High Dimensional Propensity Score and Cox Models in Anemia Risk Study Related to ADT

(1)

1 Supplemental Digital Content

eMethod 1 High Dimensional Propensity Score Analysis.

eMethod 2 Marginal Structural Cox Proportional Hazards Model.

eTable 1 Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia by Severity.

eTable 2 Crude and Adjusted HRs for the Association Between Time Since Discontinuation and the Risk of Anemia Among Past Users of Androgen Deprivation Therapy

eTable 3 Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia (Varying the Residual Effect Period).

eTable 4 Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia (Stricter Inclusion Criteria).

eTable 5 Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia (relaxed cohort inclusion criterion)

eTable 6 Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia (Excluding and Censoring on Chemotherapy, Radiotherapy, Surgery and Metastasis).

eTable 7 Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia (Censoring on No Hemoglobin Measurement).

eTable 8 Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia (Composite Outcome Definition).

eTable 9 Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia (Multiple Imputation).

eTable 10 Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia (High Density Propensity Score Analysis).

eTable 11 Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia (Marginal Structural Model).

eFigure 1 Study Flow Diagram Describing the Construction of the Study Cohort eFigure 2 Restricted Cubic Spline of Cumulative Duration of ADT Use

eFigure 3 Analyses Assessing the Association Between Current Use of ADT and Anemia Severity.

(2)

2

eFigure 4 Sensitivity Analyses for the Association Between Current Use of ADT and the Risk of Anemia in Patients with Prostate Cancer

eFigure 5 Strength of an Unmeasured Confounder Needed to Move the HR to the Null.

(3)

3 eMethod 1. High dimensional propensity score analysis

Residual confounding was assessed by stratifying subjects into mutually exclusive subsets of high, dimensional propensity score deciles. The high dimensional propensity score is a method that empirically selects covariates based on their prevalence and potential for confounding.¹ Thus, for each patient, we used multivariate logistic regression to calculate a propensity score, i.e. the probability of being exposed to ADT compared to non-use conditional, based upon use within the first 6 months of follow-up, on 500 empirically identified and 19 predefined covariates measured at cohort entry (covariates included in primary analyses as listed in text). The empirical covariates were estimated from 7 data dimensions (drug prescriptions from CPRD, procedures from CPRD and HES, diagnoses from CPRD and HES, disease history from CPRD, and administrative information from CPRD).

References

1. Schneeweiss S, Rassen JA, Glynn RJ, et al: High, dimensional propensity score adjustment in studies of treatment effects using health care claims data. Epidemiology 20:512–22, 2009

(4)

4 eMethod 2. Marginal structural Cox proportional hazards model.

We conducted a marginal structural Cox proportional hazards model to address potential residual time, dependent confounding over the 18 year follow, up period. This method is designed to adjust for time, dependent confounding associated with time, varying exposures.^{1, 2} Firstly, two pooled logistic regression models were fitted to estimate the conditional probability of being exposed to ADT at 30-day intervals during follow, up; one for the numerator and one for the denominator of the stabilized inverse, probability, of, treatment weights (IPTWs). The numerator treatment model included baseline covariates (the covariates included in the primary analysis, listed in the text) and follow-up time. The denominator model included covariates (the same as those listed in the text as well as metastases and radical prostatectomy) measured at each time interval and follow-up time. In both the numerator and denominator models, follow-up time was modelled using a restricted cubic spline with five knots to reduce bias due to model misspecification from linearity assumptions.³We also estimated inverse probability of censoring weights (IPCWs) in a similar fashion. Stabilized IPTW and IPCW for each patient were computed using the predicted probabilities from the two treatment and censoring models. The product of these stabilized IPTWs and IPCWs was then used to reweight the cohort, in which we estimated the hazard ratios of anemia associated with the use of ADT, with 95% confidence intervals, calculated using robust variance estimators.²

References

1. Robins JM, Hernán MA, Brumback B: Marginal structural models and causal inference in epidemiology. Epidemiology 11:550–60, 2000

2. Hernán MA, Brumback B, Robins JM: Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV, positive men. Epidemiology 11:561–70, 2000 3. Cole SR, Hernán MA: Constructing inverse probability weights for marginal structural models. Am J Epidemiol 168:656–64, 2008

(5)

5 Abbreviations: ADT, androgen deprivation therapy, CI, confidence interval, GnRH, gonadotropin, releasing hormone, HR, hazard ratio

a Per 100 Person, Years.

b Adjusted for age, year of prostate cancer diagnosis, alcohol, related disorders, smoking status, body mass index, prostate-specific antigen, previous cancer (other than non, melanoma skin cancer), previous chemotherapy, previous radiation therapy, chronic obstructive pulmonary disease, chronic kidney disease, Crohn’s disease, ulcerative colitis, rheumatoid arthritis, previous gastrointestinal bleed, surgery (measured in the 3 months prior to cohort entry), and the use of aspirin, other non-steroidal anti-inflammatory drugs, warfarin, and antiplatelets

* The risk for mild, moderate and severe anemia was assessed separately, with categories modelled as mutually non-exclusive events.

eTable 1 Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia by severity*

Exposure to ADT Events Person,

years Incidence rate(95% CI)^a Crude HR^b Adjusted HR (95% CI)^b Mild (110, 129g/l)

Non use 839 15, 964 5.3 (4.9, 5.6) 1.00 [Reference] 1.00 [Reference]

Current use 2048 9851 20.8 (19.9, 21.7) 3.76 2.88 (2.63, 3.15)

Past use 375 6004 6.2 (5.6, 6.9) 1.36 1.26 (1.11, 1.43)

Moderate (80, 109g/l)

Current use 761 13, 114 5.8 (5.4, 6.2) 5.54 4.00 (3.34, 4.79)

Past use 147 7766 1.9 (1.6, 2.2) 1.58 1.44 (1.15, 1.80)

Severe (< 80g/l)

Current use 68 13, 581 0.5 (0.4, 0.6) 4.50 3.43 (1.96, 5.99)

Past use 28 7972 0.4 (0.2, 0.5) 2.79 2.50 (1.36, 4.58)

(6)

6 eTable 2. Crude and Adjusted HRs for the Association Between Time Since Discontinuation and the Risk of Anemia Among Past Users of Androgen Deprivation Therapy

Events Person,

years Incidence rate(95% CI)^a Crude HR Adjusted HR (95% CI)^b

Non use 940 15, 872 5.9 (5.5, 6.3) 1.00 [Reference] 1.00 [Reference]

Time since ADT

discontinuation, months

< 6 126 1035 12.2 (10.1, 14.5) 2.12 1.88 (1.55, 2.27)

6, 12 63 808 7.8 (6.0, 10.0) 1.43 1.32 (1.02, 1.71)

13, 18 44 669 6.6 (4.8, 8.8) 1.28 1.21 (0.89, 1.65)

19, 24 39 568 6.9 (4.9, 9.4) 1.34 1.28 (0.92, 1.77)

≥ 25 148 2869 5.2 (4.4, 6.1) 1.00 0.95 (0.79, 1.15)

Abbreviations: ADT, androgen deprivation therapy; CI, confidence interval; HR, hazard ratio.

Note: This analysis was conducted among the 420 events in the past use exposure category. The current use exposure category is not displayed in the table, but was considered in the regression model for proper estimation of treatment effects.

a Per 100 person, years.

(7)

7 eTable 3. Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia (varying residual effect period)

years Incidence rate^a (95% CI) Crude HR Adjusted HR (95% CI)^b 90-day grace period

Current use 2216 9328 23.8 (22.8, 24.8) 3.80 2.91 (2.67, 3.17)

Past use 495 6375 7.8 (7.1, 8.5) 1.48 1.38 (1.23, 1.55)

1-year grace period

Current use 2372 10, 469 22.7 (21.8, 23.6) 3.69 2.84 (2.61, 3.09)

Past use 339 5234 6.5 (5.8, 7.2) 1.25 1.18 (1.03, 1.34)

Abbreviations: ADT, androgen deprivation therapy, CI, confidence interval, HR, hazard ratio

b Adjusted for age, year of prostate cancer diagnosis, alcohol, related disorders, smoking status, body mass index, prostate-specific antigen, previous cancer (other than non, melanoma skin cancer), previous chemotherapy, previous radiation therapy, chronic obstructive pulmonary disease, chronic kidney disease, Crohn’s disease, ulcerative colitis, rheumatoid arthritis, previous gastrointestinal bleed, surgery (measured in the 3 months prior to cohort entry), and the use of aspirin, other non-steroidal anti-inflammatory drugs, warfarin, and antiplatelets.

(8)

8 eTable 4. Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia (stricter inclusion criteria*)

years Incidence rate^a (95% CI) Crude HR Adjusted HR (95% CI)^b

Current use 2234 9656 23.1 (22.2, 24.1) 3.88 2.98 (2.73, 3.25)

Past use 407 5920 6.9 (6.2, 7.6) 1.35 1.26 (1.12, 1.43)

* Including patients with at least two hemoglobin results in the normal range recorded in CPRD in the year preceding prostate cancer diagnosis.

(9)

9 eTable 5 . Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia (relaxed cohort inclusion criterion)*

Exposure to ADT Events Person-

years

Incidence rate^a (95% CI)

Crude HR Adjusted HR (95% CI)^b

Non use 1766 34,534 5.1 (4.9, 5.4) 1.00 [Reference] 1.00 [Reference]

Current use 4005 19,949 20.1 (19.5, 20.7) 3.85 2.88 (2.71, 3.07)

Past use 794 12,727 6.2 (5.8, 6.7) 1.37 1.26 (1.15, 1.37)

a Per 100 Person-Years.

b Adjusted for age, year of prostate cancer diagnosis, excessive alcohol use, smoking status, body mass index, prostate-specific antigen, chronic obstructive pulmonary disease, chronic kidney disease, Crohn’s disease, ulcerative colitis, rheumatoid arthritis, previous record of GI bleeds (ever recorded prior to cohort entry) and the use of aspirin, other NSAIDs, warfarin, and antiplatelets (measured in the year prior to cohort entry)

* Cohort includes 19,423 patients

(10)

10 eTable 6. Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia (excluding and censoring on chemotherapy, radiotherapy, surgery and metastasis)

Non use 329 6059 5.4 (4.9, 6.0) 1.00 [Reference] 1.00 [Reference]

Current use 1111 5270 21.1 (19.9, 22.4) 3.73 3.00 (2.63, 3.44)

Past use 144 2198 6.6 (5.5, 7.7) 1.34 1.37 (1.11, 1.68)

b Adjusted for age, year of prostate cancer diagnosis, excessive alcohol use, smoking status, body mass index, prostate-specific antigen, chronic obstructive pulmonary disease, chronic kidney disease, Crohn’s disease, ulcerative colitis, rheumatoid arthritis, previous record of gastrointestinal bleeds and the use of aspirin, other non-steroidal anti-inflammatory drugs, warfarin, and antiplatelets .

(11)

11 eTable 7. Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia (censoring on no

haemoglobin measurement* )

Non use 538 6680 8.1 (7.4, 8.8) 1.00 [Reference] 1.00 [Reference]

Current use 1226 4905 25.0 (23.6, 26.4) 2.98 2.47

Past use 94 982 9.6 (7.7, 11.7) 1.45 1.37

* Censoring on no hemoglobin measurements in the year after cohort entry as well as those patients with no repeat hemoglobin measurements within one year of each other

(12)

12 eTable 8. Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia (composite outcome definition)*

Exposure to ADT Events Person-years Incidence rate^a (95% CI)

Crude HR Adjusted HR (95% CI)^b

Non use 2222 34,534 6.4 (6.2, 6.7) 1.00 [Reference] 1.00 [Reference]

Current use 4441 19,949 22.3 (21.6, 22.9) 3.41 2.55 (2.41, 2.70)

Past use 957 12,727 7.5 (7.1, 8.0) 1.32 1.22 (1.13, 1.32)

a Per 100 Person-Years.

b Adjusted for age, year of prostate cancer diagnosis, excessive alcohol use, smoking status, body mass index, prostate-specific antigen, chronic obstructive pulmonary disease, chronic kidney disease, Crohn’s disease, ulcerative colitis, rheumatoid arthritis, previous record of GI bleeds (ever recorded prior to cohort entry) and the use of aspirin, other NSAIDs, warfarin, and antiplatelets (measured in the year prior to cohort entry)

* Cohort defined using relaxed cohort criterion (N=19,423). Outcome defined using a diagnosis code for anemia, hemoglobin measurement below the normal range (<130g/dl) or receipt of anemia treatments or procedure (including iron supplements, folic acid, vitamin B12, erythropoietin and blood transfusion).

(13)

13 eTable 9. Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia (multiple imputation)

years

Incidence rate^a (95% CI) Crude HR Adjusted HR (95% CI)^b

Current use 2291 9755 23.5 (22.5, 24.5) 3.78 2.92 (2.68, 3.18)

Past use 420 5948 7.1 (6.4, 7.8) 1.36 1.26 (1.12, 1.43)

(14)

14 eTable 10. Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of

Anemia (High dimensional propensity score analysis) Exposure to ADT Events Person,

years

Incidence rate^a

(95% CI) Crude HR Adjusted HR (95% CI)^b No use 262 5559 4.7 (4.2, 5.3) 1.00 [Reference] 1.00 [Reference]

Current use 820 3342 24.5 (22.9, 26.3) 4.92 3.91 (3.25, 4.71)

b Stratified by HDPS deciles

(15)

15 eTable 11. Crude and Adjusted HRs for the Association Between the Use of ADT and the Risk of Anemia (Marginal structural model ) Exposure to ADT Events Person, months Incidence rate^a (95% CI) Crude HR in weighted model Adjusted HR in weighted

model (95% CI)^b

Current use 2313 124, 704 1.9 (1.8, 1.9) 3.55 2.76 (2.52, 3.02)

Past use 398 71, 630 0.6 (0.5, 0.6) 1.30 1.21 (1.06, 1.38)

(16)

16 eFigure 1 Study flow diagram describing the construction of the study cohort

Figure 1 Figure 1

6991 Excluded

3685 < 1 year of medical history prior to cohort entry 255 Date inconsistencies

8 < 40 years of age

2109 Prior use of androgen deprivation therapy 934 Metastatic disease at diagnosis

Bone (n=566) Lymph (n=132) Visceral (n=128) Other (n=108)

12,251 Excluded

9542 No hemoglobin test in the year prior to diagnosis 2709 Last hemoglobin level recorded in CPRD in the year prior to diagnosis not in normal range

10,364 Patients included in the study cohort

718 Excluded

189 History of hematological malignancies and disorders 19 Blood transfusion in the year prior

501 Medications used to treat anaemia in the year prior

9 No follow-up 11,082 Patients with prostate cancer

with normal hemoglobin levels at diagnosis

23,333 Patients with prostate cancer 30,324 Patients with a first-ever

diagnosis of prostate cancer between April 1, 1998 and September 30, 2015

(17)

17 eFigure 2 Restricted cubic spline of cumulative duration of ADT use

Smooth restricted spline curve of adjusted hazard ratio of anemia (solid line) and 95% confidence limits (dashed lines) as function of cumulative duration of ADT use

(18)

18 eFigure 3 Analyses assessing the association between current use of ADT and anemia severity.

The risk for mild, moderate and severe anemia was assessed separately, with categories modeled as mutually non-exclusive events. The reference category was non-use of androgen deprivation therapy

(19)

19 eFigure 4 Sensitivity analyses for the association between current use of ADT and the risk of anemia in patients with prostate cancer

*The reference category for all analyses was non-use of androgen deprivation therapy.

a Inclusion criteria required at least two hemoglobin measurements in the year prior to cohort entry in the normal range.

b Cohort definition included patients with no hemoglobin measurement prior to cohort entry and excluded those with a diagnosis of anemia, abnormal hemoglobin measurements or treatment for anemia in the year prior to diagnosis.

c Additional censoring included new metastases and receipt of chemotherapy during follow up.

d Utilized cohort definition outlined in ^b. Composite outcome included a diagnosis code for anemia, abnormal hemoglobin measurement or a treatment for anemia.

e Androgen deprivation therapy exposure was based on use within the first 6 months of follow-up.

(20)

20 eFigure 5: Strength of an unmeasured confounder needed to move the HR to the null.

Based on an observed HR of 2.90, an ADT prevalence of 31%, and a confounder prevalence of 20%. Blue line: observed hazard ratio (HR); Green line: lower bound of the confidence intervals. ORExposure, Confounder: odds ratio for the exposure, confounder association; RRConfounder, Disease: relative risk for the confounder, disease association.

Exposure, confounder and confounder, disease associations to the right of the curves would be necessary to bring the association down to the null.

0 5 10 15 20 25 30

ORExposure,Confounder

RRConfounder,Disease

Observed HR=2.90 Lower 95% CI= 2.67