Multistate Survival Analysis Research Articles

Comparative Effectiveness of Treatment Strategies for Bladder Cancer With Clinical Evidence of Regional Lymph Node Involvement

Patients with bladder cancer with clinical lymph node involvement (cN+) are at high risk for distant metastases, but are potentially curable. Such patients are excluded from neoadjuvant chemotherapy trials and pooled with patients with distant metastases in first-line chemotherapy trials not suited to define the role of combined-modality therapy. To address this evidence void, we performed a comparative effectiveness analysis. We included cTanyN1-3M0 bladder cancer patients from the National Cancer Data Base (2003-2012) treated with chemotherapy and/or cystectomy. We used multistate survival analysis, allowing for delayed entry, to assess overall survival (OS) according to various treatment strategies. Effectiveness was estimated with multivariable adjustment for tumor-, patient-, and facility-level characteristics. Among 1,739 patients (cN1, 48%; cN2, 45%; cN3, 7%), 1,104 underwent cystectomy and 635 were treated with chemotherapy alone. Of the cystectomy patients, 363 received preoperative and 328 received adjuvant chemotherapy. The crude 5-year OS for chemotherapy alone, cystectomy alone, preoperative chemotherapy followed by cystectomy, and cystectomy followed by adjuvant chemotherapy was 14% (95% CI, 11% to 17%), 19% (95% CI, 15% to 24%), 31% (95% CI, 25% to 38%), and 26% (95% CI, 21% to 34%), respectively. Compared with cystectomy alone, preoperative chemotherapy was associated with a significant improvement in OS (hazard ratio, 0.80; 95% CI, 0.66 to 0.97). Adjuvant chemotherapy was also associated with a significant improvement in survival compared with cystectomy alone. The survival of patients treated with chemotherapy alone was worse than those treated with cystectomy alone. A subset of patients with cN+ bladder cancer achieves long-term survival. Combined-modality therapy, with chemotherapy and cystectomy, is associated with the best outcomes.

Multistate Survival Models as Transient Electrical Networks

ABSTRACTIn multistate survival analysis, the sojourn of a patient through various clinical states is shown to correspond to the diffusion of 1 C of electrical charge through an electrical network. The essential comparison has differentials of probability for the patient to correspond to differentials of charge, and it equates clinical states to electrical nodes. Indeed, if the death state of the patient corresponds to the sink node of the circuit, then the transient current that would be seen on an oscilloscope as the sink output is a plot of the probability density for the survival time of the patient. This electrical circuit analogy is further explored by considering the simplest possible survival model with two clinical states, alive and dead (sink), that incorporates censoring and truncation. The sink output seen on an oscilloscope is a plot of the Kaplan–Meier mass function. Thus, the Kaplan–Meier estimator finds motivation from the dynamics of current flow, as a fundamental physical law, rather than as a nonparametric maximum likelihood estimate (MLE). Generalization to competing risks settings with multiple death states (sinks) leads to cause‐specific Kaplan–Meier submass functions as outputs at sink nodes. With covariates present, the electrical analogy provides for an intuitive understanding of partial likelihood and various baseline hazard estimates often used with the proportional hazards model.

Characterizing Sleep Structure Using the Hypnogram

Research on the effects of sleep-disordered breathing (SDB) on sleep structure has traditionally been based on composite sleep-stage summaries. The primary objective of this investigation was to demonstrate the utility of log-linear and multistate analysis of the sleep hypnogram in evaluating differences in nocturnal sleep structure in subjects with and without SDB. A community-based sample of middle-aged and older adults with and without SDB matched on age, sex, race, and body mass index was identified from the Sleep Heart Health Study. Sleep was assessed with home polysomnography and categorized into rapid eye movement (REM) and non-REM (NREM) sleep. Log-linear and multistate survival analysis models were used to quantify the frequency and hazard rates of transitioning, respectively, between wakefulness, NREM sleep, and REM sleep. Whereas composite sleep-stage summaries were similar between the two groups, subjects with SDB had higher frequencies and hazard rates for transitioning between the three states. Specifically, log-linear models showed that subjects with SDB had more wake-to-NREM sleep and NREM sleep-to-wake transitions, compared with subjects without SDB. Multistate survival models revealed that subjects with SDB transitioned more quickly from wake-to-NREM sleep and NREM sleep-to-wake than did subjects without SDB. The description of sleep continuity with log-linear and multistate analysis of the sleep hypnogram suggests that such methods can identify differences in sleep structure that are not evident with conventional sleep-stage summaries. Detailed characterization of nocturnal sleep evolution with event history methods provides additional means for testing hypotheses on how specific conditions impact sleep continuity and whether sleep disruption is associated with adverse health outcomes.

Additive hazards Markov regression models illustrated with bone marrow transplant data

SUMMARY When there are covariate effects to be considered, multi-state survival analysis is dominated either by parametric Markov regression models or by semiparametric Markov regression models using Cox's (1972) proportional hazards models for transition intensities between the states. The purpose of this research work is to study alternatives to Cox's model in a general finite-state Markov process setting. We shall look at two alternative models, Aalen's (1989) nonparametric additive hazards model and Lin & Ying's (1994) semiparametric additive hazards model. The former allows the effects of covariates to vary freely over time, while the latter assumes that the regression coefficients are constant over time. With the basic tools of the product integral and the functional delta-method, we present an estimator of the transition probability matrix and develop the large-sample theory for the estimator under each of these two models. Data on 1459 HLA identical sibling transplants for acute leukaemia from the International Bone Marrow Transplant Registry serve as illustration.

A random effects model for multistate survival analysis with application to bone marrow transplants

We present an extension of the non-homogeneous Markov model for a bone marrow transplant recovery process which allows for possible associations between the transition intensities. The associations between intensities are modeled by a correlated gamma frailty model. Based on a parametric model for the conditional transition intensities, we obtain estimates of the model parameters. We use these estimates to make predictions of patient’s eventual prognosis given the current medical history of the patient. Estimates of the uncertainty in our predictions are obtained by a modified bootstrap technique.

Quality-Adjusted Survival Estimation with Periodic Observations: A Multistate Survival Analysis Approach

Quality-adjusted survival is a composite measure that combines quality-of-life and survival data. Analyzing quality-adjusted survival with data collected at periodic intervals can be difficult because of incomplete information resulting from dropouts or missing visits. Dropouts could be purely random or caused by treatments or the illness itself. In a multistate model, dropout information can be incorporated into analysis by including the “dropout” state as a state of the patient's health. Under a Markovian assumption on patients' health status, we applied a multistate survival analysis approach that extends Chen and Sen's study [Chen, P.-L., Sen, P. K. (2001). Quality adjusted survival estimation with periodic observation. Biometrics 57:868–874] which estimated the mean quality-adjusted survival where the transition probability between health states and patients' expected survival time can be estimated simultaneously. Here we show that the estimator is asymptotically normal with simple variance calculation. We conducted a simulation study to investigate the behavior of the estimator, and used a long-term contraceptive study to illustrate the use of the estimator.

Prognosis for Ambulation in Cerebral Palsy: A Population-Based Study

To determine independent predictors of ambulation among children with cerebral palsy and to develop a simple tool that estimates the probability that a child will walk. In a retrospective study of all children with cerebral palsy who were not yet walking at 2 to 3(1/2) years of age, while receiving services from the California Department of Developmental Services during the years 1987-1999, we analyzed medical and functional data obtained annually by Department of Developmental Services physicians and social workers. Using logistic regression analyses, we determined independent predictors of a child's ability to walk well alone at least 20 feet, without assistive devices, by age 6. We then estimated the probabilities of walking at various levels of ability over time, using multistate survival analysis. Of 5366 study subjects, 2295 (43%) were evaluated at age 6; 12.8% could walk independently and 18.4% walked with support. Independent predictors of successful ambulation included early motor milestones such as sitting (odds ratio: 12.5; 95% confidence interval: 5.8-27.2) and pulling to a stand (odds ratio: 28.5; 95% confidence interval: 13.4-60.4) when compared with lack of rolling at age 2, cerebral palsy type other than spastic quadriparesis (odds ratio: 2.2; 95% confidence interval: 1.5-3.1), and preserved visual function (odds ratio: 2.4; 95% confidence interval: 1.1-5.4). Our ambulation charts depict the probability of remaining nonambulatory, transitioning to 1 of 3 possible ambulatory states, or expiring at all subsequent ages through age 14. The ambulation charts provide a simple straightforward way to estimate the probability that a child with cerebral palsy who is nonambulatory at 2 to 3 12 years of age will eventually walk with or without support.

Temporal process regression

SUMMARY We consider regression for response and covariates which are temporal processes observed over intervals. A functional generalised linear model is proposed which includes extensions of standard models in multi-state survival analysis. Simple nonparametric esti mators of time-indexed parameters are developed using 'working independence' estimating equations and are shown to be uniformly consistent and to converge weakly to Gaussian processes. The procedure does not require smoothing or a Markov assumption, unlike approaches based on transition intensities. The usual definition of optimal estimating equations for parametric models is then generalised to the functional model and the optimum is identified in a class of functional generalised estimating equations. Simulations demonstrate large efficiency gains relative to working independence at times where censoring is heavy. The estimators are the basis for new tests of the covariate effects and for the estimation of models in which greater structure is imposed on the parameters, providing novel goodness-of-fit tests. The methodology's practical utility is illustrated in a data analysis.

Simultaneous analysis of quality of life and survival data.

In many phase III clinical trials, particularly in the field of cancer, the comparison of treatments is based on both length of survival and quality of life. Subjects are followed over time until death and during this period, quality of life is assessed on a number of occasions. Simultaneous analysis of these two outcomes supplements the comparison of treatments in terms of each outcome independently with an assessment of the net effect. In addition, it provides a means of accounting for the informative dropout due to death of patients within the time frame of the quality of life study. The methods also have the potential to be extended to allow for informative dropout from the quality of life study prior to death. There are a number of broad approaches for the simultaneous analysis of quality of life and survival data. The most widely used approach in clinical research is quality-adjusted survival analysis, where treatments are compared in terms of a composite measure of quality and quantity of life. The paper reviews the different techniques for quality-adjusted survival analysis, illustrating the methodology by application to data from a phase III clinical trial in pancreatic cancer. In addition, alternative approaches using multistate survival analysis and joint modelling methods are also discussed.

Analytic difficulties in applying quality of life outcomes to clinical trials of therapy for HIV disease

Abstract Despite considerable enthusiasm for the concept, quality-of-life or health status outcomes are seldom employed in clinical trials. The failure of common analytic procedures to meet key requirements may have contributed to this limited acceptance. In particular, (1) results of clinical trials must be expressed in terms that clinicians, regulators, administrators, and patients find useful, (2) reasonable means of summarizing outcomes should be available a priori, (3) scale units should have real world meaning, (4) unwarranted assumptions regarding scale properties should be avoided, and (5) adequate methods for handling attrition due to death or drop-out are necessary. Our group has developed approaches to these problems. We summarize overall outcome using a weighted sum of scores for scales covering several domains and weights derived from regressions of scale scores on a reference variable. Our multistate survival analysis. an extension of standard survival analysis attempts to circumvent some of the difficulties with attrition and poor scale properties of health status/quality of life measures. Multistate survival analysis has two components, a description of survival-in-state, and significance test based on transitions-from-state. In survival-in-state analysis, we generalize the usual survival analysis to consider the proportions of participants with a health or quality status which is at least equal to that indicated by specified ordered states. In transition-from-states analysis, we generalize the Mantel-Haenszel procedure to simultaneously consider upward and downward transitions from previous health or quality state to improved or worsened states. These approaches incorporate mortality without requiring specification of a score value for death, allow reasonable handling of attrition, give results denominated in proportions or time units rather than score values, and allow assessment of net changes in status for individual participants between evaluations.

Plotting summary predictions in multistate survival models: Probabilities of relapse and death in remission for bone marrow transplantation patients

Multistate survival analysis usually involves a series of detailed regressional analyses describing transitions between various states. There is an often neglected need for the many estimates resulting from such an analysis to be re-synthesized into summary statements, such as prediction of various outcomes from specified patient histories. Arjas and Erola recently proposed a framework for dynamic probabilistic causality which has calculation of such prediction statements as a central tool. We illustrate these procedures on data from a multicentre bone marrow transplantation study, with death while in remission and relapse as terminal events and recovery of the patients's platelets to a normal level and the onset of acute graft-versus-host disease as intermediate events, using Cox regression models throughout. Among the features illustrated by the resulting plots is a strong effect on death while in remission if the platelets do not recover within the first three months.

Multistate Survival Analysis: An Application in Breast Cancer

SummaryThe extension of the proportional hazard model of Cox for survival data allows the consideration of transition times between events of interest (e.g., response, relapse, progression, etc.) and of competing risks. This paper applies these new models to a breast cancer study and gives some general remarks for the proceeding.

Some Test Statistics for use in Multistate Survival Analysis

Some Test Statistics for use in Multistate Survival Analysis

Some test statistics for use in multistate survival analysis

SUMMARY Some current nonparametric methods related to the log rank test are extended to cover ordered categories of response, e.g. response, no change, progression, and to incorporate information on duration of response. As an example, data from a protocol for the treatment of advanced breast cancer are analysed. The powers of several tests for this special case of multistate survival data are compared by Monte Carlo simulation for both small and moderate samples from exponential and Weibull distributions.