Time Varying EPTS

Data Structures

Kidney Allocation

Author

Molly H. White

Published

February 19, 2024

In the SRTR Standard Analysis Files, the CAND_KIPA file includes information on candidates listed for kidney and/or pancreas transplants. From this file, it is possible to calculate a candidate EPTS score at listing, but it does not directly account for the change in dialysis time and age during a patient’s time on the waitlist that can lead to higher EPTS scores over time. To perform analyses on EPTS scores that change over time, it is possible to request an enhanced SAF from the SRTR that includes time-varying EPTS. Alternatively, you can consctruct a discrete time dataset that can be used to calculate EPTS at different periods during a candidate’s time on the waitlist. In this post we will address how we constructed such a dataset for our manuscript Association of Race and Ethnicity with Priority for Deceased Donor Kidney Transplant.

Let’s take a look at our data:

PX_ID	min_list_date	previous_TX	dialysis	waitlist_end_date	age_months	CAN_DIAL_DT	dialysis_time_at_list	wait_time
1	2015-09-03	0	0	2016-02-09	713	2015-11-15	0	159 days
2	2012-02-03	0	1	2012-04-16	439	2011-09-20	136	73 days
3	2014-04-30	1	0	2014-12-20	339	NA	0	234 days
4	2012-07-01	0	1	2015-01-01	654	2011-07-01	366	914 days
5	2012-07-01	0	0	2015-01-01	654	2013-01-01	0	914 days
6	2012-07-01	0	0	2015-01-01	654	NA	0	914 days

Note

These data are fabricated and do not represent real patients listed for kidney transplant

PX_ID is a unique patient identifier
min_list_date is the earliest date a patient is listed for a transplant. This takes into account patients who are listed at multiple centers concurrently. We will explain how to address such patients in another post.
previous_TX is an indicator for whether the patient has received a previous transplant
dialysis is an indicator for whether the patient was on dialysis when they were listed
waitlist_end_date is the date that the patient received a transplant or was otherwise removed from the waiting list
diabetes is an indicator for whether the candidate has diabetes
age_months is the candidate’s age in months at listing
CAN_DIAL_DT is the date the candidate started dialysis (if at all)
dialysis_time_at_list is how long the patient was on dialysis before being placed on the waitlist
wait_time is the time between the candidate’s listing and their waitlist end date

With these variables we would be able to calculate a patient’s EPTS score at listing, but neither the age nor dialysis time variable captures changes over time. To address this, we can create a discrete time data set with 1 month intervals such that the age and dialysis time increase every month that the candidate is on the waitlist.

First, we will flag patient’s who were pre-emptively listed and then started dialysis during their time on the waitlist:

df_epts_varying$dialysis_during_waitlist <- ifelse(df_epts_varying$CAN_DIAL_DT > df_epts_varying$min_list_date, 1, 0)
df_epts_varying$dialysis_during_waitlist[is.na(df_epts_varying$dialysis_during_waitlist)] <- 0

We will then calculate the total months that each patient was on the waitlist:

df_epts_varying = df_epts_varying  %>% mutate(time_period = as.integer(floor((wait_time)*12/365)))

To properly encode the dialysis time for patients who begin dialysis after listing, we use a time_until_dialysis variable, which we will later compare to the patient’s time on the waitlist to trigger the dialysis_time variable to start increasing

df_epts_varying = df_epts_varying %>% mutate(time_until_dialysis = ifelse(dialysis_during_waitlist == 1, as.integer(floor((CAN_DIAL_DT - min_list_date)*12/365)), 0))

Using the time period variable, we construct a dataset which has an observation for each month the patient is on the waitlist.

expanded_data <- df_epts_varying %>%
  tidyr::uncount(weights = time_period + 1) %>%
  group_by(PX_ID) %>%
  mutate(time = ifelse(row_number() <= time_period + 1, row_number() - 1, NA),
    time = ifelse(is.na(time), max(time, na.rm = TRUE), time),
    age = age_months/12
  ) %>%
  mutate(age = age + row_number()/12)

expanded_data = expanded_data %>% 
  mutate(dialysis_after_waitlist = case_when(
    dialysis_during_waitlist == 1 & (time - time_until_dialysis) < 0 ~ 0, 
    dialysis_during_waitlist == 1 & (time - time_until_dialysis) >= 0 ~ (time - time_until_dialysis), 
    dialysis_during_waitlist == 0 & dialysis == 1 ~ (time - time_until_dialysis),
    TRUE ~ 0))

expanded_data = expanded_data %>% mutate(dialysis_time = dialysis_time_at_list + dialysis_after_waitlist/12)

As we can see below, this process allows us to determine dialysis time and age at each month of a patient’s time on the waitlist in order to accurately calculate EPTS at each time step

PX_ID	time	dialysis_time_at_list	dialysis_after_waitlist	dialysis_time	age
1	0	0	0	0.0000000	59.50000
1	1	0	0	0.0000000	59.58333
1	2	0	0	0.0000000	59.66667
1	3	0	1	0.0833333	59.75000
1	4	0	2	0.1666667	59.83333
1	5	0	3	0.2500000	59.91667
2	0	136	0	136.0000000	36.66667
2	1	136	1	136.0833333	36.75000
2	2	136	2	136.1666667	36.83333
3	0	0	0	0.0000000	28.33333
3	1	0	0	0.0000000	28.41667
3	2	0	0	0.0000000	28.50000
3	3	0	0	0.0000000	28.58333
3	4	0	0	0.0000000	28.66667
3	5	0	0	0.0000000	28.75000
3	6	0	0	0.0000000	28.83333
3	7	0	0	0.0000000	28.91667
4	0	366	0	366.0000000	54.58333
4	1	366	1	366.0833333	54.66667
4	2	366	2	366.1666667	54.75000
4	3	366	3	366.2500000	54.83333
4	4	366	4	366.3333333	54.91667
4	5	366	5	366.4166667	55.00000
4	6	366	6	366.5000000	55.08333
4	7	366	7	366.5833333	55.16667
4	8	366	8	366.6666667	55.25000
4	9	366	9	366.7500000	55.33333
4	10	366	10	366.8333333	55.41667
4	11	366	11	366.9166667	55.50000
4	12	366	12	367.0000000	55.58333
4	13	366	13	367.0833333	55.66667
4	14	366	14	367.1666667	55.75000
4	15	366	15	367.2500000	55.83333
4	16	366	16	367.3333333	55.91667
4	17	366	17	367.4166667	56.00000
4	18	366	18	367.5000000	56.08333
4	19	366	19	367.5833333	56.16667
4	20	366	20	367.6666667	56.25000
4	21	366	21	367.7500000	56.33333
4	22	366	22	367.8333333	56.41667
4	23	366	23	367.9166667	56.50000
4	24	366	24	368.0000000	56.58333
4	25	366	25	368.0833333	56.66667
4	26	366	26	368.1666667	56.75000
4	27	366	27	368.2500000	56.83333
4	28	366	28	368.3333333	56.91667
4	29	366	29	368.4166667	57.00000
4	30	366	30	368.5000000	57.08333
5	0	0	0	0.0000000	54.58333
5	1	0	0	0.0000000	54.66667
5	2	0	0	0.0000000	54.75000
5	3	0	0	0.0000000	54.83333
5	4	0	0	0.0000000	54.91667
5	5	0	0	0.0000000	55.00000
5	6	0	0	0.0000000	55.08333
5	7	0	1	0.0833333	55.16667
5	8	0	2	0.1666667	55.25000
5	9	0	3	0.2500000	55.33333
5	10	0	4	0.3333333	55.41667
5	11	0	5	0.4166667	55.50000
5	12	0	6	0.5000000	55.58333
5	13	0	7	0.5833333	55.66667
5	14	0	8	0.6666667	55.75000
5	15	0	9	0.7500000	55.83333
5	16	0	10	0.8333333	55.91667
5	17	0	11	0.9166667	56.00000
5	18	0	12	1.0000000	56.08333
5	19	0	13	1.0833333	56.16667
5	20	0	14	1.1666667	56.25000
5	21	0	15	1.2500000	56.33333
5	22	0	16	1.3333333	56.41667
5	23	0	17	1.4166667	56.50000
5	24	0	18	1.5000000	56.58333
5	25	0	19	1.5833333	56.66667
5	26	0	20	1.6666667	56.75000
5	27	0	21	1.7500000	56.83333
5	28	0	22	1.8333333	56.91667
5	29	0	23	1.9166667	57.00000
5	30	0	24	2.0000000	57.08333
6	0	0	0	0.0000000	54.58333
6	1	0	0	0.0000000	54.66667
6	2	0	0	0.0000000	54.75000
6	3	0	0	0.0000000	54.83333
6	4	0	0	0.0000000	54.91667
6	5	0	0	0.0000000	55.00000
6	6	0	0	0.0000000	55.08333
6	7	0	0	0.0000000	55.16667
6	8	0	0	0.0000000	55.25000
6	9	0	0	0.0000000	55.33333
6	10	0	0	0.0000000	55.41667
6	11	0	0	0.0000000	55.50000
6	12	0	0	0.0000000	55.58333
6	13	0	0	0.0000000	55.66667
6	14	0	0	0.0000000	55.75000
6	15	0	0	0.0000000	55.83333
6	16	0	0	0.0000000	55.91667
6	17	0	0	0.0000000	56.00000
6	18	0	0	0.0000000	56.08333
6	19	0	0	0.0000000	56.16667
6	20	0	0	0.0000000	56.25000
6	21	0	0	0.0000000	56.33333
6	22	0	0	0.0000000	56.41667
6	23	0	0	0.0000000	56.50000
6	24	0	0	0.0000000	56.58333
6	25	0	0	0.0000000	56.66667
6	26	0	0	0.0000000	56.75000
6	27	0	0	0.0000000	56.83333
6	28	0	0	0.0000000	56.91667
6	29	0	0	0.0000000	57.00000
6	30	0	0	0.0000000	57.08333

Each patient’s raw EPTS score is calculated using the following formula:

Raw EPTS = 0.047*max(Age-25,0)- 0.015*Diabetes*max(Age-25,0) \\ + 0.398*Prior Organ Transplant - 0.237*Diabetes*Prior Organ Transplant \\ + 0.315*log(Dialysis Time + 1) - 0.099*Diabetes*log(Dialysis Time + 1) \\+ 0.130*(Dialysis Time = 0) - 0.348*Diabetes*(Dialysis Time = 0) + 1.262*Diabetes

We then use the EPTS mapping table from 2021 shown here to calculate EPTS of these patients at each month on the waitlist.

If the raw EPTS is between		Then
>	<=	EPTS is

0.0000000	1.842390e-02	0
0.0184239	2.358706e-01	1
0.2358706	4.188522e-01	2
0.4188522	5.280000e-01	3
0.5280000	6.285256e-01	4
0.6285256	7.135270e-01	5
0.7135270	7.922030e-01	6
0.7922030	8.671443e-01	7
0.8671443	9.304798e-01	8
0.9304798	9.939185e-01	9
0.9939185	1.055990e+00	10
1.0559898	1.114348e+00	11
1.1143479	1.170456e+00	12
1.1704557	1.220301e+00	13
1.2203005	1.272125e+00	14
1.2721250	1.319138e+00	15
1.3191377	1.364385e+00	16
1.3643854	1.411682e+00	17
1.4116824	1.454332e+00	18
1.4543320	1.494737e+00	19
1.4947372	1.535142e+00	20
1.5351424	1.573005e+00	21
1.5730051	1.608103e+00	22
1.6081034	1.642976e+00	23
1.6429760	1.673541e+00	24
1.6735411	1.702554e+00	25
1.7025537	1.731507e+00	26
1.7315065	1.758694e+00	27
1.7586938	1.784780e+00	28
1.7847796	1.811802e+00	29
1.8118022	1.836835e+00	30
1.8368350	1.860602e+00	31
1.8606023	1.883752e+00	32
1.8837516	1.907272e+00	33
1.9072723	1.929411e+00	34
1.9294107	1.951500e+00	35
1.9514996	1.973708e+00	36
1.9737084	1.994142e+00	37
1.9941416	2.014865e+00	38
2.0148654	2.033233e+00	39
2.0332331	2.053976e+00	40
2.0539760	2.073276e+00	41
2.0732762	2.092022e+00	42
2.0920218	2.110557e+00	43
2.1105572	2.127109e+00	44
2.1271095	2.144695e+00	45
2.1446947	2.162066e+00	46
2.1620664	2.178958e+00	47
2.1789580	2.195336e+00	48
2.1953362	2.212030e+00	49
2.2120298	2.228307e+00	50
2.2283066	2.244865e+00	51
2.2448652	2.259348e+00	52
2.2593477	2.274579e+00	53
2.2745791	2.290074e+00	54
2.2900737	2.305555e+00	55
2.3055553	2.321628e+00	56
2.3216283	2.336763e+00	57
2.3367630	2.352642e+00	58
2.3526424	2.368047e+00	59
2.3680465	2.382880e+00	60
2.3828801	2.397443e+00	61
2.3974431	2.411764e+00	62
2.4117645	2.426611e+00	63
2.4266108	2.441439e+00	64
2.4414390	2.456166e+00	65
2.4561660	2.470464e+00	66
2.4704641	2.485417e+00	67
2.4854167	2.500826e+00	68
2.5008259	2.515759e+00	69
2.5157591	2.531790e+00	70
2.5317904	2.548471e+00	71
2.5484715	2.564502e+00	72
2.5645021	2.580563e+00	73
2.5805634	2.596225e+00	74
2.5962254	2.612206e+00	75
2.6122058	2.629802e+00	76
2.6298023	2.646337e+00	77
2.6463374	2.662708e+00	78
2.6627084	2.680714e+00	79
2.6807143	2.699657e+00	80
2.6996572	2.719246e+00	81
2.7192464	2.738536e+00	82
2.7385362	2.757782e+00	83
2.7577815	2.777288e+00	84
2.7772876	2.797192e+00	85
2.7971922	2.818845e+00	86
2.8188454	2.839567e+00	87
2.8395672	2.861173e+00	88
2.8611734	2.884584e+00	89
2.8845836	2.906797e+00	90
2.9067967	2.931876e+00	91
2.9318760	2.955637e+00	92
2.9556373	2.981927e+00	93
2.9819266	3.010420e+00	94
3.0104196	3.042116e+00	95
3.0421156	3.076537e+00	96
3.0765369	3.118385e+00	97
3.1183851	3.171600e+00	98
3.1715997	3.248494e+00	99
3.2484942	1.000000e+09	100

This results in our final dataset which includes each EPTS variable and the resulting EPTS score for each month a patient is on the wailist.

PX_ID	Age	Dialysis Time	Previous TX	Percentile EPTS
1	59.50000	0.0000000	0	27
1	59.58333	0.0000000	0	27
1	59.66667	0.0000000	0	28
1	59.75000	0.0833333	0	24
1	59.83333	0.1666667	0	25
1	59.91667	0.2500000	0	26
2	36.66667	136.0000000	0	43
2	36.75000	136.0833333	0	43
2	36.83333	136.1666667	0	43
3	28.33333	0.0000000	1	5
3	28.41667	0.0000000	1	5
3	28.50000	0.0000000	1	5
3	28.58333	0.0000000	1	5
3	28.66667	0.0000000	1	5
3	28.75000	0.0000000	1	5
3	28.83333	0.0000000	1	5
3	28.91667	0.0000000	1	5
4	54.58333	366.0000000	0	100
4	54.66667	366.0833333	0	100
4	54.75000	366.1666667	0	100
4	54.83333	366.2500000	0	100
4	54.91667	366.3333333	0	100
4	55.00000	366.4166667	0	100
4	55.08333	366.5000000	0	100
4	55.16667	366.5833333	0	100
4	55.25000	366.6666667	0	100
4	55.33333	366.7500000	0	100
4	55.41667	366.8333333	0	100
4	55.50000	366.9166667	0	100
4	55.58333	367.0000000	0	100
4	55.66667	367.0833333	0	100
4	55.75000	367.1666667	0	100
4	55.83333	367.2500000	0	100
4	55.91667	367.3333333	0	100
4	56.00000	367.4166667	0	100
4	56.08333	367.5000000	0	100
4	56.16667	367.5833333	0	100
4	56.25000	367.6666667	0	100
4	56.33333	367.7500000	0	100
4	56.41667	367.8333333	0	100
4	56.50000	367.9166667	0	100
4	56.58333	368.0000000	0	100
4	56.66667	368.0833333	0	100
4	56.75000	368.1666667	0	100
4	56.83333	368.2500000	0	100
4	56.91667	368.3333333	0	100
4	57.00000	368.4166667	0	100
4	57.08333	368.5000000	0	100
5	54.58333	0.0000000	0	20
5	54.66667	0.0000000	0	20
5	54.75000	0.0000000	0	20
5	54.83333	0.0000000	0	20
5	54.91667	0.0000000	0	21
5	55.00000	0.0000000	0	21
5	55.08333	0.0000000	0	21
5	55.16667	0.0833333	0	18
5	55.25000	0.1666667	0	19
5	55.33333	0.2500000	0	20
5	55.41667	0.3333333	0	20
5	55.50000	0.4166667	0	21
5	55.58333	0.5000000	0	21
5	55.66667	0.5833333	0	22
5	55.75000	0.6666667	0	22
5	55.83333	0.7500000	0	23
5	55.91667	0.8333333	0	24
5	56.00000	0.9166667	0	24
5	56.08333	1.0000000	0	25
5	56.16667	1.0833333	0	25
5	56.25000	1.1666667	0	26
5	56.33333	1.2500000	0	26
5	56.41667	1.3333333	0	27
5	56.50000	1.4166667	0	27
5	56.58333	1.5000000	0	28
5	56.66667	1.5833333	0	29
5	56.75000	1.6666667	0	29
5	56.83333	1.7500000	0	30
5	56.91667	1.8333333	0	30
5	57.00000	1.9166667	0	31
5	57.08333	2.0000000	0	31
6	54.58333	0.0000000	0	20
6	54.66667	0.0000000	0	20
6	54.75000	0.0000000	0	20
6	54.83333	0.0000000	0	20
6	54.91667	0.0000000	0	21
6	55.00000	0.0000000	0	21
6	55.08333	0.0000000	0	21
6	55.16667	0.0000000	0	21
6	55.25000	0.0000000	0	21
6	55.33333	0.0000000	0	21
6	55.41667	0.0000000	0	21
6	55.50000	0.0000000	0	21
6	55.58333	0.0000000	0	21
6	55.66667	0.0000000	0	21
6	55.75000	0.0000000	0	22
6	55.83333	0.0000000	0	22
6	55.91667	0.0000000	0	22
6	56.00000	0.0000000	0	22
6	56.08333	0.0000000	0	22
6	56.16667	0.0000000	0	22
6	56.25000	0.0000000	0	22
6	56.33333	0.0000000	0	22
6	56.41667	0.0000000	0	22
6	56.50000	0.0000000	0	23
6	56.58333	0.0000000	0	23
6	56.66667	0.0000000	0	23
6	56.75000	0.0000000	0	23
6	56.83333	0.0000000	0	23
6	56.91667	0.0000000	0	23
6	57.00000	0.0000000	0	23
6	57.08333	0.0000000	0	23

Patients 5 and 6 are an example of two patients who have the same EPTS characteristics but one patient is put on dialysis and the other is not. As we can see here, when patient 5 is put on dialysis it initially lowers their EPTS, but their EPTS soon increases to its previous level and then continues to increase at a much faster pace than patient 6 who is not on dialysis.

save(df_months, file = "time_varying_data.Rdata")