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Background: Older people in low- and middle-income countries are more susceptible to the impact of childhood experiences. This study comprehensively examines how childhood socioeconomic status (SES) and adult SES collectively influence late-life healthy longevity from a life course perspective, providing insights for shaping health-related policies. Methods: This study analyzed data from the Chinese Longitudinal Healthy Longevity Survey (1998-2018) with 37,264 individuals aged 65 and above. Using R software, we applied continuous-time multi-state models incorporating the Rockwood frailty index with 38 indicators to assess participants' health. Childhood SES or life course SES trajectories were core explanatory variables, while age and gender were controlled. Multinomial regression estimated annual transition probabilities between different states, and the multi-state life table method calculated total and frailty-specific life expectancy (LE). Results: (1) Social mobility among older people in China showed an upward trend from childhood to adulthood. (2) Transition probabilities for robust-frailty, robust-dead, and frailty-dead increased with age, while frailty-robust decreased. Transition probabilities and LE varied across different childhood SES (low, medium, high) or life-course SES trajectory categories (low-low, low-medium, low-high, medium-low, medium-medium, medium-high, high-low, high-medium, high-high), with probabilities of robust-frailty, robust-dead, and frailty-dead decreasing sequentially across different categories, and frailty-robust increasing sequentially across different categories. Total LE, robust LE, and robust LE proportion increased sequentially across different categories, while frailty LE decreased sequentially across different categories. (3) Women had higher total LE and frailty incidence, but lower recovery rate, mortality risk, robust LE, and robust LE proportion compared to men. Conclusion: Favorable childhood SES and lifelong accumulation of SES advantages protect against frailty morbidity, improve recovery rate, reduce mortality risk, and increase total LE, robust LE, and robust LE proportion. High childhood SES has a stronger protective effect than high adult SES, indicating the lasting impact of childhood conditions on healthy longevity. Systematic interventions in education, food supply, and medical accessibility for children from impoverished families are crucial.
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Longevidade , Classe Social , Humanos , Feminino , Masculino , Estudos Longitudinais , China , Idoso , Idoso de 80 Anos ou mais , Expectativa de Vida , Fragilidade , Criança , Inquéritos Epidemiológicos , População do Leste AsiáticoRESUMO
Objectives: Many studies have attempted to determine the disease severity and patterns of COVID-19. However, at the beginning of the pandemic, the complex patients' trajectories were only descriptively reported, and many analyses were worryingly prone to time-dependent-, selection-, and competing risk biases. Multi-state models avoid these biases by jointly analysing multiple clinical outcomes while taking into account their time dependency, including current cases, and modelling competing events. This paper uses a publicly available data set from the first wave in Israel as an example to demonstrate the benefits of analysing hospital data via multi-state methodology. Methods: We compared the outcome of the data analysis using multi-state models with the outcome obtained when various forms of bias are ignored. Furthermore, we used Cox regression to model the transitions among the states in a multi-state model. This allowed for the comparison of the covariates' influence on transition rates between the two states. Lastly, we calculated expected lengths of stay and state probabilities based on the multi-state model and visualised it using stacked probability plots. Results: Compared to standard methods, multi-state models avoid many biases in the analysis of real-time disease developments. The utility of multi-state models is further highlighted through the use of stacked probability plots, which visualise the results. In addition, by stratification of disease patterns by subgroups and visualisation of the distribution of possible outcomes, these models bring the data into an interpretable form. Conclusion: To accurately guide the provision of medical resources, this paper recommends the real-time collection of hospital data and its analysis using multi-state models, as this method eliminates many potential biases. By applying multi-state models to real-time data, the gained knowledge allows rapid detection of altered disease courses when new variants arise, which is essential when informing medical and political decision-makers as well as the general population.
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There is imminent refracture risk in elderly individuals for up to six years, with a decline thereafter except in women below 75 who face a constant elevated risk. Elderly men with fractures face the highest mortality risk, particularly those with hip and vertebral fractures. Targeted monitoring and treatment strategies are recommended. PURPOSE: Current management and interventions for osteoporotic fractures typically focus on bone mineral density loss, resulting in suboptimal evaluation of fracture risk. The aim of the study is to understand the progression of fractures to refractures and mortality in the elderly using multi-state models to better target those at risk. METHODS: This prospective, observational study analysed data from the AGES-Reykjavik cohort of Icelandic elderly, using multi-state models to analyse the evolution of fractures into refractures and mortality, and to estimate the probability of future events in subjects based on prognostic factors. RESULTS: At baseline, 4778 older individuals aged 65 years and older were included. Elderly men, and elderly women above 80 years of age, had a distinct imminent refracture risk that lasted between 2-6 years, followed by a sharp decline. However, elderly women below 75 continued to maintain a nearly constant refracture risk profile for ten years. Hip (30-63%) and vertebral (24-55%) fractures carried the highest 5-year mortality burden for elderly men and women, regardless of age, and for elderly men over 80, lower leg fractures also posed a significant mortality risk. CONCLUSION: The risk of refracture significantly increases in the first six years following the initial fracture. Elderly women, who experience fractures at a younger age, should be closely monitored to address their long-term elevated refracture risk. Elderly men, especially those with hip and vertebral fractures, face substantial mortality risk and require prioritized monitoring and treatment.
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Fraturas do Quadril , Fraturas por Osteoporose , Recidiva , Fraturas da Coluna Vertebral , Humanos , Fraturas por Osteoporose/mortalidade , Idoso , Masculino , Feminino , Islândia/epidemiologia , Idoso de 80 Anos ou mais , Fraturas do Quadril/mortalidade , Fraturas da Coluna Vertebral/mortalidade , Estudos Prospectivos , Medição de Risco/métodos , Progressão da Doença , Densidade Óssea/fisiologia , PrognósticoRESUMO
PURPOSE: Acute kidney injury (AKI) associated with COVID-19 is associated with poor prognosis. This study assessed the hitherto uninvestigated impact of COVID-19 on the progression and clinical outcomes of patients with AKI. METHODS: Data from 576 patients with AKI admitted between 13/3/20 and 13/5/20 were studied. Increasingly complex analyses, from logistic regressions to competing-risk and multi-state models, have revealed insights into AKI progression dynamics associated with PCR-confirmed COVID-19 acquisition and death. Meta-analyses of case fatality ratios among patients with AKI were also conducted. RESULTS: The overall case-fatality ratio was 0.33 [95% CI (0.20-0.36)]; higher in COVID-19 positive (COVID+) patients 0.52 [95% CI (0.46-0.58)] than in their negative (COVID-) counterparts 0.16 [95% CI (0.12-0.20)]. In AKI Stage-3 patients, that was 0.71 [95% CI (0.64-0.79)] among COVID+ patients with 45% dead within 14 days and 0.35 [95% CI (0.25-0.44)] in the COVID- group and 28% died within 14 days. Among patients diagnosed with AKI Stage-1 within 24 h, the probability of progression to AKI Stage-3 on day 7 post admission was 0.22 [95% CI (0.17-0.27)] among COVID+ patients, and 0.06 [95% CI (0.03, 0.09)] among those who tested negative. The probability of discharge by day 7 was 0.71 [95% CI (0.66, 0.75)] in COVID- patients, and 0.27 [95% CI (0.21, 0.32)] in COVID+ patients. By day 14, in AKI Stage-3 COVID+ patients, that was 0.35 [95% CI (0.25, 0.44)] with little change by day 10, that is, 0.38 [95% CI (0.29, 0.47)]. CONCLUSION: These results are consistent with either a rapid progression in severity, prolonged hospital care, or high case fatality ratio among AKI Stage-3 patients, significantly exacerbated by COVID-19 infection.
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Injúria Renal Aguda , COVID-19 , Progressão da Doença , Humanos , COVID-19/complicações , COVID-19/mortalidade , COVID-19/epidemiologia , COVID-19/terapia , Injúria Renal Aguda/mortalidade , Injúria Renal Aguda/terapia , Injúria Renal Aguda/epidemiologia , Injúria Renal Aguda/diagnóstico , Masculino , Feminino , Pessoa de Meia-Idade , Idoso , SARS-CoV-2 , Fatores de Risco , Prognóstico , Estudos RetrospectivosRESUMO
BACKGROUND: Real-world observational data are an important source of evidence on the treatment effectiveness for patients hospitalized with coronavirus disease 2019 (COVID-19). However, observational studies evaluating treatment effectiveness based on longitudinal data are often prone to methodological biases such as immortal time bias, confounding bias, and competing risks. METHODS: For exemplary target trial emulation, we used a cohort of patients hospitalized with COVID-19 (n = 501) in a single centre. We described the methodology for evaluating the effectiveness of a single-dose treatment, emulated a trial using real-world data, and drafted a hypothetical study protocol describing the main components. To avoid immortal time and time-fixed confounding biases, we applied the clone-censor-weight technique. We set a 5-day grace period as a period of time when treatment could be initiated. We used the inverse probability of censoring weights to account for the selection bias introduced by artificial censoring. To estimate the treatment effects, we took the multi-state model approach. We considered a multi-state model with five states. The primary endpoint was defined as clinical severity status, assessed by a 5-point ordinal scale on day 30. Differences between the treatment group and standard of care treatment group were calculated using a proportional odds model and shown as odds ratios. Additionally, the weighted cause-specific hazards and transition probabilities for each treatment arm were presented. RESULTS: Our study demonstrates that trial emulation with a multi-state model analysis is a suitable approach to address observational data limitations, evaluate treatment effects on clinically heterogeneous in-hospital death and discharge alive endpoints, and consider the intermediate state of admission to ICU. The multi-state model analysis allows us to summarize results using stacked probability plots that make it easier to interpret results. CONCLUSIONS: Extending the emulated target trial approach to multi-state model analysis complements treatment effectiveness analysis by gaining information on competing events. Combining two methodologies offers an option to address immortal time bias, confounding bias, and competing risk events. This methodological approach can provide additional insight for decision-making, particularly when data from randomized controlled trials (RCTs) are unavailable.
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COVID-19 , Humanos , Resultado do Tratamento , Viés de Seleção , Hospitalização , Razão de ChancesRESUMO
Several social dimensions including social integration, status, early-life adversity, and their interactions across the life course can predict health, reproduction, and mortality in humans. Accordingly, the social environment plays a fundamental role in the emergence of phenotypes driving the evolution of aging. Recent work placing human social gradients on a biological continuum with other species provides a useful evolutionary context for aging questions, but there is still a need for a unified evolutionary framework linking health and aging within social contexts. Here, we summarize current challenges to understand the role of the social environment in human life courses. Next, we review recent advances in comparative biodemography and propose a biodemographic perspective to address socially driven health phenotype distributions and their evolutionary consequences using a nonhuman primate population. This new comparative approach uses evolutionary demography to address the joint dynamics of populations, social dimensions, phenotypes, and life history parameters. The long-term goal is to advance our understanding of the link between individual social environments, population-level outcomes, and the evolution of aging.
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Envelhecimento , Meio Social , Animais , HumanosRESUMO
Blood-related diseases are complex diseases with diverse origins, treatments and prognosis. In haematology studies, investigators are interested in multiple outcomes and multiple prognostic variables that may change value over the course of follow-up. These time-dependent variables can be of different nature. Time-dependent events such as treatment with haematopoeitic stem cell transplant (HCT) and acute or chronic graft-versus-host disease (GVHD) typically interact with outcomes respectively after diagnosis or HCT. Longitudinal measurement such as immune response do influence survival after HCT. Effect of these time-dependent variables on outcomes can be investigated using different approaches, such as time-dependent Cox regression, landmark analysis, multi-state models or joint modelisation. In this paper we review basic principles of these different approaches using examples from haematological studies.
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Síndrome de Bronquiolite Obliterante , Humanos , Estudos Retrospectivos , Transplante de Células-TroncoRESUMO
Illness-death models are a class of stochastic models inside the multi-state framework. In those models, individuals are allowed to move over time between different states related to illness and death. They are of special interest when working with non-terminal diseases, as they not only consider the competing risk of death but also allow us to study the progression from illness to death. The intensity of each transition can be modelled including both fixed and random effects of covariates. In particular, spatially structured random effects or their multivariate versions can be used to assess spatial differences between regions and among transitions. We propose a Bayesian methodological framework based on an illness-death model with a multivariate Leroux prior for the random effects. We apply this model to a cohort study regarding progression after an osteoporotic hip fracture in elderly patients. From this spatial illness-death model, we assess the geographical variation in risks, cumulative incidences and transition probabilities related to recurrent hip fracture and death. Bayesian inference is done via the integrated nested Laplace approximation.
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Teorema de Bayes , Humanos , Idoso , Estudos de Coortes , ProbabilidadeRESUMO
Multiple randomized controlled trials, each comparing a subset of competing interventions, can be synthesized by means of a network meta-analysis to estimate relative treatment effects between all interventions in the evidence base. Here we focus on estimating relative treatment effects for time-to-event outcomes. Cancer treatment effectiveness is frequently quantified by analyzing overall survival (OS) and progression-free survival (PFS). We introduce a method for the joint network meta-analysis of PFS and OS that is based on a time-inhomogeneous tri-state (stable, progression, and death) Markov model where time-varying transition rates and relative treatment effects are modeled with parametric survival functions or fractional polynomials. The data needed to run these analyses can be extracted directly from published survival curves. We demonstrate use by applying the methodology to a network of trials for the treatment of non-small-cell lung cancer. The proposed approach allows the joint synthesis of OS and PFS, relaxes the proportional hazards assumption, extends to a network of more than two treatments, and simplifies the parameterization of decision and cost-effectiveness analyses.
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Carcinoma Pulmonar de Células não Pequenas , Neoplasias Pulmonares , Humanos , Carcinoma Pulmonar de Células não Pequenas/terapia , Metanálise em Rede , Resultado do Tratamento , Intervalo Livre de Progressão , Intervalo Livre de DoençaRESUMO
Ageing has been related to the onset of disability and dependency in older adults. There is a need to better understand the disability and dependency trajectories of older adults and their relationship with socio-demographic characteristics and institutional or cultural context. This study analyses the role of age, sex, education and self-perceived health in disability, dependency and death transitions, addressing the heterogeneity across European countries and inconsistencies when using different measures of disability. Multi-state models were adjusted to evaluate the role of risk and protective factors in the transitions to disability, dependency and death. Difficulties in performing activities of daily living (ADLs) assess disability and dependency states. Data were from the Survey of Health, Ageing and Retirement in Europe conducted in 2004-2013, considering individuals aged 65 and older at baseline from Austria, Belgium, Denmark, France, Germany, Italy, the Netherlands, Spain, Sweden and Switzerland. The results showed that transitions to disability and dependency varied with age, sex, education and self-perceived health. The probability of transition to disability and dependency states increases until the age of 70 for all countries. However, there was heterogeneity in the disability and dependency trajectories with ageing between men and women. In most countries, women live with difficulties and may need help for longer than men. Care policies should consider sex differences to decrease the burden of care of informal caregivers, particularly in countries where care systems are absent or partially developed and a high level of family obligations to care needs exist.
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BACKGROUND: Multi-state models are used to study several clinically meaningful research questions. Depending on the research question of interest and the information contained in the data, different multi-state structures and modelling choices can be applied. We aim to explore different research questions using a series of multi-state models of increasing complexity when studying repeated prescriptions data, while also evaluating different modelling choices. METHODS: We develop a series of research questions regarding the probability of being under antidepressant medication across time using multi-state models, among Swedish women diagnosed with breast cancer (n = 18,313) and an age-matched population comparison group of cancer-free women (n = 92,454) using a register-based database (Breast Cancer Data Base Sweden 2.0). Research questions were formulated ranging from simple to more composite ones. Depending on the research question, multi-state models were built with structures ranging from simpler ones, like single-event survival analysis and competing risks, up to complex bidirectional and recurrent multi-state structures that take into account the recurring start and stop of medication. We also investigate modelling choices, such as choosing a time-scale for the transition rates and borrowing information across transitions. RESULTS: Each structure has its own utility and answers a specific research question. However, the more complex structures (bidirectional, recurrent) enable accounting for the intermittent nature of prescribed medication data. These structures deliver estimates of the probability of being under medication and total time spent under medication over the follow-up period. Sensitivity analyses over different definitions of the medication cycle and different choices of timescale when modelling the transition intensity rates show that the estimates of total probabilities of being in a medication cycle over follow-up derived from the complex structures are quite stable. CONCLUSIONS: Each research question requires the definition of an appropriate multi-state structure, with more composite ones requiring such an increase in the complexity of the multi-state structure. When a research question is related with an outcome of interest that repeatedly changes over time, such as the medication status based on prescribed medication, the use of novel multi-state models of adequate complexity coupled with sensible modelling choices can successfully address composite, more realistic research questions.
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Neoplasias da Mama , Humanos , Feminino , Neoplasias da Mama/tratamento farmacológico , Recidiva Local de Neoplasia , Antidepressivos/uso terapêutico , Sistema de Registros , Prescrições de MedicamentosRESUMO
There are few computational and methodological tools available for the analysis of general multi-state models with interval censoring. Here, we propose a general framework for parametric inference with interval censored multi-state data. Our framework can accommodate any parametric model for the transition times, and covariates may be included in various ways. We present a general method for constructing the likelihood, which we have implemented in a ready-to-use R package, smms, available on GitHub. The R package also computes the required high-dimensional integrals in an efficient manner. Further, we explore connections between our modelling framework and existing approaches: our models fall under the class of semi-Markovian multi-state models, but with a different, and sparser parameterisation than what is often seen. We illustrate our framework through a dataset monitoring heart transplant patients. Finally, we investigate the effect of some forms of misspecification of the model assumptions through simulations.
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Modelos Estatísticos , Humanos , Probabilidade , Interpretação Estatística de Dados , Modelos de Riscos Proporcionais , Análise de SobrevidaRESUMO
Discrete dynamical systems in which model components take on categorical values have been successfully applied to biological networks to study their global dynamic behavior. Boolean models in particular have been used extensively. However, multi-state models have also emerged as effective computational tools for the analysis of complex mechanisms underlying biological networks. Models in which variables assume more than two discrete states provide greater resolution, but this scheme introduces discontinuities. In particular, variables can increase or decrease by more than one unit in one time step. This can be corrected, without changing fixed points of the system, by applying an additional rule to each local activation function. On the other hand, if one is interested in cyclic attractors of their system, then this rule can potentially introduce new cyclic attractors that were not observed previously. This article makes some advancements in understanding the state space dynamics of multi-state network models with synchronous, sequential, or block-sequential update schedules and establishes conditions under which no new cyclic attractors are added to networks when the additional rule is applied. Our analytical results have the potential to be incorporated into modeling software and aid researchers in their analyses of biological multi-state networks.
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Algoritmos , Software , Redes Reguladoras de GenesRESUMO
INTRODUCTION: In older patients with breast cancer, the risk of dying from other causes than breast cancer strongly increases after the age of 70. The aim of this study was to assess contributions of breast cancer mortality versus other-cause mortality after locoregional or distant recurrence in a population-based cohort of older patients analysed by multi-state models. METHODS: Surgically treated patients ≥70 years diagnosed with stage I-III breast cancer in 2003-2009 were selected from the Netherlands Cancer Registry. A novel multi-state model with locoregional and distant recurrence that incorporates relative survival was fitted. Other-cause and breast cancer mortality were indicated as population and excess mortality. RESULTS: Overall, 18,419 patients were included. Ten-year cumulative incidences of locoregional and distant recurrence were 2.8% (95%CI 2.6-3.1%) and 12.5% (95%CI 11.9-13.1%). Other-cause mortality increased from 23.9% (95%CI 23.7-24.2%) in patients 70-74 years to 73.8% (95%CI 72.2-75.4%) in those ≥80 years. Ten-year probabilities of locoregional or distant recurrence with subsequent breast cancer death were 0.4-1.3% and 10.2-14.6%, respectively. For patients with a distant recurrence in the first two years after diagnosis, breast cancer death probabilities were 95.3% (95%CI 94.2-96.4%), 93.1% (95%CI 91.6-94.6%), and 88.6% (95%CI 86.5-90.8%) in patients 70-74, 75-79, and ≥80 years. CONCLUSION: In older patients without recurrence, prognosis is driven by other-cause mortality. Although locoregional recurrence is a predictor for worse outcome, given its low incidence it contributes little to breast cancer mortality after diagnosis. For patients who develop a distant recurrence, breast cancer remains the dominant cause of death, even at old age.
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Neoplasias da Mama , Idoso , Mama/patologia , Neoplasias da Mama/patologia , Feminino , Humanos , Incidência , Recidiva Local de Neoplasia/patologia , Estadiamento de Neoplasias , PrognósticoRESUMO
BACKGROUND AND AIMS: Cardiometabolic multimorbidity has become increasingly common over the past few decades. Little is known about how risk factors affect temporal progression of cardiometabolic multimorbidity. We aim to explore the role of socioeconomic, lifestyle, and clinical risk factors in the progression of cardiometabolic multimorbidity. METHODS AND RESULTS: This prospective cohort study included 56,587 participants aged ≥45 years who were free of diabetes, stroke, and heart disease. Three clusters of risk factors were assessed and each on a 5-point scale: socioeconomic, lifestyle, and clinical factors. We used multi-state models (MSMs) to examine the roles of risk factors in five transitions of multimorbidity trajectory: from healthy to first cardiometabolic disease, first cardiometabolic disease to cardiometabolic multimorbidity, health to mortality, first cardiometabolic disease to mortality, and cardiometabolic multimorbidity to mortality. In MSMs, socioeconomic (HR: 1.21; 95% CI: 1.19-1.25) and clinical (HR: 1.53; 95% CI: 1.51-1.56) scales were associated with the transition from health to first cardiometabolic. Socioeconomic (HR: 2.39; 95% CI: 2.24-2.54) and lifestyle (HR: 1.22; 95% CI: 1.18-1.26) scales were associated with the transitions from first disease to cardiometabolic multimorbidity. In addition, socioeconomic and lifestyle scales were associated with increased risk of mortality in people without cardiometabolic disease, with first cardiometabolic disease, and with cardiometabolic multimorbidity. CONCLUSIONS: Socioeconomic and lifestyle factors were not only important predictors of multimorbidity in those with existing cardiometabolic disease, but also important in shaping risk of mortality. However, clinical factors were the only key determinants of incidence of a first cardiometabolic disease.
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Cardiopatias , Multimorbidade , China/epidemiologia , Humanos , Estilo de Vida , Estudos Prospectivos , Fatores de Risco , Fatores SocioeconômicosRESUMO
The recent availability of routine medical data, especially in a university-clinical context, may enable the discovery of typical healthcare pathways, that is, typical temporal sequences of clinical interventions or hospital readmissions. However, such pathways are heterogeneous in a large provider such as a university hospital, and it is important to identify similar care pathways that can still be considered typical pathways. We understand the pathway as a temporal process with possible transitions from a single initial treatment state to hospital readmission of different types, which constitutes a competing risks setting. In this article, we propose a multi-state model-based approach to uncover pathway similarity between two groups of individuals. We describe a new bootstrap procedure for testing the similarity of constant transition intensities from two competing risk models. In a large simulation study, we investigate the performance of our similarity approach with respect to different sample sizes and different similarity thresholds. The studies are motivated by an application from urological clinical routine and we show how the results can be transferred to the application example.
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Procedimentos Clínicos , Neoplasias da Próstata , Atenção à Saúde , Hospitais , Humanos , Masculino , Readmissão do Paciente , Neoplasias da Próstata/cirurgiaRESUMO
Multi-state models for event history analysis most commonly assume the process is Markov. This article considers tests of the Markov assumption that are applicable to general multi-state models. Two approaches using existing methodology are considered; a simple method based on including time of entry into each state as a covariate in Cox models for the transition intensities and a method involving detecting a shared frailty through a stratified Commenges-Andersen test. In addition, using the principle that under a Markov process the future rate of transitions of the process at times $t > s$ should not be influenced by the state occupied at time $s$, a new class of general tests is developed by considering summaries from families of log-rank statistics where patients are grouped by the state occupied at varying initial time $s$. An extended form of the test applicable to models that are Markov conditional on observed covariates is also derived. The null distribution of the proposed test statistics are approximated by using wild bootstrap sampling. The approaches are compared in simulation and applied to a dataset on sleeping behavior. The most powerful test depends on the particular departure from a Markov process, although the Cox-based method maintained good power in a wide range of scenarios. The proposed class of log-rank statistic based tests are most useful in situations where the non-Markov behavior does not persist, or is not uniform in nature across patient time.
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Modelos Estatísticos , Projetos de Pesquisa , Simulação por Computador , Humanos , Cadeias de Markov , Modelos de Riscos ProporcionaisRESUMO
Existing methods concerning the assessment of long-term survival outcomes in one-armed trials are commonly restricted to one primary endpoint. Corresponding adaptive designs suffer from limitations regarding the use of information from other endpoints in interim design changes. Here we provide adaptive group sequential one-sample tests for testing hypotheses on the multivariate survival distribution derived from multi-state models, while making provision for data-dependent design modifications based on all involved time-to-event endpoints. We explicitly elaborate application of the methodology to one-sample tests for the joint distribution of (i) progression-free survival (PFS) and overall survival (OS) in the context of an illness-death model, and (ii) time to toxicity and time to progression while accounting for death as a competing event. Large sample distributions are derived using a counting process approach. Small sample properties are studied by simulation. An already established multi-state model for non-small cell lung cancer is used to illustrate the adaptive procedure.
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Carcinoma Pulmonar de Células não Pequenas , Neoplasias Pulmonares , Ensaios Clínicos Fase II como Assunto , Simulação por Computador , Determinação de Ponto Final/métodos , Humanos , Projetos de Pesquisa , Tamanho da AmostraRESUMO
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.
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Probabilidade , HumanosRESUMO
Multi-state models are increasingly being used to model complex epidemiological and clinical outcomes over time. It is common to assume that the models are Markov, but the assumption can often be unrealistic. The Markov assumption is seldomly checked and violations can lead to biased estimation of many parameters of interest. This is a well known problem for the standard Aalen-Johansen estimator of transition probabilities and several alternative estimators, not relying on the Markov assumption, have been suggested. A particularly simple approach known as landmarking have resulted in the Landmark-Aalen-Johansen estimator. Since landmarking is a stratification method a disadvantage of landmarking is data reduction, leading to a loss of power. This is problematic for "less traveled" transitions, and undesirable when such transitions indeed exhibit Markov behaviour. Introducing the concept of partially non-Markov multi-state models, we suggest a hybrid landmark Aalen-Johansen estimator for transition probabilities. We also show how non-Markov transitions can be identified using a testing procedure. The proposed estimator is a compromise between regular Aalen-Johansen and landmark estimation, using transition specific landmarking, and can drastically improve statistical power. We show that the proposed estimator is consistent, but that the traditional variance estimator can underestimate the variance of both the hybrid and landmark estimator. Bootstrapping is therefore recommended. The methods are compared in a simulation study and in a real data application using registry data to model individual transitions for a birth cohort of 184 951 Norwegian men between states of sick leave, disability, education, work and unemployment.