Markov models with lognormal transition rates in the analysis of survival times

Ocón, Rafael Pérez; Castro, Juan Luis; Pérez, M. Luz Gámiz

doi:10.1007/bf02595740

Cited by 3 publications

(4 citation statements)

References 17 publications

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“…These limitations are either related to the method presented to assess the assumptions or are limited to a special type of the data: right censoring, for instance, or a special type of multi-state models: e.g. progressive model (Faddy, 1976;1988;Gentleman et al, 1994;Chen et al, 1999;Pérez-Ocón et al, 2000;Pérez-Ocón et al, 2001;Foulkes and De Gruttola, 2003;Healy and Degruttola, 2007). The present study, thus, attempted to present exhaustive methods for assessing these assumptions based on Cox-Snell residuals, Akaikie information criterion, and Schoenfeld residuals which are not limited to a special type of multi-state models and censoring mechanism and are applicable to most statistical softwares.…”

Section: Discussionmentioning

confidence: 99%

“…Assessing Markov assumption in these methods is based on the effect of sojourn time of the process in former states on the transition rate to latter states. In this method, of course, the precision and accuracy of results is based on the precision of transition times among states because observing states occurrence of in a multi-state model occur often in optional times (Kay, 1986;Pérez-Ocón et al, 2000). In these models the exact which in turn can affect the results.…”

Section: In This Equation H(t)mentioning

confidence: 99%

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Assessing Markov and Time Homogeneity Assumptions in Multi-state Models: Application in Patients with Gastric Cancer Undergoing Surgery in the Iran Cancer Institute

Zare

Mahmoodi

Mohammad³

et al. 2014

Asian Pacific Journal of Cancer Prevention

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Background: Multi-state models are appropriate for cancer studies such as gastrectomy which have high mortality statistics. These models can be used to better describe the natural disease process. But reaching that goal requires making assumptions like Markov and homogeneity with time. The present study aims to investigate these hypotheses. Materials and Methods: Data from 330 patients with gastric cancer undergoing surgery at Iran Cancer Institute from 1995 to 1999 were analyzed. To assess Markov assumption and time homogeneity in modeling transition rates among states of multi-state model, Cox-Snell residuals, Akaikie information criteria and Schoenfeld residuals were used, respectively. Results: The assessment of Markov assumption based on Cox-Snell residuals and Akaikie information criterion showed that Markov assumption was not held just for transition rate of relapse (state 1 state 2) and for other transition rates -death hazard without relapse (state 1 state 3) and death hazard with relapse (state 2 state 3) -this assumption could also be made. Moreover, the assessment of time homogeneity assumption based on Schoenfeld residuals revealed that this assumption -regarding the general test and each of the variables in the model -was held just for relapse (state 1 state 2) and death hazard with a relapse (state 2 state 3). Conclusions: Most researchers take account of assumptions such as Markov and time homogeneity in modeling transition rates. These assumptions can make the multi-state model simpler but

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Section: Discussionmentioning

confidence: 99%

Section: In This Equation H(t)mentioning

confidence: 99%

Assessing Markov and Time Homogeneity Assumptions in Multi-state Models: Application in Patients with Gastric Cancer Undergoing Surgery in the Iran Cancer Institute

Zare

Mahmoodi

Mohammad³

et al. 2014

Asian Pacific Journal of Cancer Prevention

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show abstract

“…In models under aging effects, frequent in the literature, the transition rates are time-dependent, and the exponential distribution is not applicable; in these cases, the Markov model is not appropriated. A way to overcome this problem is to consider non-homogeneous Markov processes, fitting distributions to the staying times in states [20][21][22], or to consider semi-Markov processes [23][24][25]. When the number of states increases, the calculations using these processes are cumbersome.…”

Section: State-space Modelsmentioning

confidence: 99%

A Longitudinal Study of the Bladder Cancer Applying a State-Space Model with Non-Exponential Staying Time in States

2021

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A longitudinal study for 847 bladder cancer patients for a period of fifteen years is presented. After the first surgery, the patients undergo successive ones (recurrences). A state-model is selected for analyzing the evolution of the cancer, based on the distribution of the times between recurrences. These times do not follow exponential distributions, and are approximated by phase-type distributions. Under these conditions, a multidimensional Markov process governs the evolution of the disease. The survival probability and mean times in the different states (levels) of the disease are calculated empirically and also by applying the Markov model, the comparison of the results indicate that the model is well-fitted to the data to an acceptable significance level of 0.05. Two sub-cohorts are well-differenced: those reaching progression (the bladder is removed) and those that do not. These two cases are separately studied and performance measures calculated, and the comparison reveals details about the characteristics of the patients in these groups.

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“…6(3), 347-358 (2006) Since the landmark article by Beck and Pauker [1] that introduced its application in medicine, Markov modeling has become the paradigm for studying the progression of patients through various states of health following an intervention or treatment. These models form the basis for decision analyses in clinical medicine [2,3], economic evaluation [4] and for studying the dynamics of disease progression as in natural history studies of cancer [5][6][7][8][9][10]. Markov models are ubiquitous in cost-effectiveness analysis (CEA), which seeks to compare competing healthcare interventions on health outcomes with their costs.…”

mentioning

confidence: 99%

A stochastic framework for estimation of summary measures in cost–effectiveness analyses

Gardiner¹,

Luo²,

Liu³

2006

Expert Review of Pharmacoeconomics & Outcomes Research

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Stochastic modeling of patient health and cost outcomes is a useful tool in identifying and assessing the important individual characteristics that influence these outcomes. It is a critical step in cost-effectiveness analysis that aims to structure comparisons between competing healthcare interventions on both health outcomes and costs. The authors use a continuous-time finite-state nonhomogeneous Markov process to describe the occurrence of patient events as they unfold over time. States of the process represent health conditions or health states (e.g., well, ill or dead). Commonly used measures of health outcome, such as life expectancy and quality-adjusted survival, are defined in terms of expected values of functions of the process. Costs are incurred through medical resource use while sojourning in health states, and in transitions between health states. By combining these expenditure streams, the authors define net present values for expected total cost over a specified time period. Metrics used in cost-effectiveness analyses, such as net health benefit, net health cost and the cost-effectiveness ratio are defined as functions of expected values. In this longitudinal framework the authors describe regression models for estimation of these summary statistics and quantifying the impact thereupon of explanatory variables. With increasing attention being given to longitudinal studies for gathering economic data alongside clinical investigations, these models can be applied to analyze jointly both costs and patient outcomes and more fully exploit the dynamic mechanisms that engender cost and health outcome data.

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Markov models with lognormal transition rates in the analysis of survival times

Abstract: Covariates, lognormal distribution, maximum-likelihood estimate, nonhomogeneous Markov process, survival data, 62M05, 62N05,

Cited by 3 publications

References 17 publications

Assessing Markov and Time Homogeneity Assumptions in Multi-state Models: Application in Patients with Gastric Cancer Undergoing Surgery in the Iran Cancer Institute

Assessing Markov and Time Homogeneity Assumptions in Multi-state Models: Application in Patients with Gastric Cancer Undergoing Surgery in the Iran Cancer Institute

A Longitudinal Study of the Bladder Cancer Applying a State-Space Model with Non-Exponential Staying Time in States

A stochastic framework for estimation of summary measures in cost–effectiveness analyses

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