Asymptotic properties of mean survival estimate based on the Kaplan-Meier curve with an extrapolated tail

Cost-effectiveness model of trastuzumab deruxtecan as second-line treatment in HER2-positive unresectable and/or metastatic breast cancer in Finland

OBJECTIVES

Trastuzumab deruxtecan (T-DXd) was recently recommended by the Committee for Medicinal Products for Human Use as a treatment for adult patients with unresectable or metastatic HER2-positive breast cancer, who had received a prior anti-HER2-based regimen. In our study, we evaluated the cost-effectiveness of T-DXd compared with ado-trastuzumab emtansine (T-DM1) for this indication in Finland.

METHODS

A three-state partitioned survival analysis model was developed with a payer's perspective. Time to event data from the DESTINY-Breast03 (DB-03) trial were extrapolated over a lifetime horizon either directly-for progression-free survival and time to treatment discontinuation-or using an alternative approach utilizing long-term T-DM1 survival data and DB-03 data-for overall survival. Discount rates of 3% were applied for costs and effects. Inputs were sourced from the Medicinal Products Database from Kela, Helsinki University Hospital service price list, Finnish Medicines Agency assessments, clinical experts, and DB-03. Sensitivity analyses were performed to characterize and demonstrate parameter uncertainties in the model.

RESULTS

Total quality-adjusted life years (QALYs) and life years (LYs) gained for T-DXd compared with T-DM1 were 1.93 and 2.56, respectively. Incremental costs for T-DXd compared with T-DM1 were €106,800, resulting in an ICER of €55,360 per QALY gained and an ICER of €41,775 per LY gained. One-way sensitivity analysis showed the hazard ratio of T-DXd vs T-DM1 for OS was the most influential parameter. The probabilistic sensitivity analysis showed similar results to the base case.

CONCLUSIONS

T-DXd is cost-effective based on surrogate WTP thresholds of €72,000 and €139,000 per QALY.

Socioeconomic Disparities in Individual-Level Quality-Adjusted Life Years throughout Remaining Lifetimes: A National Representative Longitudinal Survey in China

Socioeconomic disparities in health within and across low- and middle-income countries pose a significant global public health concern. While prior research has demonstrated the importance of socioeconomic status on health outcomes, few studies have employed comprehensive measures of individual-level health such as quality-adjusted life years (QALYs) in exploring the quantitative relationship. In our study, we employed QALYs to measure individual-level health, using health-related quality of life scores based on the Short Form 36 and predicted remaining life years through individual-specific Weibull survival analysis. We then constructed a linear regression model to explore the socioeconomic factors that influence QALYs, providing a predictive model of individual-level QALYs throughout remaining lifetimes. This practical tool can help individuals predict their remaining healthy life years. Using data from the China Health and Retirement Longitudinal Study between 2011 and 2018, we found that education and occupation were the primary factors influencing health outcomes among individuals aged 45 and above, while income appeared to have less of an impact when education and occupation were simultaneously controlled for. To promote the health status of this population, low- and middle-income countries should prioritize the long-term advancement of their population's education while controlling unemployment rates in the short term.

On the use of extreme value tail modeling for generalized pairwise comparisons with censored outcomes

In randomized clinical trials, methods of pairwise comparisons such as the 'Net Benefit' or the 'win ratio' have recently gained much attention when interests lies in assessing the effect of a treatment as compared to a standard of care. Among other advantages, these methods are usually praised for delivering a treatment measure that can easily handle multiple outcomes of different nature, while keeping a meaningful interpretation for patients and clinicians. For time-to-event outcomes, a recent suggestion emerged in the literature for estimating these treatment measures by providing a natural handling of censored outcomes. However, this estimation procedure may lead to biased estimates when tails of survival functions cannot be reliably estimated using Kaplan-Meier estimators. The problem then extrapolates to the other outcomes incorporated in the pairwise comparison construction. In this work, we suggest to extend the procedure by the consideration of a hybrid survival function estimator that relies on an extreme value tail model through the Generalized Pareto distribution. We provide an estimator of treatment effect measures that notably improves on bias and remains easily apprehended for practical implementation. This is illustrated in an extensive simulation study as well as in an actual trial of a new cancer immunotherapy.

Transcription factors linked to the molecular signatures in the development of hepatocellular carcinoma on a cirrhotic background

Mechanisms underlying the regulation of gene expression in cancer have been surveyed for decades to find novel prognostic factors and new targets for molecular targeted therapies in cancer. Because most cases of liver cancer are associated with liver cirrhosis, we aimed to analyze the gene expression signatures and the gene regulatory mechanism in hepatocellular carcinoma (HCC) on a cirrhotic background using high-throughput data analysis. In the present study, three valid array-based datasets containing HCC and liver cirrhosis samples were obtained to identify common differentially expressed genes (DEGs). Moreover, a comprehensive data analysis was conducted based on RNA-Seq data and using Kaplan-Meier curve analysis to find molecular signatures that reduce patients' survival rate. Furthermore, we proposed a gene regulatory network (GRN) to explore the possible regulatory mechanism of these molecular signatures by transcription factors in HCC progression from cirrhosis. Besides, we analyzed protein-protein interactions, gene ontology (GO), and pathway enrichment to elucidate the cellular and molecular function of the GRN elements in HCC. In this way, we found a list of 231 molecular signatures in HCC derived from cirrhosis. We also found the importance of TCF4, RUNX1, HINFP, KDM2B, MAF, JUN, NR5A2, NFYA, and AR as key differentially expressed transcription factors (DETFs) in the progression of HCC from cirrhosis. In conclusion, the identified molecular signatures and their transcription factors propose candidate prognostic markers and possible molecular targets in the progression of HCC.

Threshold regression to accommodate a censored covariate

In several common study designs, regression modeling is complicated by the presence of censored covariates. Examples of such covariates include maternal age of onset of dementia that may be right censored in an Alzheimer's amyloid imaging study of healthy subjects, metabolite measurements that are subject to limit of detection censoring in a case-control study of cardiovascular disease, and progressive biomarkers whose baseline values are of interest, but are measured post-baseline in longitudinal neuropsychological studies of Alzheimer's disease. We propose threshold regression approaches for linear regression models with a covariate that is subject to random censoring. Threshold regression methods allow for immediate testing of the significance of the effect of a censored covariate. In addition, they provide for unbiased estimation of the regression coefficient of the censored covariate. We derive the asymptotic properties of the resulting estimators under mild regularity conditions. Simulations demonstrate that the proposed estimators have good finite-sample performance, and often offer improved efficiency over existing methods. We also derive a principled method for selection of the threshold. We illustrate the approach in application to an Alzheimer's disease study that investigated brain amyloid levels in older individuals, as measured through positron emission tomography scans, as a function of maternal age of dementia onset, with adjustment for other covariates. We have developed an R package, censCov, for implementation of our method, available at CRAN.

An application of restricted mean survival time in a competing risks setting: comparing time to ART initiation by injection drug use

Background

Restricted mean survival time (RMST) is an underutilized estimand in time-to-event analyses. Herein, we highlight its strengths by comparing time to (1) all-cause mortality and (2) initiation of antiretroviral therapy (ART) for HIV-infected persons who inject drugs (PWID) and persons who do not inject drugs.

Methods

RMST to death was determined by integrating the Kaplan-Meier survival curve to 5 years of follow-up. To account for the competing risks of death and loss-to-clinic when estimating time to ART, we calculated RMST to ART initiation by estimating the area between the survival curve for ART initiation and the cumulative incidence curve for death or loss-to-clinic. We standardized all curves using inverse probability of exposure weights.

Results

We followed 3044 HIV-positive, ART-naive persons from enrollment into the Johns Hopkins HIV Clinical Cohort from 1996 to 2014. PWID had a − 0.19 year (95% confidence interval (CI): − 0.29, − 0.10) difference in survival over 5 years of follow-up compared to persons who did not inject drugs. There was no difference between the two groups in time not on ART while alive and in clinic (RMST difference = 0.08, 95% CI: -0.10, 0.36).

Conclusions

PWID have similar expected time to ART initiation after properly accounting for their greater risk of death and loss-to-clinic.

Electronic supplementary material

The online version of this article (10.1186/s12874-018-0484-z) contains supplementary material, which is available to authorized users.

Tobit regression for modeling mean survival time using data subject to multiple sources of censoring

Mean survival time is often of inherent interest in medical and epidemiologic studies. In the presence of censoring and when covariate effects are of interest, Cox regression is the strong default, but mostly due to convenience and familiarity. When survival times are uncensored, covariate effects can be estimated as differences in mean survival through linear regression. Tobit regression can validly be performed through maximum likelihood when the censoring times are fixed (ie, known for each subject, even in cases where the outcome is observed). However, Tobit regression is generally inapplicable when the response is subject to random right censoring. We propose Tobit regression methods based on weighted maximum likelihood which are applicable to survival times subject to both fixed and random censoring times. Under the proposed approach, known right censoring is handled naturally through the Tobit model, with inverse probability of censoring weighting used to overcome random censoring. Essentially, the re-weighting data are intended to represent those that would have been observed in the absence of random censoring. We develop methods for estimating the Tobit regression parameter, then the population mean survival time. A closed form large-sample variance estimator is proposed for the regression parameter estimator, with a semiparametric bootstrap standard error estimator derived for the population mean. The proposed methods are easily implementable using standard software. Finite-sample properties are assessed through simulation. The methods are applied to a large cohort of patients wait-listed for kidney transplantation.

Burden of disease associated with lower levels of income among US adults aged 65 and older

BACKGROUND

Persons aged 65 years and older represent a heterogeneous group whose prevalence in the USA is expected to markedly increase. Few investigations have examined the total burden of disease attributable to lower levels of income in a single number that accounts for morbidity and mortality.

METHODS

We ascertained respondents' health-related quality of life (HRQOL) scores and mortality status from the 2003 to 2004, 2005 to 2006, 2007 to 2008 and 2009 to 2010 cohorts of the National Health and Nutrition Examination Survey (NHANES) with mortality follow-up through 31 December 2011. A mapping algorithm based on respondents' age and answers to the 4 core Healthy Days questions was used to obtain values of a preference-based measure of HRQOL, the EuroQol five dimensions questionnaire (EQ-5D) index, which enables quality-adjusted life years (QALYs) to be calculated. We included only respondents aged 65 years and older at the baseline, yielding a total sample size of 4952. We estimated mean QALYs according to different categories of income based on the percentage of Federal Poverty Level (FPL).

RESULTS

After adjusting for age, gender and education, the remaining QALYs decreased with each successive decrement of category of income, ranging from 18.4 QALY (≥500% FPL) to 8.6 QALY (<100% FPL). Compared with participants with a mean income of ≥250% FPL, participants with an income <250% FPL had significant losses in QALY for most of the sociodemographic groups examined. In contrast, persons with a lower educational attainment did not show a corresponding loss in QALY according to income category.

CONCLUSIONS

This study confirmed the association between lower income category and greater burden of disease, as measured by QALYs lost, among the US population aged 65 years and older. Our findings provide additional evidence of the role played by other key determinants of health and how factors not traditionally addressed by the healthcare system impact the life cycle of individuals and communities.

Incremental decreases in quality-adjusted life years (QALY) associated with higher levels of depressive symptoms for U.S. Adults aged 65 years and older

Background

Quality-adjusted life years (QALY) is a single value index that quantifies the overall burden of disease. It reflects all aspects of heath, including nonfatal illness and mortality outcomes by weighting life-years lived with health-related quality of life (HRQOL) scores. This study examine the burden of disease due to increasing levels of depressive symptoms by examining the association between the 9-item Patient Health Questionnaire (PHQ-9) scores and QALY for U.S. adults aged 65 years and older.

Methods

We ascertained respondents’ HRQOL scores and mortality status from the 2005–2006, 2007–2008, and 2009–2010 cohorts of the National Health and Nutrition Examination Survey (NHANES) with mortality follow-up data through December 31, 2011. This analysis included respondents aged 65 years and older (n = 3,680). We estimated the mean QALY throughout the remaining lifetime according to participants’ depression severity categories: none or minimal (PHQ-9 score 0–4), mild (5–9), moderate (10–14), and moderately severs and severe (15 or higher). We estimated QALY loss due to major depressive disorder (PHQ-9 score 10 or higher) and to mild depression (5–9).

Results

The QALY for persons with none/minimal, mild, moderate, and moderately severe/severe depression were 14.0, 7.8, 4.7, and 3.3 years, respectively. Compared to persons without major depressive disorder, persons with major depressive disorder had 8.3 fewer QALY (12.7 vs. 4.4), or a 65% loss. Compared to persons who reported “none” or minimal depressive symptoms, persons who reported mild depressive symptoms had 6.2 fewer QALY (14.0 vs. 7.8), or a 44% loss. The same patterns were noted in demographic and socioeconomic subgroups and according to number of comorbidities.

Conclusions

This study not only confirmed the significant burden of disease for major depressive disorder among the U.S. elderly, but also showed an incremental decrease in QALY with an increasing severity of depressive symptoms as well as significant QALY loss due to mild depression. Specifically, individuals with higher (or more impaired) PHQ-9 scores had significantly fewer QALYs and our findings of fewer years of QALY for persons with major depressive disorder and mild depression were not only statistically significant but also clinically important.

Bias and precision of methods for estimating the difference in restricted mean survival time from an individual patient data meta-analysis

Background

The difference in restricted mean survival time (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ rmstD\left({t}^{\ast}\right) $$\end{document}rmstDt∗), the area between two survival curves up to time horizon \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {t}^{\ast } $$\end{document}t∗, is often used in cost-effectiveness analyses to estimate the treatment effect in randomized controlled trials. A challenge in individual patient data (IPD) meta-analyses is to account for the trial effect. We aimed at comparing different methods to estimate the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ rmstD\left({t}^{\ast}\right) $$\end{document}rmstDt∗ from an IPD meta-analysis.

Methods

We compared four methods: the area between Kaplan-Meier curves (experimental vs. control arm) ignoring the trial effect (Naïve Kaplan-Meier); the area between Peto curves computed at quintiles of event times (Peto-quintile); the weighted average of the areas between either trial-specific Kaplan-Meier curves (Pooled Kaplan-Meier) or trial-specific exponential curves (Pooled Exponential). In a simulation study, we varied the between-trial heterogeneity for the baseline hazard and for the treatment effect (possibly correlated), the overall treatment effect, the time horizon \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {t}^{\ast } $$\end{document}t∗, the number of trials and of patients, the use of fixed or DerSimonian-Laird random effects model, and the proportionality of hazards. We compared the methods in terms of bias, empirical and average standard errors. We used IPD from the Meta-Analysis of Chemotherapy in Nasopharynx Carcinoma (MAC-NPC) and its updated version MAC-NPC2 for illustration that included respectively 1,975 and 5,028 patients in 11 and 23 comparisons.

Results

The Naïve Kaplan-Meier method was unbiased, whereas the Pooled Exponential and, to a much lesser extent, the Pooled Kaplan-Meier methods showed a bias with non-proportional hazards. The Peto-quintile method underestimated the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ rmstD\left({t}^{\ast}\right) $$\end{document}rmstDt∗, except with non-proportional hazards at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {t}^{\ast } $$\end{document}t∗= 5 years. In the presence of treatment effect heterogeneity, all methods except the Pooled Kaplan-Meier and the Pooled Exponential with DerSimonian-Laird random effects underestimated the standard error of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ rmstD\left({t}^{\ast}\right) $$\end{document}rmstDt∗. Overall, the Pooled Kaplan-Meier method with DerSimonian-Laird random effects formed the best compromise in terms of bias and variance. The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ rmstD\left({t}^{\ast },=,10,\kern0.5em ,\mathrm{years}\right) $$\end{document}rmstDt∗=10years estimated with the Pooled Kaplan-Meier method was 0.49 years (95 % CI: [−0.06;1.03], p = 0.08) when comparing radiotherapy plus chemotherapy vs. radiotherapy alone in the MAC-NPC and 0.59 years (95 % CI: [0.34;0.84], p < 0.0001) in the MAC-NPC2.

Conclusions

We recommend the Pooled Kaplan-Meier method with DerSimonian-Laird random effects to estimate the difference in restricted mean survival time from an individual-patient data meta-analysis.

Electronic supplementary material

The online version of this article (doi:10.1186/s12874-016-0137-z) contains supplementary material, which is available to authorized users.

Difference in Restricted Mean Survival Time for Cost-Effectiveness Analysis Using Individual Patient Data Meta-Analysis: Evidence from a Case Study

Objective

In economic evaluation, a commonly used outcome measure for the treatment effect is the between-arm difference in restricted mean survival time (rmstD). This study illustrates how different survival analysis methods can be used to estimate the rmstD for economic evaluation using individual patient data (IPD) meta-analysis. Our aim was to study if/how the choice of a method impacts on cost-effectiveness results.

Methods

We used IPD from the Meta-Analysis of Radiotherapy in Lung Cancer concerning 2,000 patients with locally advanced non-small cell lung cancer, included in ten trials. We considered methods either used in the field of meta-analysis or in economic evaluation but never applied to assess the rmstD for economic evaluation using IPD meta-analysis. Methods were classified into two approaches. With the first approach, the rmstD is estimated directly as the area between the two pooled survival curves. With the second approach, the rmstD is based on the aggregation of the rmstDs estimated in each trial.

Results

The average incremental cost-effectiveness ratio (ICER) and acceptability curves were sensitive to the method used to estimate the rmstD. The estimated rmstDs ranged from 1.7 month to 2.5 months, and mean ICERs ranged from € 24,299 to € 34,934 per life-year gained depending on the chosen method. At a ceiling ratio of € 25,000 per life year-gained, the probability of the experimental treatment being cost-effective ranged from 31% to 68%.

Conclusions

This case study suggests that the method chosen to estimate the rmstD from IPD meta-analysis is likely to influence the results of cost-effectiveness analyses.

Impact of nine chronic conditions for US adults aged 65 years and older: an application of a hybrid estimator of quality-adjusted life years throughout remainder of lifetime

PURPOSE

To estimate quality-adjusted life years (QALY) loss due to each of the following nine chronic conditions-depression, diabetes mellitus, hypertension, heart disease, stroke, emphysema, asthma, arthritis, and cancer.

METHODS

We ascertained respondents' health-related quality of life scores and mortality status from the 2005 to 2008 National Health and Nutrition Examination Survey (NHANES) with mortality follow-up data through December 31, 2011. We included respondents aged 65 years and older (n = 2380). A hybrid estimator was used to calculate QALY from two parts: QALY during the follow-up period and QALY beyond the follow-up period. We calculated QALY by each of the nine chronic conditions.

RESULTS

For persons aged 65 and older, QALY throughout the reminder of lifetime was 12.3 years. After adjusting for age- and sex-related differences, depression had an associated 8.2 years of QALY loss; diabetes, 5.6 years; hypertension, 2.5 years; heart disease, 5.4 years; stroke, 6.4 years; emphysema, 8.0 years; asthma, 4.8 years; arthritis, 0.3 years; and cancer, 2.5 years. Compared to persons without any chronic conditions, persons with one condition had an associated 4.7 years of QALY loss; persons with two conditions, 7.9 years; and persons with three or more conditions, 10.8 years.

CONCLUSIONS

This study presents a QALY estimator for respondents in the NHANES-Linked Mortality File and demonstrates the utility of this method to other follow-up data. Continued application of our method would enable the burden of disease to be compared for a range of health conditions and risk factors in the ongoing effort to improve population health.

Bias and precision of measures of survival gain from right-censored data

In cost-effectiveness analyses of drugs or health technologies, estimates of life years saved or quality-adjusted life years saved are required. Randomised controlled trials can provide an estimate of the average treatment effect; for survival data, the treatment effect is the difference in mean survival. However, typically not all patients will have reached the endpoint of interest at the close-out of a trial, making it difficult to estimate the difference in mean survival. In this situation, it is common to report the more readily estimable difference in median survival. Alternative approaches to estimating the mean have also been proposed. We conducted a simulation study to investigate the bias and precision of the three most commonly used sample measures of absolute survival gain--difference in median, restricted mean and extended mean survival--when used as estimates of the true mean difference, under different censoring proportions, while assuming a range of survival patterns, represented by Weibull survival distributions with constant, increasing and decreasing hazards. Our study showed that the three commonly used methods tended to underestimate the true treatment effect; consequently, the incremental cost-effectiveness ratio (ICER) would be overestimated. Of the three methods, the least biased is the extended mean survival, which perhaps should be used as the point estimate of the treatment effect to be inputted into the ICER, while the other two approaches could be used in sensitivity analyses. More work on the trade-offs between simple extrapolation using the exponential distribution and more complicated extrapolation using other methods would be valuable.

Summarising censored survival data using the mean residual life function

The mean residual life function provides a clear and simple summary of the effect of a treatment or a risk factor in units of time, avoiding hazard ratios or probability scales, which require careful interpretation. Estimation of the mean residual life is complicated by the upper tail of the survival distribution not being observed as, for example, patients may still be alive at the end of the follow-up period. Various approaches have been developed to estimate the mean residual life in the presence of such right censoring. In this work, a novel semi-parametric method that combines existing non-parametric methods and an extreme value tail model is presented, where the limited sample information in the tail (prior to study termination) is used to estimate the upper tail behaviour. This approach will be demonstrated with simulated and real-life examples.