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In many applications of survival analysis techniques there are intermediate events whose occurrence may effect a patient's prognosis. The occurrence of these intermediate events can be modeled using a proportional hazards model with time dependent covariates or by a model using distinct hazards for each event that allows for non proportional hazard...
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Multivariate Adaptive Regression Splines (MARS) are a generalization of stepwise linear regression method that is often employed to improve the efficiency of regression models. It is a useful tool to identify linear/nonlinear and interactions effects between a set of metrical and categorical covariates in regression models. In this study, the use o...
Citations
... Therefore, it is often necessary to accommodate the influence of these covariates on transition intensities through a regression model. In this regard, there are a number of models for transition intensities that have been proposed in the literature including parametric models [5][6][7][8][9], semiparametric Markov regression models where transition intensities are modeled by the Cox [10] proportional hazards regression model [11][12][13][14][15], or the Aalen additive hazards regression model [2,13,16]. However, most of the time, there are large correlations between covariates as well as non-linear or multivariable relations especially in high dimension settings. ...
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Background
This study aimed to introduce recursively imputed survival trees into multistate survival models (MSRIST) to analyze these types of data and to identify the prognostic factors influencing the disease progression in patients with intermediate events. The proposed method is fully nonparametric and can be used for estimating transition probabilities.
Methods
A general algorithm was provided for analyzing multi-state data with a focus on the illness-death and progressive multi-state models. The model considered both beyond Markov and Non-Markov settings. We also proposed a multi-state random survival method (MSRSF) and compared their performance with the classical multi-state Cox model. We applied the proposed method to a dataset related to HIV/AIDS patients based on a retrospective cohort study extracted in Tehran from April 2004 to March 2014 consist of 2473 HIV-infected patients.
Results
The results showed that MSRIST outperformed the classical multistate method using Cox Model and MSRSF in terms of integrated Brier score and concordance index over 500 repetitions. We also identified a set of important risk factors as well as their interactions on different states of HIV and AIDS progression.
Conclusions
There are different strategies for modelling the intermediate event. We adapted two newly developed data mining technique (RSF and RIST) for multistate models (MSRSF and MSRIST) to identify important risk factors in different stages of the diseases. The methods can capture any complex relationship between variables and can be used as a useful tool for identifying important risk factors in different states of this disease.
... In the next section, we show how we can use the three parameter GG distribution to identify h 13 0 (s − ) and h 23 (t − s) and how the properties of this distribution can be used to do the calculations related to RLL due to each stroke type using the concept of RT. More examples of multistate models with additive hazards extensions can be found in Klein et al. 14 and in Shu et al. 15 Variance estimation for some of these models can be found in Klein et al. 16 Large-sample properties of three different additive hazards extension models can be found in Shu. 17 Likewise, examples with a nonparametric semi-Markov model and a semi-Markov model incorporating covariate information are illustrated in Voelkel et al. 18 and Andersen et al., 19 respectively. Estimation and prediction in a semi-Markov model in a Cox regression framework with baseline hazards and covariates depending on recurrence times has been illustrated in Dabrowska. ...
Time-dependent covariates can be modeled within the Cox regression framework and can allow both proportional and nonproportional hazards for the risk factor of research interest. However, in many areas of health services research, interest centers on being able to estimate residual longevity after the occurrence of a particular event such as stroke. The survival trajectory of patients experiencing a stroke can be potentially influenced by stroke type (hemorrhagic or ischemic), time of the stroke (relative to time zero), time since the stroke occurred, or a combination of these factors. In such situations, researchers are more interested in estimating lifetime lost due to stroke rather than merely estimating the relative hazard due to stroke. To achieve this, we propose an ensemble approach using the generalized gamma distribution by means of a semi-Markov type model with an additive hazards extension. Our modeling framework allows stroke as a time-dependent covariate to affect all three parameters (location, scale, and shape) of the generalized gamma distribution. Using the concept of relative times, we answer the research question by estimating residual life lost due to ischemic and hemorrhagic stroke in the chronic dialysis population.
... For each treatment pathway, we estimated the probability over time of a given treatment pathway using the data from the AF cohort (e.g. the probability of a patient first being treated with an antithrombotic medication and then with rate-limiting medication and then not treated). A finite state Markov process model was used to model the hazard rates for each possible transition using a separate (left truncated) Cox proportional hazard model (24,25). The transition probabilities were calculated using the base line hazard function (26,27). ...
Although there has been growing concordance over what constitutes best practice in recent guidelines for treatment of atrial fibrillation (AF), notably regarding anticoagulant use, it remains unclear whether patients are being treated accordingly.
The aims of this study were to explore the pattern of treatment pathways - i.e. how patients are treated over time - for patients with AF, and to test the hypothesis that comparative to patients in lower stroke-risk categories (as measured by CHADS(2) score), patients with higher CHADS(2) scores are less likely to discontinue anticoagulant therapy or, if not started on anticoagulant treatment, more likely to be transferred to anticoagulant therapy, in keeping with guideline recommendations.
A total of 67,857 patients with a diagnosis of AF in practices registered with the General Practice Research Database.
A series of possible treatment pathways were identified, and for each initial treatment, we estimated the probability of treatment change and the average time that a patient newly diagnosed with AF spent on a particular treatment, projected across 5 years and stratified by CHADS(2) score.
There was no relationship between CHADS(2) score and maintenance or discontinuation of particular approaches to antithrombotic treatment. While those beginning on antiplatelet therapy were more likely to change treatment than those on anticoagulants (approximately 60% vs. 50% within the first year), as much as one-third of treatment time of all those starting on a therapeutic approach involving anticoagulants featured no use of anticoagulants (either as monotherapy or in combination) over the 5-year period, and whether treatment was discontinued or maintained did not vary by CHADS(2) score. No difference was found in treatment pathways controlling for post-2002 diagnoses as against the whole sample.
Although there is more evidence of treatment maintenance than treatment change, especially in the first year after diagnosis, the amount of therapeutic change remains noteworthy and appears higher than in some previous studies. Prescription patterns for AF therapy suggest that too few high-risk patients are receiving best practice treatment, and particularly of concern is that some of these patients are being transferred away from best practice treatment over time.
... Since the papers of Klein et al. [21], Keiding et al. [22] the multi-state approach, is becoming more popular but remain solely in hematopoeitic stem cell transplantation (HSCT). The use of multistate in HSCT is not particlularly new [21,23]. One possible reason is that a multi-state model regression analysis typically involves the modelling of each transition intensity separately. ...
... When there are covariates which may affect the rate of transition from one state to the next, a number of Markov models have been proposed in the literature. These include parametric models for the transition intensities (Begg & Larson, 1982; Kalbfleisch & Lawless, 1985; Marshall & Jones, 1995; Alioum & Commenges, 2001; Pérez-Ocón et al., 2001) or semiparametric Markov regression models where transition intensities are modelled by the Cox (1972) proportional hazards regression models (Andersen, 1988; Andersen et al., 1991; Klein et al., 1993; Klein & Qian, 1996; Andersen et al., 2000). In this paper, we focus on the semiparametric case. ...
... In the bone marrow transplant example this approach requires the fitting of four Cox models. The transition probability estimators and their asymptotics for this model can be found in Klein & Qian (1996). Recently, Aalen et al. (2001 They suggested that the transition intensities be modelled by Aalen's (1989) additive hazards regression models rather than Cox's proportional hazards regression models. ...
When there are covariate effects to be considered, multi-state survival analysis is dominated either by parametric Markov regression models or by semiparametric Markov regression models using Cox's (1972) proportional hazards models for transition intensities between the states. The purpose of this research work is to study alternatives to Cox's model in a general finite-state Markov process setting. We shall look at two alternative models, Aalen's (1989) nonparametric additive hazards model and Lin & Ying's (1994) semiparametric additive hazards model. The former allows the effects of covariates to vary freely over time, while the latter assumes that the regression coefficients are constant over time. With the basic tools of the product integral and the functional delta-method, we present an estimator of the transition probability matrix and develop the large-sample theory for the estimator under each of these two models. Data on 1459 HLA identical sibling transplants for acute leukaemia from the International Bone Marrow Transplant Registry serve as illustration. Copyright 2005, Oxford University Press.
Background
Understanding the progression of kidney disease is of great interest among clinicians. The multi-state model is an adequate tool to model the effects of covariates that influence the onset, progression, and regression of kidney function.
Objective
The goal of the present study is to propose a stochastic model for kidney disease progression and to demonstrate the application of the same.
Methodology
We proposed a semi-parametric continuous time homogeneous multi-state Markov model for the kidney disease progression data obtained from a retrospective study of 225 patients prescribed with colistin (a re-emerging antibiotic) in a tertiary care hospital in coastal Karnataka. Different stages of kidney disease were defined based on the Kidney Disease Improving Global Outcome (KDIGO) score. The model consists of three transient states, and an absorbing state death. Covariate effects on the bidirectional transition rates were estimated using the multi-state model.
Results
We used the data of 225 patients to see their kidney disease progression. All the patients were under colistin therapy. The median length of hospital stay was 21 days. A total of 83 (36.89%) patients died in the hospital. The prognostic factors such as gender, hypertension, sepsis, and surgery are significant factors affecting kidney disease in different stages.
Conclusion
The findings of the study will be useful for public health policymakers to implement the policies and treatment plans to improve the survival of the patients. Moreover, modelling the disease progression helps in understanding the expected burden of the disease.
Healthcare spending in Australia has increased rapidly in recent decades, partly due to the prevalence of lifestyle related illness, as physical inactivity and ageing have become common. Diabetes is a chronic and costly illness resulting from poor lifestyle choice and ageing. In this study, we estimate the long-run cumulative costs of a complication of diabetes, diabetic kidney disease, using well-known techniques from health economics. We find that spending on treatment for diabetic kidney disease will amount to $9.2 billion over the next 30 years. Most of the cost from this complication comes from the clinical stage of diabetic kidney disease.
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.
In many cancer studies we are interested the survival experience of the patient. This survival experience may be the time until response to therapy, the duration of remission, the length of time free of disease or toxic effects of the treatment or simply the overall survival experience of the patient. We are interested in estimation of the distribution of these times, in comparing these outcomes between two or more treatments, or in finding models for these outcomes that allow us to predict outcome based on a particular patient profile.
We present an extension of the non-homogeneous Markov model for a bone marrow transplant recovery process which allows for possible associations between the transition intensities. The associations between intensities are modeled by a correlated gamma frailty model. Based on a parametric model for the conditional transition intensities, we obtain estimates of the model parameters. We use these estimates to make predictions of patient's eventual prognosis given the current medical history of the patient. Estimates of the uncertainty in our predictions are obtained by a modified bootstrap technique.
