Regression analysis of incomplete medical cost data

A Tutorial on Net Benefit Regression for Real-World Cost-Effectiveness Analysis Using Censored Data from Randomized or Observational Studies

HIGHLIGHTS

We illustrate the steps involved in carrying out cost-effectiveness analysis using net benefit regressions with possibly censored demo data by providing step-by-step guidance and code applied to a data set.We demonstrate the importance of these new methods by illustrating how naïve methods for handling censoring can lead to biased cost-effectiveness results.

Longitudinal varying coefficient single-index model with censored covariates

It is of interest to health policy research to estimate the population-averaged longitudinal medical cost trajectory from initial cancer diagnosis to death, and understand how the trajectory curve is affected by patient characteristics. This research question leads to a number of statistical challenges because the longitudinal cost data are often non-normally distributed with skewness, zero-inflation, and heteroscedasticity. The trajectory is nonlinear, and its length and shape depend on survival, which are subject to censoring. Modeling the association between multiple patient characteristics and nonlinear cost trajectory curves of varying lengths should take into consideration parsimony, flexibility, and interpretation. We propose a novel longitudinal varying coefficient single-index model. Multiple patient characteristics are summarized in a single-index, representing a patient's overall propensity for healthcare use. The effects of this index on various segments of the cost trajectory depend on both time and survival, which is flexibly modeled by a bivariate varying coefficient function. The model is estimated by generalized estimating equations with an extended marginal mean structure to accommodate censored survival time as a covariate. We established the pointwise confidence interval of the varying coefficient and a test for the covariate effect. The numerical performance was extensively studied in simulations. We applied the proposed methodology to medical cost data of prostate cancer patients from the Surveillance, Epidemiology, and End Results-Medicare-Linked Database.

Economic evaluation of pharmacogenomic-guided antiplatelet treatment in Spanish patients suffering from acute coronary syndrome participating in the U-PGx PREPARE study

BACKGROUND

Cardiovascular diseases and especially Acute Coronary Syndrome (ACS) constitute a major health issue impacting millions of patients worldwide. Being a leading cause of death and hospital admissions in many European countries including Spain, it accounts for enormous amounts of healthcare expenditures for its management. Clopidogrel is one of the oldest antiplatelet medications used as standard of care in ACS.

METHODS

In this study, we performed an economic evaluation study to estimate whether a genome-guided clopidogrel treatment is cost-effective compared to conventional one in a large cohort of 243 individuals of Spanish origin suffering from ACS and treated with clopidogrel. Data were derived from the U-PGx PREPARE clinical trial. Effectiveness was measured as survival of individuals while study data on safety and efficacy, as well as on resource utilization associated with each adverse drug reaction were used to measure costs to treat these adverse drug reactions. A generalized linear regression model was used to estimate cost differences for both study groups.

RESULTS

Based on our findings, PGx-guided treatment group is cost-effective. PGx-guided treatment demonstrated to have 50% less hospital admissions, reduced emergency visits and almost 13% less ADRs compared to the non-PGx approach with mean QALY 1.07 (95% CI, 1.04-1.10) versus 1.06 (95% CI, 1.03-1.09) for the control group, while life years for both groups were 1.24 (95% CI, 1.20-1.26) and 1.23 (95% CI, 1.19-1.26), respectively. The mean total cost of PGx-guided treatment was 50% less expensive than conventional therapy with clopidogrel [€883 (95% UI, €316-€1582), compared to €1,755 (95% UI, €765-€2949)].

CONCLUSION

These findings suggest that PGx-guided clopidogrel treatment represents a cost-effective option for patients suffering from ACS in the Spanish healthcare setting.

Association Between Positive Airway Pressure Adherence and Health Care Costs Among Individuals With OSA

BACKGROUND

The impact of positive airway pressure (PAP) therapy for OSA on health care costs is uncertain.

RESEARCH QUESTION

Are 3-year health care costs associated with PAP adherence in participants from the Tele-OSA clinical trial?

STUDY DESIGN AND METHODS

Participants with OSA and prescribed PAP in the Tele-OSA study were stratified into three PAP adherence groups based on usage patterns over 3 years: (1) high (consistently ≥ 4 h/night), (2) moderate (2-3.9 h/night or inconsistently ≥ 4 h/night), and (3) low (< 2 h/night). Using data from 3 months of the Tele-OSA trial and 33 months of posttrial follow up, average health care costs (2020 US dollars) in 6-month intervals were derived from electronic health records and analyzed using multivariable generalized linear models.

RESULTS

Of 543 participants, 25% were categorized as having high adherence, 22% were categorized as having moderate adherence, and 52% were categorized as having low adherence to PAP therapy. Average PAP use mean ± SD was 6.5 ± 1.0 h, 3.7 ± 1.2 h, and 0.5 ± 0.5 h for the high, moderate, and low adherence groups, respectively. The high adherence group had the lowest average covariate-adjusted 6-month health care costs ± SE ($3,207 ± $251) compared with the moderate ($3,638 ± $363) and low ($4,040 ± $304) adherence groups. Significant cost differences were observed between the high and low adherence groups ($832; 95% CI, $127 to $1,538); differences between moderate and low adherence were nonsignificant ($401; 95% CI, -$441 to $1,243).

INTERPRETATION

In participants with OSA, better PAP adherence was associated with significantly lower health care costs over 3 years. Findings support the importance of strategies to enhance long-term PAP adherence.

Net-benefit regression with censored cost-effectiveness data from randomized or observational studies

Cost-effectiveness analysis is an essential part of the evaluation of new medical interventions. While in many studies both costs and effectiveness (eg, survival time) are censored, standard survival analysis techniques are often invalid due to the induced dependent censoring problem. We propose methods for censored cost-effectiveness data using the net-benefit regression framework, which allow covariate-adjustment and subgroup identification when comparing two intervention groups. The methods provide a straightforward way to construct cost-effectiveness acceptability curves with censored data. We also propose a more efficient doubly robust estimator of average causal incremental net benefit, which increases the likelihood that the results will represent a valid inference in observational studies. Lastly, we conduct extensive numerical studies to examine the finite-sample performance of the proposed methods, and illustrate the proposed methods with a real data example using both survival time and quality-adjusted survival time as the measures of effectiveness.

Age, morbidity, or something else? A residual approach using microdata to measure the impact of technological progress on health care expenditure

This study measures the increment of health care expenditure (HCE) that can be attributed to technological progress and change in medical practice by using a residual approach and microdata. We examine repeated cross-sections of individuals experiencing an initial health shock at different point in time over a 10-year window and capture the impact of unobservable technology and medical practice to which they are exposed after allowing for differences in health and socioeconomic characteristics. We decompose the residual increment in the part that is due to the effect of delaying time to death, that is, individuals surviving longer after a health shock and thus contributing longer to the demand of care, and the part that is due to increasing intensity of resource use, that is, the basket of services becoming more expensive to allow for the cost of innovation. We use data from the Danish National Health System that offers universal coverage and is free of charge at the point of access. We find that technological progress and change in medical practice can explain about 60% of the increment of HCE, in line with macroeconomic studies that traditionally investigate this subject.

Health care costs in a randomized trial of antimicrobial duration among cystic fibrosis patients with pulmonary exacerbations

BACKGROUND

The purpose of these analyses was to determine whether overall costs were reduced in cystic fibrosis (CF) patients experiencing pulmonary exacerbation (PEx) who received shorter versus longer durations of treatment.

METHODS

Among people with CF experiencing PEx, we calculated 30-day inpatient, outpatient, emergency room, and medication costs and summed these to derive total costs in 2020 USD. Using the Kaplan-Meier sample average (KMSA) method, we calculated adjusted costs and differences in costs within two pairs of randomized groups: early robust responders (ERR) randomized to receive treatment for 10 days (ERR-10 days) or 14 days (ERR-14 days), and non-early robust responders (NERR) randomized to receive treatment for 14 days (NERR-14 days) or 21 days (NERR-21 days).

RESULTS

Patients in the shorter treatment duration groups had shorter lengths of stay per hospitalization (mean ± standard deviation (SD) for ERR-10 days: 7.9 ± 3.0 days per hospitalization compared to 10.1 ± 4.2 days in ERR-14 days; for NERR-14 days: 8.7 ± 4.9 days per hospitalization compared to 9.6 ± 6.5 days in NERR-21 days). We found statistically significantly lower adjusted mean costs (95% confidence interval) among those who were randomized to receive shorter treatment durations (ERR-10 days: $60,800 ($59,150 - $62,430) vs $74,420 ($72,610 - $76,450) in ERR-14 days; NERR-14 days: $66,690 ($65,960-$67,400) versus $74,830 ($73,980-$75,650) in NERR-21 days).

CONCLUSIONS

Tied with earlier evidence that shorter treatment duration was not associated with worse clinical outcomes, our analyses indicate that treating with shorter antimicrobial durations can reduce costs without diminishing clinical outcomes.

Early-stage economic analysis of research-based comprehensive genomic sequencing for advanced cancer care

Genomic research is driving discovery for future population benefit. Limited evidence exists on immediate patient and health system impacts of research participation. This study uses real-world data and quasi-experimental matching to examine early-stage cost and health impacts of research-based genomic sequencing. British Columbia’s Personalized OncoGenomics (POG) single-arm program applies whole genome and transcriptome analysis (WGTA) to characterize genomic landscapes in advanced cancers. Our cohort includes POG patients enrolled between 2014 and 2015 and 1:1 genetic algorithm–matched usual care controls. We undertake a cost consequence analysis and estimate 1-year effects of WGTA on patient management, patient survival, and health system costs reported in 2015 Canadian dollars. WGTA costs are imputed and forecast using system of equations modeling. We use Kaplan-Meier survival analysis to explore survival differences and inverse probability of censoring weighted linear regression to estimate mean 1-year survival times and costs. Non-parametric bootstrapping simulates sampling distributions and enables scenario analysis, revealing drivers of incremental costs, survival, and net monetary benefit for assumed willingness to pay thresholds. We identified 230 POG patients and 230 matched controls for cohort inclusion. The mean period cost of research-funded WGTA was $26,211 (SD: $14,191). Sequencing costs declined rapidly, with WGTA forecasts hitting $13,741 in 2021. The incremental healthcare system effect (non-research expenditures) was $5203 (95% CI: 75, 10,424) compared to usual care. No overall survival differences were observed, but outcome heterogeneity was present. POG patients receiving WGTA-informed treatment experienced incremental survival gains of 2.49 months (95% CI: 1.32, 3.64). Future cost consequences became favorable as WGTA cost drivers declined and WGTA-informed treatment rates improved to 60%. Our study demonstrates the ability of real-world data to support evaluations of only-in-research health technologies. We identify situations where precision oncology research initiatives may produce survival benefit at a cost that is within healthcare systems’ willingness to pay. This economic evidence informs the early-stage healthcare impacts of precision oncology research.

Matching methods in precision oncology: An introduction and illustrative example

BACKGROUND

Randomized controlled trials (RCTs) are uncommon in precision oncology. We provide an introduction and illustrative example of matching methods for evaluating precision oncology in the absence of RCTs. We focus on British Columbia's Personalized OncoGenomics (POG) program, which applies whole-genome and transcriptome analysis (WGTA) to inform advanced cancer care.

METHODS

Our cohort comprises 230 POG patients enrolled between 2014 and 2015 and matched POG-naive controls. We generated our matched cohort using 1:1 propensity score matching (PSM) and genetic matching prior to exploring survival differences.

RESULTS

We find that genetic matching outperformed PSM when balancing covariates. In all cohorts, overall survival did not significantly differ across POG and POG-naive patients (p > 0.05). Stratification by WGTA-informed treatment indicated unmatched survival differences. Patients whose WGTA information led to treatment change were at a reduced hazard of death compared to POG-naive controls in all cohorts, with estimated hazard ratios ranging from 0.33 (95% CI: 0.13, 0.81) to 0.41 (95% CI: 0.17, 0.98).

CONCLUSION

These results signal that clinical effectiveness of precision oncology approaches will depend on rates of genomics-informed treatment change. Our study will guide future evaluations of precision oncology and support reliable effect estimation when RCT data are unavailable.

Empirical likelihood-based inferences for median medical cost regression models with censored data

Recent studies show that medical cost data can be heavily censored and highly skewed, which leads to have more complex cost data analysis. In this paper, we propose influence function and empirical likelihood (EL)-based methods to construct confidence regions for regression parameters in median cost regression models with censored data. We further propose confidence intervals for the median cost with given covariates using the proposed EL-based confidence regions. Simulation studies are conducted to compare the proposed EL-based confidence regions with the existing normal approximation-based confidence regions in terms of coverage probabilities. The new EL-based methods are observed to have better finite sample performances than existing methods particularly when the censoring proportion is high. The new methods are also illustrated through a real data example.

Nested g-computation: A causal approach to analysis of censored medical costs in the presence of time-varying treatment

Rising medical costs are an emerging challenge in policy decisions and resource allocation planning. When cumulative medical cost is the outcome, right-censoring induces informative missingness due to heterogeneity in cost accumulation rates across subjects. Inverse-weighting approaches have been developed to address the challenge of informative cost trajectories in mean cost estimation, though these approaches generally ignore post-baseline treatment changes. In post-hysterectomy endometrial cancer patients, data from a linked database of Medicare records and the Surveillance, Epidemiology, and End Results program of the National Cancer Institute reveal substantial within-subject variation in treatment over time. In such a setting, the utility of existing intent-to-treat approaches is generally limited. Estimates of population mean cost under a hypothetical time-varying treatment regime can better assist with resource allocation when planning for a treatment policy change; such estimates must inherently take time-dependent treatment and confounding into account. In this paper, we develop a nested g-computation approach to cost analysis to address this challenge, while accounting for censoring. We develop a procedure to evaluate sensitivity to departures from baseline treatment ignorability. We further conduct a variety of simulations and apply our nested g-computation procedure to two-year costs from endometrial cancer patients.

A joint modeling approach for analyzing marker data in the presence of a terminal event

In many medical studies, markers are contingent on recurrent events and the cumulative markers are usually of interest. However, the recurrent event process is often interrupted by a dependent terminal event, such as death. In this article, we propose a joint modeling approach for analyzing marker data with informative recurrent and terminal events. This approach introduces a shared frailty to specify the explicit dependence structure among the markers, the recurrent, and terminal events. Estimation procedures are developed for the model parameters and the degree of dependence, and a prediction of the covariate-specific cumulative markers is provided. The finite sample performance of the proposed estimators is examined through simulation studies. An application to a medical cost study of chronic heart failure patients from the University of Virginia Health System is illustrated.

Reference-based multiple imputation for missing data sensitivity analyses in trial-based cost-effectiveness analysis

Missing data are a common issue in cost-effectiveness analysis (CEA) alongside randomised trials and are often addressed assuming the data are 'missing at random'. However, this assumption is often questionable, and sensitivity analyses are required to assess the implications of departures from missing at random. Reference-based multiple imputation provides an attractive approach for conducting such sensitivity analyses, because missing data assumptions are framed in an intuitive way by making reference to other trial arms. For example, a plausible not at random mechanism in a placebo-controlled trial would be to assume that participants in the experimental arm who dropped out stop taking their treatment and have similar outcomes to those in the placebo arm. Drawing on the increasing use of this approach in other areas, this paper aims to extend and illustrate the reference-based multiple imputation approach in CEA. It introduces the principles of reference-based imputation and proposes an extension to the CEA context. The method is illustrated in the CEA of the CoBalT trial evaluating cognitive behavioural therapy for treatment-resistant depression. Stata code is provided. We find that reference-based multiple imputation provides a relevant and accessible framework for assessing the robustness of CEA conclusions to different missing data assumptions.

Estimating cost-effectiveness from claims and registry data with measured and unmeasured confounders

The analysis of observational data to determine the cost-effectiveness of medical treatments is complicated by the need to account for skewness, censoring, and the effects of measured and unmeasured confounders. We quantify cost-effectiveness as the Net Monetary Benefit (NMB), a linear combination of the treatment effects on cost and effectiveness that denominates utility in monetary terms. We propose a parametric estimation approach that describes cost with a Gamma generalized linear model and survival time (the canonical effectiveness variable) with a Weibull accelerated failure time model. To account for correlation between cost and survival, we propose a bootstrap procedure to compute confidence intervals for NMB. To examine sensitivity to unmeasured confounders, we derive simple approximate relationships between naïve parameters, assuming only measured confounders, and the values those parameters would take if there was further adjustment for a single unmeasured confounder with a specified distribution. A simulation study shows that the method returns accurate estimates for treatment effects on cost, survival, and NMB under the assumed model. We apply our method to compare two treatments for Stage II/III bladder cancer, concluding that the NMB is sensitive to hypothesized unmeasured confounders that represent smoking status and personal income.

Estimating the Effectiveness of DPYD Genotyping in Italian Individuals Suffering from Cancer Based on the Cost of Chemotherapy-Induced Toxicity

Fluoropyrimidines (FLs) have been widely used for more than 60 years against a range of solid tumors and still remains the cornerstone for the treatment of colorectal, gastric, and breast cancer. Here, we performed an economic analysis to estimate the cost of DPYD-guided toxicity management and the clinical benefit expressed as quality adjusted life years (QALYs) in a large group of 571 individuals of Italian origin suffering from cancer and treated with a fluoropyrimidines-based chemotherapy. Individuals suffering from cancer with a histologically confirmed diagnosis of cancer, who received a fluoropyrimidines-based treatment, were retrospectively genotyped in the DPYD gene. Effectiveness was measured as survival of individuals from chemotherapy, while study data on safety and efficacy as well as on resource utilization associated with each adverse drug reaction were used to measure costs to treat these adverse drug reactions. A generalized linear regression model was used to estimate cost differences for both study groups. DPYD extensive metabolizers (528 individuals) had greater effectiveness and lesser cost, representing a cost-saving option over DPYD intermediate and poor metabolizers (43 individuals) with mean QALYs of 4.18 (95%CI: 3.16-5.55) versus 3.02 (95%CI: 1.94-4.25), respectively. Our economic analysis showed that there are some indications for differences in survival between the two groups (p > 0.05), while the cost of DPYD extensive metabolizers was significantly lower (p < 0.01) compared with those belonging to the group of intermediate/poor metabolizers. These findings suggest that DPYD-guided fluoropyrimidines treatment represent a cost-saving choice for individuals suffering from cancer in the Italian healthcare setting.

Clinical and Economic Benefits of Stent Grafts in Dysfunctional and Thrombosed Hemodialysis Access Graft Circuits in the REVISE Randomized Trial

PURPOSE

To compare reinterventions and associated costs to maintain arteriovenous graft hemodialysis access circuits after rescue with percutaneous transluminal angioplasty (PTA), with or without concurrent Viabahn stent grafts, over 24 months.

MATERIALS AND METHODS

This multicenter (n = 30 sites) study evaluated reintervention number, type, and cost in 269 patients randomized to undergo placement of stent grafts or PTA alone. Outcomes were 24-month average cumulative number of reinterventions, associated costs, and total costs for all patients and in 4 groups based on index treatment and clinical presentation (thrombosed or dysfunctional).

RESULTS

Over 24 months, the patients in the stent graft arm had a 27% significant reduction in the average number of reinterventions within the circuit compared to the PTA arm (3.7 stent graft vs 5.1 PTA; P = .005) and similar total costs ($27,483 vs $28,664; P = .49). In thrombosed grafts, stent grafts significantly reduced the number of reinterventions (3.7 stent graft vs 6.2 PTA; P = .022) and had significantly lower total costs compared to the PTA arm ($30,329 vs $37,206; P = .027). In dysfunctional grafts, no statistical difference was observed in the number of reinterventions or total costs (3.7 stent graft vs 4.4 PTA; P = .12, and $25,421 stent graft and $22,610 PTA; P = .14).

CONCLUSIONS

Over 24 months, the use of stent grafts significantly reduced the number of reinterventions for all patients, driven by patients presenting with thrombosed grafts. Compared to PTA, stent grafts reduced overall treatment costs for patients presenting with thrombosed grafts and had similar costs for stenotic grafts.

Quantifying the totality of treatment effect with multiple event-time observations in the presence of a terminal event from a comparative clinical study

To evaluate the totality of one treatment's benefit/risk profile relative to an alternative treatment via a longitudinal comparative clinical study, the timing and occurrence of multiple clinical events are typically collected during the patient's follow-up. These multiple observations reflect the patient's disease progression/burden over time. The standard practice is to create a composite endpoint from the multiple outcomes, the timing of the occurrence of the first clinical event, to evaluate the treatment via the standard survival analysis techniques. By ignoring all events after the composite outcome, this type of assessment may not be ideal. Various parametric or semiparametric procedures have been extensively discussed in the literature for the purposes of analyzing multiple event-time data. Many existing methods were developed based on extensive model assumptions. When the model assumptions are not plausible, the resulting inferences for the treatment effect may be misleading. In this article, we propose a simple, nonparametric inference procedure to quantify the treatment effect, which has an intuitive clinically meaningful interpretation. We use the data from a cardiovascular clinical trial for heart failure to illustrate the procedure. A simulation study is also conducted to evaluate the performance of the new proposal.

Analyzing medical costs with time-dependent treatment: The nested g-formula

As medical expenses continue to rise, methods to properly analyze cost outcomes are becoming of increasing relevance when seeking to compare average costs across treatments. Inverse probability weighted regression models have been developed to address the challenge of cost censoring in order to identify intent-to-treat effects (i.e., to compare mean costs between groups on the basis of their initial treatment assignment, irrespective of any subsequent changes to their treatment status). In this paper, we describe a nested g-computation procedure that can be used to compare mean costs between two or more time-varying treatment regimes. We highlight the relative advantages and limitations of this approach when compared with existing regression-based models. We illustrate the utility of this approach as a means to inform public policy by applying it to a simulated data example motivated by costs associated with cancer treatments. Simulations confirm that inference regarding intent-to-treat effects versus the joint causal effects estimated by the nested g-formula can lead to markedly different conclusions regarding differential costs. Therefore, it is essential to prespecify the desired target of inference when choosing between these two frameworks. The nested g-formula should be considered as a useful, complementary tool to existing methods when analyzing cost outcomes.

Semiparametric Estimation of Longitudinal Medical Cost Trajectory

Estimating the average monthly medical costs from disease diagnosis to a terminal event such as death for an incident cohort of patients is a topic of immense interest to researchers in health policy and health economics because patterns of average monthly costs over time reveal how medical costs vary across phases of care. The statistical challenges to estimating monthly medical costs longitudinally are multifold; the longitudinal cost trajectory (formed by plotting the average monthly costs from diagnosis to the terminal event) is likely to be nonlinear, with its shape depending on the time of the terminal event, which can be subject to right censoring. The goal of this paper is to tackle this statistically challenging topic by estimating the conditional mean cost at any month t given the time of the terminal event s. The longitudinal cost trajectories with different terminal event times form a bivariate surface of t and s, under the constraint t ≤ s. We propose to estimate this surface using bivariate penalized splines in an Expectation-Maximization algorithm that treats the censored terminal event times as missing data. We evaluate the proposed model and estimation method in simulations and apply the method to the medical cost data of an incident cohort of stage IV breast cancer patients from the Surveillance, Epidemiology and End Results-Medicare Linked Database.

[Methods for the analysis and treatment of cost data by micro- and gross-costing approaches]

This work addresses the analysis of individual cost data in the setting of interventional or observational studies using statistical analysis software once the costs per patient have been estimated. It is in fact necessary to be able to present and describe data in an appropriate manner in each of the studied health strategies and to test whether the difference in costs observed between treatment groups is due to chance or not. Furthermore, cost analysis differs from conventional statistical analysis in that cost data have a certain number of specific properties, including their use by health decision-makers. This work also addresses the difficulties that generally arise in regard to the distribution of cost; it explains why the mathematical average constitutes the only relevant measure for economists; and it outlines which analyses are required for inter-strategy cost comparisons. It also covers the issue of missing or censored data, features that are inherent to information collected regarding costs and to sensitivity analyses.

Healthcare utilization and costs among patients with herpes zoster and solid tumor malignancy on chemotherapy: A retrospective cohort study

Immunosuppressed patients with solid tumor malignancies (STMs) are particularly vulnerable to herpes zoster (HZ). This study estimated the incidence of HZ and evaluated healthcare resource utilization and costs for persons with STM receiving chemotherapy with and without incident HZ.We conducted a retrospective claims study of adults with STM receiving chemotherapy between January 1, 2010 and June 30, 2014. Patients were followed from their first chemotherapy date through development of HZ, health plan disenrollment, the study end date, or 24 months. HZ incidence was calculated and stratified by patient characteristics. Adjusted HZ incidence was estimated using Poisson regression. Healthcare resource utilization and costs were compared between patients with HZ (cases) and propensity score-matched controls without HZ during a variable follow-up period. Adjusted healthcare costs were estimated using Lin regression to control for informative censoring.Of 155,480 patients with STM receiving chemotherapy, 3100 (2.0%) developed HZ, yielding an adjusted HZ incidence rate of 13.8/1000 person-years (PY). HZ cases (n = 3004) had significantly higher healthcare resource utilization than matched controls (n = 15,020). Adjusted annual costs were $48,077 for cases vs $41,645 for matched controls, corresponding to a differential cost of $6432 annually.After adjustment for potential confounders, patients with STM receiving chemotherapy had an HZ incidence of 13.8/1000 PY; those who developed HZ used more healthcare resources and incurred higher costs than those who did not. These findings suggest that HZ prevention by vaccination could improve outcomes and reduce costs in this population.

A doubly robust approach for cost-effectiveness estimation from observational data

Estimation of common cost-effectiveness measures, including the incremental cost-effectiveness ratio and the net monetary benefit, is complicated by the need to account for informative censoring and inherent skewness of the data. In addition, since the two components of these measures, medical costs and survival are often collected from observational claims data, one must account for potential confounders. We propose a novel doubly robust, unbiased estimator for cost-effectiveness based on propensity scores that allow the incorporation of cost history and time-varying covariates. Further, we use an ensemble machine learning approach to obtain improved predictions from parametric and non-parametric cost and propensity score models. Our simulation studies demonstrate that the proposed doubly robust approach performs well even under mis-specification of either the propensity score model or the outcome model. We apply our approach to a cost-effectiveness analysis of two competing lung cancer surveillance procedures, CT vs. chest X-ray, using SEER-Medicare data.

Double robust estimator of average causal treatment effect for censored medical cost data

In observational studies, estimation of average causal treatment effect on a patient's response should adjust for confounders that are associated with both treatment exposure and response. In addition, the response, such as medical cost, may have incomplete follow-up. In this article, a double robust estimator is proposed for average causal treatment effect for right censored medical cost data. The estimator is double robust in the sense that it remains consistent when either the model for the treatment assignment or the regression model for the response is correctly specified. Double robust estimators increase the likelihood the results will represent a valid inference. Asymptotic normality is obtained for the proposed estimator, and an estimator for the asymptotic variance is also derived. Simulation studies show good finite sample performance of the proposed estimator and a real data analysis using the proposed method is provided as illustration. Copyright © 2016 John Wiley & Sons, Ltd.

The ProFHER (PROximal Fracture of the Humerus: Evaluation by Randomisation) trial - a pragmatic multicentre randomised controlled trial evaluating the clinical effectiveness and cost-effectiveness of surgical compared with non-surgical treatment for proximal fracture of the humerus in adults

BACKGROUND

Proximal humeral fractures account for 5-6% of all fractures in adults. There is considerable variation in whether or not surgery is used in the management of displaced fractures involving the surgical neck.

OBJECTIVE

To evaluate the clinical effectiveness and cost-effectiveness of surgical compared with non-surgical treatment of the majority of displaced fractures of the proximal humerus involving the surgical neck in adults.

DESIGN

A pragmatic parallel-group multicentre randomised controlled trial with an economic evaluation. Follow-up was for 2 years.

SETTING

Recruitment was undertaken in the orthopaedic departments of 33 acute NHS hospitals in the UK. Patient care pathways included outpatient and community-based rehabilitation.

PARTICIPANTS

Adults (aged ≥ 16 years) presenting within 3 weeks of their injury with a displaced fracture of the proximal humerus involving the surgical neck.

INTERVENTIONS

The choice of surgical intervention was left to the treating surgeons, who used techniques with which they were experienced. Non-surgical treatment was initial sling immobilisation followed by active rehabilitation. Provision of rehabilitation was comparable in both groups.

MAIN OUTCOME MEASURES

The primary outcome was the Oxford Shoulder Score (OSS) assessed at 6, 12 and 24 months. Secondary outcomes were the 12-item Short Form health survey, surgical and other shoulder fracture-related complications, secondary surgery to the shoulder or increased/new shoulder-related therapy, medical complications during inpatient stay and mortality. European Quality of Life-5 Dimensions data and treatment costs were also collected.

RESULTS

The mean age of the 250 trial participants was 66 years and 192 (77%) were female. Independent assessment using the Neer classification identified 18 one-part fractures, 128 two-part fractures and 104 three- or four-part fractures. OSS data were available for 215 participants at 2 years. We found no statistically or clinically significant differences in OSS scores between the two treatment groups (scale 0-48, with a higher score indicating a better outcome) over the 2-year period [difference of 0.75 points in favour of the surgery group, 95% confidence interval (CI) -1.33 to 2.84; p = 0.479; data from 114 surgery and 117 non-surgery participants] or at individual time points. We found no statistically significant differences between surgical and non-surgical group participants in SF-12 physical or mental component summary scores; surgical or shoulder fracture-related complications (30 vs. 23 respectively); those undergoing further shoulder-related therapy, either surgery (11 vs. 11 respectively) or other therapy (seven vs. four respectively); or mortality (nine vs. five respectively). The base-case economic analysis showed that, at 2 years, the cost of surgical intervention was, on average, £1780.73 more per patient (95% CI £1152.71 to £2408.75) than the cost of non-surgical intervention. It was also slightly less beneficial in terms of utilities, although this difference was not statistically significant. The net monetary benefit associated with surgery is negative. There was only a 5% probability of surgery achieving the criterion of costing < £20,000 to gain a quality-adjusted life-year, which was confirmed by extensive sensitivity analyses.

CONCLUSIONS

Current surgical practice does not result in a better outcome for most patients with displaced fractures of the proximal humerus involving the surgical neck and is not cost-effective in the UK setting. Two areas for future work are the setting up of a national database of these fractures, including the collection of patient-reported outcomes, and research on the best ways of informing patients with these and other upper limb fractures about initial self-care.

TRIAL REGISTRATION

Current Controlled Trials ISRCTN50850043.

FUNDING

This project was funded by the NIHR Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 19, No. 24. See the NIHR Journals Library website for further project information.

Propensity score and doubly robust methods for estimating the effect of treatment on censored cost

The estimation of treatment effects on medical costs is complicated by the need to account for informative censoring, skewness, and the effects of confounders. Because medical costs are often collected from observational claims data, we investigate propensity score (PS) methods such as covariate adjustment, stratification, and inverse probability weighting taking into account informative censoring of the cost outcome. We compare these more commonly used methods with doubly robust (DR) estimation. We then use a machine learning approach called super learner (SL) to choose among conventional cost models to estimate regression parameters in the DR approach and to choose among various model specifications for PS estimation. Our simulation studies show that when the PS model is correctly specified, weighting and DR perform well. When the PS model is misspecified, the combined approach of DR with SL can still provide unbiased estimates. SL is especially useful when the underlying cost distribution comes from a mixture of different distributions or when the true PS model is unknown. We apply these approaches to a cost analysis of two bladder cancer treatments, cystectomy versus bladder preservation therapy, using SEER-Medicare data. Copyright © 2015 John Wiley & Sons, Ltd.

VenUS IV (Venous leg Ulcer Study IV) - compression hosiery compared with compression bandaging in the treatment of venous leg ulcers: a randomised controlled trial, mixed-treatment comparison and decision-analytic model

BACKGROUND

Compression is an effective and recommended treatment for venous leg ulcers. Although the four-layer bandage (4LB) is regarded as the gold standard compression system, it is recognised that the amount of compression delivered might be compromised by poor application technique. Also the bulky nature of the bandages might reduce ankle or leg mobility and make the wearing of shoes difficult. Two-layer compression hosiery systems are now available for the treatment of venous leg ulcers. Two-layer hosiery (HH) may be advantageous, as it has reduced bulk, which might enhance ankle or leg mobility and patient adherence. Some patients can also remove and reapply two-layer hosiery, which may encourage self-management and could reduce costs. However, little robust evidence exists about the effectiveness of two-layer hosiery for ulcer healing and no previous trials have compared two-layer hosiery delivering 'high' compression with the 4LB.

OBJECTIVES

Part I To compare the clinical effectiveness and cost-effectiveness of HH and 4LB in terms of time to complete healing of venous leg ulcers. Part II To synthesise the relative effectiveness evidence (for ulcer healing) of high-compression treatments for venous leg ulcers using a mixed-treatment comparison (MTC). Part III To construct a decision-analytic model to assess the cost-effectiveness of high-compression treatments for venous leg ulcers.

DESIGN

Part I A multicentred, pragmatic, two-arm, parallel, open randomised controlled trial (RCT) with an economic evaluation. Part II MTC using all relevant RCT data - including Venous leg Ulcer Study IV (VenUS IV). Part III A decision-analytic Markov model.

SETTINGS

Part I Community nurse teams or services, general practitioner practices, leg ulcer clinics, tissue viability clinics or services and wound clinics within England and Northern Ireland.

PARTICIPANTS

Part I Patients aged ≥ 18 years with a venous leg ulcer, who were willing and able to tolerate high compression.

INTERVENTIONS

Part I Participants in the intervention group received HH. The control group received the 4LB, which was applied according to standard practice. Both treatments are designed to deliver 40 mmHg of compression at the ankle. Part II and III All relevant high-compression treatments including HH, the 4LB and the two-layer bandage (2LB).

MAIN OUTCOME MEASURES

Part I The primary outcome measure was time to healing of the reference ulcer (blinded assessment). Part II Time to ulcer healing. Part III Quality-adjusted life-years (QALYs) and costs.

RESULTS

Part I A total of 457 participants were recruited. There was no evidence of a difference in time to healing of the reference ulcer between groups in an adjusted analysis [hazard ratio (HR) 0.99, 95% confidence interval (CI) 0.79 to 1.25; p = 0.96]. Time to ulcer recurrence was significantly shorter in the 4LB group (HR = 0.56, 95% CI 0.33 to 0.94; p = 0.026). In terms of cost-effectiveness, using QALYs as the measure of benefit, HH had a > 95% probability of being the most cost-effective treatment based on the within-trial analysis. Part II The MTC suggests that the 2LB has the highest probability of ulcer healing compared with other high-compression treatments. However, this evidence is categorised as low to very low quality. Part III Results suggested that the 2LB had the highest probability of being the most cost-effective high-compression treatment for venous leg ulcers.

CONCLUSIONS

Trial data from VenUS IV found no evidence of a difference in venous ulcer healing between HH and the 4LB. HH may reduce ulcer recurrence rates compared with the 4LB and be a cost-effective treatment. When all available high-compression treatments were considered, the 2LB had the highest probability of being clinically effective and cost-effective. However, the underpinning evidence was sparse and more research is needed. Further research should thus focus on establishing, in a high-quality trial, the effectiveness of this compression system in particular.

TRIAL REGISTRATION

Current Controlled Trials ISRCTN49373072.

FUNDING

This project was funded by the National Institute for Health Research (NIHR) Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 18, No. 57. See the NIHR Journals Library website for further project information.

Does Higher Spending Improve Survival Outcomes for Myocardial Infarction? Examining the Cost-Outcomes Relationship Using Time-Varying Covariates

OBJECTIVES

Previous patient-level acute myocardial infarction (AMI) research has found higher hospital spending to be associated with improved survival; however, survivor-treatment selection bias traditionally has been overlooked. The purpose of this study was to examine the AMI cost-outcome relationship, taking into account this form of bias.

DATA SOURCES

Hospital Discharge Abstract data tracked costs for AMI hospitalizations. Ontario Vital Statistics data tracked patient mortality.

STUDY DESIGN

A standard Cox survival model was compared to an extended Cox model using hospital costs as a time-varying covariate to examine the impact of cost on 1-year survival in a cohort of 30,939 first-time AMI patients in Ontario, Canada, from 2007 to 2010.

PRINCIPAL FINDINGS

Higher patient-level AMI spending decreased the hazard of dying (Standard Model: log-cost hazard ratio: 0.513, 95 percent CI: 0.479-0.549; Extended Model: log-cost hazard ratio: 0.700, 95 percent CI: 0.645-0.758); however, the protective effect was overestimated by 62 percent when survivor-treatment bias was overlooked. In the extended model, a 10 percent increase in spending was associated with a 3.6 percent decrease in hazard of death.

CONCLUSION

The findings of this study suggest that if survivor-treatment bias is overlooked, future research may materially overstate the protective effect of patient-level spending on outcomes.

Considerations for observational research using large data sets in radiation oncology

The radiation oncology community has witnessed growing interest in observational research conducted using large-scale data sources such as registries and claims-based data sets. With the growing emphasis on observational analyses in health care, the radiation oncology community must possess a sophisticated understanding of the methodological considerations of such studies in order to evaluate evidence appropriately to guide practice and policy. Because observational research has unique features that distinguish it from clinical trials and other forms of traditional radiation oncology research, the International Journal of Radiation Oncology, Biology, Physics assembled a panel of experts in health services research to provide a concise and well-referenced review, intended to be informative for the lay reader, as well as for scholars who wish to embark on such research without prior experience. This review begins by discussing the types of research questions relevant to radiation oncology that large-scale databases may help illuminate. It then describes major potential data sources for such endeavors, including information regarding access and insights regarding the strengths and limitations of each. Finally, it provides guidance regarding the analytical challenges that observational studies must confront, along with discussion of the techniques that have been developed to help minimize the impact of certain common analytical issues in observational analysis. Features characterizing a well-designed observational study include clearly defined research questions, careful selection of an appropriate data source, consultation with investigators with relevant methodological expertise, inclusion of sensitivity analyses, caution not to overinterpret small but significant differences, and recognition of limitations when trying to evaluate causality. This review concludes that carefully designed and executed studies using observational data that possess these qualities hold substantial promise for advancing our understanding of many unanswered questions of importance to the field of radiation oncology.

Cost-effectiveness of a primary care intervention to treat obesity

BACKGROUND

Data on the cost-effectiveness of the behavioral treatment of obesity are not conclusive. The cost-effectiveness of treatment in primary care settings is particularly relevant.

METHODS

We conducted a within-trial cost-effectiveness analysis of a primary care-based obesity intervention. Study participants were randomized to: Usual Care (UC; quarterly visits with their primary care provider); Brief Lifestyle Counseling (BLC; quarterly provider visits plus monthly weight loss counseling visits) or Enhanced Brief Lifestyle Counseling (EBLC; all above interventions, plus choice of meal replacements or weight loss medication). A health-care payer perspective was used. Intervention costs were estimated from tracking data obtained prospectively. Quality-adjusted life years (QALYs) were estimated with the EuroQol-5D. We estimated cost per kilogram-year of weight loss and cost per QALY.

RESULTS

Weight losses after 2 years were 1.7, 2.9 and 4.6 kg for UC, BLC and EBLC, respectively (P=0.003 for comparison of EBLC vs UC). The incremental cost per kilogram-year lost was $292 for EBLC compared with UC (95% confidence interval (CI): $219-$437). The short-term incremental cost per QALY was $115,397, but the 95% CI were undefined. Comparison of short-term cost per kg with published estimates of longer-term cost per QALY suggested that the intervention could be cost-effective over the long term (≥ 10 years).

CONCLUSIONS

A primary care intervention that includes monthly counseling visits and a choice of meal replacements or weight loss medication could be a cost-effective treatment for obesity over the long term. However, additional studies are needed on the cost-effectiveness of behavioral treatment of obesity.

EVALUATING COSTS WITH UNMEASURED CONFOUNDING: A SENSITIVITY ANALYSIS FOR THE TREATMENT EFFECT

Estimates of the effects of treatment on cost from observational studies are subject to bias if there are unmeasured confounders. It is therefore advisable in practice to assess the potential magnitude of such biases. We derive a general adjustment formula for loglinear models of mean cost and explore special cases under plausible assumptions about the distribution of the unmeasured confounder. We assess the performance of the adjustment by simulation, in particular, examining robustness to a key assumption of conditional independence between the unmeasured and measured covariates given the treatment indicator. We apply our method to SEER-Medicare cost data for a stage II/III muscle-invasive bladder cancer cohort. We evaluate the costs for radical cystectomy vs. combined radiation/chemotherapy, and find that the significance of the treatment effect is sensitive to plausible unmeasured Bernoulli, Poisson and Gamma confounders.

A flexible model for the mean and variance functions, with application to medical cost data

Medical cost data are often skewed to the right and heteroscedastic, having a nonlinear relation with covariates. To tackle these issues, we consider an extension to generalized linear models by assuming nonlinear associations of covariates in the mean function and allowing the variance to be an unknown but smooth function of the mean. We make no further assumption on the distributional form. The unknown functions are described by penalized splines, and the estimation is carried out using nonparametric quasi-likelihood. Simulation studies show the flexibility and advantages of our approach. We apply the model to the annual medical costs of heart failure patients in the clinical data repository at the University of Virginia Hospital System.

Generalized Redistribute-to-the-Right Algorithm: Application to the Analysis of Censored Cost Data

Medical cost estimation is a challenging task when censoring of data is present. Although researchers have proposed methods for estimating mean costs, these are often derived from theory and are not always easy to understand. We provide an alternative method, based on a replace-from-the-right algorithm, for estimating mean costs more efficiently. We show that our estimator is equivalent to an existing one that is based on the inverse probability weighting principle and semiparametric efficiency theory. We also propose an alternative method for estimating the survival function of costs, based on the redistribute-to-the-right algorithm, that was originally used for explaining the Kaplan-Meier estimator. We show that this second proposed estimator is equivalent to a simple weighted survival estimator of costs. Finally, we develop a more efficient survival estimator of costs, using the same redistribute-to-the-right principle. This estimator is naturally monotone, more efficient than some existing survival estimators, and has a quite small bias in many realistic settings. We conduct numerical studies to examine the finite sample property of the survival estimators for costs, and show that our new estimator has small mean squared errors when the sample size is not too large. We apply both existing and new estimators to a data example from a randomized cardiovascular clinical trial.

Joint modeling of medical cost and survival in complex sample surveys

Medical cost data are typically highly skewed to the right with a large proportion of zero costs. It is also common for these data to be censored because of incomplete follow-up and death. In the case of censoring due to death, it is important to consider the potential dependence between cost and survival. This association can occur because patients who incur a greater amount of medical cost tend to be frailer and hence are more likely to die. To handle this informative censoring issue, joint modeling of cost and survival with shared random effects has been proposed. In this paper, we extend this joint modeling approach to handle a final feature of many medical cost data sets, i.e., Specifically, the fact that data were obtained via a complex survey design. Specifically, we extend the joint model by incorporating the sample weights when estimating the parameters and using the Taylor series linearization approach when calculating the standard errors. We use a simulation study to compare the joint modeling approach with and without these adjustments. The simulation study shows that parameter estimates can be seriously biased when information about the complex survey design is ignored. It also shows that standard errors based on the Taylor series linearization approach provide satisfactory confidence interval coverage. The proposed joint model is applied to monthly hospital costs obtained from the 2004 National Long Term Care Survey.

Economic evaluation of pemetrexed versus erlotinib as second-line treatment of patients with advanced/metastatic non-small cell lung cancer in Greece: a cost minimization analysis

OBJECTIVES

An economic evaluation was conducted in conjunction with a prospective, multicenter, randomized trial, to compare pemetrexed with erlotinib in pretreated patients with metastatic non-small cell lung cancer (NSCLC) in Greece.

METHODS

The effectiveness of treatments examined was comparable; thus, cost minimization analysis was conducted to evaluate which option is less costly. Patient-level resource utilization data were combined with unit cost data, which were aggregated to compute the total treatment cost for each patient. The analysis was conducted with respect to the individual incurring the cost. Due to the limited life-expectancy of the patients, discounting was unnecessary. Since data were right censored, the Bang and Tsiatis method was employed to identify unbiased estimators of the mean cost per treatment arm, while other methods were employed for sensitivity analysis. To analyze uncertainty and to construct uncertainty intervals (UI), stochastic analysis was performed based on 5000 bootstrap replications.

RESULTS

The one-year survival rate was 28.3% in the pemetrexed arm and 31.7% in the erlotinib arm, while the corresponding median survival over the follow-up period was 7.1 and 6.7 months, respectively (P = 0.765). Total cost in the pemetrexed arm was €10508 (95% UI: €9552-€11488), while in the erlotinib arm the cost was €9563 (95% UI: €8499-€10711); thus, no statistically significant difference was found between the comparators (P = 0.206). Results remained constant for all sensitivity analyses.

CONCLUSIONS

There is no survival or cost difference between erlotinib and pemetrexed; thus, these therapies are equivalent. Further studies are needed to determine whether other parameters, such as quality of life, differ among treatment options.

Techniques for estimating health care costs with censored data: an overview for the health services researcher

Objective

The aim of this study was to review statistical techniques for estimating the mean population cost using health care cost data that, because of the inability to achieve complete follow-up until death, are right censored. The target audience is health service researchers without an advanced statistical background.

Methods

Data were sourced from longitudinal heart failure costs from Ontario, Canada, and administrative databases were used for estimating costs. The dataset consisted of 43,888 patients, with follow-up periods ranging from 1 to 1538 days (mean 576 days). The study was designed so that mean health care costs over 1080 days of follow-up were calculated using naïve estimators such as full-sample and uncensored case estimators. Reweighted estimators – specifically, the inverse probability weighted estimator – were calculated, as was phase-based costing. Costs were adjusted to 2008 Canadian dollars using the Bank of Canada consumer price index (http://www.bankofcanada.ca/en/cpi.html).

Results

Over the restricted follow-up of 1080 days, 32% of patients were censored. The full-sample estimator was found to underestimate mean cost ($30,420) compared with the reweighted estimators ($36,490). The phase-based costing estimate of $37,237 was similar to that of the simple reweighted estimator.

Conclusion

The authors recommend against the use of full-sample or uncensored case estimators when censored data are present. In the presence of heavy censoring, phase-based costing is an attractive alternative approach.

Economic impact of healthcare resource utilisation patterns among patients diagnosed with advanced melanoma in the United Kingdom, Italy, and France: results from a retrospective, longitudinal survey (MELODY study)

OBJECTIVE

To describe patterns of healthcare resource utilisation and associated costs for patients with advanced melanoma in the United Kingdom (UK), Italy, and France.

METHODS

For patients receiving systemic treatment, or supportive care, data describing hospitalisations, hospice care, and outpatient visits were retrieved retrospectively from advanced disease diagnosis as part of a multicountry observational study. Costs were estimated by multiplying utilisation level by unit cost. In an exploratory analysis, costs were compared between individuals who died within one year of initiating first-line treatment (short-term survivors) and those with ≥ 1 year follow-up (long-term survivors).

RESULTS

Hospitalisation costs were highest in France (€6262 per-person compared with €3225 in the UK and €2486 in Italy), reflecting higher rates of hospitalisation. In contrast, outpatient costs were highest in the UK (€782 per-person, compared with €115 in France and €72 in Italy), reflecting the highest rate and frequency of outpatient visits and the highest cost per visit. Hospitalisation rates were consistently higher during supportive care compared with systemic therapy. Roughly one-third of patients entered clinical trials and were not included in the analysis. In exploratory analysis, total costs were generally higher for long-term survivors, but monthly per-patient costs were generally lower for long-term survivors, consistent with a hypothesis that resource utilisation and costs do not necessarily increase proportionally with extended survival.

CONCLUSION

Total costs associated with resource utilisation for advanced melanoma patients varied across countries. Overall cost differences were due to differences in frequency and intensity of utilisation patterns and variation in unit costs of health resources.

The relationship between baseline health and longitudinal costs of hospital use

In this paper, we investigate the relationship between baseline health and costs of hospital use over a period of eight years. We combine cross-sectional survey data with information from the Dutch national hospital register. Four different indicators of health (self-perceived health, long-term impairments, ADL limitations and comorbidity) are considered. We find that for ages 50 to 70, differences in hospital costs between good health and bad health are substantial and persist during the whole time period. However, for higher ages expected hospital costs for individuals in bad health decline rapidly and become lower than those for people in good health after about six to seven years. The higher mortality rate among people in bad health is the primary cause here. Our results are confirmed for all four health indicators. We conclude that relying on better health to contain healthcare expenditures is too optimistic, and the interaction between health and mortality should be taken into account when projecting healthcare costs. Healthy ageing is important, but more for health gains than for cost savings.

Some insight on censored cost estimators

Censored survival data analysis has been studied for many years. Yet, the analysis of censored mark variables, such as medical cost, quality-adjusted lifetime, and repeated events, faces a unique challenge that makes standard survival analysis techniques invalid. Because of the 'informative' censorship imbedded in censored mark variables, the use of the Kaplan-Meier (Journal of the American Statistical Association 1958; 53:457-481) estimator, as an example, will produce biased estimates. Innovative estimators have been developed in the past decade in order to handle this issue. Even though consistent estimators have been proposed, the formulations and interpretations of some estimators are less intuitive to practitioners. On the other hand, more intuitive estimators have been proposed, but their mathematical properties have not been established. In this paper, we prove the analytic identity between some estimators (a statistically motivated estimator and an intuitive estimator) for censored cost data. Efron (1967) made similar investigation for censored survival data (between the Kaplan-Meier estimator and the redistribute-to-the-right algorithm). Therefore, we view our study as an extension of Efron's work to informatively censored data so that our findings could be applied to other marked variables.