Part 1 Multistate modelling theory: recap
Multistate models for intermittentlyobserved data
More information about the msm
package in
A more indepth treatment of this kind of modelling can be found in

 applications in lifecourse / ageing epidemiology

 more advanced mathematically, greater variety of models
1.1 Multistate processes
Multistate models represent processes that can be described as discrete states that change through time.
The msm
package can be used for any state and transition structure.
Examples in the course represent stages of a disease.
For example, a progressive disease with death from any state (CAV after heart transplantation, from Sharples et al. )
Progression through stages of an irreversible nonfatal condition (psoriatic arthritis, from Gladman and Farewell)
A relapsingremitting condition with no “final” state (also in psoriatic arthritis, from Jackson et al.)
1.2 msm
models work in continuous time
Model represents movement between discrete states in continuous time
1.2.1 Transition intensities
Continuoustime Markov models are defined by transition intensities \(q_{rs}(t)\) between pairs of states \(r,s\).
Transition intensity matrix \(Q\) with diagonals \(q_{rr}(t) = \sum_{s!=r} q_{rs}(t)\).
1.2.2 Transition probabilities
If \(Q(t) = Q\) is constant over time, we can compute the transition probability matrix over any time unit as \(P(t) = Exp(tQ)\) where Exp is the matrix exponential.
Entries \(p_{rs}(t)\) define the probability someone in state \(r\) now is in state \(s\) at a time \(t\) years from now.
Discretetime models (not covered in this course) are defined by transition probabilities \(p_{rs}\) over one unit of time. Less common than continuoustime models in medical applications, since data are not generally on a regular discretetime grid.
Be careful of these distinctions!
1.3 Intermittentlyobserved data
msm
is mainly designed for data that are intermittently observed
1.4 Timetoevent data (not covered in this course)
In multistate timetoevent data, we know the exact times of transitions between all states, potentially with rightcensoring
Patient  Months  Event 

1  0  Start of follow up 
1  50  Disease diagnosis 
1  60  Death 
Competing risks analyses are a special case: e.g. survival data with one “alive” state and multiple “death” states for different causes of death.
msm
can be used for this kind of data, but relies on strong assumptions:
 intensites are piecewise constant, i.e. constant over a series of time intervals, or a step function of time.
 models are Markov
Other R packages are better designed for multistate timetoevent data:
1.5 Examples used for illustration
1.5.1 Psoriatic arthritis
Factors governing progression of joint damage, an irreversible condition.
Available as psor
in the msm
package.
1.5.2 Cardiac allograft vasculopathy after heart transplantation
A condition similar to coronary artery disease that occurs in people who have had heart transplants. Clinically irreversible, but measured state (diagnosed by angiography) can go backwards or forwards
Available as cav
in the msm
package.