Regression Models for the Mean of the Quality-of-Life-Adjusted Restricted Survival Time Using Pseudo-Observations

A comparison of quality-adjusted life years in older adults after heart transplantation versus long-term mechanical support: Findings from the SUSTAIN-IT study

BACKGROUND

The quality-adjusted life year (QALY) measures disease burden and treatment, combining overall survival and health-related quality of life (HRQOL). We estimated QALYs in 3 groups of older patients (60-80 years) with heart failure (HF) who underwent heart transplantation (HT, with pre-transplant mechanical circulatory support [HT MCS] or HT without pre-transplant MCS [HT Non-MCS]) or long-term MCS (destination therapy). We also identified factors associated with gains in QALYs through 24 months follow-up.

METHODS

Of 393 eligible patients enrolled (10/1/15-12/31/18) at 13 U.S. sites, 161 underwent HT (n = 68 HT MCS, n = 93 HT Non-MCS) and 144 underwent long-term MCS. Survival and HRQOL data were collected through 24 months. QALY health utilities were based on patient self-report of EQ-5D-3L dimensions. Mean-restricted QALYs were compared among groups using generalized linear models.

RESULTS

For the entire cohort, mean age in years closest to surgery was 67 (standard deviation, SD: 4.7), 78% were male, and 83% were White. By 18 months post-surgery, sustained significant differences in adjusted average ± SD QALYs emerged across groups, with the HT Non-MCS group having the highest average QALYs (24-month window: HT Non-MCS = 22.58 ± 1.1, HT MCS = 19.53 ± 1.33, Long-term MCS = 19.49 ± 1.3, p = 0.003). At 24 months post-operatively, a lower gain in QALYs was associated with HT MCS, long-term MCS, a lower pre-operative LVEF, NYHA class III or IV before surgery, and an ischemic or other etiology of HF.

CONCLUSIONS

Determination of QALYs may provide important information for policy makers and clinicians to consider regarding benefits of HT and long-term MCS as treatment options for older patients with HF.

Analysis of survival data with cure fraction and variable selection: A pseudo-observations approach

In biomedical studies, survival data with a cure fraction (the proportion of subjects cured of disease) are commonly encountered. The mixture cure and bounded cumulative hazard models are two main types of cure fraction models when analyzing survival data with long-term survivors. In this article, in the framework of the Cox proportional hazards mixture cure model and bounded cumulative hazard model, we propose several estimators utilizing pseudo-observations to assess the effects of covariates on the cure rate and the risk of having the event of interest for survival data with a cure fraction. A variable selection procedure is also presented based on the pseudo-observations using penalized generalized estimating equations for proportional hazards mixture cure and bounded cumulative hazard models. Extensive simulation studies are conducted to examine the proposed methods. The proposed technique is demonstrated through applications to a melanoma study and a dental data set with high-dimensional covariates.

A semiparametric modeling approach for analyzing clinical biomarkers restricted to limits of detection

Before biomarkers can be used in clinical trials or patients' management, the laboratory assays that measure their levels have to go through development and analytical validation. One of the most critical performance metrics for validation of any assay is related to the minimum amount of values that can be detected and any value below this limit is referred to as below the limit of detection (LOD). Most of the existing approaches that model such biomarkers, restricted by LOD, are parametric in nature. These parametric models, however, heavily depend on the distributional assumptions, and can result in loss of precision under the model or the distributional misspecifications. Using an example from a prostate cancer clinical trial, we show how a critical relationship between serum androgen biomarker and a prognostic factor of overall survival is completely missed by the widely used parametric Tobit model. Motivated by this example, we implement a semiparametric approach, through a pseudo-value technique, that effectively captures the important relationship between the LOD restricted serum androgen and the prognostic factor. Our simulations show that the pseudo-value based semiparametric model outperforms a commonly used parametric model for modeling below LOD biomarkers by having lower mean square errors of estimation.

Causal inference for recurrent event data using pseudo-observations

Recurrent event data are commonly encountered in observational studies where each subject may experience a particular event repeatedly over time. In this article, we aim to compare cumulative rate functions (CRFs) of two groups when treatment assignment may depend on the unbalanced distribution of confounders. Several estimators based on pseudo-observations are proposed to adjust for the confounding effects, namely inverse probability of treatment weighting estimator, regression model-based estimators, and doubly robust estimators. The proposed marginal regression estimator and doubly robust estimators based on pseudo-observations are shown to be consistent and asymptotically normal. A bootstrap approach is proposed for the variance estimation of the proposed estimators. Model diagnostic plots of residuals are presented to assess the goodness-of-fit for the proposed regression models. A family of adjusted two-sample pseudo-score tests is proposed to compare two CRFs. Simulation studies are conducted to assess finite sample performance of the proposed method. The proposed technique is demonstrated through an application to a hospital readmission data set.

Regression analysis of recurrent-event-free time from multiple follow-up windows

This research develops multivariable restricted time models appropriate for analysis of recurrent events data, where data is repurposed into censored longitudinal time-to-first-event outcomes in τ-length follow-up windows. We develop two approaches for addressing the censored nature of the outcomes: a pseudo-observation (PO) approach and a multiple-imputation (MI) approach. Each of these approaches allows for complete data methods, such as generalized estimating equations, to be used for the analysis of the newly constructed correlated outcomes. Through simulation, this manuscript assesses the performance of the proposed PO and MI methods. Both PO and MI approaches show attractive results with either correlated or independent gap times in an individual. We also demonstrate how to apply the proposed methods in the data from azithromycin in Chronic Obstructive Pulmonary Disease Trial.

A flexible semiparametric modeling approach for doubly censored data with an application to prostate cancer

Doubly censored data often arise in medical studies of disease progression involving two related events for which both an originating and a terminating event are interval-censored. Although regression modeling for such doubly censored data may be complicated, we propose a simple semiparametric regression modeling strategy based on jackknife pseudo-observations obtained using nonparametric estimators of the survival function. Inference is carried out via generalized estimating equations. Simulations studies show that the proposed method produces virtually unbiased covariate effect estimates, even for moderate sample sizes. A prostate cancer study example illustrates the practical advantages of the proposed approach.

Effects of Recipient Age and Diagnosis on Health-related Quality-of-Life Benefit of Lung Transplantation

RATIONALE

The average age of lung transplant recipients is increasing, and the mix of recipient indications for transplantation is changing.

OBJECTIVES

To determine whether the health-related quality-of-life (HRQL) benefit of lung transplantation differs by recipient age and diagnosis.

METHODS

In this prospective cohort study, we obtained serial HRQL measurements in adults with advanced lung disease who subsequently underwent lung transplantation (2004-2012). HRQL assessments included the St. George's Respiratory Questionnaire, 36-Item Short-Form Health Survey (SF-36), EQ-5D, Standard Gamble, and Visual Analog Scale for current health. We used linear mixed effects models for associations between age or diagnosis and changes in HRQL with transplantation. To address potential survivorship bias, we fitted Markov models to the distribution of discrete post-transplant health states (HRQL better than pretransplant, not better, or dead) and estimated quality-adjusted life-years post-transplant.

MEASUREMENTS AND MAIN RESULTS

A total of 430 subjects were listed, 387 were transplanted, and 326 provided both pretransplant and post-transplant data. Transplantation conferred large improvements in all HRQL measures: St. George's change of -47 units (95% confidence interval, -48 to -44), 36-Item Short-Form Health Survey physical component summary score of 17.7 (16.5-18.9), EQ-5D of 0.27 (0.24-0.30), Standard Gamble of 0.48 (0.44-0.51), and Visual Analog of 44 (42-47). Age was not associated with meaningful differences in the HRQL benefits of transplantation. There was less HRQL benefit in interstitial lung disease than in cystic fibrosis.

CONCLUSIONS

Lung transplantation confers large HRQL benefits, which vary by recipient diagnosis, but do not differ substantially in older recipients.

The k-sample problem in a multi-state model and testing transition probability matrices

The choice of multi-state models is natural in analysis of survival data, e.g., when the subjects in a study pass through different states like 'healthy', 'in a state of remission', 'relapse' or 'dead' in a health related quality of life study. Competing risks is another common instance of the use of multi-state models. Statistical inference for such event history data can be carried out by assuming a stochastic process model. Under such a setting, comparison of the event history data generated by two different treatments calls for testing equality of the corresponding transition probability matrices. The present paper proposes solution to this class of problems by assuming a non-homogeneous Markov process to describe the transitions among the health states. A class of test statistics are derived for comparison of [Formula: see text] treatments by using a 'weight process'. This class, in particular, yields generalisations of the log-rank, Gehan, Peto-Peto and Harrington-Fleming tests. For an intrinsic comparison of the treatments, the 'leave-one-out' jackknife method is employed for identifying influential observations. The proposed methods are then used to develop the Kolmogorov-Smirnov type supremum tests corresponding to the various extended tests. To demonstrate the usefulness of the test procedures developed, a simulation study was carried out and an application to the Trial V data provided by International Breast Cancer Study Group is discussed.

Quality-adjusted time without symptoms or toxicity (Q-TWiST): patient-reported outcome or mathematical model? A systematic review in cancer

OBJECTIVE

Successful cancer treatment is defined as an increase in overall survival and/or progression-free survival. Despite their importance, these metrics omit patient quality of life. Quality-adjusted time without symptoms or toxicity (Q-TWiST) was developed to adjust survival gained, accounting for quality of life. The purpose of this systematic review was to assess the methods reported in cancer literature to determine Q-TWiST values and how these are currently translated to the clinic.

METHODS

The Preferred Reporting Items for Systematic Reviews and Meta-analyses guidelines were used to conduct a systematic review of studies indexed on MEDLINE and Web of Science through April 2013. Cancer studies that measured Q-TWiST either as a primary outcome or retrospectively and determined utility coefficients from a patient population were identified, and their methods reviewed to determine how the utility coefficient was calculated. Additionally, other relevant factors such as definitions of health states and significant findings were collected and summarized.

RESULTS

Out of 284 studies, 11 were identified that calculated patient-defined utility coefficients. Several methods to determine utility coefficients were reported, and multiple definitions of health state toxicity were applied. Of these studies, seven reported significant differences (p < 0.05) in quality-adjusted survival. No studies, however, directly discussed the clinical relevance of their findings.

CONCLUSIONS

Currently, Q-TWiST is utilized as a mathematical theory rather than a clinical tool. Standardization of terminology plus reliability and validity testing of determining both utility coefficients and time frame definitions must be performed before Q-TWiST can become clinically useful to physicians and patients alike for making treatment decisions.

Pseudo-observations in survival analysis

We review recent work on the application of pseudo-observations in survival and event history analysis. This includes regression models for parameters like the survival function in a single point, the restricted mean survival time and transition or state occupation probabilities in multi-state models, e.g. the competing risks cumulative incidence function. Graphical and numerical methods for assessing goodness-of-fit for hazard regression models and for the Fine—Gray model in competing risks studies based on pseudo-observations are also reviewed. Sensitivity to covariate-dependent censoring is studied. The methods are illustrated using a data set from bone marrow transplantation.