Estimation and assessment of markov multistate models with intermittent observations on individuals

Maximum likelihood estimation for semiparametric regression models with interval-censored multistate data

Interval-censored multistate data arise in many studies of chronic diseases, where the health status of a subject can be characterized by a finite number of disease states and the transition between any two states is only known to occur over a broad time interval. We relate potentially time-dependent covariates to multistate processes through semiparametric proportional intensity models with random effects. We study nonparametric maximum likelihood estimation under general interval censoring and develop a stable expectation-maximization algorithm. We show that the resulting parameter estimators are consistent and that the finite-dimensional components are asymptotically normal with a covariance matrix that attains the semiparametric efficiency bound and can be consistently estimated through profile likelihood. In addition, we demonstrate through extensive simulation studies that the proposed numerical and inferential procedures perform well in realistic settings. Finally, we provide an application to a major epidemiologic cohort study.

Risk factors for stroke-related functional disability and mortality at Felege Hiwot Referral Hospital, Ethiopia

BACKGROUND

Stroke is one of the top causes of functional disability around the world. The main objective was to identify stroke-related functional outcomes and risk factors. A good functional outcome is defined as the absence of problems secondary to the stroke event, a poor functional outcome as the presence of complications, and mortality as the existence of complications.

METHOD

A retrospective cohort analysis was used to observe factors in 298 eligible adult (18 or older) stroke patients who attend outpatient clinics every three months at Felege Hiwot Referral Hospital between September 2019 and August 2021 to predict outcomes.

RESULT

The likelihood of dying from a poor outcome was 9%, and the likelihood of recovering was 24%. The average time spent on good and poor outcomes for different levels of independent variables varies according to their risk. During the first three years of follow-up, the instantaneous risk with a 95% confidence interval of transitioning from good to poor outcome in the women, aged 60 or older, with hypertension, atrial fibrillation, and hemorrhage stroke versus men stroke patients, aged 18 to 59, without hypertension, atrial fibrillation, and ischemic stroke were 1.54 (1.10, 2.15), 1.73 (1.19, 2.52), 2.34 (1.55, 3.53), 2.74 (1.64, 4.56), and 1.52 (1.10, 2.19) respectively. The hazard ratio of transitioning from poor outcome to death for patients with diabetes mellitus and atrial fibrillation versus those without diabetes mellitus and atrial fibrillation was estimated to be 1.95 (1.10, 3.46) and 3.39 (1.67, 6.89), respectively.

CONCLUSION

Women over 60 with hypertension, atrial fibrillation, and hemorrhagic stroke were more likely to progress from a good to a poor outcome. Diabetes and atrial fibrillation were also risk factors for progressing from a poor outcome to death. The states and transitions, as well as a clinical control of the hazards for the transition through states, should improve the physician's decision-making process. Since gender and age are difficult to control, early intervention by patients and the hospital may be critical in influencing functional outcomes.

Risk factors for neonatal hypothermia at Arba Minch General Hospital, Ethiopia

BACKGROUND

The first few minutes after birth are the most dangerous for the survival of an infant. Babies in neonatal intensive care units are either under heated or overheated, and hypothermic infants remain hypothermic or develop a fever. As a result, special attention must be paid to monitoring and maintaining the time of recovery from hypothermia states. Despite numerous studies, only a few have examined the transition from neonatal hypothermia and associated risk factors in depth.

METHOD

A retrospective observational study was conducted to track axillary temperatures taken at the time of neonatal intensive care unit admission, which were then tracked every 30 minutes until the newborn's temperature stabilized. All hypothermic neonates admitted to the neonatal intensive care unit between January 2018 and December 2020 was included in the study. Temperature data were available at birth and within the first three hours of admission for 391 eligible hypothermic neonates. The effect of factors on the transition rate in different states of hypothermia was estimated using a multi-state Markov model.

RESULT

The likelihood of progressing from mild to severe hypothermia was 5%, while the likelihood of progressing to normal was 34%. The average time spent in a severe hypothermia state was 48, 35, and 24 minutes for three different levels of birth weight, and 53, 41, and 31 minutes for low, moderate, and normal Apgar scores, respectively. Furthermore, the mean sojourn time in a severe hypothermia state was 48, 39, and 31 minutes for three different levels of high, normal, and low pulse rate, respectively.

CONCLUSION

For hypothermic survivors within the first three hours of life, very low birth weight, low Apgar, and high pulse rate had the strongest association with hypothermia and took the longest time to improve/recover. As a result, there is an urgent need to train all levels of staff dealing with maintaining the time of recovery from neonatal hypothermia.

Likelihood function for estimating parameters in multistate disease process with Laplace-transformation-based transition probabilities

Multistate statistical models are often used to characterize the complex multi-compartment progression of the disease such as cancer. However, the derivation of multistate transition kernels is often involved with the intractable convolution that requires intensive computation. Moreover, the estimation of parameters pertaining to transition kernel requires the individualized time-stamped history data while the traditional likelihood function forms are constructed. In this paper, we came up with a novel likelihood function derived from Laplace transformation-based transition probabilities in conjunction with Expectation-Maximization algorithm to estimate parameters. The proposed method was applied to two large population-based screening data with only aggregated count data without relying on individual time-stamped history data.

Multistate Models for Examining the Progression of Intermittently Measured Patient-Reported Symptoms Among Patients With Cancer: The Importance of Accounting for Interval Censoring

CONTEXT

Patients with cancer in Ontario, Canada, receive symptom monitoring in a standardized fashion using the Edmonton Symptom Assessment System (ESAS). These measurements can be used to understand symptom progression during the cancer trajectory.

OBJECTIVES

This study demonstrates the implementation of multistate models for examining symptom progression, while appropriately accounting for intermittent observation. We also compare the estimates when the panel nature of the data is ignored.

METHODS

This was a population-based retrospective cohort study using linked administrative health-care databases. The cohort consisted of patients who were newly diagnosed with a primary cancer and had at least one ESAS assessment completed between 2007 and 2015 in Ontario, Canada. A 5-state model was developed to examine the progression of symptom severity, where estimation was conducted with and without accommodating for the panel nature of the symptom data.

RESULTS

The study cohort consisted of 212,615 patients diagnosed with cancer, collectively having 1,006,360 ESAS assessments within the first year after diagnosis. The median (interquartile range) of the number of ESAS assessments per patient was 3 (1-6), and the average gap time between consecutive assessments was approximately three months. The estimated mean sojourn time in each state was consistently and significantly greater when ignoring interval censoring than when accounting for it. This held true for all states and symptoms.

CONCLUSION

Our work demonstrates the use of multistate models and the importance of accommodating for intermittent observation when examining symptom progression using ESAS among patients with cancer. This work serves as a methodological guide for applied researchers interested in modeling disease progression under the presence of intermittent observation.

Tracing studies in cohorts with attrition: Selection models for efficient sampling

Cohort studies of chronic diseases involve recruitment and longitudinal follow-up of affected individuals with a view to studying the effect of risk factors on disease progression and death. When the time to withdrawal from the cohort is conditionally independent of the disease process the primary consequence is a loss of information on the parameters of interest. This loss can sometimes be mitigated through the conduct of tracing studies in which a subsample of those lost to follow up are contacted and some information is obtained on their disease and survival status. We describe the use of selection models to sample individuals for tracing who will yield more efficient estimators than those obtained by simple random sampling. Efficient sampling schemes featuring cost constraints are also developed and shown to perform well. An application to data from the University of Toronto Psoriatic Arthritis Cohort illustrates how to apply the method in a real setting.

Poverty dynamics, poverty thresholds and mortality: An age-stage Markovian model

Recent studies have examined the risk of poverty throughout the life course, but few have considered how transitioning in and out of poverty shape the dynamic heterogeneity and mortality disparities of a cohort at each age. Here we use state-by-age modeling to capture individual heterogeneity in crossing one of three different poverty thresholds (defined as 1×, 2× or 3× the “official” poverty threshold) at each age. We examine age-specific state structure, the remaining life expectancy, its variance, and cohort simulations for those above and below each threshold. Survival and transitioning probabilities are statistically estimated by regression analyses of data from the Health and Retirement Survey RAND data-set, and the National Longitudinal Survey of Youth. Using the results of these regression analyses, we parameterize discrete state, discrete age matrix models. We found that individuals above all three thresholds have higher annual survival than those in poverty, especially for mid-ages to about age 80. The advantage is greatest when we classify individuals based on 1× the “official” poverty threshold. The greatest discrepancy in average remaining life expectancy and its variance between those above and in poverty occurs at mid-ages for all three thresholds. And fewer individuals are in poverty between ages 40-60 for all three thresholds. Our findings are consistent with results based on other data sets, but also suggest that dynamic heterogeneity in poverty and the transience of the poverty state is associated with income-related mortality disparities (less transience, especially of those above poverty, more disparities). This paper applies the approach of age-by-stage matrix models to human demography and individual poverty dynamics. In so doing we extend the literature on individual poverty dynamics across the life course.

A stochastic estimation procedure for intermittently-observed semi-Markov multistate models with back transitions

Multistate models provide an important method for analyzing a wide range of life history processes including disease progression and patient recovery following medical intervention. Panel data consisting of the states occupied by an individual at a series of discrete time points are often used to estimate transition intensities of the underlying continuous-time process. When transition intensities depend on the time elapsed in the current state and back transitions between states are possible, this intermittent observation process presents difficulties in estimation due to intractability of the likelihood function. In this manuscript, we present an iterative stochastic expectation-maximization algorithm that relies on a simulation-based approximation to the likelihood function and implement this algorithm using rejection sampling. In a simulation study, we demonstrate the feasibility and performance of the proposed procedure. We then demonstrate application of the algorithm to a study of dementia, the Nun Study, consisting of intermittently-observed elderly subjects in one of four possible states corresponding to intact cognition, impaired cognition, dementia, and death. We show that the proposed stochastic expectation-maximization algorithm substantially reduces bias in model parameter estimates compared to an alternative approach used in the literature, minimal path estimation. We conclude that in estimating intermittently observed semi-Markov models, the proposed approach is a computationally feasible and accurate estimation procedure that leads to substantial improvements in back transition estimates.

Effects of antiretroviral treatment and nadir CD4 count in progression to cardiovascular events and related comorbidities in a HIV Brazilian cohort: a multi-stage approach

The use of highly active antiretroviral therapy has resulted in changes of comorbidity profile in people living with HIV (PLHIV), increasing non-AIDS-related events. The occurrence of cardiovascular events is greater in PLHIV, but the mechanism responsible for it is still controversial. This article aimed to investigate factors associated with the progression to cardiovascular events in PLHIV using HAART. A 15-years cohort study with 1135 PLHIV was conducted in Rio de Janeiro-Brazil. Clinical progression was stratified in five states: No comorbidities (s₁), arterial hypertension (s₂), lipid abnormalities (s₃), hypertension and lipid abnormalities (s₄) and major cardiovascular events (stroke, coronary artery disease, thrombosis or death) (s₅). Semi-Markov models evaluated the effects of cardiovascular traditional factors, treatment and clinical covariates on transitions between these states. Hazard Ratios (HR) and 95% confidence intervals (CI) were provided. In addition to traditional factors (age, sex, educational level and skin color), the development of one comorbidity (lipid abnormalities or hypertension) increased in patients with low nadir CD4 (<50 cells/mm³), (HR = 1.59, CI 1.11-2.28 and 1.36, CI 1.11-1.66, respectively). The risk to experience a second comorbidity (s₃→s₄) increased 75% with low nadir CD4. Age was the only factor that increased the risk of major cardiovascular events once having lipid abnormalities with or without hypertension (s₃,s₄→s₅). The prolonged use of certain antiretroviral drugs (abacavir, didanosine, ritonavir, lopinavir, amprenavir and fosamprenavir) increased the risk of direct transition (s₁→s₅) to major cardiovascular events (HR = 5.29, CI 1.16-24.05). This analysis suggests that prolonged use of certain antiretroviral drugs led directly to major cardiovascular events, while low nadir CD4 only affected the occurrence of lipid abnormalities and hypertension. Management strategies, including rational use of complex exams (such as, computed-tomography angiography), statins and antihypertensives, should be developed based on the distinct roles of antiretroviral use and of HIV infection itself on the progression to cardiovascular events.

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.