Inference for outcome probabilities in multi-state models

Weighted reverse counting process (WRCP): A novel approach to quantify the overall treatment effect with multiple time-to-event outcomes by adaptive weighting

In a longitudinal randomized study where multiple time-to-event outcomes are collected, the overall treatment effect may be quantified by a composite endpoint defined as the time to the first occurrence of any of the selected events including death. The reverse counting process (RCP) was recently proposed to extend the restricted mean survival time (RMST) approach with an advantage of utilizing observations of events beyond the "first-occurrence" endpoint. However, the interpretation may be questionable because RCP treats all events equally without considering their different associations with the overall survival. In this work, we propose a novel approach, the weighted reverse counting process (WRCP), to construct a weighted composite endpoint to evaluate the overall treatment effect. A multi-state transition model is used to model the association between events, and an adaptive weighting algorithm is developed to determine the weight for individual endpoints based on the association between the nonfatal endpoints and death using the trial data. Simulation studies are presented to compare the performance of WRCP with RCP, log-rank test and RMST approach. The results show that WRCP is a powerful and robust method to detect the overall treatment effect while controlling the clinically false positive rate well across different simulation scenarios.

Activities of Daily Living Disability Transition Patterns in Older Adults with Chronic Diseases: A Four-Year Cohort Study in China

BACKGROUND

Older adults with chronic diseases often experience higher rates of Activities of Daily Living (ADL) disability, with research primarily examining the transition between states of ADL disability and non-disability. The current study aims to analyze the patterns and factors of mutual transitions between multiple different ADL disability states in older adults with chronic diseases.

METHODS

This longitudinal study utilized data from the Shanghai Elderly Care Unified Needs Assessment (SECUNA) spanning 2014 to 2017, with 2014 being the baseline. The study included older adults aged 60 years and older with chronic diseases. Using the Markov model, individuals were classified into three states: no ADL disability, mild ADL disability, and severe ADL disability. Transition patterns were analyzed by calculating the frequency, intensity, and probability of transition, and the influencing factors of six transition scenarios were evaluated.

RESULTS

Older adults with mild ADL disability were more likely to experience improvement (transition intensity: 0.4731) rather than deterioration (transition intensity: 0.2226) in their ADL disability states. However, those with severe ADL disability faced challenges in improving their states (transition intensities: 0.0068 and 0.1204). Among the six ADL disability transition scenarios, place of residence was associated with four scenarios, age and economic sources were associated with three scenarios, sex was associated with two scenarios, and other factors were associated with one scenario.

CONCLUSIONS

The transition patterns and factors differ among individuals with varying ADL disability states. It is essential for relevant agencies to implement tailored preventive healthcare strategies to effectively manage the health status of older adults with chronic diseases.

Association Between Variables and Transitions Among No Opioid Use, Opioid Use, and Subsequent Dropout Among Participants on Methadone Treatment: A Retrospective Study Utilizing a Multistate Model

BACKGROUND

Although previous studies have reported the variables that influence opioid use or dropout among participants receiving methadone treatment, limited attention has been given to the variables related to transitions among no opioid use, opioid use, and dropout.

METHODS

This retrospective study utilized data collected from June 2010 to June 2022 at 11 methadone treatment clinics in Guangdong Province, China. Two transient states (no opioid use and opioid use) and 1 absorbing state (dropout) were defined based on monthly urine morphine test results and daily methadone intake records. We used a multistate model to explore the variables associated with transitions among no opioid use, opioid use, and dropout among participants.

RESULTS

Among 3136 participants, with an average treatment duration of 497 days, 1646 (52.49%) underwent at least 1 period of opioid use, resulting in 3283 transitions from no opioid use to opioid use. The transitions between no opioid use and opioid use were significantly associated with variables such as age, gender, employment status, marital status, living situation, travel time to the clinic, human immunodeficiency virus and hepatitis C virus infection statuses, average methadone dosage, and attendance rates. The variables influencing participants' dropout varied depending on their opioid use behaviors. Additionally, the probability of a specified opioid use state remaining unchanged or transitioning to a different state at a defined time point would change over time.

CONCLUSIONS

The opioid use behaviors of participants are dynamic. Methadone providers should offer targeted interventions based on participants' opioid use behaviors to effectively decrease rates of opioid use and improve retention.

Association between chronic disease status and transitions in depressive symptoms among middle-aged and older Chinese population: Insights from a Markov model-based cohort study

BACKGROUND

The relationship between chronic disease status (CDS) and transitions in depressive symptoms (DS) remains unclear. This study explores the association between CDS and DS transitions.

METHODS

This cohort study analyzed data from 8175 participants aged 45+, sourced from China Family Panel Studies (2016, 2018, 2020). DS were assessed using a brief version of Center for Epidemiologic Studies Depression Scale (CES-D). CDS was categorized into healthy, single disease, and multimorbidity. Markov models were used to estimate state transition intensities, mean sojourn times and hazard ratios (HRs).

RESULTS

DS transitions occurred between adjacent and non-adjacent states, but transition intensity between adjacent states was higher than among non-adjacent states. Self-transition intensities of severe-DS, mild-DS, and non-DS progressively increased, with average durations of 1.365, 1.482, and 7.854 years, respectively. Both single disease and multimorbidity were significantly associated with an increased risk of transitioning from non-DS to mild-DS, with multimorbidity showing a stronger association. In contrast, HRs for single diseases transitioning from mild-DS to severe-DS were significantly lower than 1. Furthermore, their HRs were almost <1 in recovery transitions but not statistically significant.

LIMITATIONS

Specific chronic diseases and their combinations were not analyzed.

CONCLUSIONS

The progression of DS exhibits various pathways. CDS is associated with DS transitions, but the roles of single disease and multimorbidity may differ across different DS progression stages. Both conditions were significantly linked to the risk of new-onset DS, with multimorbidity posing a greater association. However, this relationship is not observed in other progression stages. These findings could provide insights for early prevention and intervention for DS.

Statistical methods applied for the assessment of the HIV cascade and continuum of care: a systematic scoping review

OBJECTIVES

This scoping review aims to identify and synthesise existing statistical methods used to assess the progress of HIV treatment programmes in terms of the HIV cascade and continuum of care among people living with HIV (PLHIV).

DESIGN

Systematic scoping review.

DATA SOURCES

Published articles were retrieved from PubMed, Cumulative Index to Nursing and Allied Health Literature (CINAHL) Complete and Excerpta Medica dataBASE (EMBASE) databases between April and July 2022. We also strategically search using the Google Scholar search engine and reference lists of published articles.

ELIGIBILITY CRITERIA

This scoping review included original English articles that estimated and described the HIV cascade and continuum of care progress in PLHIV. The review considered quantitative articles that evaluated either HIV care cascade progress in terms of the Joint United Nations Programme on HIV and AIDS targets or the dynamics of engagement in HIV care.

DATA EXTRACTION AND SYNTHESIS

The first author and the librarian developed database search queries and screened the retrieved titles and abstracts. Two independent reviewers and the first author extracted data using a standardised data extraction tool. The data analysis was descriptive and the findings are presented in tables and visuals.

RESULTS

This review included 300 articles. Cross-sectional study design methods were the most commonly used to assess the HIV care cascade (n=279, 93%). In cross-sectional and longitudinal studies, the majority used proportions to describe individuals at each cascade stage (276/279 (99%) and 20/21 (95%), respectively). In longitudinal studies, the time spent in cascade stages, transition probabilities and cumulative incidence functions was estimated. The logistic regression model was common in both cross-sectional (101/279, 36%) and longitudinal studies (7/21, 33%). Of the 21 articles that used a longitudinal design, six articles used multistate models, which included non-parametric, parametric, continuous-time, time-homogeneous and discrete-time multistate Markov models.

CONCLUSIONS

Most literature on the HIV cascade and continuum of care arises from cross-sectional studies. The use of longitudinal study design methods in the HIV cascade is growing because such methods can provide additional information about transition dynamics along the cascade. Therefore, a methodological guide for applying different types of longitudinal design methods to the HIV continuum of care assessments is warranted.

Adjusting for informative cluster size in pseudo-value-based regression approaches with clustered time to event data

Informative cluster size (ICS) arises in situations with clustered data where a latent relationship exists between the number of participants in a cluster and the outcome measures. Although this phenomenon has been sporadically reported in the statistical literature for nearly two decades now, further exploration is needed in certain statistical methodologies to avoid potentially misleading inferences. For inference about population quantities without covariates, inverse cluster size reweightings are often employed to adjust for ICS. Further, to study the effect of covariates on disease progression described by a multistate model, the pseudo-value regression technique has gained popularity in time-to-event data analysis. We seek to answer the question: "How to apply pseudo-value regression to clustered time-to-event data when cluster size is informative?" ICS adjustment by the reweighting method can be performed in two steps; estimation of marginal functions of the multistate model and fitting the estimating equations based on pseudo-value responses, leading to four possible strategies. We present theoretical arguments and thorough simulation experiments to ascertain the correct strategy for adjusting for ICS. A further extension of our methodology is implemented to include informativeness induced by the intracluster group size. We demonstrate the methods in two real-world applications: (i) to determine predictors of tooth survival in a periodontal study and (ii) to identify indicators of ambulatory recovery in spinal cord injury patients who participated in locomotor-training rehabilitation.

A nomogram for predicting cause-specific mortality among patients with cecal carcinoma: a study based on SEER database

OBJECTIVE

Classical Cox proportional hazard models tend to overestimate the event probability in a competing risk setup. Due to the lack of quantitative evaluation of competitive risk data for colon cancer (CC), the present study aims to evaluate the probability of CC-specific death and construct a nomogram to quantify survival differences among CC patients.

METHODS

Data on patients diagnosed with CC between 2010 and 2015 were collected from the Surveillance, Epidemiology, and End Results Program (SEER) database. Patients were divided into a training dataset for the establishment of the model and a validation dataset to evaluate the performance the model at a ratio of 7:3. To evaluate the ability of multiple variables to predict cause-specific death in CC patients, univariate and multivariate analyses with Fine-Gray models were performed to screen the predictors of cause-specific death, and a nomogram for predicting cause-specific mortality was constructed. Then, the receiver operating characteristic (ROC) curve and the calibration curve were plotted to evaluate the prognostic performance of the nomogram.

RESULTS

The dataset was randomly divided into a training (n = 16,655) dataset and a validation (n = 7,139) dataset at a ratio of 7:3. In the training dataset, variables including pathological subtypes of tumors, pathological grading (degree of differentiation), AJCC staging, T-staging, surgical type, lymph node surgery, chemotherapy, tumor deposits, lymph node metastasis, liver metastasis, and lung metastasis were identified as independent risk factors for cause-specific death of CC patients. Among these factors, the AJCC stage had the strongest predictive ability, and these features were used to construct the final model. In the training dataset, the consistency index (C-index) of the model was 0.848, and the areas under the receiver operating characteristic curve (AUC) at 1, 3, and 5 years was 0.852, 0.861, and 0.856, respectively. In the validation dataset, the C-index of the model was 0.847, and the AUC at 1 year, 3 years, and 5 years was 0.841, 0.862, and 0.852, respectively, indicating that this nomogram had an excellent and robust predictive performance.

CONCLUSION

This study can help clinical doctors make better clinical decisions and provide better support for patients with CC.

Semiparametric copula method for semi-competing risks data subject to interval censoring and left truncation: Application to disability in elderly

We aim to evaluate the marginal effects of covariates on time-to-disability in the elderly under the semi-competing risks framework, as death dependently censors disability, not vice versa. It becomes particularly challenging when time-to-disability is subject to interval censoring due to intermittent assessments. A left truncation issue arises when the age time scale is applied. We develop a flexible two-parameter copula-based semiparametric transformation model for semi-competing risks data subject to interval censoring and left truncation. The two-parameter copula quantifies both upper and lower tail dependence between two margins. The semiparametric transformation models incorporate proportional hazards and proportional odds models in both margins. We propose a two-step sieve maximum likelihood estimation procedure and study the sieve estimators' asymptotic properties. Simulations show that the proposed method corrects biases in the marginal method. We demonstrate the proposed method in a large-scale Chinese Longitudinal Healthy Longevity Study and provide new insights into preventing disability in the elderly. The proposed method could be applied to the general semi-competing risks data with intermittently assessed disease status.

Estimation in discrete time coarsened multivariate longitudinal models

We consider the analysis of longitudinal data of multiple types of events where some of the events are observed on a coarser level (e.g. grouped) at some time points during the follow-up, for example, when certain events, such as disease progression, are only observable during parts of follow-up for some subjects, causing gaps in the data, or when the time of death is observed but the cause of death is unknown. In this case, there is missing data in key characteristics of the event history such as onset, time in state, and number of events. We derive the likelihood function, score and observed information under independent and non-informative coarsening, and conduct a simulation study where we compare bias, empirical standard errors, and confidence interval coverage of estimators based on direct maximum likelihood, Monte Carlo Expectation Maximisation, ignoring the coarsening thus acting as if no event occurred, and artificial right censoring at the first time of coarsening. Longitudinal data on drug prescriptions and survival in men receiving palliative treatment for prostate cancer is used to estimate the parameters of one of the data-generating models. We demonstrate that the performance depends on several factors, including sample size and type of coarsening.

Inference for transition probabilities in non-Markov multi-state models

Multi-state models are frequently used when data come from subjects observed over time and where focus is on the occurrence of events that the subjects may experience. A convenient modeling assumption is that the multi-state stochastic process is Markovian, in which case a number of methods are available when doing inference for both transition intensities and transition probabilities. The Markov assumption, however, is quite strict and may not fit actual data in a satisfactory way. Therefore, inference methods for non-Markov models are needed. In this paper, we review methods for estimating transition probabilities in such models and suggest ways of doing regression analysis based on pseudo observations. In particular, we will compare methods using land-marking with methods using plug-in. The methods are illustrated using simulations and practical examples from medical research.

Motivational Drivers of Temporal Dynamics in Postretirement Work

OBJECTIVES

Many retirees continue to work in retirement, but the temporal dynamics of this process are not well understood. This article examined the extent to which retirees increase, decrease, and exit their work engagement over time. We hypothesized that different motives for postretirement work-financial, social, personal, and organizational-have differential affects on changes in work extent.

METHODS

We analyzed 7 waves of the HEalth, Aging and Retirement Transitions in Sweden study (n = 3,123). Postretirement work was defined as working for pay while receiving pension benefits. Changes in work extent were estimated with multistate models and examined in relation to the 4 motives.

RESULTS

Results showed a gradual decrease in work extent following retirement. Financial motives increased the likelihood to take up more work and decreased the likelihood to reduce work hours. Social motives increased the likelihood to reduce and exit work, while personal motives decreased the likelihood for those same pathways. Organizational (demand-driven) motives increased the likelihood to stop working.

DISCUSSION

Our findings suggest that financial motives constitute an important driver for taking up more work in retirement, while motives related to the personal meaning of work explain why retirees maintain their level of engagement over time. The social function of work, on the other hand, may be gradually replaced by social activities outside of work, resulting in a gradual disengagement from work. Finally, demand-driven motives appear insufficient to remain in the labor force, highlighting the need to acknowledge the diversity of motives for continuing to work.

Longitudinal transition of body mass index status and its associated factors among Chinese middle-aged and older adults in Markov model

Introduction

Body mass index (BMI) has a strong correlation with chronic diseases and all-cause mortality. However, few studies have previously reported the longitudinal transition of BMI status and its influential factors, especially among Chinese middle-aged and older adults.

Methods

This population-based cohort study involved 6,507 participants derived from the China Health and Retirement Longitudinal Study from 2011 to 2015, including objectively measured BMI recorded in 26,028 person-year of all observations followed up. Multistate Markov model was performed to estimate the BMI state transition intensity and hazard ratios of each potential exposure risk.

Results

The mean intensity of the population that shifted from normal to overweight was more than twice than shifted to underweight. Besides, a predicted probability was up to 16.16% that the population with overweight would suffer from obesity and more than half of the population with underweight would return to normal weight over a 6-year interval. The study also implied significant effects of baseline age, gender, marital status, education level, alcohol consumption, smoking, depression symptoms, and activities of daily living impairment on BMI status transition to varying degrees.

Conclusions

Findings of this study indicated that the mean transition probability between different BMI statuses varied, specific exposure factors serving as barriers or motivators to future transitions based on current BMI status was clarified for the health promotion strategies.

The transitions and predictors of cognitive frailty with multi-state Markov model: a cohort study

BACKGROUND

Cognitive frailty (CF) is characterized by the simultaneous presence of physical frailty and cognitive impairment. Previous studies have investigated its prevalence and impact on different adverse health-related outcomes. Few studies have focused on the progression and reversibility of CF and their potential predictors.

METHODS

Data were derived from the China Health and Retirement Longitudinal Study (CHARLS). A total of 4051 older adults with complete data on three waves of the survey (2011, 2013, and 2015) were included and categorized into four groups: normal state (NS), cognitive impairment (CI) only, physical frailty (PF) only and CF (with both PF and CI). A multi-state Markov model was constructed to explore the transitions and predicting factors of CF.

RESULTS

The incidence and improvement rates of CF were 1.70 and 11.90 per 100 person-years, respectively. The 1-year transition probability of progression to CF in those with CI was higher than that in the PF population (0.340 vs. 0.054), and those with CF were more likely to move to PF (0.208). Being female [hazard ratio (HR) = 1.46, 95%CI = 1.06, 2.02)], dissatisfied with life (HR = 4.94, 95%CI = 1.04, 23.61), had a history of falls (HR = 2.36, 95%CI = 1.02, 5.51), rural household registration (HR = 2.98, 95%CI = 1.61, 5.48), multimorbidity (HR = 2.17, 95%CI = 1.03, 4.59), and depression (HR = 1.75, 95%CI = 1.26, 2.45) increased the risk of progression to CF, whereas literacy (HR = 0.46, 95%CI = 0.33, 0.64) decreased such risk. Depression (HR = 0.43, 95%CI = 0.22, 0.84) reduced the likelihood of CF improvement, whereas literacy (HR = 2.23, 95%CI = 1.63, 3.07) increased such likelihood.

CONCLUSIONS

Cognitive frailty is a dynamically changing condition in older adults. Possible interventions aimed at preventing the onset and facilitating the recovery of cognitive frailty should focus on improving cognitive function in older adults.

A multistate competing risks framework for preconception prediction of pregnancy outcomes

Background

Preconception pregnancy risk profiles—characterizing the likelihood that a pregnancy attempt results in a full-term birth, preterm birth, clinical pregnancy loss, or failure to conceive—can provide critical information during the early stages of a pregnancy attempt, when obstetricians are best positioned to intervene to improve the chances of successful conception and full-term live birth. Yet the task of constructing and validating risk assessment tools for this earlier intervention window is complicated by several statistical features: the final outcome of the pregnancy attempt is multinomial in nature, and it summarizes the results of two intermediate stages, conception and gestation, whose outcomes are subject to competing risks, measured on different time scales, and governed by different biological processes. In light of this complexity, existing pregnancy risk assessment tools largely focus on predicting a single adverse pregnancy outcome, and make these predictions at some later, post-conception time point.

Methods

We reframe the individual pregnancy attempt as a multistate model comprised of two nested multinomial prediction tasks: one corresponding to conception and the other to the subsequent outcome of that pregnancy. We discuss the estimation of this model in the presence of multiple stages of outcome missingness and then introduce an inverse-probability-weighted Hypervolume Under the Manifold statistic to validate the resulting multivariate risk scores. Finally, we use data from the Effects of Aspirin in Gestation and Reproduction (EAGeR) trial to illustrate how this multistate competing risks framework might be utilized in practice to construct and validate a preconception pregnancy risk assessment tool.

Results

In the EAGeR study population, the resulting risk profiles are able to meaningfully discriminate between the four pregnancy attempt outcomes of interest and represent a significant improvement over classification by random chance.

Conclusions

As illustrated in our analysis of the EAGeR data, our proposed prediction framework expands the pregnancy risk assessment task in two key ways—by considering a broader array of pregnancy outcomes and by providing the predictions at an earlier, preconception intervention window—providing obstetricians and their patients with more information and opportunities to successfully guide pregnancy attempts.

Integrating relative survival in multi-state models—a non-parametric approach

Multi-state models provide an extension of the usual survival/event-history analysis setting. In the medical domain, multi-state models give the possibility of further investigating intermediate events such as relapse and remission. In this work, a further extension is proposed using relative survival, where mortality due to population causes (i.e. non-disease-related mortality) is evaluated. The objective is to split all mortality in disease and non-disease-related mortality, with and without intermediate events, in datasets where cause of death is not recorded or is uncertain. To this end, population mortality tables are integrated into the estimation process, while using the basic relative survival idea that the overall mortality hazard can be written as a sum of a population and an excess part. Hence, we propose an upgraded non-parametric approach to estimation, where population mortality is taken into account. Precise definitions and suitable estimators are given for both the transition hazards and probabilities. Variance estimating techniques and confidence intervals are introduced and the behaviour of the new method is investigated through simulations. The newly developed methodology is illustrated by the analysis of a cohort of patients followed after an allogeneic hematopoietic stem cell transplantation. The work has been implemented in the R package mstate.

Treatment response after palliative radiotherapy for bleeding gastric cancer: a multicenter prospective observational study (JROSG 17-3)

BACKGROUND

Palliative radiotherapy seems to be rarely performed for incurable gastric cancer. In this first multicenter study, we examined the effectiveness of palliative radiotherapy and investigated whether biologically effective dose (BED) is associated with survival, response, or re-bleeding.

METHODS

Eligibility criteria included blood transfusion or hemoglobin levels < 8.0 g/dL. The primary endpoint was the intention-to-treat (ITT) bleeding response rate at 4 weeks. Response entailed all of the following criteria: (i) hemoglobin levels ≥ 8.0 g/dL; (ii) 7 consecutive days without blood transfusion anytime between enrollment and blood sampling; and (iii) no salvage treatment (surgery, endoscopic treatment, transcatheter embolization, or re-irradiation) for bleeding gastric cancer. Re-bleeding was defined as the need for blood transfusion or salvage treatment.

RESULTS

We enrolled 55 patients from 15 institutions. The ITT response rates were 47%, 53%, and 49% at 2, 4, and 8 weeks, respectively. The per-protocol response rates were 56%, 78%, and 90% at 2, 4, and 8 weeks, respectively. Neither response nor BED (α/β = 10) predicted overall survival. Multivariable Fine-Gray model showed that BED was not a significant predictor of response. Univariable Cox model showed that BED was not significantly associated with re-bleeding. Grades 1, 2, 3, and, ≥ 4 radiation-related adverse events were reported in 11, 9, 1, and 0 patients, respectively.

CONCLUSIONS

The per-protocol response rate increased to 90% during the 8-week follow-up. The frequent occurrence of death starting shortly after enrollment lowered the ITT response rate. BED was not associated with survival, bleeding response, or re-bleeding.

Development of a dynamic interactive web tool to enhance understanding of multi-state model analyses: MSMplus

BACKGROUND

Multi-state models are used in complex disease pathways to describe a process where an individual moves from one state to the next, taking into account competing states during each transition. In a multi-state setting, there are various measures to be estimated that are of great epidemiological importance. However, increased complexity of the multi-state setting and predictions over time for individuals with different covariate patterns may lead to increased difficulty in communicating the estimated measures. The need for easy and meaningful communication of the analysis results motivated the development of a web tool to address these issues.

RESULTS

MSMplus is a publicly available web tool, developed via the Shiny R package, with the aim of enhancing the understanding of multi-state model analyses results. The results from any multi-state model analysis are uploaded to the application in a pre-specified format. Through a variety of user-tailored interactive graphs, the application contributes to an improvement in communication, reporting and interpretation of multi-state analysis results as well as comparison between different approaches. The predicted measures that can be supported by MSMplus include, among others, the transition probabilities, the transition intensity rates, the length of stay in each state, the probability of ever visiting a state and user defined measures. Representation of differences, ratios and confidence intervals of the aforementioned measures are also supported. MSMplus is a useful tool that enhances communication and understanding of multi-state model analyses results.

CONCLUSIONS

Further use and development of web tools should be encouraged in the future as a means to communicate scientific research.

The Value of the Illness-Death Model for Predicting Outcomes in Patients with Non‒Small Cell Lung Cancer

Purpose

The illness-death model (IDM) is a comprehensive approach to evaluate the relationship between relapse and death. This study aimed to illustrate the value of the IDM for identifying risk factors and evaluating predictive probabilities for relapse and death in patients with non–small cell lung cancer (NSCLC) in comparison with the disease-free survival (DFS) model.

Materials and Methods

We retrospectively analyzed 612 NSCLC patients who underwent a curative operation. Using the IDM, the risk factors and predictive probabilities for relapse, death without relapse, and death after relapse were simultaneously evaluated and compared to those obtained from a DFS model.

Results

The IDM provided more detailed risk factors according to the patient’s disease course, including relapse, death without relapse, and death after relapse, in patients with resected lung cancer. In the IDM, history of malignancy (other than lung cancer) was related to relapse and smoking history was associated with death without relapse; both were indistinguishable in the DFS model. In addition, the IDM was able to evaluate the predictive probability and risk factors for death after relapse; this information could not be obtained from the DFS model.

Conclusion

Compared to the DFS model, we found that the IDM provides more comprehensive information on transitions between states and disease stages and provides deeper insights with respect to understanding the disease process among lung cancer patients.

Bayesian survival analysis with BUGS

Survival analysis is one of the most important fields of statistics in medicine and biological sciences. In addition, the computational advances in the last decades have favored the use of Bayesian methods in this context, providing a flexible and powerful alternative to the traditional frequentist approach. The objective of this article is to summarize some of the most popular Bayesian survival models, such as accelerated failure time, proportional hazards, mixture cure, competing risks, multi-state, frailty, and joint models of longitudinal and survival data. Moreover, an implementation of each presented model is provided using a BUGS syntax that can be run with JAGS from the R programming language. Reference to other Bayesian R-packages is also discussed.

Competitive Risk Analysis of Prognosis in Patients With Cecum Cancer: A Population-Based Study

Background:

The presence of competing risks means that the results obtained using the classic Cox proportional-hazards model for the factors affecting the prognosis of patients diagnosed with cecum cancer (CC) may be biased.

Objective:

The purpose of this study was to establish a competitive risk model for patients diagnosed with CC to evaluate the relevant factors affecting the prognosis of patients, and to compare the results with the classical COX proportional risk model.

Methods:

We extracted data on patients diagnosed with CC registered between 2004 and 2016 in the Surveillance, Epidemiology, and End Results (SEER) database. The univariate analysis utilized the cumulative incidence function and Gray’s test, while a multivariate analysis was performed using the Fine-Gray, cause-specific (CS), and Cox proportional-hazards models.

Results:

The 54463 eligible patients diagnosed with CC included 24387 who died: 12087 from CC and 12300 from other causes. The multivariate Fine-Gray analysis indicated that significant factors affecting the prognosis of patients diagnosed with CC include: age, race, AJCC stage, differentiation grade, tumor size, surgery, radiotherapy, chemotherapy and regional lymph nodes metastasis. Due to the presence of competitive risk events, COX model results could not provide accurate estimates of effects and false-negative results occurred. In addition, COX model misestimated the direction of association between regional lymph node metastasis and cumulative risk of death in patients diagnosed with CC. Competitive risk models tend to be more advantageous when analyzing clinical survival data with multiple endpoints.

Conclusions:

The present study can help clinicians to make better clinical decisions and provide patients diagnosed with CC with better support.

High hopes: lower risk of death due to mental disorders and self-harm in a century-long US Olympian cohort compared with the general population

OBJECTIVE

To determine the risk of death due to prominent mental disorders, substance abuse, and self-harm among US Olympians compared with the general population.

METHODS

All female (n=2301) and male (n=5823) US Olympians who participated in the summer or winter Games between 1912 and 2012 were followed until 2016. The National Death Index certified their vital statuses and causes of death. We performed a Standard Mortality Ratio (SMR) analysis for all causes studied and applied the years-saved (YS) method to quantify differences in the risk of death for (1) anxiety, depression and self-harm and (2) substance abuse and eating disorders. Additionally, we examined the YS across sports with greater than 100 total deaths and between medalists and non-medalists.

RESULTS

US Olympians had a 32% (SMR=0.68, 95% CI 0.49 to 0.91) lower risk of death compared with the general population, resulting in a longevity advantage of 0.21 YS (95% CI 0.14 to 0.29) for deaths by depression, anxiety and self-harm and 0.12 years (95% CI 0.08 to 0.15) for substance abuse and eating disorders. There were no significant differences between medalists and non-medalists, but findings varied by sports. Most sports (eg, athletics, swimming, rowing) had significantly lower risks of deaths than the general population with the exceptions of fencing and shooting. Shooting showed a trend towards a higher risk through suicide by firearm.

CONCLUSION

Olympians have a lower risk of death, favouring an increased longevity compared with the general population for mental disorders, substance abuse and suicides.

Midlife Forgetfulness and Risk of Dementia in Old Age: Results from the Danish Working Environment Cohort Study

BACKGROUND

Despite the current evidence of a high prevalence of forgetfulness in middle-aged individuals, and the evidence of a link between midlife memory complaints and biological changes in the brain, no previous study has yet investigated midlife forgetfulness in relation to risk of dementia in old age.

AIMS

We investigated whether midlife forgetfulness was an indicator of an increased risk of dementia in old age.

METHODS

We used data from 3,136 employed men and women who participated in the Danish Work Environment Cohort Study in 1990. These data were linked to Danish national registers. Participants were asked whether their closest relative had ever told them that they were forgetful. Incidence rate ratios (IRR) were estimated using Poisson regression analysis.

RESULTS

At baseline, 749 (24%) study participants were categorized as forgetful, and 86 (2.7%) participants were diagnosed with dementia during a total of 31,724 person-years at risk. After adjusting for sociodemographic factors, comorbidities, and work-related factors, midlife forgetfulness was associated with a higher risk of dementia (IRR = 1.82; 95% CI: 1.12-2.97).

CONCLUSIONS

This study is the first to investigate midlife forgetfulness and dementia, and the results suggest that midlife forgetfulness is an early indicator of an increased risk of dementia in old age.

Natural History of Pediatric Low-Grade Glioma Disease - First Multi-State Model Analysis

Background: Pediatric low-grade glioma [PLGG] is often a chronic progressive disease requiring multiple treatments, i.e. surgery, chemotherapy and irradiation. The multi-state model [MSM] allows an extended analysis of disease-states, that patients may undergo, incorporating competing risks over the course of time.

Purpose: We studied disease-state-probabilities of the German SIOP-LGG 2004 cohort from the initial state “diagnosis” to the final state “death”. Transient “disease-states” incorporated successive surgical and non-surgical treatments. We evaluated clinical risk factors for highly progressive disease requiring multiple interventions and death.

Results: We identified 22 states within 1587 patients (median follow-up 6.3 years). For robust statistical calculation, we reduced the model to 7 states and eventually to three levels of disease-progressiveness: non, low and highly progressive. Five years after diagnosis state-probabilities were: 0.11 no therapy, 0.49 one and 0.11 two or more surgeries only, 0.19 one and 0.06 two or more non-surgical interventions with or without prior surgery. At this time point higher probability for highly progressive disease was found in infants (0.30), supratentorial-midline location (0.17) and diffuse astrocytoma WHO-grade II (0.12). Neurofibromatosis type-1 patients were most likely not to be treated (0.36) or to have received only non-surgical therapy (0.45). Two years after diagnosis 3-year predictions for highly progressive disease and death increased with the number of interventions patients underwent in the first 2 years after diagnosis.

Conclusion: In this first MSM analysis we delineated a refined description of PLGG disease course over time, identifying three levels of progressiveness. Growth behavior in the first two years predicted future progressiveness and death.

Landmark estimation of transition probabilities in non-Markov multi-state models with covariates

In non-Markov multi-state models, the traditional Aalen-Johansen (AJ) estimator for state transition probabilities is generally not valid. An alternative, suggested by Putter and Spitioni, is to analyse a subsample of the full data, consisting of the individuals present in a specific state at a given landmark time-point. The AJ estimator of occupation probabilities is then applied to the landmark subsample. Exploiting the result by Datta and Satten, that the AJ estimator is consistent for state occupation probabilities even in non-Markov models given that censoring is independent of state occupancy and times of transition between states, the landmark Aalen-Johansen (LMAJ) estimator provides consistent estimates of transition probabilities. So far, this approach has only been studied for non-parametric estimation without covariates. In this paper, we show how semi-parametric regression models and inverse probability weights can be used in combination with the LMAJ estimator to perform covariate adjusted analyses. The methods are illustrated by a simulation study and an application to population-wide registry data on work, education and health-related absence in Norway. Results using the traditional AJ estimator and the LMAJ estimator are compared, and show large differences in estimated transition probabilities for highly non-Markov multi-state models.

Social Relations at Work and Incident Dementia: 29-Years' Follow-Up of the Copenhagen Male Study

Objective:

We investigated whether social relations at work were associated with incident dementia in old age.

Methods:

One thousand five hundred seventy-two occupationally active men from the Copenhagen Male Study Cohort were followed from 1986 to 2014. Participants underwent a clinical examination at baseline and answered questionnaires on whether they (1) had possibilities to be in contact with coworkers, (2) could get along with coworkers, and (3) were satisfied with supervisor. Poisson regression was used to estimate incidence rate ratios (IRR).

Results:

Two hundred forty five (15.6%) men were diagnosed with dementia during an average of 15.8 years of follow-up. After adjusting for potential confounders, limited contact with coworkers was associated with a higher risk of dementia (IRR = 2.49, 95% confidence interval [CI] 1.14 to 5.44), but the other two measures were not.

Conclusions:

Our data partially support that social relations at work are associated with incident dementia.

Modeling the hazard of transition into the absorbing state in the illness-death model

The illness-death model is the simplest multistate model where the transition from the initial state 0 to the absorbing state 2 may involve an intermediate state 1 (e.g., disease relapse). The impact of the transition into state 1 on the subsequent transition hazard to state 2 enables insight to be gained into the disease evolution. The standard approach of analysis is modeling the transition hazards from 0 to 2 and from 1 to 2, including time to illness as a time-varying covariate and measuring time from origin even after transition into state 1. The hazard from 1 to 2 can be also modeled separately using only patients in state 1, measuring time from illness and including time to illness as a fixed covariate. A recently proposed approach is a model where time after the transition into state 1 is measured in both scales and time to illness is included as a time-varying covariate. Another possibility is a model where time after transition into state 1 is measured only from illness and time to illness is included as a fixed covariate. Through theoretical reasoning and simulation protocols, we discuss the use of these models and we develop a practical strategy aiming to (a) validate the properties of the illness-death process, (b) estimate the impact of time to illness on the hazard from state 1 to 2, and (c) quantify the impact that the transition into state 1 has on the hazard of the absorbing state. The strategy is also applied to a literature dataset on diabetes.

The population-attributable fraction for time-dependent exposures and competing risks-A discussion on estimands

The population-attributable fraction (PAF) quantifies the public health impact of a harmful exposure. Despite being a measure of significant importance, an estimand accommodating complicated time-to-event data is not clearly defined. We discuss current estimands of the PAF used to quantify the public health impact of an internal time-dependent exposure for data subject to competing outcomes. To overcome some limitations, we proposed a novel estimand that is based on dynamic prediction by landmarking. In a profound simulation study, we discuss interpretation and performance of the various estimands and their estimators. The methods are applied to a large French database to estimate the health impact of ventilator-associated pneumonia for patients in intensive care.

Regression analysis in an illness-death model with interval-censored data: A pseudo-value approach

Pseudo-values provide a method to perform regression analysis for complex quantities with right-censored data. A further complication, interval-censored data, appears when events such as dementia are studied in an epidemiological cohort. We propose an extension of the pseudo-value approach for interval-censored data based on a semi-parametric estimator computed using penalised likelihood and splines. This estimator takes interval-censoring and competing risks into account in an illness-death model. We apply the pseudo-value approach to three mean value parameters of interest in studies of dementia: the probability of staying alive and non-demented, the restricted mean survival time without dementia and the absolute risk of dementia. Simulation studies are conducted to examine properties of pseudo-values based on this semi-parametric estimator. The method is applied to the French cohort PAQUID, which included more than 3,000 non-demented subjects, followed for dementia for more than 25 years.

Quantifying the association between progression-free survival and overall survival in oncology trials using Kendall's τ

This paper considers methods for estimating the association between progression-free and overall survival in oncology trials. Copula-based, nonparametric, and illness-death model-based methods are reviewed. In addition, the approach based on an underlying illness-death model is generalized to allow general parametric models. The performance of these methods, in terms of bias and efficiency, is investigated through simulation and also illustrated using data from a clinical trial of treatments for colon cancer. The simulations suggest that the illness-death model-based method provides good estimates of Kendall's τ across several scenarios. In some situations, copula-based methods perform well but their performance is sensitive to the choice of copula. The Clayton copula is most appropriate in scenarios, which might realistically reflect an oncology trial, but the use of copula models in practice is questionable.

Risk factors of transition from mild cognitive impairment to Alzheimer's disease and death: A cohort study

BACKGROUND

Knowledge of risk factors is essential for developing strategies that prevent or minimise transitions from mild cognitive impairment (MCI) to Alzheimer's disease (AD) and death. The aim of this study was to assess risk factors for progression to AD and death among Chinese individuals with cognitive impairment.

METHODS

We conducted a multisite, population-based cohort study on 437 community-dwelling elderly MCI residents in Taiyuan, China from 2010 to 2014. MCI, AD, death from AD and death from a cause other than AD were specified as disease states during the natural history of dementia. Transition-specific Cox model was fitted and hazard ratio (HR) with 95% confidence intervals (CIs) was estimated.

RESULTS

Analyses showed that risk factors played different roles in affecting transitions to AD and death. Risk factors for transition from MCI to AD were being female (HR: 1.82; 95%CI: 1.20-2.77), older age (HR: 3.09; 95%CI: 1.81-5.25), reading occasionally (HR: 1.79; 95%CI: 1.11-2.89), current smoking (HR: 1.74; 95%CI: 1.15-2.65), light-moderate alcohol drinker (HR: 2.24; 95%CI: 1.42-3.53), cerebrovascular disease (HR: 2.70; 95%CI: 1.68-4.34), hyperlipidemia (HR: 1.87; 95%CI: 1.16-3.02) and diabetes (HR: 1.81; 95%CI: 1.18-2.77). Only cerebrovascular disease (HR: 3.04; 95%CI: 1.22-7.58) was a significant risk factor for transition from MCI to death from a cause other than AD. Older age (HR: 10.68; 95%CI: 1.16-97.93) and low level education (HR: 0.14; 95%CI: 0.05-0.44) were significant predictors for transition from AD to death from a cause other than AD.

CONCLUSIONS

Participants with advanced age, low-level education, history of harmful alcohol consumption or smoking, cerebrovascular disease, hyperlipidemia, diabetes or who were female were at increased risk of transitioning to AD or death. Strategies to control modifiable risk factors in specific disease stage should be implemented to decrease the conversion to AD or death among Chinese patients with MCI.

Current recommendations on the estimation of transition probabilities in Markov cohort models for use in health care decision-making: a targeted literature review

OBJECTIVE

Although Markov cohort models represent one of the most common forms of decision-analytic models used in health care decision-making, correct implementation of such models requires reliable estimation of transition probabilities. This study sought to identify consensus statements or guidelines that detail how such transition probability matrices should be estimated.

METHODS

A literature review was performed to identify relevant publications in the following databases: Medline, Embase, the Cochrane Library, and PubMed. Electronic searches were supplemented by manual-searches of health technology assessment (HTA) websites in Australia, Belgium, Canada, France, Germany, Ireland, Norway, Portugal, Sweden, and the UK. One reviewer assessed studies for eligibility.

RESULTS

Of the 1,931 citations identified in the electronic searches, no studies met the inclusion criteria for full-text review, and no guidelines on transition probabilities in Markov models were identified. Manual-searching of the websites of HTA agencies identified ten guidelines on economic evaluations (Australia, Belgium, Canada, France, Germany, Ireland, Norway, Portugal, Sweden, and UK). All identified guidelines provided general guidance on how to develop economic models, but none provided guidance on the calculation of transition probabilities. One relevant publication was identified following review of the reference lists of HTA agency guidelines: the International Society for Pharmacoeconomics and Outcomes Research taskforce guidance. This provided limited guidance on the use of rates and probabilities.

CONCLUSIONS

There is limited formal guidance available on the estimation of transition probabilities for use in decision-analytic models. Given the increasing importance of cost-effectiveness analysis in the decision-making processes of HTA bodies and other medical decision-makers, there is a need for additional guidance to inform a more consistent approach to decision-analytic modeling. Further research should be done to develop more detailed guidelines on the estimation of transition probabilities.

Basic parametric analysis for a multi-state model in hospital epidemiology

Background

The extended illness-death model is a useful tool to study the risks and consequences of hospital-acquired infections (HAIs). The statistical quantities of interest are the transition-specific hazard rates and the transition probabilities as well as attributable mortality (AM) and the population-attributable fraction (PAF). In the most general case calculation of these expressions is mathematically complex.

Methods

When assuming time-constant hazards calculation of the quantities of interest is facilitated. In this situation the transition probabilities can be expressed in closed mathematical forms. The estimators for AM and PAF can be easily derived from these forms.

Results

In this paper, we show how to explicitly calculate all the transition probabilities of an extended-illness model with constant hazards. Using a parametric model to estimate the time-constant transition specific hazard rates of a data example, the transition probabilities, AM and PAF can be directly calculated. With a publicly available data example, we show how the approach provides first insights into principle time-dynamics and data structure.

Conclusion

Assuming constant hazards facilitates the understanding of multi-state processes. Even in a non-constant hazards setting, the approach is a helpful first step for a comprehensive investigation of complex data.

Electronic supplementary material

The online version of this article (doi:10.1186/s12874-017-0379-4) contains supplementary material, which is available to authorized users.

IQ and mental health are vital predictors of work drop out and early mortality. Multi-state analyses of Norwegian male conscripts

BACKGROUND

Disability benefits and sick leave benefits represents huge costs in western countries. The pathways and prognostic factors for receiving these benefits seen in recent years are complex and manifold. We postulate that mental health and IQ, both alone and concurrent, influence subsequent employment status, disability benefits and mortality.

METHODS

A cohort of 918 888 Norwegian men was followed for 16 years from the age of 20 to 55. Risk for health benefits, emigration, and mortality were studied. Indicators of mental health and IQ at military enrolment were used as potential risk factors. Multi-state models were used to analyze transitions between employment, sick leave, time limited benefits, disability benefits, emigration, and mortality.

RESULTS

During follow up, there were a total of 3 908 397 transitions between employment and different health benefits, plus 12 607 deaths. Men with low IQ (below 85), without any mental health problems at military enrolment, had an increased probability of receiving disability benefits before the age of 35 (HRR = 4.06, 95% CI: 3.88-4.26) compared to men with average IQ (85 to 115) and no mental health problems. For men with both low IQ and mental health problems, there was an excessive probability of receiving disability benefits before the age of 35 (HRR = 14.37, 95% CI: 13.59-15.19), as well as an increased probability for time limited benefits and death before the age of 35 compared to men with average IQ (85 to 115) and no mental health problems.

CONCLUSION

Low IQ and mental health problems are strong predictors of future disability benefits and early mortality for young men.

Non-parametric regression in clustered multistate current status data with informative cluster size

Datasets examining periodontal disease records current (disease) status information of tooth-sites, whose stochastic behavior can be attributed to a multistate system with state occupation determined at a single inspection time. In addition, the tooth-sites remain clustered within a subject, and the number of available tooth-sites may be representative of the true PD status of that subject, leading to an 'informative cluster size' scenario. To provide insulation against incorrect model assumptions, we propose a nonparametric regression framework to estimate state occupation probabilities at a given time and state exit/entry distributions, utilizing weighted monotonic regression and smoothing techniques. We demonstrate the superior performance of our proposed weighted estimators over the un-weighted counterparts via. a simulation study, and illustrate the methodology using a dataset on periodontal disease.

Methodological issues in the design and analyses of neonatal research studies: Experience of the NICHD Neonatal Research Network

Impressive advances in neonatology have occurred over the 30 years of life of The Eunice Kennedy Shriver National Institute of Child Health and Human Development Neonatal Research Network (NRN). However, substantial room for improvement remains in investigating and further developing the evidence base for improving outcomes among the extremely premature. We discuss some of the specific methodological challenges in the statistical design and analysis of randomized trials and observational studies in this population. Challenges faced by the NRN include designing trials for unusual or rare outcomes, accounting for and explaining center variations, identifying other subgroup differences, and balancing safety and efficacy concerns between short-term hospital outcomes and longer-term neurodevelopmental outcomes. In conclusion, the constellation of unique patient characteristics in neonates calls for broad understanding and careful consideration of the issues identified in this article for conducting rigorous studies in this population.

Transitions Between Compensated Work Disability, Joblessness, and Self-Sufficiency: A Cohort Study 1997-2010 of Those Jobless in 1995

Associations between unemployment, work, and disability have been researched in many studies. The findings are often based on cross-sectional data and single outcomes. The present study analysed multiple outcomes over a period of 15 years among long-term unemployed individuals. Based on all individuals aged 20–40 living in Sweden in 1995, prospective cohort analyses were conducted. Individual annual labour market proximity 1995–2010 was estimated and categorised into three mutually exclusive categories: “Jobless”, “Self-sufficient” (i.e. main income from work), or “Disabled”. Individuals in the category “Jobless” (n = 638,622) in 1995 constituted the study population. Using autoregressive multinomial logistic regression, transitions between the three states during 1997–2010 were analysed. Socio-economic factors, previous inpatient care, and national unemployment rates in different time periods were included in the regression models. Among those “Jobless” in 1995, 17 % were also “Jobless” in 2010, while 10 % were “Disabled” and 61 % “Self-sufficient”. The transitions were stable over time periods for transitions into “Self-sufficient” and “Disabled” but less so for “Jobless”. Previous state was the best predictor of subsequent state. “Jobless” individuals with previous morbidity had a higher transition probability into “Disabled” and a lower transition probability into “Self-sufficient”. The transition rates into “Self-sufficient” were higher in periods with lower unemployment levels. The study supports the interpretation that return to work was affected both by the individuals’ previous health status and by the national unemployment level. Transition from being “Jobless” into “Disability” may be influenced by previous ill health and by negative health effects of being “Jobless”.

A marginal structural model for recurrent events in the presence of time-dependent confounding: non-specific effects of vaccines on child hospitalisations

Using a Danish register-based study on childhood vaccination and hospitalisation as motivation, a marginal structural model for recurrent events is studied. The model addresses a number of challenges which may be seen more generally in large register-based cohort studies. One is to adjust for a time-dependent confounder when studying the effect of a time-varying exposure on a recurrent event based on an analysis in continuous time. Another is to report results via a measure which is easy to interpret and communicate even though quite elaborate treatment regimes are considered. Lastly, the implementation of continuously updated weights implies a substantial computationally demanding workload. Copyright © 2016 John Wiley & Sons, Ltd.

Boosting multi-state models

One important goal in multi-state modelling is to explore information about conditional transition-type-specific hazard rate functions by estimating influencing effects of explanatory variables. This may be performed using single transition-type-specific models if these covariate effects are assumed to be different across transition-types. To investigate whether this assumption holds or whether one of the effects is equal across several transition-types (cross-transition-type effect), a combined model has to be applied, for instance with the use of a stratified partial likelihood formulation. Here, prior knowledge about the underlying covariate effect mechanisms is often sparse, especially about ineffectivenesses of transition-type-specific or cross-transition-type effects. As a consequence, data-driven variable selection is an important task: a large number of estimable effects has to be taken into account if joint modelling of all transition-types is performed. A related but subsequent task is model choice: is an effect satisfactory estimated assuming linearity, or is the true underlying nature strongly deviating from linearity? This article introduces component-wise Functional Gradient Descent Boosting (short boosting) for multi-state models, an approach performing unsupervised variable selection and model choice simultaneously within a single estimation run. We demonstrate that features and advantages in the application of boosting introduced and illustrated in classical regression scenarios remain present in the transfer to multi-state models. As a consequence, boosting provides an effective means to answer questions about ineffectiveness and non-linearity of single transition-type-specific or cross-transition-type effects.

Survival Analysis of Breast Cancer Patients after Surgery with an Intermediate Event: Application of Illness-Death Model

BACKGROUND

Breast cancer (BC) is the second most commonly diagnosed cancer after lung cancer. Survival of BC patients is affected by intermediate events. This study was aimed to investigate the disease course of primary nonmetastatic BC patients with first recurrence of the tumor (FRT) as the intermediate event using the illness- death model.

METHODS

This retrospective cohort study was conducted on 529 Iranian females with BC underwent surgery, from 1995 to 2013. Patients, tumor and treatment characteristics were collected from medical records of the patients. The illness-death model were used to investigate the relationship between these factors and survival time. Data were analyzed using version 3.1.1 of R software.

RESULTS

The risk of FRT in patients who had tumors size in the range of 2-5 cm and >5 cm was 1.3 and 3.5 times higher than that of patients with tumor size ≤2 cm, respectively (P<0.001). Furthermore, risk of death in patients aged ≥50 years was 1.6 times higher compared to patients aged less than 50 years (P =0.012). Risk of death after metastasis in patients with tumor size >5 cm was 2.1 times higher than patients with tumor size ≤2 cm (P =0.019).

CONCLUSIONS

The stage of the disease and tumor size have statistically significant effects on patients' survival before occurrence of the FRT. Furthermore, illness-death model was found to be a useful tool in modeling the disease course of BC patients.

Survival probabilities with time-dependent treatment indicator: quantities and non-parametric estimators

The 'landmark' and 'Simon and Makuch' non-parametric estimators of the survival function are commonly used to contrast the survival experience of time-dependent treatment groups in applications such as stem cell transplant versus chemotherapy in leukemia. However, the theoretical survival functions corresponding to the second approach were not clearly defined in the literature, and the use of the 'Simon and Makuch' estimator was criticized in the biostatistical community. Here, we review the 'landmark' approach, showing that it focuses on the average survival of patients conditional on being failure free and on the treatment status assessed at the landmark time. We argue that the 'Simon and Makuch' approach represents counterfactual survival probabilities where treatment status is forced to be fixed: the patient is thought as under chemotherapy without possibility to switch treatment or as under transplant since the beginning of the follow-up. We argue that the 'Simon and Makuch' estimator leads to valid estimates only under the Markov assumption, which is however less likely to occur in practical applications. This motivates the development of a novel approach based on time rescaling, which leads to suitable estimates of the counterfactual probabilities in a semi-Markov process. The method is also extended to deal with a fixed landmark time of interest.

A systematic model specification procedure for an illness-death model without recovery

Multi-state models are a flexible tool for analyzing complex time-to-event problems with multiple endpoints. Compared to the Cox regression model with a single endpoint or a summarizing composite endpoint, they can provide a more detailed insight into the disease process. Furthermore, prognosis can be improved by including information from intermediate events occurring during the course of the disease. Different model variants, options and additional assumptions provide many possibilities, but at the same time complicate the implementation of multi-state techniques. So far, no guiding literature is available to specify a multi-state model systematically. The objective of this work was to set up a general specification procedure for an illness-death model that optimizes the model fit and predictive accuracy by stepwise reduction of the model. As an application example, we reanalyzed data from an observational study of 434 ovarian cancer patients with progression as intermediate and death as absorbing state. The technique is described in general terms and can be applied to other illness-death models without recovery. The clock-reset approach was used, implicating that the time was reset to zero after progression. The non-homogeneous semi-Markov characteristic stated that the present time as well as the time between surgery and progression influenced survival after progression. Covariate effects on transitions were estimated and proportionality of transition baseline hazards was tested. The finally developed model optimized the accuracy of predictions for two simulated patients. This stepwise procedure yields parsimonious but targeted multi-state models with well interpretable coefficients and optimized predictive ability, even for smaller data sets.

Bayesian path specific frailty models for multi-state survival data with applications

Multi-state models can be viewed as generalizations of both the standard and competing risks models for survival data. Models for multi-state data have been the theme of many recent published works. Motivated by bone marrow transplant data, we propose a Bayesian model using the gap times between two successive events in a path of events experienced by a subject. Path specific frailties are introduced to capture the dependence structure of the gap times in the paths with two or more states. Under improper prior distributions for the parameters, we establish propriety of the posterior distribution. An efficient Gibbs sampling algorithm is developed for drawing samples from the posterior distribution. An extensive simulation study is carried out to examine the empirical performance of the proposed approach. A bone marrow transplant data set is analyzed in detail to further demonstrate the proposed methodology.

Stroke in Patients With Aortic Stenosis

Background and Purpose—

There are limited data on risk stratification of stroke in aortic stenosis. This study examined predictors of stroke in aortic stenosis, the prognostic implications of stroke, and how aortic valve replacement (AVR) with or without concomitant coronary artery bypass grafting influenced the predicted outcomes.

Methods—

Patients with mild-to-moderate aortic stenosis enrolled in the Simvastatin and Ezetimibe in Aortic Stenosis (SEAS) study. Diabetes mellitus, known atherosclerotic disease, and oral anticoagulation were exclusion criteria. Ischemic stroke was the primary end point, and poststroke survival a secondary outcome. Cox models treating AVR as a time-varying covariate were adjusted for atrial fibrillation and congestive heart failure, hypertension, age ≥75 years, diabetes mellitus, stroke/transient ischemic attack, vascular disease, age 65–74 years and female sex (CHA 2 DS 2 -VASc) scores.

Results—

One thousand five hundred nine patients were followed for 4.3±0.8 years (6529 patient-years). Rates of stroke were 5.6 versus 21.8 per 1000 patient-years pre- and post-AVR; 429 (28%) underwent AVR and 139 (9%) died. Atrial fibrillation (hazard ratio [HR], 2.7; 95% confidence interval [CI], 1.1–6.6), CHA 2 DS 2 -VASc score (HR 1.4 per unit; 95% CI, 1.1–1.8), diastolic blood pressure (HR, 1.4 per 10 mm Hg; 95% CI, 1.1–1.8), and AVR with concomitant coronary artery bypass grafting (HR, 3.2; 95% CI, 1.4–7.2, all P ≤0.026) were independently associated with stroke. Incident stroke predicted death (HR, 8.1; 95% CI, 4.7–14.0; P <0.001).

Conclusions—

In patients with aortic stenosis not prescribed oral anticoagulation, atrial fibrillation, AVR with concomitant coronary artery bypass grafting, and CHA 2 DS 2 -VASc score were the major predictors of stroke. Incident stroke was strongly associated with mortality.

Clinical Trial Registration—

URL: http://www.clinicaltrials.gov . Unique identifier: NCT00092677.