Using multistate models with clinical trial data for a deeper understanding of complex disease processes.

A clinical trial represents a large commitment from all individuals involved and a huge financial obligation given its high cost; therefore, it is wise to make the most of all collected data by learning as much as possible. A multistate model is a generalized framework to describe longitudinal events; multistate hazards models can treat multiple intermediate/final clinical endpoints as outcomes and estimate the impact of covariates simultaneously. Proportional hazards models are fitted (one per transition), which can be used to calculate the absolute risks, that is, the probability of being in a state at a given time, the expected number of visits to a state, and the expected amount of time spent in a state. Three publicly available clinical trial datasets, colon, myeloid, and rhDNase, in the survival package in R were used to showcase the utility of multistate hazards models. In the colon dataset, a very well-known and well-used dataset, we found that the levamisole+fluorouracil treatment extended time in the recurrence-free state more than it extended overall survival, which resulted in less time in the recurrence state, an example of the classic "compression of morbidity." In the myeloid dataset, we found that complete response (CR) is durable, patients who received treatment B have longer sojourn time in CR than patients who received treatment A, while the mutation status does not impact the transition rate to CR but is highly influential on the sojourn time in CR. We also found that more patients in treatment A received transplants without CR, and more patients in treatment B received transplants after CR. In addition, the mutation status is highly influential on the CR to transplant transition rate. The observations that we made on these three datasets would not be possible without multistate models. We want to encourage readers to spend more time to look deeper into clinical trial data. It has a lot more to offer than a simple yes/no answer if only we, the statisticians, are willing to look for it.

Comparison of nonparametric estimators of the expected number of recurrent events.

We compare the performance of nonparametric estimators for the mean number of recurrent events and provide a systematic overview for different recurrent event settings. The mean number of recurrent events is an easily interpreted marginal feature often used for treatment comparisons in clinical trials. Incomplete observations, dependencies between successive events, terminating events acting as competing risk, or gaps between at risk periods complicate the estimation. We use survival multistate models to represent different complex recurrent event situations, profiting from recent advances in nonparametric estimation for non-Markov multistate models, and explain several estimators by using multistate intensity processes, including the common Nelson-Aalen-type estimators with and without competing mortality. In addition to building on estimation of state occupation probabilities in non-Markov models, we consider a simple extension of the Nelson-Aalen estimator by allowing for dependence on the number of prior recurrent events. We pay particular attention to the assumptions required for the censoring mechanism, one issue being that some settings require the censoring process to be entirely unrelated while others allow for state-dependent or event-driven censoring. We conducted extensive simulation studies to compare the estimators in various complex situations with recurrent events. Our practical example deals with recurrent chronic obstructive pulmonary disease exacerbations in a clinical study, which will also be used to illustrate two-sample-inference using resampling.

On restricted mean time in favor of treatment.

The restricted mean time in favor (RMT-IF) of treatment is a nonparametric effect size for complex life history data. It is defined as the net average time the treated spend in a more favorable state than the untreated over a prespecified time window. It generalizes the familiar restricted mean survival time (RMST) from the two-state life-death model to account for intermediate stages in disease progression. The overall estimand can be additively decomposed into stage-wise effects, with the standard RMST as a component. Alternate expressions of the overall and stage-wise estimands as integrals of the marginal survival functions for a sequence of landmark transitioning events allow them to be easily estimated by plug-in Kaplan-Meier estimators. The dynamic profile of the estimated treatment effects as a function of follow-up time can be visualized using a multilayer, cone-shaped "bouquet plot." Simulation studies under realistic settings show that the RMT-IF meaningfully and accurately quantifies the treatment effect and outperforms traditional tests on time to the first event in statistical efficiency thanks to its fuller utilization of patient data. The new methods are illustrated on a colon cancer trial with relapse and death as outcomes and a cardiovascular trial with recurrent hospitalizations and death as outcomes. The R-package rmt implements the proposed methodology and is publicly available from the Comprehensive R Archive Network (CRAN).

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.

MSMpred: interactive modelling and prediction of individual evolution via multistate models.

BACKGROUND: Modelling the course of a disease regarding severe events and identifying prognostic factors is of great clinical relevance. Multistate models (MSM) can be used to describe diseases or processes that change over time using different states and the transitions between them. Specifically, they are useful to analyse a disease with an increasing degree of severity, that may precede death. The complexity of these models changes depending on the number of states and transitions taken into account. Due to that, a web tool has been developed making easier to work with those models. RESULTS: MSMpred is a web tool created with the shiny R package that has two main features: 1) to allow to fit a MSM from specific data; 2) to predict the clinical evolution for a given subject. To fit the model, the data to be analysed must be upload in a prespecified format. Then, the user has to define the states and transitions as well as the covariates (e.g., age or gender) involved in each transition. From this information, the app returns histograms or barplots, as appropriate, to represent the distributions of the selected covariates and boxplots to show the patient' length of stay (for uncensored data) in each state. To make predictions, the values of selected covariates from a new subject at baseline has to be provided. From these inputs, the app provides some indicators of the subject's evolution such as the probability of 30-day death or the most likely state at a fixed time. Furthermore, visual representations (e.g., the stacked transition probabilities plot) are given to make predictions more understandable. CONCLUSIONS: MSMpred is an intuitive and visual app that eases the work of biostatisticians and facilitates to the medical personnel the interpretation of MSMs.

Racial, Ethnic, Nativity, and Educational Disparities in Cognitive Impairment and Activity Limitations in the United States, 1998-2016.

Despite extensive research on cognitive impairment and limitations in basic activities of daily living, no study has investigated the burden of their co-occurrence (co-impairment). Using the Health and Retirement Study data and incidence-based multistate models, we study the population burden of co-impairment using three key indicators: mean age at onset, lifetime risk, and health expectancy. We examine patterns by gender, race, ethnicity, nativity, education, and their interactions for U.S. residents aged 50-100. Furthermore, we analyze what fractions of racial, ethnic, and nativity disparities in co-impairment are attributable to inequalities in educational attainment. Results reveal that an estimated 56% of women and 41% of men aged 50 will experience co-impairment in their remaining life expectancy. Men experience an earlier onset of co-impairment than women (74 vs. 77 years), and women live longer in co-impairment than men (3.4 vs. 1.9 years). Individuals who are Black, Latinx, and lower educated, especially those experiencing intersecting disadvantages, have substantially higher lifetime risk of co-impairment, earlier co-impairment onset, and longer life in co-impairment than their counterparts. Up to 75% of racial, ethnic, and nativity disparity is attributable to inequality in educational attainment. This study provides novel insights into the burden of co-impairment and offers evidence of dramatic disparities in the older U.S. population.

Transitions in health care settings for frequent and infrequent users of emergency departments: a population-based retrospective cohort study.

BACKGROUND: Efforts to reduce emergency department (ED) volumes often target frequent users. We examined transitions in care across ED, hospital, and community settings, and in-hospital death, for high system users (HSUs) compared to controls. METHODS: Population-based databases provided ED visits and hospitalizations in Alberta and Ontario, Canada. The retrospective cohort included the top 10% of all the ED users during 2015/2016 (termed HSUs) and a random sample of controls (4 per each HSU) from the bottom 90% per province. Rates of transitions among ED, hospitalization, community settings, and in-hospital mortality were adjusted for sociodemographic and ED variables in a multistate statistical model. RESULTS: There were 2,684,924 patients and 579,230 (21.6%) were HSUs. Patient characteristics associated with shorter community to ED transition times for HSUs included Alberta residence (ratio of hazard ratio [RHR] = 1.11, 95% confidence interval [CI] 1.11,1.12), living in areas in the lower income quintile (RHR = 1.06, 95%CI 1.06,1.06), and Ontario residents without a primary health care provider (RHR = 1.13, 95%CI 1.13,1.14). Once at the ED, characteristics associated with shorter ED to hospital transition times for HSUs included higher acuity (e.g., RHR = 1.70, 95% CI 1.61, 1.81 for emergent), and for many diagnoses including chest pain (RHR = 1.71, 95%CI 1.65,1.76) and gastrointestinal (RHR = 1.66, 95%CI 1.62,1.71). Once admitted to hospital, HSUs did not necessarily have longer stays except for conditions such as chest pain (RHR = 0.90, 95% CI 0.86, 0.95). HSUs had shorter times to death in the ED if they presented for cancer (RHR = 2.51), congestive heart failure (RHR = 1.93), myocardial infarction (RHR = 1.53), and stroke (RHR = 1.84), and shorter times to death in-hospital if they presented with cancer (RHR = 1.29). CONCLUSIONS: Differences between HSUs and controls in predictors of transitions among care settings were identified. Co-morbidities and limitations in access to primary care are associated with more rapid transitions from community to ED and hospital among HSUs. Interventions targeting these challenges may better serve patients across health systems.. TRIAL REGISTRATION: Not applicable.

Flexible transition timing in discrete-time multistate life tables using Markov chains with rewards.

Discrete-time multistate life tables are attractive because they are easier to understand and apply in comparison with their continuous-time counterparts. While such models are based on a discrete time grid, it is often useful to calculate derived magnitudes (e.g. state occupation times), under assumptions which posit that transitions take place at other times, such as mid-period. Unfortunately, currently available models allow very few choices about transition timing. We propose the use of Markov chains with rewards as a general way of incorporating information on the timing of transitions into the model. We illustrate the usefulness of rewards-based multistate life tables by estimating working life expectancies using different retirement transition timings. We also demonstrate that for the single-state case, the rewards approach matches traditional life-table methods exactly. Finally, we provide code to replicate all results from the paper plus R and Stata packages for general use of the method proposed.

Deconstructing the Treatment Effect of Remdesivir in the Adaptive Coronavirus Disease 2019 (COVID-19) Treatment Trial-1: Implications for Critical Care Resource Utilization.

BACKGROUND: The Adaptive Coronavirus Disease 2019 (COVID-19) Treatment Trial-1 (ACTT-1) found that remdesivir therapy hastened recovery in patients hospitalized with COVID-19, but the pathway for this improvement was not explored. We investigated how the dynamics of clinical progression changed along 4 pathways: recovery, improvement in respiratory therapy requirement, deterioration in respiratory therapy requirement, and death. METHODS: We analyzed trajectories of daily ordinal severity scores reflecting oxygen requirements of 1051 patients hospitalized with COVID-19 who participated in ACTT-1. We developed competing risks models that estimate the effect of remdesivir therapy on cumulative incidence of clinical improvement and deterioration, and multistate models that utilize the entirety of each patient's clinical course to characterize the effect of remdesivir on progression along the 4 pathways above. RESULTS: Based on a competing risks analysis, remdesivir reduced clinical deterioration (hazard ratio [HR], 0.73; 95% confidence interval [CI]: .59-.91) and increased clinical improvement (HR, 1.22; 95% CI: 1.08, 1.39) relative to baseline. Our multistate models indicate that remdesivir inhibits worsening to ordinal scores of greater clinical severity among patients on room air or low-flow oxygen (HR, 0.74; 95% CI: .57-.94) and among patients receiving mechanical ventilation or high-flow oxygen/noninvasive positive-pressure ventilation (HR, 0.73; 95% CI: .53-1.00) at baseline. We also find that remdesivir reduces expected intensive care respiratory therapy utilization among patients not mechanically ventilated at baseline. CONCLUSIONS: Remdesivir speeds time to recovery by preventing worsening to clinical states that would extend the course of hospitalization and increase intensive respiratory support, thereby reducing the overall demand for hospital care.

Transitions Between Preexposure Prophylaxis Eligibility States and HIV Infection in the Lisbon Cohort of HIV-Negative Men Who Have Sex With Men: A Multistate Model Analysis.

We aimed to describe transitions between preexposure prophylaxis (PrEP) eligibility and human immunodeficiency virus (HIV) infection among HIV-negative men who have sex with men (MSM). We used data from 1,885 MSM, who had not used PrEP, enrolled in the Lisbon Cohort of MSM, with at least 2 consecutive measurements of PrEP eligibility from 2014-2020. A time-homogeneous Markov multistate model was applied to describe the transitions between states of PrEP eligibility-eligible and ineligible-and from these to HIV infection (HIV). The intensities of the transitions were closer for ineligible-to-eligible and eligible-to-ineligible transitions (intensity ratio, 1.107, 95% confidence interval (CI): 1.080, 1.176), while the intensity of the eligible-to-HIV transition was higher than that for ineligible-to-HIV transition (intensity ratio, 9.558, 95% CI: 0.738, 65.048). The probabilities of transitions increased with time; for 90 days, the probabilities were similar for the ineligible-to-eligible and eligible-to-ineligible transitions (0.285 (95% CI: 0.252, 0.319) vs. 0.258 (95% CI: 0.228, 0.287)), while the eligible-to-HIV transition was more likely than ineligible-to-HIV (0.004 (95% CI: 0.003, 0.007) vs. 0.001 (95% CI: 0.001, 0.008)) but tended to become closer with time. Being classified as ineligible was a short-term indicator of a lower probability of acquiring HIV. Once an individual moved to eligible, he was at a higher risk of seroconversion, demanding a timely delivery ofPrEP.

A multistate model incorporating estimation of excess hazards and multiple time scales.

As cancer patient survival improves, late effects from treatment are becoming the next clinical challenge. Chemotherapy and radiotherapy, for example, potentially increase the risk of both morbidity and mortality from second malignancies and cardiovascular disease. To provide clinically relevant population-level measures of late effects, it is of importance to (1) simultaneously estimate the risks of both morbidity and mortality, (2) partition these risks into the component expected in the absence of cancer and the component due to the cancer and its treatment, and (3) incorporate the multiple time scales of attained age, calendar time, and time since diagnosis. Multistate models provide a framework for simultaneously studying morbidity and mortality, but do not solve the problem of partitioning the risks. However, this partitioning can be achieved by applying a relative survival framework, allowing us to directly quantify the excess risk. This article proposes a combination of these two frameworks, providing one approach to address (1) to (3). Using recently developed methods in multistate modeling, we incorporate estimation of excess hazards into a multistate model. Both intermediate and absorbing state risks can be partitioned and different transitions are allowed to have different and/or multiple time scales. We illustrate our approach using data on Hodgkin lymphoma patients and excess risk of diseases of the circulatory system, and provide user-friendly Stata software with accompanying example code.

Markov modelling of viral load adjusting for CD4 orthogonal variable and multivariate conditional autoregressive mapping of the HIV immunological outcomes among ART patients in Zimbabwe.

BACKGROUND: This study aimed to jointly model HIV disease progression patterns based on viral load (VL) among adult ART patients adjusting for the time-varying "incremental transients states" variable, and the CD4 cell counts orthogonal variable in a single 5-stage time-homogenous multistate Markov model. We further jointly mapped the relative risks of HIV disease progression outcomes (detectable VL (VL ≥ 50copies/uL) and immune deterioration (CD4 < 350cells/uL) at the last observed visit) conditional not to have died or become loss to follow-up (LTFU). METHODS: Secondary data analysis of individual-level patients on ART was performed. Adjusted transition intensities, hazard ratios (HR) and regression coefficients were estimated from the joint multistate model of VL and CD4 cell counts. The mortality and LTFU transition rates defined the extent of patients' retention in care. Joint mapping of HIV disease progression outcomes after ART initiation was done using the Bayesian intrinsic Multivariate Conditional Autoregressive prior model. RESULTS: The viral rebound from the undetectable state was 1.78times more likely compared to viral suppression among patients with VL ranging from 50-1000copies/uL. Patients with CD4 cell counts lower than expected had a higher risk of viral increase above 1000copies/uL and death if their VL was above 1000copies/uL (state 2 to 3 (λ23): HR = 1.83 and (λ34): HR = 1.42 respectively). Regarding the time-varying effects of CD4 cell counts on the VL transition rates, as the VL increased, (λ12 and λ23) the transition rates increased with a decrease in the CD4 cell counts over time. Regardless of the individual's VL, the transition rates to become LTFU decreased with a decrease in CD4 cell counts. We observed a strong shared geographical pattern of 66% spatial correlation between the relative risks of detectable VL and immune deterioration after ART initiation, mainly in Matabeleland North. CONCLUSION: With high rates of viral rebound, interventions which encourage ART adherence and continual educational support on the barriers to ART uptake are crucial to achieve and sustain viral suppression to undetectable levels. Area-specific interventions which focus on early ART screening through self-testing, behavioural change campaigns and social support strategies should be strengthened in heavily burdened regions to sustain the undetectable VL. Sustaining undetectable VL lowers HIV transmission in the general population and this is a step towards achieving zero HIV incidences by 2030.

Predicting Potential Prevention Effects on Hospital Burden of Nosocomial Infections: A Multistate Modeling Approach.

OBJECTIVES: Hospital-acquired infections (HAIs) place a substantial burden on health systems. Tools are required to quantify the change in this burden as a result of a preventive intervention. We aim to estimate how much a reduction in the rate of hospital-acquired infections translates into a change in hospital mortality and length of stay. METHODS: Using multistate modelling and competing risks methodology, we created a tool to estimate the reduction in burden after the introduction of a preventive effect on the infection rate. The tool requires as inputs the patients' length of hospital stay, patients' infection information (status, time), patients' final outcome (discharged alive, dead), and a preventive effect. We demonstrated the methods on both simulated data and 3 published data sets from Germany, France, and Spain. RESULTS: A hypothetical prevention that cuts the infection rate in half would result in 21 lives and 2212 patient-days saved in French ventilator-associated pneumonia data, 61 lives and 3125 patient-days saved in Spanish nosocomial infection data, and 20 lives and 1585 patient-days saved in German nosocomial pneumonia data. CONCLUSIONS: Our tool provides a quick and easy means of acquiring an impression of the impact a preventive measure would have on the burden of an infection. The tool requires quantities routinely collected and computation can be done with a calculator. R code is provided for researchers to determine the burden in various settings with various effects. Furthermore, cost data can be used to get the financial benefit of the reduction in burden.

Fitting a shared frailty illness-death model to left-truncated semi-competing risks data to examine the impact of education level on incident dementia.

BACKGROUND: Semi-competing risks arise when interest lies in the time-to-event for some non-terminal event, the observation of which is subject to some terminal event. One approach to assessing the impact of covariates on semi-competing risks data is through the illness-death model with shared frailty, where hazard regression models are used to model the effect of covariates on the endpoints. The shared frailty term, which can be viewed as an individual-specific random effect, acknowledges dependence between the events that is not accounted for by covariates. Although methods exist for fitting such a model to right-censored semi-competing risks data, there is currently a gap in the literature for fitting such models when a flexible baseline hazard specification is desired and the data are left-truncated, for example when time is on the age scale. We provide a modeling framework and openly available code for implementation. METHODS: We specified the model and the likelihood function that accounts for left-truncated data, and provided an approach to estimation and inference via maximum likelihood. Our model was fully parametric, specifying baseline hazards via Weibull or B-splines. Using simulated data we examined the operating characteristics of the implementation in terms of bias and coverage. We applied our methods to a dataset of 33,117 Kaiser Permanente Northern California members aged 65 or older examining the relationship between educational level (categorized as: high school or less; trade school, some college or college graduate; post-graduate) and incident dementia and death. RESULTS: A simulation study showed that our implementation provided regression parameter estimates with negligible bias and good coverage. In our data application, we found higher levels of education are associated with a lower risk of incident dementia, after adjusting for sex and race/ethnicity. CONCLUSIONS: As illustrated by our analysis of Kaiser data, our proposed modeling framework allows the analyst to assess the impact of covariates on semi-competing risks data, such as incident dementia and death, while accounting for dependence between the outcomes when data are left-truncated, as is common in studies of aging and dementia.

Progression of myopic maculopathy in a Caucasian cohort of highly myopic patients with long follow-up: a multistate analysis.

PURPOSE: This study aims to determine the probability of progression of myopic maculopathy according to age. METHODS: This is a longitudinal observational study of single-center retrospective cohort of Caucasian patients formed by 212 consecutive adults with high myopia. Main outcome measures were age, visual acuity (VA), refractive error (RE), follow-up time, and the macular status assessed at least 5 years apart according to the Meta-Analysis of Pathologic Myopia Study Group. The progression rate was calculated based on per 1000 eyes/year. Multistate models were fitted to identify the predictive factors and to calculate the most probable age of progression onset using the Aalen-Johansen estimator. RESULTS: We studied 220 eyes of 122 Caucasian patients. Mean age was 48.18 ± 14.1, mean follow-up 12.73 ± 5.81 years. One-hundred and fifty-two (69.1%) eyes progressed of category, and 96 (44%) worsened a mean of 0.3 logMAR units during follow-up. The progression rate was 32.21/1000 eyes/year. The probability of progressing increased with age; it was higher in women if there was a family history of myopia, worse VA, higher RE, or wide macular staphyloma. The probability of progressing from category 1 was > 0.6 after 70 years of age; from category 2, it was 0.7 after 70 years; and 0.5 from category 3 after 75 years. If choroidal neovascularization (CNV) appeared, this probability exceeded 0.7 between ages 45 and 55 for all categories. CONCLUSION: The progression rate is lower than in a Japanese series. The vision worsened with disease progression, and the probability of both happening increased after the age of 70-75. If CNV appears, the risk of progression is very high at the age of 45-55.

Evaluating the transitions in care for children presenting with acute asthma to emergency departments: a retrospective cohort study.

BACKGROUND: Acute asthma is a common presentation to emergency departments (EDs) worldwide and, due to overcrowding, delays in treatment often occur. This study deconstructs the total ED length of stay into stages and estimates covariate effects on transition times for children presenting with asthma. METHODS: We extracted ED presentations in 2019 made by children in Alberta, Canada for acute asthma. We used multivariable Cox regressions in a multistate model to model transition times among the stages of start, physician initial assessment (PIA), disposition decision, and ED departure. RESULTS: Data from 6598 patients on 8270 ED presentations were extracted. The individual PIA time was longer (i.e., HR < 1) when time to the crowding metric (hourly PIA) was above 1 h (HR = 0.32; 95% CI:0.30,0.34), for tertiary (HR = 0.65; 95% CI:0.61,0.70) and urban EDs (HR = 0.77; 95% CI:0.70,0.84), for younger patients (HR = 0.99 per year; 95% CI:0.99,1.00), and for patients triaged less urgent/non-urgent (HR = 0.89; 95% CI:0.84,0.95). It was shorter for patients arriving by ambulance (HR = 1.22; 95% CI:1.04,1.42). Times from PIA to disposition decision were longer for tertiary (HR = 0.47; 95% CI:0.44,0.51) and urban (HR = 0.69; 95% CI:0.63,0.75) EDs, for patients triaged as resuscitation/emergent (HR = 0.51; 95% CI:0.48,0.54), and for patients arriving by ambulance (HR = 0.78; 95% CI:0.70,0.87). Times from disposition decision to ED departure were longer for patients who were admitted (HR = 0.16; 95% CI:0.13,0.20) or transferred (HR = 0.42; 95% CI:0.35,0.50), and for tertiary EDs (HR = 0.93; 95% CI:0.92,0.94). CONCLUSIONS: All transition times were impacted by ED presentation characteristics. The sole key patient characteristic was age and it only impacted time to PIA. ED crowding demonstrated strong effects of time to PIA but not for the transition times involving disposition decision and ED departure stages.

EM algorithms for fitting multistate cure models.

Multistate cure models are multistate models in which transitions into one or more of the states cannot occur for a fraction of the population. In the study of cancer, multistate cure models can be used to identify factors related to the rate of cancer recurrence, the rate of death before and after recurrence, and the probability of being cured by initial treatment. However, the previous method for fitting multistate cure models requires substantial custom programming, making these valuable models less accessible to analysts. In this article, we present an Expectation-Maximization (EM) algorithm for fitting the multistate cure model using maximum likelihood. The proposed algorithm makes use of a weighted likelihood representation allowing it to be easily implemented with standard software and can incorporate either parametric or non-parametric baseline hazards for the state transition rates. A common complicating feature in cancer studies is that the follow-up times for recurrence and death may differ. Additionally, we may have missingness in the covariates. We propose a Monte Carlo EM (MCEM) algorithm for fitting the multistate cure model in the presence of covariate missingness and/or unequal follow-up of the two outcomes, we describe a novel approach for obtaining standard errors, and we provide some software. Simulations demonstrate good algorithmic performance as long as the modeling assumptions are sufficiently restrictive. We apply the proposed algorithm to a study of recurrence and death in patients with head and neck cancer.

Dynamic Multistate Models With Constant Cross-Product Ratios: Applications to Poverty Status.

Cross-product ratios (αs), which are structurally analogous to odds ratios, are statistically sound and demographically meaningful measures. Assuming constant cross-product ratios in the elements of a matrix of multistate transition probabilities provides a new basis both for calculating probabilities from minimal data and for modeling populations with changing demographic rates. Constant-α estimation parallels log linear modeling, in which the αs are the fixed interactions, and the main effects are calculated from relevant data. Procedures are presented showing how an N state model's matrix of transition probabilities can be found from the constant αs and (1) the state composition of adjacent populations, (2) (N - 1) known probabilities, (3) (N - 1) known transfer rates, or (4) (2N - 1) known numbers of transfers. The scope and flexibility of constant-α models makes them applicable to a broad range of demographic subjects, including marital/union status, political affiliation, residential status, and labor force status. Here, an application is provided to the important but understudied topic of poverty status. Census data, separately for men and women, provide age-specific numbers of persons in three poverty statuses for the years 2009 and 2014. Using an estimated transition matrix that furnishes a set of cross-product ratios, the constant-α approach allows the calculation of male and female poverty status life tables for the 2009-2014 period. The results describe the time spent in each poverty state and the transitions between states over the entire life course.

Working and disability expectancies at older ages: The role of childhood circumstances and education.

The ability to work at older ages depends on health and education. Both accumulate starting very early in life. We assess how childhood disadvantages combine with education to affect working and health trajectories. Applying multistate period life tables to data from the Health and Retirement Study (HRS) for the period 2008-2014, we estimate how the residual life expectancy at age 50 is distributed in number of years of work and disability, by number of childhood disadvantages, gender, and race/ethnicity. Our findings indicate that number of childhood disadvantages is negatively associated with work and positively with disability, irrespective of gender and race/ethnicity. Childhood disadvantages intersect with low education resulting in shorter lives, and redistributing life years from work to disability. Among the highly educated, health and work differences between groups of childhood disadvantage are small. Combining multistate models and inverse probability weighting, we show that the return of high education is greater among the most disadvantaged.

Confidence bands for multiplicative hazards models: Flexible resampling approaches.

We propose new resampling-based approaches to construct asymptotically valid time-simultaneous confidence bands for cumulative hazard functions in multistate Cox models. In particular, we exemplify the methodology in detail for the simple Cox model with time-dependent covariates, where the data may be subject to independent right-censoring or left-truncation. We use simulations to investigate their finite sample behavior. Finally, the methods are utilized to analyze two empirical examples with survival and competing risks data.