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.

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.

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.

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.

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

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

A weighted cumulative sum (WCUSUM) to monitor medical outcomes with dependent censoring.

We develop a weighted cumulative sum (WCUSUM) to evaluate and monitor pre-transplant waitlist mortality of facilities in the context where transplantation is considered to be dependent censoring. Waitlist patients are evaluated multiple times in order to update their current medical condition as reflected in a time-dependent variable called the Model for End-Stage Liver Disease (MELD) score. Higher MELD scores are indicative of higher pre-transplant death risk. Moreover, under the current liver allocation system, patients with higher MELD scores receive higher priority for liver transplantation. To evaluate the waitlist mortality of transplant centers, it is important to take this dependent censoring into consideration. We assume a 'standard' transplant practice through a transplant model and utilize inverse probability censoring weights to construct a WCUSUM. We evaluate the properties of a weighted zero-mean process as the basis of the proposed WCUSUM. We then discuss a resampling technique to obtain control limits. The proposed WCUSUM is illustrated through the analysis of national transplant registry data.

CONFIDENCE INTERVALS UNDER ORDER RESTRICTIONS.

In this paper, we consider the problem of constructing confidence intervals (CIs) for G independent normal population means subject to linear ordering constraints. For this problem, CIs based on asymptotic distributions, likelihood ratio tests and bootstraps do not have good properties particularly when some of the population means are close to each other. We propose a new method based on defining intermediate random variables that are related to the original observations and using the CIs of the means of these intermediate random variables to restrict the original CIs from the separate groups. The coverage rates of the intervals are shown to exceed, but be close to, the nominal level for two groups, when the ratio of the variances is assumed known. Simulation studies show that the proposed CIs have coverage rates close to nominal levels with reduced average widths. Data on half-lives of an antibiotic are analyzed to illustrate the method.

Decision Making in Kidney Paired Donation Programs with Altruistic Donors.

In recent years, kidney paired donation (KPD) has been extended to include living non-directed or altruistic donors, in which an altruistic donor donates to the candidate of an incompatible donor-candidate pair with the understanding that the donor in that pair will further donate to the candidate of a second pair, and so on; such a process continues and thus forms an altruistic donor-initiated chain. In this paper, we propose a novel strategy to sequentially allocate the altruistic donor (or bridge donor) so as to maximize the expected utility; analogous to the way a computer plays chess, the idea is to evaluate different allocations for each altruistic donor (or bridge donor) by looking several moves ahead in a derived look-ahead search tree. Simulation studies are provided to illustrate and evaluate our proposed method.

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.

Kernel Estimation of Bivariate Time-varying Coefficient Model for Longitudinal Data with Terminal Event.

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 follow a finite-dimensional normal distribution asymptotically under mild regularity conditions, and provide an easily computed sandwich covariance matrix 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.

A risk-adjusted O-E CUSUM with monitoring bands for monitoring medical outcomes.

In order to monitor a medical center's survival outcomes using simple plots, we introduce a risk-adjusted Observed-Expected (O-E) Cumulative SUM (CUSUM) along with monitoring bands as decision criterion.The proposed monitoring bands can be used in place of a more traditional but complicated V-shaped mask or the simultaneous use of two one-sided CUSUMs. The resulting plot is designed to simultaneously monitor for failure time outcomes that are "worse than expected" or "better than expected." The slopes of the O-E CUSUM provide direct estimates of the relative risk (as compared to a standard or expected failure rate) for the data being monitored. Appropriate rejection regions are obtained by controlling the false alarm rate (type I error) over a period of given length. Simulation studies are conducted to illustrate the performance of the proposed method. A case study is carried out for 58 liver transplant centers. The use of CUSUM methods for quality improvement is stressed.

Repeated randomization and matching in multi-arm trials.

Cluster randomized trials with relatively few clusters have been widely used in recent years for evaluation of health-care strategies. The balance match weighted (BMW) design, introduced in Xu and Kalbfleisch (2010, Biometrics 66, 813-823), applies the optimal full matching with constraints technique to a prospective randomized design with the aim of minimizing the mean squared error (MSE) of the treatment effect estimator. This is accomplished through consideration of M independent randomizations of the experimental units and then selecting the one which provides the most balance evaluated by matching on the estimated propensity scores. Often in practice, clinical trials may involve more than two treatment arms and multiple treatment options need to be evaluated. Therefore, we consider extensions of the BMW propensity score matching method to allow for studies with three or more arms. In this article, we propose three approaches to extend the BMW design to clinical trials with more than two arms and evaluate the property of the extended design in simulation studies.

An estimating function approach to the analysis of recurrent and terminal events.

In clinical and observational studies, the event of interest can often recur on the same subject. In a more complicated situation, there exists a terminal event (e.g., death) which stops the recurrent event process. In many such instances, the terminal event is strongly correlated with the recurrent event process. We consider the recurrent/terminal event setting and model the dependence through a shared gamma frailty that is included in both the recurrent event rate and terminal event hazard functions. Conditional on the frailty, a model is specified only for the marginal recurrent event process, hence avoiding the strong Poisson-type assumptions traditionally used. Analysis is based on estimating functions that allow for estimation of covariate effects on the recurrent event rate and terminal event hazard. The method also permits estimation of the degree of association between the two processes. Closed-form asymptotic variance estimators are proposed. The proposed method is evaluated through simulations to assess the applicability of the asymptotic results in finite samples and the sensitivity of the method to its underlying assumptions. The methods can be extended in straightforward ways to accommodate multiple types of recurrent and terminal events. Finally, the methods are illustrated in an analysis of hospitalization data for patients in an international multi-center study of outcomes among dialysis patients.

Sleep apnea treatment after stroke (SATS) trial: is it feasible?

Sleep apnea affects more than half of patients with acute ischemic stroke and is associated with poor stroke outcome. This pilot study assessed the feasibility of a randomized, sham-controlled continuous positive airway pressure (CPAP) trial in subjects with acute ischemic stroke. Subjects identified with sleep apnea based on an apnea-hypopnea index≥5 on overnight polysomnography or portable respiratory monitoring within 7 days of onset of stroke symptoms were randomized to receive active or sham CPAP for a 3-month period. Objective usage was ascertained by compliance data cards. Subjects, treating physicians, and outcome assessors were masked to intervention allocation. Among 87 subjects who provided consent, 74 were able to complete sleep apnea screening, 54 (73%) of whom had sleep apnea. Thirty-two subjects agreed to randomization. Of the 15 subjects who commenced active titration, 11 (73%) took the device home, and 8 (53%) completed the 3-month follow-up. Of the 17 subjects who commenced sham titration, 11 (65%) took the sham device home and completed the 3-month follow-up. The median cumulative usage hours over the 90 days were similar in the active group (53 hours; interquartile range, 22-173 hours) and the sham group (74 hours; interquartile range, 17-94 hours), and blinding to subject condition was successfully maintained. This first-ever randomized, sham-controlled trial of CPAP in patients with recent stroke and sleep apnea demonstrates that sham treatment can be an effective placebo.

Dialysis outcomes and analysis of practice patterns suggests the dialysis schedule affects day-of-week mortality.

The risk of death for hemodialysis patients is thought to be highest on the days following the longest interval without dialysis (usually Mondays and Tuesdays); however, existing results are inconclusive. To clarify this we analyzed Dialysis Outcomes and Practice Patterns Study (DOPPS) data of 22,163 hemodialysis patients from the United States, Europe, and Japan. Our study focused on the association between dialysis schedule and day of the week of all-cause, cardiovascular, and noncardiovascular mortality with day-of-week coded as a time-dependent covariate. The models were adjusted for dialysis schedule, age, country, DOPPS phase I or II, and other demographic and clinical covariates, and compared mortality on each day to the 7-day average. Patients on a Monday-Wednesday-Friday (MWF) schedule had elevated all-cause mortality on Mondays, and those on a Tuesday-Thursday-Saturday (TTS) schedule had increased risk of mortality on Tuesdays in all three regions. The association between day-of-week mortality and schedule was generally stronger for cardiovascular than noncardiovascular mortality, and was most pronounced in the United States. Unexpectedly, Japanese patients on a MWF schedule had a higher risk of noncardiovascular mortality on Fridays, and European patients on a TTS schedule experienced an elevated cardiovascular mortality on Saturdays. Thus, future studies are needed to evaluate the influence of practice patterns on schedule-specific mortality and factors that could modulate this effect.

Pregnancy-onset habitual snoring, gestational hypertension, and preeclampsia: prospective cohort study.

OBJECTIVE: This study aimed to prospectively examine the impact of chronic vs pregnancy-onset habitual snoring on gestational hypertension, preeclampsia, and gestational diabetes. STUDY DESIGN: Third-trimester pregnant women were recruited from a large, tertiary medical center from March 2007 through December 2010 and screened for the presence and duration of habitual snoring, as a known marker for sleep-disordered breathing. Clinical diagnoses of gestational hypertension, preeclampsia, and gestational diabetes were obtained. RESULTS: Of 1719 pregnant women, 34% reported snoring, with 25% reporting pregnancy-onset snoring. After adjusting for confounders, pregnancy-onset, but not chronic, snoring was independently associated with gestational hypertension (odds ratio, 2.36; 95% confidence interval, 1.48-3.77; P < .001) and preeclampsia (odds ratio, 1.59; 95% confidence interval, 1.06-2.37; P = .024) but not gestational diabetes. CONCLUSION: New-onset snoring during pregnancy is a strong risk factor for gestational hypertension and preeclampsia. In view of the significant morbidity and health care costs associated with hypertensive diseases of pregnancy, simple screening of pregnant women may have clinical utility.

Computationally efficient marginal models for clustered recurrent event data.

Large observational databases derived from disease registries and retrospective cohort studies have proven very useful for the study of health services utilization. However, the use of large databases may introduce computational difficulties, particularly when the event of interest is recurrent. In such settings, grouping the recurrent event data into prespecified intervals leads to a flexible event rate model and a data reduction that remedies the computational issues. We propose a possibly stratified marginal proportional rates model with a piecewise-constant baseline event rate for recurrent event data. Both the absence and the presence of a terminal event are considered. Large-sample distributions are derived for the proposed estimators. Simulation studies are conducted under various data configurations, including settings in which the model is misspecified. Guidelines for interval selection are provided and assessed using numerical studies. We then show that the proposed procedures can be carried out using standard statistical software (e.g., SAS, R). An application based on national hospitalization data for end-stage renal disease patients is provided.

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.