Models and methods for analysing clustered recurrent hospitalisations in the presence of COVID-19 effects.

Recurrent events such as hospitalisations are outcomes that can be used to monitor dialysis facilities' quality of care. However, current methods are not adequate to analyse data from many facilities with multiple hospitalisations, especially when adjustments are needed for multiple time scales. It is also controversial whether direct or indirect standardisation should be used in comparing facilities. This study is motivated by the need of the Centers for Medicare and Medicaid Services to evaluate US dialysis facilities using Medicare claims, which involve almost 8,000 facilities and over 500,000 dialysis patients. This scope is challenging for current statistical software's computational power. We propose a method that has a flexible baseline rate function and is computationally efficient. Additionally, the proposed method shares advantages of both indirect and direct standardisation. The method is evaluated under a range of simulation settings and demonstrates substantially improved computational efficiency over the existing R package survival. Finally, we illustrate the method with an important application to monitoring dialysis facilities in the U.S., while making time-dependent adjustments for the effects of COVID-19.

Pitfalls of the concordance index for survival outcomes.

Prognostic models are useful tools for assessing a patient's risk of experiencing adverse health events. In practice, these models must be validated before implementation to ensure that they are clinically useful. The concordance index (C-Index) is a popular statistic that is used for model validation, and it is often applied to models with binary or survival outcome variables. In this paper, we summarize existing criticism of the C-Index and show that many limitations are accentuated when applied to survival outcomes, and to continuous outcomes more generally. We present several examples that show the challenges in achieving high concordance with survival outcomes, and we argue that the C-Index is often not clinically meaningful in this setting. We derive a relationship between the concordance probability and the coefficient of determination under an ordinary least squares model with normally distributed predictors, which highlights the limitations of the C-Index for continuous outcomes. Finally, we recommend existing alternatives that more closely align with common uses of survival models.

Concordance indices with left-truncated and right-censored data.

In the context of time-to-event analysis, a primary objective is to model the risk of experiencing a particular event in relation to a set of observed predictors. The Concordance Index (C-Index) is a statistic frequently used in practice to assess how well such models discriminate between various risk levels in a population. However, the properties of conventional C-Index estimators when applied to left-truncated time-to-event data have not been well studied, despite the fact that left-truncation is commonly encountered in observational studies. We show that the limiting values of the conventional C-Index estimators depend on the underlying distribution of truncation times, which is similar to the situation with right-censoring as discussed in Uno et al. (2011) [On the C-statistics for evaluating overall adequacy of risk prediction procedures with censored survival data. Statistics in Medicine 30(10), 1105-1117]. We develop a new C-Index estimator based on inverse probability weighting (IPW) that corrects for this limitation, and we generalize this estimator to settings with left-truncated and right-censored data. The proposed IPW estimators are highly robust to the underlying truncation distribution and often outperform the conventional methods in terms of bias, mean squared error, and coverage probability. We apply these estimators to evaluate a predictive survival model for mortality among patients with end-stage renal disease.

COVID-19 and Hospitalization Among Maintenance Dialysis Patients: A Retrospective Cohort Study Using Time-Dependent Modeling.

Rationale & Objective: The coronavirus disease 2019 (COVID-19) pandemic has had a profound impact on hospitalizations in general and on dialysis patients in particular. This study modeled the impact of COVID-19 on hospitalizations of dialysis patients in 2020. Study Design: Retrospective cohort study. Setting & Participants: Medicare patients on dialysis in calendar year 2020. Predictors: COVID-19 status was divided into 4 stages: COVID1 (first 10 days after initial diagnosis), COVID2 (extends until the Post-COVID stage), Post-COVID (after 21 days with no COVID-19 diagnosis), and Late-COVID (begins after a hospitalization with a COVID-19 diagnosis); demographic and clinical characteristics; and dialysis facilities. Outcome: The sequence of hospitalization events. Analytical Approach: A proportional rate model with a nonparametric baseline rate function of calendar time on the study population. Results: A total of 509,609 patients were included in the study, 63,521 were observed to have a SARS-CoV-2 infection, 34,375 became Post-COVID, and 1,900 became Late-COVID. Compared with No-COVID, all 4 stages had significantly greater adjusted risks of hospitalizations with relative rates of 18.50 (95% CI, 18.19-18.81) for COVID1, 2.03 (95% CI, 1.99-2.08) for COVID2, 1.37 (95% CI, 1.35-1.40) for Post-COVID, and 2.00 (95% CI, 1.89-2.11) for Late-COVID. Limitations: For Medicare Advantage patients, we only had inpatient claim information. The analysis was based on data from the year 2020, and the effects may have changed due to vaccinations, new treatments, and new variants. The COVID-19 effects may be somewhat overestimated due to missing information on patients with few or no symptoms and possible delay in COVID-19 diagnosis. Conclusions: We discovered a marked time dependence in the effect of COVID-19 on hospitalization of dialysis patients, beginning with an extremely high risk for a relatively short period, with more moderate but continuing elevated risks later, and never returning to the No-COVID level.

Analysis of hospital readmissions with competing risks.

The 30-day hospital readmission rate has been used in provider profiling for evaluating inter-provider care coordination, medical cost effectiveness, and patient quality of life. Current profiling analyzes use logistic regression to model 30-day readmission as a binary outcome, but one disadvantage of this approach is that this outcome is strongly affected by competing risks (e.g., death). Thus, one, perhaps unintended, consequence is that if two facilities have the same rates of readmission, the one with the higher rate of competing risks will have the lower 30-day readmission rate. We propose a discrete time competing risk model wherein the cause-specific readmission hazard is used to assess provider-level effects. This approach takes account of the timing of events and focuses on the readmission rates which are of primary interest. The quality measure, then is a standardized readmission ratio, akin to a standardized mortality ratio. This measure is not systematically affected by the rate of competing risks. To facilitate the estimation and inference of a large number of provider effects, we develop an efficient Blockwise Inversion Newton algorithm, and a stabilized robust score test that overcomes the conservative nature of the classical robust score test. An application to dialysis patients demonstrates improved profiling, model fitting, and outlier detection over existing methods.

The Impact of COVID-19 on Postdischarge Outcomes for Dialysis Patients in the United States: Evidence from Medicare Claims Data.

Background: Recent investigations have shown that, on average, patients hospitalized with coronavirus disease 2019 (COVID-19) have a poorer postdischarge prognosis than those hospitalized without COVID-19, but this effect remains unclear among patients with end-stage kidney disease (ESKD) who are on dialysis. Methods: Leveraging a national ESKD patient claims database administered by the US Centers for Medicare and Medicaid Services, we conducted a retrospective cohort study that characterized the effects of in-hospital COVID-19 on all-cause unplanned readmission and death within 30 days of discharge for patients on dialysis. Included in this study were 436,745 live acute-care hospital discharges of 222,154 Medicare beneficiaries on dialysis from 7871 Medicare-certified dialysis facilities between January 1 and October 31, 2020. Adjusting for patient demographics, clinical characteristics, and prevalent comorbidities, we fit facility-stratified Cox cause-specific hazard models with two interval-specific (1-7 and 8-30 days after hospital discharge) effects of in-hospital COVID-19 and effects of prehospitalization COVID-19. Results: The hazard ratios due to in-hospital COVID-19 over the first 7 days after discharge were 95% CI, 1.53 to 1.65 for readmission and 95% CI, 1.38 to 1.70 for death, both with P<0.001. For the remaining 23 days, the hazard ratios were 95% CI, 0.89 to 0.96 and 95% CI, 0.86 to 1.07, with P<0.001 and P=0.50, respectively. Effects of prehospitalization COVID-19 were mostly nonsignificant. Conclusions: In-hospital COVID-19 had an adverse effect on both postdischarge readmission and death over the first week. With the surviving patients having COVID-19 substantially selected from those hospitalized, in-hospital COVID-19 was associated with lower rates of readmission and death starting from the second week.

Kidney Paired Donation Chains Initiated by Deceased Donors.

Introduction: Rather than generating 1 transplant by directly donating to a candidate on the waitlist, deceased donors (DDs) could achieve additional transplants by donating to a candidate in a kidney paired donation (KPD) pool, thereby, initiating a chain that ends with a living donor (LD) donating to a candidate on the waitlist. We model outcomes arising from various strategies that allow DDs to initiate KPD chains. Methods: We base simulations on actual 2016 to 2017 US DD and waitlist data and use simulated KPD pools to model DD-initiated KPD chains. We also consider methods to assess and overcome the primary criticism of this approach, namely the potential to disadvantage blood type O-waitlisted candidates. Results: Compared with shorter DD-initiated KPD chains, longer chains increase the number of KPD transplants by up to 5% and reduce the number of DDs allocated to the KPD pool by 25%. These strategies increase the overall number of blood type O transplants and make LDs available to candidates on the waitlist. Restricting allocation of blood type O DDs to require ending KPD chains with LD blood type O donations to the waitlist markedly reduces the number of KPD transplants achieved. Conclusion: Allocating fewer than 3% of DD to initiate KPD chains could increase the number of kidney transplants by up to 290 annually. Such use of DDs allows additional transplantation of highly sensitized and blood type O KPD candidates. Collectively, patients of each blood type, including blood type O, would benefit from the proposed strategies.

Deceased donors as nondirected donors in kidney paired donation.

As proof of concept, we simulate a revised kidney allocation system that includes deceased donor (DD) kidneys as chain-initiating kidneys (DD-CIK) in a kidney paired donation pool (KPDP), and estimate potential increases in number of transplants. We consider chains of length 2 in which the DD-CIK gives to a candidate in the KPDP, and that candidate's incompatible donor donates to theDD waitlist. In simulations, we vary initial pool size, arrival rates of candidate/donor pairs and (living) nondirected donors (NDDs), and delay time from entry to the KPDP until a candidate is eligible to receive a DD-CIK. Using data on candidate/donor pairs and NDDs from the Alliance for Paired Kidney Donation, and the actual DDs from the Scientific Registry of Transplant Recipients (SRTR) data, simulations extend over 2 years. With an initial pool of 400, respective candidate and NDD arrival rates of 2 per day and 3 per month, and delay times for access to DD-CIK of 6 months or less, including DD-CIKs increases the number of transplants by at least 447 over 2 years, and greatly reduces waiting times of KPDP candidates. Potential effects on waitlist candidates are discussed as are policy and ethical issues.

The profile inter-unit reliability.

To assess the quality of health care, patient outcomes associated with medical providers (eg, dialysis facilities) are routinely monitored in order to identify poor (or excellent) provider performance. Given the high stakes of such evaluations for payment as well as public reporting of quality, it is important to assess the reliability of quality measures. A commonly used metric is the inter-unit reliability (IUR), which is the proportion of variation in the measure that comes from inter-provider differences. Despite its wide use, however, the size of the IUR has little to do with the usefulness of the measure for profiling extreme outcomes. A large IUR can signal the need for further risk adjustment to account for differences between patients treated by different providers, while even measures with an IUR close to zero can be useful for identifying extreme providers. To address these limitations, we propose an alternative measure of reliability, which assesses more directly the value of a quality measure in identifying (or profiling) providers with extreme outcomes. The resulting metric reflects the extent to which the profiling status is consistent over repeated measurements. We use national dialysis data to examine this approach on various measures of dialysis facilities.

KPDGUI: An interactive application for optimization and management of a virtual kidney paired donation program.

BACKGROUND AND OBJECTIVES: The aim in kidney paired donation (KPD) is typically to maximize the number of transplants achieved through the exchange of donors in a pool comprising incompatible donor-candidate pairs and non-directed (or altruistic) donors. With many possible options in a KPD pool at any given time, the most appropriate set of exchanges cannot be determined by simple inspection. In practice, computer algorithms are used to determine the optimal set of exchanges to pursue. Here, we present our software application, KPDGUI (Kidney Paired Donation Graphical User Interface), for management and optimization of KPD programs. METHODS: While proprietary software platforms for managing KPD programs exist to provide solutions to the standard KPD problem, our application implements newly investigated optimization criteria that account for uncertainty regarding the viability of selected transplants and arrange for fallback options in cases where potential exchanges cannot proceed, with intuitive resources for visualizing alternative optimization solutions. RESULTS: We illustrate the advantage of accounting for uncertainty and arranging for fallback options in KPD using our application through a case study involving real data from a paired donation program, comparing solutions produced under different optimization criteria and algorithmic priorities. CONCLUSIONS: KPDGUI is a flexible and powerful tool for offering decision support to clinicians and researchers on possible KPD transplant options to pursue under different user-specified optimization schemes.

Inter-Unit Reliability for Quality Measure Testing.

Facility-specific quality measures are commonly used to monitor dialysis facilities. To successfully develop, test and validate quality measures, a subset of facilities are often recruited for preliminary evaluations. To ensure that the facility-specific measures will achieve a desirable precision, it is often of interest to determine a minimum number of facilities that should be recruited. To achieve this, we propose a method based on the inter-unit reliability (IUR), which is commonly used to assess quality measures. In particular, the confidence intervals of the IUR are calculated, with the width of this confidence interval measuring the precision of the estimate of the IUR. To assess the performance of the estimated IUR with various numbers of facilities, a simulation study is conducted. The IURs are then computed to develop and implement a quality measure that is used to guard against high ultrafiltration rates for adult dialysis patient with End-Stage Renal Disease. The estimated values are helpful to determine a minimum number of facilities that should be recruited in the measure testing process.

An efficient algorithm to enumerate sets with fallbacks in a kidney paired donation program.

Kidney paired donation is a partial solution to overcoming biological incompatibility preventing kidney transplants. A kidney paired donation (KPD) program consists of altruistic or non-directed donors (NDDs) and pairs, each of which comprises a candidate in need of a kidney transplant and her/his willing but incompatible donor. Potential transplants from NDDs or donors in pairs to compatible candidates in other pairs are determined by computer assessment, though various situations involving either the donor, candidate, or proposed transplant may lead to a potential transplant failing to proceed. A KPD program can be viewed as a directed graph with NDDs and pairs as vertices and potential transplants as edges, where failure probabilities are associated with each vertex and edge. Transplants are carried out in the form of directed cycles among pairs and directed paths initiated by NDDs, which we refer to respectively as cycles and chains. Previous research shows that selecting disjoint subgraphs with a view to creating fallback options when failures occur generates more realized transplants than optimal selection of disjoint chains and cycles. In this paper, we define such subgraphs, which are called locally relevant (LR) subgraphs, and present an efficient algorithm to enumerate all LR subgraphs. Its computational efficiency is significantly better than the previous, more restrictive, algorithms.

Inter-unit reliability for nonlinear models.

In monitoring dialysis facilities, various quality measures are used in order to assess the performance and quality of care. The inter-unit reliability (IUR) describes the proportion of variation in the quality measure that is due to the between-facility variation. If the measure under evaluation is a simple average across normally distributed patient outcomes for each facility, the IUR is based on a one-way analysis of variance (ANOVA). However, more complex quality measures are not simple averages of individual outcomes. Even the standard bootstrap methods are inadequate because the computational burden increases quickly as the sample size grows, prohibiting its application in large-scale studies. To generalize the IUR to complex quality measures used in nonlinear models, we propose an approach combining the strengths of ANOVA and resampling. The proposed method is computationally efficient and can be applied to large-scale biomedical data with complex data structures. The method is exemplified in various measures of dialysis facilities using national dialysis data.

Reevaluation of the Kidney Donor Risk Index.

BACKGROUND: The Kidney Donor Risk Index (KDRI) is a score applicable to deceased kidney donors which reflects relative graft failure risk associated with deceased donor characteristics. The KDRI is widely used in kidney transplant outcomes research. Moreover, an abbreviated version of KDRI is the basis, for allocation purposes, of the "top 20%" designation for deceased donor kidneys. Data upon which the KDRI model was based used kidney transplants performed between 1995 and 2005. Our purpose in this report was to evaluate the need to update the coefficients in the KDRI formula, with the objective of either (a) proposing new coefficients or (b) endorsing continued used of the existing formula. METHODS: Using data obtained from the Scientific Registry of Transplant Recipients, we analyzed n = 156069 deceased donor adult kidney transplants occurring from 2000 to 2016. Cox regression was used to model the risk of graft failure. We then tested for differences between the original and updated regression coefficients and compared the performance of the original and updated KDRI formulas with respect to discrimination and predictive accuracy. RESULTS: In testing for equality between the original and updated KDRIs, few coefficients were significantly different. Moreover, the original and updated KDRI yielded very similar risk discrimination and predictive accuracy. CONCLUSIONS: Overall, our results indicate that the original KDRI is robust and is not meaningfully improved by an update derived through modeling analogous to that originally employed.

Valuing Sets of Potential Transplants in a Kidney Paired Donation Network.

In kidney paired donation (KPD), incompatible donor-candidate pairs and non-directed (also known as altruistic) donors are pooled together with the aim of maximizing the total utility of transplants realized via donor exchanges. We consider a setting in which disjoint sets of potential transplants are selected at regular intervals, with fallback options available within each proposed set in the case of individual donor, candidate or match failure. We develop methods for calculating the expected utility for such sets under a realistic probability model for the KPD. Exact expected utility calculations for these sets are compared to estimates based on Monte Carlo samples of the underlying network. Models and methods are extended to include transplant candidates who join KPD with more than one incompatible donor. Microsimulations demonstrate the superiority of accounting for failure probability and fallback options, as well as candidates joining with additional donors, in terms of realized transplants and waiting time for candidates.

Discussion of "Survival models and health sequences" by Walter Dempsey and Peter McCullagh.

This is a discussion of the paper by Dempsey and McCullagh.

Conditional modeling of longitudinal data with terminal event.

We consider a random effects model for longitudinal data with the occurrence of an informative terminal event that is subject to right censoring. Existing methods for analyzing such data include the joint modeling approach using latent frailty and the marginal estimating equation approach using inverse probability weighting; in both cases the effect of the terminal event on the response variable is not explicit and thus not easily interpreted. In contrast, we treat the terminal event time as a covariate in a conditional model for the longitudinal data, which provides a straight-forward interpretation while keeping the usual relationship of interest between the longitudinally measured response variable and covariates for times that are far from the terminal event. A two-stage semiparametric likelihood-based approach is proposed for estimating the regression parameters; first, the conditional distribution of the right-censored terminal event time given other covariates is estimated and then the likelihood function for the longitudinal event given the terminal event and other regression parameters is maximized. The method is illustrated by numerical simulations and by analyzing medical cost data for patients with end-stage renal disease. Desirable asymptotic properties are provided.

A Look-Ahead Strategy for Non-Directed Donors in Kidney Paired Donation.

While there is a growing need for kidney transplants to treat end stage kidney disease, the supply of transplantable kidneys is in serious shortage. Kidney paired donation (KPD) programs serve as platforms for candidates with willing but incompatible donors to assess the possibility of exchanging donors, thus opening up new transplant opportunities for these candidates. In recent years, non-directed (or altruistic) donors (NDDs) have been incorporated into KPD programs beginning chains of transplants that benefit many candidates. In such programs, making optimal decisions in transplant exchange selection is of critical importance. With the aim of improving the selection of chains beginning with an NDD, this paper introduces a look-ahead multiple decision strategy to select chains, that are easy to extend in the future. Simulation studies are adopted to assess performance of this strategy. Taking into account the extensibility of chains increases the number of realized transplants.

A Kidney Graft Survival Calculator that Accounts for Mismatches in Age, Sex, HLA, and Body Size.

BACKGROUND AND OBJECTIVES: Outcomes for transplants from living unrelated donors are of particular interest in kidney paired donation (KPD) programs where exchanges can be arranged between incompatible donor-recipient pairs or chains created from nondirected/altruistic donors. DESIGN, SETTING, PARTICIPANTS, & MEASUREMENTS: Using Scientific Registry of Transplant Recipients data, we analyzed 232,705 recipients of kidney-alone transplants from 1998 to 2012. Graft failure rates were estimated using Cox models for recipients of kidney transplants from living unrelated, living related, and deceased donors. Models were adjusted for year of transplant and donor and recipient characteristics, with particular attention to mismatches in age, sex, human leukocyte antigens (HLA), body size, and weight. RESULTS: The dependence of graft failure on increasing donor age was less pronounced for living-donor than for deceased-donor transplants. Male donor-to-male recipient transplants had lower graft failure, particularly better than female to male (5%-13% lower risk). HLA mismatch was important in all donor types. Obesity of both the recipient (8%-18% higher risk) and donor (5%-11% higher risk) was associated with higher graft loss, as were donor-recipient weight ratios of <75%, compared with transplants where both parties were of similar weight (9%-12% higher risk). These models are used to create a calculator of estimated graft survival for living donors. CONCLUSIONS: This calculator provides useful information to donors, candidates, and physicians of estimated outcomes and potentially in allowing candidates to choose among several living donors. It may also help inform candidates with compatible donors on the advisability of joining a KPD program.