Markov状态转移模型在慢性患者平均寿命预测中的应用

目的探讨Markov状态转移模型在慢性病平均寿命预测中的应用.方法建立三状态的Markov模型,采用队列分析方法计算慢性鼻衄患者的平均寿命.结果通过专家假定的状态转移概率预测目前处于疾病状态的一个固定队列的人群今后50年处于疾病状态的平均时间是7.756年,处于健康状态的平均时间是8.135年,总的平均寿命为15.891年.结论Markov状态转移模型不仅可以预测慢性病平均寿命,还可预测患者处在疾病或健康不同状态的平均时间.     

A Bayesian semiparametric Markov regression model for juvenile dermatomyositis

Juvenile dermatomyositis (JDM) is a rare autoimmune disease that may lead to serious complications, even to death. We develop a 2‐state Markov regression model in a Bayesian framework to characterise disease progression in JDM over time and gain a better understanding of the factors influencing disease risk. The transition probabilities between disease and remission state (and vice versa) are a function of time‐homogeneous and time‐varying covariates. These latter types of covariates are introduced in the model through a latent health state function, which describes patient‐specific health over time and accounts for variability among patients. We assume a nonparametric prior based on the Dirichlet process to model the health state function and the baseline transition intensities between disease and remission state and vice versa. The Dirichlet process induces a clustering of the patients in homogeneous risk groups. To highlight clinical variables that most affect the transition probabilities, we perform variable selection using spike and slab prior distributions. Posterior inference is performed through Markov chain Monte Carlo methods. Data were made available from the UK JDM Cohort and Biomarker Study and Repository, hosted at the UCL Institute of Child Health.     

State‐space size considerations for disease‐progression models

Markov models of disease progression are widely used to model transitions in patients' health state over time. Usually, patients' health status may be classified according to a set of ordered health states. Modelers lump together similar health states into a finite and usually small, number of health states that form the basis of a Markov chain disease‐progression model. This increases the number of observations used to estimate each parameter in the transition probability matrix. However, lumping together observably distinct health states also obscures distinctions among them and may reduce the predictive power of the model. Moreover, as we demonstrate, precision in estimating the model parameters does not necessarily improve as the number of states in the model declines. This paper explores the tradeoff between lumping error introduced by grouping distinct health states and sampling error that arises when there are insufficient patient data to precisely estimate the transition probability matrix. Copyright © 2013 John Wiley & Sons, Ltd.     

A counting process approach to the analysis of the course of non-Hodgkin's lymphoma

Non-Hodgkin's lymphoma is a neoplastic disease with a course including remission and relapse. Therefore, a mortality analysis of overall survival time alone may conceal important differences between the forces of mortality (hazard functions) associated with distinct states of active disease, for example pre-remission state and first relapse. Further, prognostic factors for overall survival time may fail to contribute significantly to the pre-remission force of mortality. Our approach to analysis is based on a non-homogeneous Markov illness-death process as a stochastic model of the course of disease. It exploits the statistical theory of counting processes.     

Parametric multistate survival models: Flexible modelling allowing transition‐specific distributions with application to estimating clinically useful measures of effect differences

Multistate models are increasingly being used to model complex disease profiles. By modelling transitions between disease states, accounting for competing events at each transition, we can gain a much richer understanding of patient trajectories and how risk factors impact over the entire disease pathway. In this article, we concentrate on parametric multistate models, both Markov and semi‐Markov, and develop a flexible framework where each transition can be specified by a variety of parametric models including exponential, Weibull, Gompertz, Royston‐Parmar proportional hazards models or log‐logistic, log‐normal, generalised gamma accelerated failure time models, possibly sharing parameters across transitions. We also extend the framework to allow time‐dependent effects. We then use an efficient and generalisable simulation method to calculate transition probabilities from any fitted multistate model, and show how it facilitates the simple calculation of clinically useful measures, such as expected length of stay in each state, and differences and ratios of proportion within each state as a function of time, for specific covariate patterns. We illustrate our methods using a dataset of patients with primary breast cancer. User‐friendly Stata software is provided.     

Active life expectancy for elderly Japanese by chewing ability

OBJECTIVE: Panel interview surveys of nationally representative elderly people aged 65 years or above in Japan were conducted three times at 2-year intervals since 1999 (Nihon University Japanese Longitudinal Study of Aging) to estimate health expectancy for males and females separately according to their chewing ability. METHOD: Multistate life table methods were applied to estimate health expectancy. Three health states, namely, active, inactive and dead, were defined according to the ability to perform specified daily activities. Living respondents were considered to be in an "inactive state" if they responded "very difficult" or "unable" for performance of at least one ADL or IADL. Otherwise they were considered to be in an "active state". 4,323 sampled persons who responded to the baseline survey were included in the study. Based on estimated transition probabilities over the survey period between active and inactive states, and active and inactive states to death, both population- and status-based multistate life tables were constructed according to chewing ability. Those who could chew relatively hard foods at the baseline survey were classified as Group A and those who could chew only relatively soft foods were classified as Group B. RESULTS: The population-based multistate life tables indicated that at age 65, total life expectancy was 19.3/23.2 (males/females) years for Group A and 16.7/21.1 years for Group B. Active life expectancy was 16.8/18.6 years and 13.6/16.3 years, and inactive life expectancy was 2.4/4.6 years and 3.1/4.8 years for Groups A and B respectively. A statistically significant difference was observed between the two groups only in terms of active life expectancy. From status-based multistate life tables, similar patterns were observed for those whose status at the baseline was "active". CONCLUSION: These results suggest that maintenance or recovery of sufficient chewing ability for elderly people is related to a longer total life expectancy and even more strongly related to a longer active life expectancy.     

Multi-state models and diabetic retinopathy

This paper discusses the application of a multi-state model to diabetic retinopathy under the assumption that a continuous time Markov process determines the transition times between disease stages. The multi-state model consists of three transient states that represent the early stages of retinopathy, and one final absorbing state that represent the irreversible stage of retinopathy. By using a model with covariables, we explore the effects of factors that influence the onset, progression, and regression of diabetic retinopathy among subjects with insulin-dependent diabetes mellitus. We can also introduce time-dependent covariables in the model by assuming that the covariables remain constant between two observations. We can also obtain survival-type curves from each stage of the disease and for any combination of patient risk factors.     

A dynamic model for estimating changes in health status and costs

We develop an innovative method to assess total treatment costs over a finite period of time while incorporating the dynamics of change in the health status of patients. Costs are incurred through medical care use while patients sojourn in health states. Because complete ascertainment of costs and observation of events are not always feasible, some patient utilization will be incomplete and events will also be censored. A Markov model is used to estimate the transition probabilities between health states and the impact of patient variables on transition intensities. A mixed-effects model is used for sojourn costs with transition times as random effects and patient variables as fixed effects. The models are combined to estimate net present values (NPVs) of expenditures over a finite time interval as a function of patient characteristics. The method is applied to a data set of 624 incident cases of cancer. Physical functioning after cancer diagnosis was assessed periodically through structured interviews. The outcomes of interest are normal physical function, impaired physical function, or the terminal state, dead. Charges were obtained from Medicare claim files for 2 years following cancer diagnosis. For demonstration purposes, we estimate NPVs for charges incurred over 2 years by cancer site and cancer stage. Our method, a joint regression model, provides a flexible approach to assessing the influence of patient characteristics on both cost and health outcomes while accommodating heteroscedasticity, skewness and censoring in the data.     

Modeling the impact of adjustable gastric banding on survival in patients with morbid obesity

OBJECTIVE: Morbid obesity is associated with premature death. Adjustable gastric banding may lead to substantial weight loss in patients with morbid obesity. Little is known about the impact of weight loss on survival after adjustable gastric banding. We therefore developed a mathematical model to estimate life expectancy in patients with a body mass index (BMI) > or =40 kg/m(2) undergoing bariatric surgery. RESEARCH METHODS AND PROCEDURES: We developed a nonhomogeneous Markov chain consisting of five states: the absorbing state ("dead") and the four recurrent states BMI > or =40 kg/m(2), BMI 36 to 39 kg/m(2), BMI 32 to 35 kg/m(2), and BMI 25 to 31 kg/m(2). Scenarios of weight loss and age- and sex-dependent risk of death, as well as BMI-dependent excess mortality were extracted from life tables and published literature. All patients entered the model through the state of BMI > or =40 kg/m(2). RESULTS: In men aged either 18 or 65 years at the time of surgery, who moved from the state BMI > or =40 kg/m(2) to the next lower state of BMI 36 to 39 kg/m(2), life expectancy increased by 3 and 0.7 years, respectively. In women aged either 18 or 65 years at the time of surgery, who moved from the state BMI > or =40 kg/m(2) to the next lower state BMI 36 to 39 kg/m(2), life expectancy increased by 4.5 and 2.6 years, respectively. Weight loss to lower BMI strata resulted in further gains of life expectancy in both men and women. DISCUSSION: Within the limitations of the modeling study, adjustable gastric banding in patients with morbid obesity may substantially increase life expectancy.     

Multi-state models and outcome prediction in bone marrow transplantation.

Multi-state models have proved versatile and useful in the statistical analysis of the complicated course of events after bone marrow transplantation. Working from data from the International Bone Marrow Transplant Registry, we show that summary probability calculations may be useful to explore hypothetical scenarios where some transition intensities are set by the researcher. A multi-state Markov process model is specified with six states: the initial state 0; acute; chronic and both acute and chronic graft-versus-host disease A, C and AC; relapse R and death in remission D. Transition rates between the states are estimated using Nelson-Aalen estimators and Cox regression models and combined to transition probability estimators using Aalen-Johansen product integration. Besides the estimated transition probabilities to D and R we explore hypothetical probabilities obtained by artificially changing certain transition intensities, with the general purposes of getting summary views of the development for actual patients 'in this world' and of exploring the intrinsic information from real patients about consequences of various changed conditions.     

Model to assess the cost-effectiveness of new treatments for depression

OBJECTIVES: The objective of this study was to develop a model to assess the cost-effectiveness of a new treatment for patients with depression. METHODS: A Markov simulation model was constructed to evaluate standard care for depression as performed in clinical practice compared with a new treatment for depression. Costs and effects were estimated for time horizons of 6 months to 5 years. A naturalistic longitudinal observational study provided data on costs, quality of life, and transition probabilities. Data on long-term consequences of depression and mortality risks were collected from the literature. Cost-effectiveness was quantified as quality-adjusted life-years (QALYs) gained from the new treatment compared with standard care, and the societal perspective was taken. Probabilistic analyses were conducted to present the uncertainty in the results, and sensitivity analyses were conducted on key parameters used in the model. RESULTS: Compared with standard care, the new hypothetical therapy was predicted to substantially decrease costs and was also associated with gains in QALYs. With an improved treatment effect of 50 percent on achieving full remission, the net cost savings were 20,000 Swedish kronor over a 5-year follow-up time, given equal costs of treatments. Patients gained .073 QALYs over 5 years. The results are sensitive to changes in assigned treatment effects. CONCLUSIONS: The present study provides a new model for assessing the cost-effectiveness of treatments for depression by incorporating full remission as the treatment goal and QALYs as the primary outcome measure. Moreover, we show the usefulness of naturalistic real-life data on costs and quality of life and transition probabilities when modeling the disease over time.     

A piecewise Markov process for analysing survival from breast cancer in different risk groups

A study of the relapse and survival times for 300 breast cancer patients submitted to post-surgical treatments is presented. After surgery, these patients were given three treatments: chemotherapy; radiotherapy; hormonal therapy and a combination of them. From the data set, a non-homogeneous Markov model is selected as suitable for the evolution of the disease. The model is applied considering two time periods during the observation of the cohort where the disease is well differentiated with respect to death and relapse. The effect of the treatments on the patients is introduced into the model via the transition intensity functions. A piecewise Markov process is applied, the likelihood function is built and the parameters are estimated, following a parametric methodological procedure. As a consequence, a survival table for different treatments is given, and survival functions for different treatments are plotted and compared with the corresponding empirical survival function. The fit of the different curves is good, and predictions can be made on the survival probabilities to post-surgical treatments for different risk groups.     

Cox regression models for quality adjusted survival analysis

We develop a method for incorporating covariates as regressors in a quality adjusted survival analysis (Q-TWiST) using Cox's proportional hazards model. The standard Q-TWiST method assumes that patients progress through a series of health states which differ in quality of life. The Kaplan—Meier product limit method is used to estimate the mean duration of each state by estimating the survival curves for the health state transition times. These estimates provide the basis for quality adjusted survival analysis. In this paper, the survival curves are modelled using Cox's proportional hazards regression. Quality adjusted survival is estimated given sets of covariate values, allowing one to profile patients. The results are useful for investigating how prognostic factors affect treatment benefits in terms of quality of life. We give a brief review of the standard Q-TWiST method and illustrate the extended methodology with an example from the International Breast Cancer Study Group Trial V comparing short duration versus long duration chemotherapy in the treatment of node-positive breast cancer.     

基于多状态Markov模型的老年人认知损害转归研究

目的将多状态Markov模型应用于轻度认知损害(mild cognitive impairment,MCI)转归研究,为慢性病转归研究提供方法学借鉴。方法通过MCI患者IQ变化反映随访人群认知功能的变化趋势,构建一个四状态模型。根据多状态Markov模型分析原理,获得各状态转移影响因素、逗留时间、生存曲线,并进行模型拟合优度评价。结果 MCI病人处于认知功能稳定、认知轻度恶化和认知好转的时间大约分别为6.4年、3.6年和5.2年;生存曲线显示预后由好到差为认知功能好转、认知功能稳定、认知功能轻度恶化;多状态Markov模型拟合结果较好。结论多状态Markov模型是多状态、多阶段慢性病转归研究的有效分析方法。     

Comparison of smoothing techniques for CD4 data in a Markov model with states defined by CD4: an example on the estimation of the HIV incubation time distribution.

Multi-state models defined in terms of CD4 counts are useful for modelling HIV disease progression. A Markov model with six progressive CD4-based states and an absorbing state (AIDS) was used to estimate the cumulative probability of progressing to AIDS in 158 HIV-1 infected haemophiliacs with known seroconversion (SC) dates. A problem arising in such analysis is how to define CD4-based states, since this marker is subject to measurement error and short timescale variability. Four approaches were used: no smoothing, ad hoc smoothing (to move to a later/previous state two consecutive measurements to later/previous states are needed), kernel smoothing and random effects (RE) models. The estimates were compared with the Kaplan-Meier estimate based solely on data concerning time to AIDS. There was an apparent lack of agreement between the Kaplan-Meier and the "no smoothing" estimate. With the exception of the "no smoothing" method, "ad hoc", kernel and RE estimates fell within the range of the 95 per cent CIs of the Kaplan-Meier curve. Simulations demonstrated that the use of raw CD4 counts provides overestimated transition intensities. Compared to the kernel method, ad hoc is easier to implement and overcomes the problem of the choice of bandwidth. The RE approach leads to simple models, since it usually results in very few transitions to previous states, and can handle individuals with sparse data by smoothing their predictions towards the population mean. Ad hoc was the method that performed better, in terms of bias, than the other smoothing approaches.     

Analyzing longitudinal data with patients in different disease states during follow‐up and death as final state

This paper considers the analysis of longitudinal data complicated by the fact that during follow‐up patients can be in different disease states, such as remission, relapse or death. If both the response of interest (for example, quality of life (QOL)) and the amount of missing data depend on this disease state, ignoring the disease state will yield biased means. Death as the final state is an additional complication because no measurements after death are taken and often the outcome of interest is undefined after death. We discuss a new approach to model these types of data. In our approach the probability to be in each of the different disease states over time is estimated using multi‐state models. In each different disease state, the conditional mean given the disease state is modeled directly. Generalized estimation equations are used to estimate the parameters of the conditional means, with inverse probability weights to account for unobserved responses. This approach shows the effect of the disease state on the longitudinal response. Furthermore, it yields estimates of the overall mean response over time, either conditionally on being alive or after imputing predefined values for the response after death. Graphical methods to visualize the joint distribution of disease state and response are discussed. As an example, the analysis of a Dutch randomized clinical trial for breast cancer is considered. In this study, the long‐term impact on the QOL for two different chemotherapy schedules was studied with three disease states: alive without relapse, alive after relapse and death. Copyright © 2009 John Wiley & Sons, Ltd.     

Estimation of markov chain transition probabilities and rates from fully and partially observed data: uncertainty propagation, evidence synthesis, and model calibration.

Markov transition models are frequently used to model disease progression. The authors show how the solution to Kolmogorov's forward equations can be exploited to map between transition rates and probabilities from probability data in multistate models. They provide a uniform, Bayesian treatment of estimation and propagation of uncertainty of transition rates and probabilities when 1) observations are available on all transitions and exact time at risk in each state (fully observed data) and 2) observations are on initial state and final state after a fixed interval of time but not on the sequence of transitions (partially observed data). The authors show how underlying transition rates can be recovered from partially observed data using Markov chain Monte Carlo methods in WinBUGS, and they suggest diagnostics to investigate inconsistencies between evidence from different starting states. An illustrative example for a 3-state model is given, which shows how the methods extend to more complex Markov models using the software WBDiff to compute solutions. Finally, the authors illustrate how to statistically combine data from multiple sources, including partially observed data at several follow-up times and also how to calibrate a Markov model to be consistent with data from one specific study.     

Disorders requiring nursing care and the period before recognized as needing nursing care (active life expectancy) in relation to nursing care insurance

PURPOSE: To measure the state of health of the elderly population, active and dependent life expectancies were calculated based on the number of people needing nursing care. For this purpose, active life expectancy was defined as the period before nursing care was recognized by insurers as being required. Moreover, to cast light on disorders requiring nursing care, age-adjusted nursing time needed for different ailments per ten thousand elderly population was calculated. SUBJECTS AND METHODS: Subjects were those 65 years or over living in Taihaku-ku, Sendai City, recognized as needing nursing care by nursing care insurers. The period before being recognized as needing nursing care was calculated using the Sullivan method, and termed the active life expectancy. Dependent life expectancy = life expectancy - active life expectancy. The number of those needing nursing care caused by each disorder diagnosed by attending physicians, was also age-adjusted by the reference population and multiplied by the nursing time needed for each level of nursing, resulting in the age-adjusted nursing time needed per ten thousand elderly population. RESULTS: Those recognized as needing nursing care were 7.5% (7.7% after age adjustment) of the male elderly population, and 12.5% of the female population (10.7% after age adjustment). For men, the active life expectancy was 16.1 years for the age of 65, 9.2 years for 75 and 4.4 years for 85, while the dependent one was 2.0-2.1 years for all ages. For women, the active life expectancy was 19.3 years for the age of 65, 11.1 years for 75 and 4.8 years for 85, while the dependent one was 4.6-5.3 years. The age-adjusted nursing time needed per ten thousand elderly population was 874 hours for men and 1,125 hours for women: of the time 51% was for men with cerebrovascular disease (40% for cerebral infarction), 11% for men with dementia; 37% for women with cerebrovascular disease (26% for cerebral infarction), 20% for women with skeletal diseases, 18% for women with dementia. CONCLUSIONS: The active life expectancy for women is longer than for men, by 3.7 years for the age of 65, by 2.3 years for 75 and by 0.5 years for 85. The dependent life expectancy for women is also longer than for men, by 3.2 years for the ages of 65 and 75 and by 2.6 years for 85. Thus, nursing prevention is an urgent issue, especially for women. The disorders requiring particularly long age-adjusted nursing time are carebrovascular disease (particularly cerebral infarction), dementia and skeletal disorders (particularly among women).     

Virtual randomized study comparing lobectomy and particle beam therapy for clinical stage IA non-small cell lung cancer in operable patients

To the best of our knowledge there have been no randomized controlled trials comparing lobectomy—a standard treatment for patients with early-stage non-small cell lung cancer (NSCLC)—and particle beam therapy (PBT), the best performing existing radiotherapy. We conducted a virtual randomized trial in medically operable patients with stage IA NSCLC to compare lobectomy and PBT effectiveness. A Markov model was developed to predict life expectancy after lobectomy and PBT in a cohort of patients with stage IA NSCLC. Ten thousand virtual patients were randomly assigned to each group. Sensitivity analyses were performed as model variables and scenarios changed to determine which treatment strategy was best for improving life expectancy. All estimated model parameters were determined using variables extracted from a systematic literature review of previously published articles. The preferred strategy differed depending on patient age. In young patients, lobectomy showed better life expectancy than that of PBT. The difference in life expectancy between lobectomy and PBT was statistically insignificant in older patients. Our model predicted lobectomy as the preferred strategy when operative mortality was under 5%. However, the preferred strategy changed to PBT if operative mortality post lobectomy was over 5%. For medically operable patients with stage IA NSCLC, our Markov model revealed the preferred strategy of lobectomy or PBT regarding operative mortality changed with varying age and comorbidity. Until randomized controlled trial results become available, we hope the current results will provide a rationale background for clinicians to decide treatment modalities for patients with stage IA NSCLC.     

The analysis of asthma control under a Markov assumption with use of covariates

In studies of disease states and their relation to evolution, data on the state are usually obtained at in frequent time points during follow-up. Moreover in many applications, there are measured covariates on each individual under study and interest centres on the relationship between these covariates and the disease evolution. We developed a continuous-time Markov model with use of time-dependent covariates and a Markov model with piecewise constant intensities to model asthma evolution. Methods to estimate the effect of covariates on transition intensities, to test the assumption of time homogeneity and to assess goodness-of-fit are proposed. We apply these methods to asthma control. We consider a three-state model and we discuss in detail the analysis of asthma control evolution.