Multistate Markov Models

WHAT ARE MULTISTATE MARKOV MODELS?

Multistate models are defined by states (represented by the boxes in Figure 1) and transitions between them (represented by arrows).

States can be transient, in which individuals can enter and exit, or absorbing, in which individuals never exit once they enter (e.g. dead).

The simplest model contains two states, for example, alive and dead or healthy and ill, and is commonly called the mortality model. This type of model can be analyzed using survival analysis methods.^{[1, 2]}

Multistate models enable the analysis of longitudinal data in which individuals may experience more than one health event.

Multistate Markov models can be used to estimate the transition hazard (the instantaneous risk of transitioning from one state into another), as well as transition probabilities and the mean sojourn time in a given state.

Markov models are used most frequently due to their simplicity. A multistate model is considered Markov if it assumes that the probability of transitioning to a new state depends only on the current value of the model.^{[1, 3]}

In general, a random process can be described as a Markov if it determines future probabilities solely based on its current values.

This means that the past, current, and future states of the system are all independent of one another. For this reason, Markov processes are sometimes described as “memoryless.”^{[1, 3]}

Advantages of multistate Markov models

• Allows easy understanding ‘centile crossing’ probabilities. For example, we can calculate the probability of crossing the 90th percentile for LAZ.
• Can allow for movement between states in both directions (except for absorbing states, like death). This allows the same model to estimate the hazard rate of recovery as well as illness.

Disadvantages of multistate Markov models

• Requires categorization of states. For example, in modeling stunting based on a continuous length-for-age z-score (LAZ) variable, it requires binning the continuous variable into discrete categories.

Ki UTILIZATION OF MULTISTATE MARKOV MODEL TO DESCRIBE LONGITUDINAL CHANGES IN LAZ

Model to describe how probability of transitioning between three states—defined as stunted, at-risk for stunting, and not stunted—changes from birth to two years of age.

This models LAZ outcomes, categorized into 4 bins.

Resource Links

• Example Of Multistate Markov Models Used To Describe Stunting (as measured by LAZ) And Wasting (as measured by WAZ) During First Five Years Of Life Among A Cohort In A Cameroon(4)