Mean Time in Illness Death Model
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I would like to calculate the mean time "alive" for a progressive, time homogenous, three state Markov model in continous time. It is an illness-death model with three states: healthy, ill, dead. Illness cannot be reversed. Death is absorbing.
The initial numbers of patients in the three states are $S_0={N_h,N_i,0}$. The transition rate matrix is
$Q=begin{bmatrix}
-a-b & a & b\
0 &-c & c\
0 & 0 & 0
end{bmatrix}$.
The transition probability matrix is calculated using the matrix exponential, $P(t) = e^{Qt}$.
Is there a way to calculate the mean time in the "alive" state, that is healthy or alive?
markov-chains markov-process
asked Nov 23 at 17:28
MPahuta
1598
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I would like to calculate the mean time "alive" for a progressive, time homogenous, three state Markov model in continous time. It is an illness-death model with three states: healthy, ill, dead. Illness cannot be reversed. Death is absorbing.
The initial numbers of patients in the three states are $S_0={N_h,N_i,0}$. The transition rate matrix is
$Q=begin{bmatrix}
-a-b & a & b\
0 &-c & c\
0 & 0 & 0
end{bmatrix}$.
The transition probability matrix is calculated using the matrix exponential, $P(t) = e^{Qt}$.
Is there a way to calculate the mean time in the "alive" state, that is healthy or alive?
markov-chains markov-process
asked Nov 23 at 17:28
MPahuta
1598
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I would like to calculate the mean time "alive" for a progressive, time homogenous, three state Markov model in continous time. It is an illness-death model with three states: healthy, ill, dead. Illness cannot be reversed. Death is absorbing.
The initial numbers of patients in the three states are $S_0={N_h,N_i,0}$. The transition rate matrix is
$Q=begin{bmatrix}
-a-b & a & b\
0 &-c & c\
0 & 0 & 0
end{bmatrix}$.
The transition probability matrix is calculated using the matrix exponential, $P(t) = e^{Qt}$.
Is there a way to calculate the mean time in the "alive" state, that is healthy or alive?
markov-chains markov-process
asked Nov 23 at 17:28
MPahuta
1598
I would like to calculate the mean time "alive" for a progressive, time homogenous, three state Markov model in continous time. It is an illness-death model with three states: healthy, ill, dead. Illness cannot be reversed. Death is absorbing.
The initial numbers of patients in the three states are $S_0={N_h,N_i,0}$. The transition rate matrix is
$Q=begin{bmatrix}
-a-b & a & b\
0 &-c & c\
0 & 0 & 0
end{bmatrix}$.
The transition probability matrix is calculated using the matrix exponential, $P(t) = e^{Qt}$.
Is there a way to calculate the mean time in the "alive" state, that is healthy or alive?
markov-chains markov-process
markov-chains markov-process
asked Nov 23 at 17:28
MPahuta
1598
asked Nov 23 at 17:28
MPahuta
1598
asked Nov 23 at 17:28
MPahuta
1598
asked Nov 23 at 17:28
MPahuta
1598
asked Nov 23 at 17:28
MPahuta
1598
1598
add a comment |
add a comment |
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