Estimating Causal Effects of Organ Transplantation Treatment Regimes

Transcription

1 Estimating Causal Effects of Organ Transplantation Treatment Regimes David M. Vock, Jeffrey A. Verdoliva Boatman Division of Biostatistics University of Minnesota July 31, / 27

2 Hot off the Press Biometrics DOI: /biom Estimating the Causal Effect of Treatment Regimes for Organ Transplantation Jeffrey A. Boatman and David M. Vock * Division of Biostatistics, School of Public Health, University of Minnesota, A460 Mayo Building, MMC 303, 420 Delaware St. SE, Minneapolis, Minnesota 55455, U.S.A. vock@umn.edu Summary. Patients awaiting cadaveric organ transplantation face a difficult decision if offered a low-quality organ: accept the organ or remain on the waiting list and hope a better organ is offered in the future. A dynamic treatment regime (DTR) for transplantation is a rule that determines whether a patient should decline an offered organ. Existing methods can estimate the effect of DTRs on survival outcomes, but these were developed for applications where treatment is abundantly available. For transplantation, organ availability is limited, and existing methods can only estimate the effect of a DTR assuming a single patient follows the DTR. We show for transplantation that the effect of a DTR depends on whether other patients follow the DTR. To estimate the anticipated survival if the entire population awaiting transplantation were to adopt a DTR, we develop a novel inverse probability weighted estimator (IPCW) which re-weights patients based on the probability of following their transplant history in the counterfactual world in which all patients follow the DTR of interest. We estimate this counterfactual probability using hot deck imputation to fill in data that is not observed for patients who are artificially censored by IPCW once they no longer follow the DTR of interest. We show via simulation that our proposed method has good finite-sample properties, and we apply our method to a lung transplantation observational registry. Key words: Causal inference; Dynamic treatment regimes; Inverse probability weighting; Lung transplantation. 1. Introduction Determining an optimal rule or regime that dictates when a patient should start treatment is an important step in personalizing medicine (Cain et al., 2010). However, determining Although accepting low-quality lungs may lead to poor posttransplant prognosis, declining offered lungs and remaining on the waiting list is not without risk: the LAS system effectively allocates lungs to patients most in need, but it does 2 / 27

3 Deceased Donor Organ Offers in the United States More patients in need organ transplant than organs available In 2015, 122,071 waiting at year end, 30,975 transplants performed, and 15,068 donors recovered United Network for Organ Sharing (UNOS) responsible for orderly offering deceased donor organs Order in which deceased donor organs offered to recipients a deterministic function (urgency, benefit, geography, organ quality, fairness) 3 / 27

4 Donor Lung Offers in the United States Lung Allocation in the United States. Left figure from Colvin-Adams (2012) 4 / 27

5 Organ Acceptance Each time an organ is offered to a recipient it may be turned down Many competing factors go into organ acceptance 1. Patient 2. Surgeon 3. Transplant Center 4. Organ Procurement Organization 5. Other Patients on Waiting List 5 / 27

6 Treatment Regimes for Organ Transplantation Patients awaiting organ transplantation face a difficult decision if offered a low-quality organ: Accept the organ Decline the organ, hope to be offered a higher quality one in the future Testing the effect of personalized decision rules (dynamic transplant regimes) would be helpful here. 6 / 27

7 Transplant Regimes Treatment regimes of interest: Rules which dictate when an offered organ should be declined Treatment regimes for transplantation tend to be poorly-defined : There is not a 1-to-1 correspondence between patient covariate history and treatment Transplants are not available at any time We cannot easily specify treatment regimes such as Get a transplant as soon as LAS > 50 because these regimes are not clinically meaningful Avoid regimes which dictate if an organ should be accepted 7 / 27

8 Time-varying Treatment and Time-varying Confounding No randomized trials of different transplant regimes Necessitates the use observational datasets and appropriate methods Inverse probability of compliance estimators 1. Patient s follow-up time is considered only while she is compliant with a regime of interest 2. Once non-compliant, her follow-up time is artificially censored 3. Observations are weighted according to the inverse of probability of compliance to correct for the potential selection bias introduced by the artificial censoring 8 / 27

9 Limitations of Existing Methods Problem: Anticipated survival for a given DTR depends on the quality and availability of organs, and these depend on the strategies that other patients follow to accept or decline an organ Here the probability of initiating treatment depends on the treatment regime other patients follow Conceptually similar, although not identical, to the spillover effect described in other contexts Refer to this as transplant regime spillover Existing methods have a major limitation here: They estimate the causal effect of a treatment regime for a single random participant who adopts the treatment regime But the causal effect if all patients were to adopt the treatment regime may have more public health relevance 9 / 27

10 Goal and Outline Develop weighted causal estimators for both cases: One follows All follow Develop estimators: Assuming we have data from an observational registry Avoid modeling the many random processes: patient arrival, organ arrival, etc / 27

11 Notation Notation: L i : listing time for ith patient N ij, Y ij : failure and at-risk indicators for ith patient on jth study day X ij : patient characteristics including confounders A ijk : indicator for accepting kth organ on the jth study day A ij : treatment history through the jth day O ijk : indicator for offered kth organ on jth study E jk to be the collection of information on all subjects prior to assigning the kth organ on the jth study day day Causal estimand: λ t (g, g ): hazard of death t days after entering the waiting list, and the associated survival S t (g, g ) 11 / 27

12 Components of the weights π (, ) ij ( Aij, E jsj ) = j j =1 S j k=1 π(, ) ijk ( ) Aij k, E j k : The probability of the observed treatment history assuming all patients follow regime (no changes in propensity to accept or decline organs) π (g,g ) ij ( Aij, E jsj ) = j j =1 S j k=1 π(g,g ) ijk ( ) Aij k, E j k :The probability of the observed treatment history in the counterfactual world where ith patient follows regime g and all others follow g 12 / 27

13 Estimating λ t (g, g ) We can estimate λ t (g, g ) by solving the estimating equation m n j=1 i=1 π (g,g ) ij π (, ) ij ( Aij, E jsj ) ( Aij, E jsj ) { N ij Y ij λ t (g, g ) } I (j L i = t) = 0 Intuition for the weights π(g,g ij Similar to IPCW π (, ) ij ) ) (A ij,e jsj ) : (A ij,e jsj Standardize to the target population where probability of A ij is different Mean zero estimating function estimator for λ t (g, g ) is CAN 13 / 27

14 Estimating π (, ) ( ) ij Aij, E jsj with the Observed Data π (, ) ij ( Aij, E jsj ) is a function of the probability of being offered, and the probability of accepting if offered: Pr(A ij = 1) = Pr(O ij = 1) Pr(A ij = 1 O ij = 1) Pr(A ij = 0) = 1 Pr(O ij = 1) Pr(A ij = 1 O ij = 1) Estimating Pr(O = 1) is straightforward provided I have a model for Pr(A = 1 O = 1) 14 / 27

15 Estimating π (g,g ) ( ) ij Aij, E jsj with the Observed Data This is more challenging. The numerator is the expectation of the probability of being offered and accepting organs in the hypothetical world where all patients follow regime g given the observed data. π (g,g ) ijk (1, E jk ) = E(π (g,g ) ijk (1, E (g,g ) jk ) E jk ) If all patients follow regime g : We don t know which patients would be on the waiting list We don t know what their characteristics would be The probability of being offered an organ can t be directly computed from the observed data Sample E (g,g ) jk from E jk use Monte Carlo integration to evaluare expectation 15 / 27

16 Estimating π (g,g ) ( ) ij Aij, E jsj ID LAS A Pr(A = 1 O = 1) Pr(O = 1) Pr(A) ??? 0.437? ?? 491????? ?? ?? ?? 16 / 27

17 Estimating π (g,g ) ( ) ij Aij, E jsj Hot Deck Imputation: For all transplant recipients, impute missing data assuming never transplanted by borrowing data from their nearest neighbor, the lender Simulate the organ allocation when everyone follows g, assuming model for accepting organs holds Assume low quality organs are accepted with probability 0 We ve created a hypothetical data set where all patients follow g. 17 / 27

18 After Imputation Assume the organ is defined as high quality under g ID LAS A Pr(A = 1 O = 1) Pr(O = 1) Pr(A) / 27

19 After Assigning Organ Under g, g Assume the organ is defined as high quality under g ID LAS A A (g,g ) Pr(A = 1 O = 1) Pr(O = 1) Pr(A) / 27

20 Simulation Study Estimation: Estimated survival for regime g: decline all low- quality organs Estimated survival assuming one follows and all follow Hot deck ( imputation: lender i for patient i selected as arg min Xij X i j : j L i = j ) L i i Nonparametric bootstrap to estimate standard errors (SEs) and form 95% confidence intervals (CI) 20 / 27

21 Simulation Results Bias Target t Truth Ŝ t (g, ) Ŝ t (g, g) Ŝ t (g, ) Ŝ t (g, g) S t (g, ) S t (g, g) CP 21 / 27

22 Application Data are from an observational registry maintained by the United Network for Organ Sharing May 4, 2005-Sept 30, ,091 transplants 13,039 patients total Treatment regimes: Decline organs below pth percentile of donor quality while LAS < M; if LAS M, any organ is acceptable p and M can both vary Estimated anticipated survival assuming one follows the regime, or all follow the regime. 22 / 27

23 Application Results Cumulative Probability of Death (a) Decline All Organs Until LAS Exceeds 50 Kaplan Meier Survival One Participant Follows Regime All Participants Follow Regime Years From Entering Waitlist 23 / 27

24 Application Results Cumulative Probability of Death (b) All Follow Regime 'Decline All Organs Until LAS Exceeds Cutoff' Kaplan Meier Survival LAS Cutoff = 35 LAS Cutoff = 40 LAS Cutoff = 45 LAS Cutoff = Years From Entering Waitlist 24 / 27

25 Application Results Cumulative Probability of Death (d) One Follows Regime 'Decline Worst p% of Organs Until LAS Exceeds 50' Kaplan Meier Survival p = 25 p = 50 p = 75 p = Years From Entering Waitlist 25 / 27

26 Summary Simulation shows: Estimators have little bias for their target Causal estimand must be specified with care Application One follows and all follows are different Patients may gain a modest increase in survival probability by declining transplantation while LAS is low Effect may be greater if the entire population adopts the strategy 26 / 27

27 Summary Thank you! 27 / 27