Learn about tunnel states (Time in Markov cohort simulation)

Summary

In this video, the speaker discusses the concept of time in Markov cohort simulations, with a focus on tunnel states. They explain two types of time: model time, or system time, and sojourn time (time since entering a state). Tunnel states are introduced as a workaround for tracking sojourn time while maintaining the Markov property. The speaker explains how these states are used in health models, such as disease progression, and how to decide when to stop adding tunnel states. The video also touches on mid-cycle transitions and provides advice on implementing these concepts in tools like Excel or R.

Takeaways

• 😀 Time in Markov cohort simulations can refer to either the model time (system time) or sojourn time in a specific state.
• 😀 Model time refers to the time elapsed since the model started, while sojourn time tracks how long a cohort has been in a given state.
• 😀 The two types of time are equal only for states that cannot be revisited once entered.
• 😀 Model time is particularly useful for analyzing age-dependent risks, such as disease and mortality rates.
• 😀 Sojourn time is useful for understanding disease-specific survival or treatment costs that change over time.
• 😀 The Markov property makes it challenging to track sojourn time directly in a standard model, requiring a workaround.
• 😀 Tunnel states serve as the workaround, breaking a health state into multiple phases to track sojourn time without violating the Markov property.
• 😀 In a Markov model, tunnel states represent distinct periods in a state, such as time spent in a diseased state, and must be exited by the end of each cycle.
• 😀 The number of tunnel states to include in a model should be determined by when additional states stop significantly affecting outcomes or when few people reach later states.
• 😀 Transition probabilities and payoffs may become constant over time, reducing the need for additional tunnel states after a certain point.
• 😀 When adjusting for mid-cycle transitions, careful attention is needed, especially when using half-cycle corrections to avoid confusing calculations.

Q & A

What is the difference between model time and sojourn time in Markov cohort simulations?

Model time refers to the total time since the model started, while sojourn time is the time spent in a specific state within the model. These two times are only equal when a state cannot be re-entered after starting in it.

Why is sojourn time important in Markov modeling, and how does it differ from model time?

Sojourn time is important for modeling conditions like disease-specific survival, treatment costs, and quality of life changes, as it reflects the time spent in a particular health state. It differs from model time because it focuses on time within a specific state rather than since the model started.

What are tunnel states, and why are they used in Markov models?

Tunnel states are temporary states introduced in Markov models to account for sojourn time while maintaining the Markov property. These states force transitions to other states at the end of each cycle, preventing the model from tracking time spent in the state directly.

How are tunnel states represented in a Markov model?

Tunnel states are represented as intermediate states within a health state, often depicted with dashed edges in diagrams. These states represent different durations of time spent in the diseased state, such as less than one year, one to two years, and over two years.

What is the key characteristic of tunnel states in terms of transitions?

The key characteristic of tunnel states is that individuals cannot remain in them indefinitely. They must transition to the next state or to death by the end of the cycle, ensuring that the Markov model maintains its transition structure.

When should you stop adding tunnel states in a Markov model?

You should stop adding tunnel states when adding more does not significantly impact the model outcomes. This typically happens when subsequent transition probabilities and payoffs stabilize, or when very few individuals reach those later tunnel states.

What happens if you add too many tunnel states to a Markov model?

Adding too many tunnel states can make the model unnecessarily complex without improving accuracy, especially if the transition probabilities and payoffs become nearly constant, or if the proportion of individuals reaching those states is negligible.

How does the cycle length affect the use of tunnel states in Markov models?

The cycle length influences the duration of each health state and can impact the number of tunnel states needed. Shorter cycle lengths may require more detailed tunnel states to capture the finer nuances of disease progression, while longer cycle lengths may require fewer tunnel states.

What are mid-cycle corrections, and why are they important in Markov models?

Mid-cycle corrections, such as half-cycle adjustments, are used to refine the calculation of transition probabilities when they are not evenly distributed across the cycle. These corrections help improve the accuracy of models, especially when dealing with transitions that do not occur at the start or end of each cycle.

What is the next step after learning about tunnel states in Markov models?

The next step is to implement tunnel states in a Markov model using software like Excel or R. Additionally, learning how to adjust cycle lengths and apply mid-cycle transition corrections will further improve the model's accuracy and usefulness in simulations.