I assume that you have a Markov model wherein the states correspond to combinations of medical impairments, perhaps including levels of these impairments, and other factors such as age. And I assume that your model includes at least one transition matrix, likely based on empirical data, that describes how the disease is likely to progress. You might have one transition matrix for an untreated patient, and other transition matrices for various regimens of treatment. Thus, in general, you may have a set of Markov models. I think the methodology probably can apply to any possibly-fatal disease.

In this context, there will be at least one absorbing state representing death. If there is interest in accounting for various modes or final causes of death, there can be an absorbing state for each such mode or cause, and perhaps one for “none of the above”, or “all other” modes. Given such a formal representation of death, the formal representation of survival will be the set of non-absorbing states.

Mathematically, we begin with an initial state vector S(0) at time = 0, which describes the initial probabilities for each state. Then for a regimen for which transition matrix Tr applies, the state vector S(t) for time t will be S(t) = Tr * S(t-1), for t > 0. Or, S(t) = Trt * S(0).

Given that Sd(t) is the element of the S(t) vector that is the absorbing state representing death, this value represents the probability that death has occurred at time t or earlier. If individual states Sdm(t) are defined for each mode of death, then more detailed probabilities are available, and the probabilities for all Sdm(t) can be summed to get Sd(t), the probability of death at time t or earlier for all modes of death. Since at any time t, the sum of the probabilities for all states equals one, the probability of survival at time t will be equal to 1 – Sd(t).

The average time of death, or lifespan, is the weighted average Ta = Sum(Px(t) * t), where Px(t) is the exit probability at time t, or the sum of the transition probabilities for all transitions to the death state Sd(t) at time t.

Which such mathematics, the outcomes of various regimens can be compared, which the validity of the conclusions resting upon the validity of the Markov model, primarily the values assigned to the transition matrices.

I assume that you have a Markov model wherein the states correspond to combinations of medical impairments, perhaps including levels of these impairments, and other factors such as age. And I assume that your model includes at least one transition matrix, likely based on empirical data, that describes how the disease is likely to progress. You might have one transition matrix for an untreated patient, and other transition matrices for various regimens of treatment. Thus, in general, you may have a set of Markov models. I think the methodology probably can apply to any possibly-fatal disease.

In this context, there will be at least one absorbing state representing death. If there is interest in accounting for various modes or final causes of death, there can be an absorbing state for each such mode or cause, and perhaps one for “none of the above”, or “all other” modes. Given such a formal representation of death, the formal representation of survival will be the set of non-absorbing states.

Mathematically, we begin with an initial state vector S(0) at time = 0, which describes the initial probabilities for each state. Then for a regimen for which transition matrix Tr applies, the state vector S(t) for time t will be S(t) = Tr * S(t-1), for t > 0. Or, S(t) = Trt * S(0).

Given that Sd(t) is the element of the S(t) vector that is the absorbing state representing death, this ed e t or earlier. If individual states Sdm(t) are defined for each mode of death, then more detailed probabilities are available, and the probabilities for all Sdm(t) can be summed to get Sd(t), the probability of death at time t or earlier for all modes of death. Since at any time t, the sum of the probabilities for all states equals one, the probability of survival at time t will be equal to 1 ndash; Sd(t).

The average time of death, or lifespan, is the weighted average Ta = Sum(Px(t) * t), where Px(t) is the exit probability at time t, or the sum of the transition probabilities for all transitions to the death state Sd(t) at time t.

Which such mathematics, the outcomes of various regimens can be compared, which the validity of the conclusions resting upon the validity of the Markov model, primarily the values assigned to the transition matrices.

The link below is the raw survival data for HIV in malaysia. If you refer to this data. what can you analysis for this data? what i interest are comparing the discrete-time-homogenous Markov Chain method and continuous-time- homogenous Markov Chain method for analysis this data. so i will ask which one is the best one? or are these two method gt the same answer? so, i also will apply the simulation method on these to compare. but how to compare it still a problems to me. since all the journal said the continous-time model would be more realistic representation of the clinical data ( but its complex and difficult) so most of the researcher only use the discrete model to analysis this model by adding the states to the model maybe useful when the situation possibly violate the markovian assumption.

so, now my problem are the continuous-time- homogenous Markov Chain method. any ideas? and how to apply to the data below? thanks

How about the censor data?

check www.libgen.info and get some books on stochastic processes

Discrete time modeling is easier and also adequate, because the data is coarsely defined.

The raw database file does not provide much of a basis for defining a Markov process. Sex and Erhnicity does not vary with time, so they cannot define states. But they could distinguish different Markov processes. For example, you could define a process for Maylay males, another for Indian females, etc. The only factor that clearly varies with time is life/death, and the death date is unkown for many of the individuals. There is no date information for risk factors. Many of these could be either events or series of events -- it is unclear..

The raw database file seems to be more amenable to ANOVA.

If you had complete case history data for a collection of individuals then you might be able to express the case history as a sequence of states/

Because now i'm interest in study on Markov Chain. So, I will stay on this. thanks.

Or you have any good data suggest to me?

What you mean for the Sex and Ethnicity does not vary with time? and

you suggest me to do distinguish the different btw Markov processes. For example, you said can define a process for Malay males, another for Indian females, etc. i still not so clear about that. Can you give some graphical example so that i can see it. thanks.

first read the a HMM tutorial paper of the Rabiner tnan try to solve problem if u still face problem then mail me i suggest u solution.

Between the years 1998 and 2004 some colleagues and myself published several papers studying the survival to breast cancer using continuous Markov process, homogeneous and non-homogeneous. Different Markov models were applied to a dataset and the survival of the patients in terms of the received treatments: chemotherapy, radiotherapy, hormonal therapy, and combinations of them were calculated. The effect of these treatments were incorporated to the model as covariates, similar to the procedure of the Cox model. The Markovian assumption was tested and it was not rejected.

The size of the dataset was of 518 patients, the observation period was five years, and the data were censored. The procedure of estimation of the survival was the maximum likelihood method. The models were well-fitted, the empirical survival of the different cohorts and the corresponding ones calculated via the Markov process have graphics very near and they could not be rejected using a test of goodness of fit. The rates of relapse were also estimated. Predictions were established for the different risk groups. The study was performed with a narrow colaboration with a medical team of oncologists.

i don't know what type are the data u have . i will help u but first u read a paper of Rabiner 15 pafe uuto the forward method and make the HMM model and then we can estimate the value ie very easy .