ
.ÿpreserve

.ÿ
.ÿbsampleÿ//ÿ,ÿstrata(sex)ÿ

.ÿtempfileÿsampled_elapsed_days

.ÿquietlyÿsaveÿ`sampled_elapsed_days'

.ÿ
.ÿwhileÿ_Nÿ<ÿ`target_N'ÿ{
ÿÿ2.ÿÿÿÿÿÿÿÿÿrestore
ÿÿ3.ÿÿÿÿÿÿÿÿÿpreserve
ÿÿ4.ÿ
.ÿÿÿÿÿÿÿÿÿbsampleÿ//,ÿstrata(sex)
ÿÿ5.ÿÿÿÿÿÿÿÿÿappendÿusingÿ`sampled_elapsed_days'
ÿÿ6.ÿÿÿÿÿÿÿÿÿquietlyÿsaveÿ`sampled_elapsed_days',ÿreplace
ÿÿ7.ÿ}

.ÿrestoreÿ,ÿnot

.ÿquietlyÿkeepÿinÿ1/`target_N'

.ÿgenerateÿlongÿrowÿ=ÿ_n

.ÿquietlyÿsaveÿ`sampled_elapsed_days',ÿreplace

.ÿ
.ÿ//ÿApplyÿtheÿsampledÿfollow-upÿelapsedÿdaysÿtoÿunexposedÿpatients
.ÿuseÿ`unexposed',ÿclear

.ÿgenerateÿlongÿrowÿ=ÿ_n

.ÿmergeÿ1:1ÿrowÿusingÿ`sampled_elapsed_days',ÿassert(match)ÿnogenerateÿnoreport

.ÿdropÿrow

.ÿ
.ÿgenerateÿintÿstart_dateÿ=ÿenddateÿ-ÿdelta

.ÿformatÿ*dateÿ%tdCY-N-D

.ÿ
.ÿlistÿinÿ1/5,ÿnoobs

ÿÿ+---------------------------------------------------------+
ÿÿ|ÿIDÿÿÿÿÿÿÿÿÿÿdobÿÿÿsexÿÿÿÿÿÿenddateÿÿÿdeltaÿÿÿstart_dateÿ|
ÿÿ|---------------------------------------------------------|
ÿÿ|ÿÿ1ÿÿÿ1947-07-01ÿÿÿÿÿMÿÿÿ2021-11-01ÿÿÿÿÿ153ÿÿÿ2021-06-01ÿ|
ÿÿ|ÿÿ2ÿÿÿ1946-07-01ÿÿÿÿÿMÿÿÿ2006-09-11ÿÿÿÿ3828ÿÿÿ1996-03-19ÿ|
ÿÿ|ÿÿ3ÿÿÿ1956-07-01ÿÿÿÿÿMÿÿÿ2017-05-08ÿÿÿÿ6556ÿÿÿ1999-05-27ÿ|
ÿÿ|ÿÿ4ÿÿÿ1940-07-01ÿÿÿÿÿMÿÿÿ2013-05-30ÿÿÿÿ2977ÿÿÿ2005-04-05ÿ|
ÿÿ|ÿÿ5ÿÿÿ1929-07-01ÿÿÿÿÿMÿÿÿ2010-08-04ÿÿÿÿÿ453ÿÿÿ2009-05-08ÿ|
ÿÿ+---------------------------------------------------------+

.ÿ
.ÿexit

endÿofÿdo-file


.

help bsample

[Dana MS]

Carlo Lazzaro Many thanks for posting the code.

I tried your code and have the distribution for both groups but how do I assign the start of followup for unexposed group based on the distribution? In other words what is the next step