A semi-competing risks model for data with interval-censoring and informative observation: an application to the MRC cognitive function and ageing study

Semiparametric regression of the illness-death model with interval censored disease incidence time: An application to the ACLS data

To investigate the effect of fitness on cardiovascular disease and all-cause mortality using the Aerobics Center Longitudinal Study, we develop a semiparametric illness-death model account for intermittent observations of the cardiovascular disease incidence time and the right censored data of all-cause mortality. The main challenge in estimation is to handle the intermittent observations (interval censoring) of cardiovascular disease incidence time and we develop a semiparametric estimation method based on the expectation-maximization algorithm for a Markov illness-death regression model. The variance of the parameters is estimated using profile likelihood methods. The proposed method is evaluated using extensive simulation studies and illustrated with an application to the Aerobics Center Longitudinal Study data.

Tailored optimal posttreatment surveillance for cancer recurrence

A substantial rise in the number of cancer survivors has led to urgent management questions regarding effective posttreatment imaging-based surveillance strategies for cancer recurrence. Current surveillance guidelines provided by a number of professional societies all warn against overly aggressive surveillance, especially for low-risk patients, but all fail to provide more specific directions to accommodate underlying heterogeneity of cancer recurrence. Therefore it is imperative to develop data-driven strategies that can tailor the surveillance schedules to recurrence risk in this era of stricter insurance regulations, provider shortages, and rising costs of health care. Due to a lack of statistical methods for optimizing surveillance scheduling in presence of competing risks, we propose a general approach that uses an intuitive loss function for optimization of early detection of recurrence before death. The proposed strategies can tailor to patient risks of recurrence, in terms of both intensity and amount of surveillance. Using general three-state Markov models, our method is flexible and includes earlier works as special cases. We illustrate our method in both simulation studies and an application to breast cancer surveillance.

A multi-state model based reanalysis of the Framingham Heart Study: Is dementia incidence really declining?

Recent research by Satizabal and colleagues using data from the Framingham Heart Study demonstrated a linear decline in dementia incidence since the 1970s. The aim of this study is to re-examine these findings, given concerns that bias resulted from failure to account for the probability of acquiring dementia between the last dementia-free observation and death. This analysis included 5118 persons 60+ years of age, and determined the 5-year dementia incidence during four non-overlapping epochs. In addition to a replication using Cox proportional hazards, we applied separate Cox models (given unequal hazards across epochs) and a Spline-based penalized likelihood approach based on the illness-death multi-state model. In addition, we present a simulation study demonstrating the bias associated with the use of standard survival models. The simulation showed that estimates of disease incidence derived from the multi-state model-based approach were consistent with the true disease incidence, whereas Cox regression 'censoring' observations at death or at last observation consistently underestimated it. Using the Framingham data, the 5-year age- and sex-adjusted cumulative hazard rates for dementia as derived from the multi-state model-based approach were 3.84, 2.66, 3.29 and 3.13 per 100 persons in epochs 1, 2, 3 and 4 respectively. The findings do not support the conclusion that dementia incidence has declined in the Framingham Heart Study over the given time period. Previous findings of a decline may have been an artefact resulting from improper treatment of those cases in which death precluded the observation of dementia onset.

Additive-multiplicative hazards regression models for interval-censored semi-competing risks data with missing intermediate events

BACKGROUND

In clinical trials and survival analysis, participants may be excluded from the study due to withdrawal, which is often referred to as lost-to-follow-up (LTF). It is natural to argue that a disease would be censored due to death; however, when an LTF is present it is not guaranteed that the disease has been censored. This makes it important to consider both cases; the disease is censored or not censored. We also note that the illness process can be censored by LTF. We will consider a multi-state model in which LTF is not regarded as censoring but as a non-fatal event.

METHODS

We propose a multi-state model for analyzing semi-competing risks data with interval-censored or missing intermediate events. More precisely, we employ the additive and multiplicative hazards model with log-normal frailty and construct the conditional likelihood to estimate the transition intensities among states in the multi-state model. Marginalization of the full likelihood is accomplished using adaptive importance sampling, and the optimal solution of the regression parameters is achieved through the iterative quasi-Newton algorithm.

RESULTS

Simulation is performed to investigate the finite-sample performance of the proposed estimation method in terms of the relative bias and coverage probability of the regression parameters. The proposed estimators turned out to be robust to misspecifications of the frailty distribution. PAQUID data have been analyzed and yielded somewhat prominent results.

CONCLUSIONS

We propose a multi-state model for semi-competing risks data for which there exists information on fatal events, but information on non-fatal events may not be available due to lost to follow-up. Simulation results show that the coverage probabilities of the regression parameters are close to a nominal level of 0.95 in most cases. Regarding the analysis of real data, the risk of transition from a healthy state to dementia is higher for women; however, the risk of death after being diagnosed with dementia is higher for men.

Beyond Composite Endpoints Analysis: Semicompeting Risks as an Underutilized Framework for Cancer Research

BACKGROUND

Composite endpoints (CEP), such as progression-free survival, are commonly used in cancer research. Notwithstanding their popularity, however, CEP analyses suffer from a number of drawbacks, especially when death is combined with a nonterminal event (ie, progression or recurrence), exemplifying the semicompeting risks setting. We investigated the semicompeting risks framework as a complementary analysis strategy that avoids certain drawbacks of CEPs.

METHODS

The illness-death model under the semicompeting risks framework was compared with standard analysis approaches: CEP analyses and (separate) univariate analyses for each component endpoint. Data from a previously published phase III randomized clinical trial in metastatic colon cancer including 1419 participants in the N9741 trial (conducted between 1997 and 2003) were used to determine the impact of the loss of information associated with combining multiple endpoints, as well as of ignoring the potentially informative role of death. A simulation study was conducted to further explore these issues.

RESULTS

Failure to account for critical features of semicompeting risks data can lead to potentially severely misleading conclusions. Advantages of semicompeting risks analyses include a clear delineation of treatment effects on both events, the ability to draw conclusions about a patient's joint risk of the two events, and an assessment of the dependence between the two event types.

CONCLUSIONS

Embedding and analyzing component outcomes in the semicompeting risks framework, either as a supplement or alternative to CEP analyses, represents an important, underutilized, and feasible opportunity for cancer research.

Estimation of state occupancy probabilities in multistate models with dependent intermittent observation, with application to HIV viral rebounds

In follow-up studies on chronic disease cohorts, individuals are often observed at irregular visit times that may be related to their previous disease history and other factors. This can produce bias in standard methods of estimation. Working in the context of multistate models, we consider a method of nonparametric estimation for state occupancy probabilities that adjusts for dependent follow-up through the use of inverse-intensity-of-visit weighted estimating functions and smoothing. The methodology is applied to the estimation of viral rebound probabilities in the Canadian Observational Cohort on HIV-positive persons. Copyright © 2016 John Wiley & Sons, Ltd.

Semi-Competing Risks Data Analysis: Accounting for Death as a Competing Risk When the Outcome of Interest Is Nonterminal

Hospital readmission is a key marker of quality of health care. Notwithstanding its widespread use, however, it remains controversial in part because statistical methods used to analyze readmission, primarily logistic regression and related models, may not appropriately account for patients who die before experiencing a readmission event within the time frame of interest. Toward resolving this, we describe and illustrate the semi-competing risks framework, which refers to the general setting where scientific interest lies with some nonterminal event (eg, readmission), the occurrence of which is subject to a terminal event (eg, death). Although several statistical analysis methods have been proposed for semi-competing risks data, we describe in detail the use of illness-death models primarily because of their relation to well-known methods for survival analysis and the availability of software. We also describe and consider in detail several existing approaches that could, in principle, be used to analyze semi-competing risks data, including composite end point and competing risks analyses. Throughout we illustrate the ideas and methods using data on N=49 763 Medicare beneficiaries hospitalized between 2011 and 2013 with a principle discharge diagnosis of heart failure.

Bayesian Semi-parametric Analysis of Semi-competing Risks Data: Investigating Hospital Readmission after a Pancreatic Cancer Diagnosis

In the U.S., the Centers for Medicare and Medicaid Services uses 30-day readmission, following hospitalization, as a proxy outcome to monitor quality of care. These efforts generally focus on treatable health conditions, such as pneumonia and heart failure. Expanding quality of care systems to monitor conditions for which treatment options are limited or non-existent, such as pancreatic cancer, is challenging because of the non-trivial force of mortality; 30-day mortality for pancreatic cancer is approximately 30%. In the statistical literature, data that arise when the observation of the time to some non-terminal event is subject to some terminal event are referred to as 'semi-competing risks data'. Given such data, scientific interest may lie in at least one of three areas: (i) estimation/inference for regression parameters, (ii) characterization of dependence between the two events, and (iii) prediction given a covariate profile. Existing statistical methods focus almost exclusively on the first of these; methods are sparse or non-existent, however, when interest lies with understanding dependence and performing prediction. In this paper we propose a Bayesian semi-parametric regression framework for analyzing semi-competing risks data that permits the simultaneous investigation of all three of the aforementioned scientific goals. Characterization of the induced posterior and posterior predictive distributions is achieved via an efficient Metropolis-Hastings-Green algorithm, which has been implemented in an R package. The proposed framework is applied to data on 16,051 individuals diagnosed with pancreatic cancer between 2005-2008, obtained from Medicare Part A. We found that increased risk for readmission is associated with a high comorbidity index, a long hospital stay at initial hospitalization, non-white race, male, and discharge to home care.

Cognitive and social lifestyle: links with neuropathology and cognition in late life

Many studies report an association of cognitive and social experiential factors and related traits with dementia risk. Further, many clinical-pathologic studies find a poor correspondence between levels of neuropathology and the presence of dementia and level of cognitive impairment. The poor correspondence suggests that other factors contribute to the maintenance or loss of cognitive function, with factors associated with the maintenance of function referred to as neural or cognitive reserve. This has led investigators to examine the associations of cognitive and social experiential factors with neuropathology as a first step in disentangling the complex associations between these experiential risk factors, neuropathology, and cognitive impairment. Despite the consistent associations of a range of cognitive and social lifestyle factors with cognitive decline and dementia risk, the extant clinical-pathologic data find only a single factor from one cohort, linguistic ability, related to AD pathology. Other factors, including education, harm avoidance, and emotional neglect, are associated with cerebrovascular disease. Overall, the associations are weak. Some factors, such as education, social networks, and purpose in life, modify the relation of neuropathology to cognition. Finally, some factors such as cognitive activity appear to bypass known pathologies altogether suggesting a more direct association with biologic indices that promote person-specific differences in reserve and resilience. Future work will first need to replicate findings across more studies to ensure the veracity of the existing data. Second, effort is needed to identify the molecular substrates of neural reserve as potential mediators of the association of lifestyle factors with cognition.

Interval-censored time-to-event and competing risk with death: is the illness-death model more accurate than the Cox model?

BACKGROUND

In survival analyses of longitudinal data, death is often a competing event for the disease of interest, and the time-to-disease onset is interval-censored when the diagnosis is made at intermittent follow-up visits. As a result, the disease status at death is unknown for subjects disease-free at the last visit before death. Standard survival analysis consists in right-censoring the time-to-disease onset at that visit, which may induce an underestimation of the disease incidence. By contrast, an illness-death model for interval-censored data accounts for the probability of developing the disease between that visit and death, and provides a better incidence estimate. However, the two approaches have never been compared for estimating the effect of exposure on disease risk.

METHODS

This paper compares through simulations the accuracy of the effect estimates from a semi-parametric illness-death model for interval-censored data and the standard Cox model. The approaches are also compared for estimating the effects of selected risk factors on the risk of dementia, using the French elderly PAQUID cohort data.

RESULTS

The illness-death model provided a more accurate effect estimate of exposures that also affected mortality. The direction and magnitude of the bias from the Cox model depended on the effects of the exposure on disease and death. The application to the PAQUID cohort confirmed the simulation results.

CONCLUSION

If follow-up intervals are wide and the exposure has an impact on death, then the illness-death model for interval-censored data should be preferred to the standard Cox regression analysis.

A semi-Markov model for stroke with piecewise-constant hazards in the presence of left, right and interval censoring

This paper presents a parametric method of fitting semi-Markov models with piecewise-constant hazards in the presence of left, right and interval censoring. We investigate transition intensities in a three-state illness–death model with no recovery. We relax the Markov assumption by adjusting the intensity for the transition from state 2 (illness) to state 3 (death) for the time spent in state 2 through a time-varying covariate. This involves the exact time of the transition from state 1 (healthy) to state 2. When the data are subject to left or interval censoring, this time is unknown. In the estimation of the likelihood, we take into account interval censoring by integrating out all possible times for the transition from state 1 to state 2. For left censoring, we use an Expectation–Maximisation inspired algorithm. A simulation study reflects the performance of the method. The proposed combination of statistical procedures provides great flexibility. We illustrate the method in an application by using data on stroke onset for the older population from the UK Medical Research Council Cognitive Function and Ageing Study. Copyright © 2012 John Wiley & Sons, Ltd.