In analyzing clustered data, random effects (RE) and fixed effects (FE) models are two primary approaches. The RE model assumes that the cluster-specific effects are random and uncorrelated with individual characteristics. If this assumption is violated, the RE approach can lead to biased estimates of the coefficients of individual covariates and cluster effects. In contrast, the FE approach, which models cluster effects as fixed effects, yields unbiased estimates even if the cluster effects are correlated with individual covariates. Numerous studies have compared the FE and RE approaches. However, the practical importance of the biases observed in RE-based methods remains unclear. Some studies have demonstrated significant biases in RE models when the assumption of no correlation is violated, whereas others have found these biases to be negligible. These differences may be due to variations in study design, with some evaluations focusing on settings that may not reflect realistic data scenarios. In this paper, we compare FE and RE models through theoretical evaluation, simulation studies, and real-data applications. Specifically, we derive an approximate formula to quantify the asymptotic bias in the RE model and verify its accuracy through simulations. These results help to explain the different conclusions reached in the existing literature. Our goal is not to propose a new estimator or a fundamentally new inferential framework, but to provide an analytical clarification and practical quantification of the bias incurred by the standard RE estimator under a specific, interpretable dependence model, and to clarify how this bias relates to fixed-effects and correlated random-effects/between-within specifications.

In this work we study the lifetime Medicare spending patterns of patients with end-stage renal disease (ESRD). We extract the information of patients who started their ESRD services in 2007-2011 from the United States Renal Data System (USRDS). Patients are partitioned into three groups based on their kidney transplant status: 1-unwaitlisted and never transplanted, 2waitlisted but never transplanted, and 3-waitlisted and then transplanted. To study their Medicare cost trajectories, we use a semiparametric regression model with both fixed and bivariate time-varying coefficients to compare groups 1 and 2 as well as a bivariate time-varying coefficient model with different starting times (time since the first ESRD service and time since the kidney transplant) to compare groups 2 and 3. In addition to demographics and other medical conditions, these regression models are conditional on the survival time, which ideally depict the lifetime Medicare spending patterns. For estimation we extend the profile weighted least squares (PWLS) estimator to longitudinal data for the first comparison and propose a two-stage estimating method for the second comparison. We use sandwich variance estimators to construct confidence intervals and validate inference procedures through simulations. Our analysis of the Medicare claims data reveals that waitlisting is associated with a lower daily medical cost at the beginning of ESRD service among waitlisted patients, which gradually increases over time. Averaging over lifespan, however, there is no difference between waitlisted and unwaitlisted groups. A kidney transplant, on the other hand, reduces the medical cost significantly after an initial spike.

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.

The coronavirus disease 2019 (COVID-19) pandemic has exerted a profound impact on patients with end-stage renal disease relying on kidney dialysis to sustain their lives. A preliminary analysis of dialysis patient postdischarge hospital readmissions and deaths in 2020 revealed that the COVID-19 effect has varied significantly with postdischarge time and time since the pandemic onset. However, the complex dynamics cannot be characterized by existing varying coefficient models. To address this issue, we propose a bivariate varying coefficient model for competing risks, where tensor-product B-splines are used to estimate the surface of the COVID-19 effect. An efficient proximal Newton algorithm is developed to facilitate the fitting of the new model to the massive data for Medicare beneficiaries on dialysis. Difference-based anisotropic penalization is introduced to mitigate model overfitting and effect wiggliness; a cross-validation method is derived to determine optimal tuning parameters. Hypothesis testing procedures are designed to examine whether the COVID-19 effect varies significantly with postdischarge time and the time since the pandemic onset, either jointly or separately. Applications to Medicare dialysis patients demonstrate the real-world performance of the proposed methods. Simulation experiments are conducted to evaluate the estimation accuracy, Type I error rate, statistical power, and model selection procedures. Supplementary materials for this article are available online.

We propose a nonparametric bivariate time-varying coefficient model for longitudinal measurements with the occurrence of a terminal event that is subject to right censoring. The time-varying coefficients capture the longitudinal trajectories of covariate effects along with both the followup time and the residual lifetime. The proposed model extends the parametric conditional approach given terminal event time in recent literature, and thus avoids potential model misspecification. We consider a kernel smoothing method for estimating regression coefficients in our model and use cross-validation for bandwidth selection, applying undersmoothing in the final analysis to eliminate the asymptotic bias of the kernel estimator. We show that the kernel estimates are asymptotically normal under mild regularity conditions, and provide an easily computable sandwich variance estimator. We conduct extensive simulations that show desirable performance of the proposed approach, and apply the method to analyzing the medical cost data for patients with end-stage renal disease.

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.

On average, randomization achieves balance in covariate distributions between treatment groups; yet in practice, chance imbalance exists post randomization, which increases the error in estimating treatment effects. This is an important issue, especially in cluster randomized trials, where the experimental units (the clusters) are highly heterogeneous and relatively few in number. To address this, several restricted randomization designs have been proposed to balance on a few covariates of particular interest. More recently, approaches involving rerandomization have been proposed that aim to achieve simultaneous balance on several important prognostic factors. In this article, we comment on some properties of rerandomized designs and propose a new design for comparing two or more treatments. This design combines optimal nonbipartite matching of the subjects together with rerandomization, both aimed at minimizing a measure of distance between elements in blocks to achieve reductions in the mean squared error of estimated treatment effects. Compared with the existing alternatives, the proposed design can substantially reduce the mean squared error of the estimated treatment effect. This enhanced efficiency is evaluated both theoretically and empirically, and robustness properties are also noted. The design is generalized to three or more treatment arms.

The Cox model is now 50 years old. The seminal paper of Sir David Cox has had an immeasurable impact on the analysis of censored survival data, with applications in many different disciplines. This work has also stimulated much additional research in diverse areas and led to important theoretical and practical advances. These include semiparametric models, nonparametric efficiency, and partial likelihood. In addition to quickly becoming the go-to method for estimating covariate effects, Cox regression has been extended to a vast number of complex data structures, to all of which the central idea of sampling from the set of individuals at risk at time t can be applied. In this article, we review the Cox paper and the evolution of the ideas surrounding it. We then highlight its extensions to competing risks, with attention to models based on cause-specific hazards, and to hazards associated with the subdistribution or cumulative incidence function. We discuss their relative merits and domains of application. The analysis of recurrent events is another major topic of discussion, including an introduction to martingales and complete intensity models as well as the more practical marginal rate models. We include several worked examples to illustrate the main ideas.

Key Points We studied the effect of coronavirus disease 2019 (COVID-19) on the 30-day postdischarge outcomes of patients with end-stage kidney disease who are on dialysis.During the first postdischarge week, patients on dialysis who were hospitalized with COVID-19 were more likely to experience readmission and death.After the first week, there was no marked difference in the risks of readmission and death between patients with COVID-19 and those without. 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.

Monitoring outcomes of health care providers, such as patient deaths, hospitalizations and hospital readmissions, helps in assessing the quality of health care. We consider a large database on patients being treated at dialysis facilities in the United States, and the problem of identifying facilities with outcomes that are better than or worse than expected. Analyses of such data have been commonly based on random or fixed facility effects, which have shortcomings that can lead to unfair assessments. A primary issue is that they do not appropriately account for variation between providers that is outside the providers' control due, for example, to unobserved patient characteristics that vary between providers. In this article, we propose a smoothed empirical null approach that accounts for the total variation and adapts to different provider sizes. The linear model provides an illustration that extends easily to other nonlinear models for survival or binary outcomes, for example. The empirical null method is generalized to allow for some variation being due to quality of care. These methods are examined with numerical simulations and applied to the monitoring of survival in the dialysis facility data.

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.

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.

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.

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.

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.

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.

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.

Background and objectivesThe 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.MethodsWhile 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.ResultsWe 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.ConclusionsKPDGUI 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.

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.

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.