Cycle

Cycle: Concept Architecture

Follow a model through repeated intervals

A cycle is one defined interval in a discrete-time state-transition model. This page explains how the model updates health states, counts outcomes and costs, and chooses an interval short enough for the events under study.

Define the interval and the people in each state

A cohort model starts a cycle with a specified number or proportion of people in each health state. It then applies transition probabilities for that interval to determine the state distribution at the next boundary. A cycle might last a week, a month, or a year; its duration must match the clinical process and the model's time horizon.

If the row vector $\mathbf{s}_k$ gives state occupancy at the beginning of cycle $k$ and $P_k$ is the transition matrix for that interval, the next distribution is:

$$\mathbf{s}_{k+1}=\mathbf{s}_kP_k.$$

Each row of $P_k$ contains nonnegative probabilities summing to one across mutually exclusive destinations. Time-varying probabilities can be represented by a different matrix for each cycle. A cycle is the time step itself, whereas a health state is a condition occupied during or at a boundary of that step.

See one monthly update

Suppose 100 people begin a month in a stable state. Over that month, the model assigns probabilities of 0.80 to remaining stable, 0.15 to progressing, and 0.05 to dying. At the next boundary, expected occupancy is 80 stable, 15 progressed, and 5 dead.

These are expected cohort counts, not a claim that each individual makes exactly one clinical move. A one-step transition matrix must represent the intended probability of each destination at the cycle boundary; a coarse cycle may hide clinically important sequences, such as progression followed by death within the same month.

Choose a duration that matches the evidence

The interval should be short enough to represent treatment schedules, event timing, changes in risk, and clinically meaningful sequences. It should also be workable for the available data and the model's computational requirements. ISPOR–SMDM state-transition modelling guidance discusses the choice and reporting of cycle length, while methodological work on time in economic evaluation explains why long intervals can introduce approximation error.

Transition probabilities belong to a specified interval and cannot simply be reused for a different duration. Under a constant hazard $r$ for a single event, the interval probability is $p(\Delta t)=1-e^{-r\Delta t}$; for a probability $p_1$ observed over duration $t_1$, the corresponding probability over $t_2$ under that same assumption is $1-(1-p_1)^{t_2/t_1}$. Competing transitions and multi-state processes require a coherent joint conversion, not separate conversion of every destination probability; research on changing cycle lengths examines the limitations.

Count time, costs, and outcomes within cycles

Occupancy at a boundary is only a snapshot, while quality-adjusted life years and ongoing costs accumulate over time. For a one-month interval, 100 people spending the whole month in a state with utility 0.8 would contribute $100\times0.8/12\approx6.67$ undiscounted quality-adjusted life years. Event costs and one-off treatment costs should be assigned at the appropriate time rather than automatically spread over the full cycle.

People may change states between boundaries, so valuing the entire interval from the start or end occupancy alone can misstate time in each state. A half-cycle or other within-cycle correction can approximate accrued outcomes when justified; shorter cycles or continuous-time methods may reduce that approximation error. Within-cycle correction research shows that the choice of correction and interval length can affect estimates.

Check the model's clock

Report the duration, number of cycles, initial time point, transition timing, and how costs, outcomes, discounting, and partial final intervals are handled. These choices determine whether ten annual cycles represent ten years and whether a 28-day cycle has inadvertently been treated as a calendar month.

Test whether plausible shorter intervals change the estimated costs, outcomes, or preferred strategy. If results shift materially, inspect the probability conversion, events occurring within an interval, and within-cycle accumulation before interpreting the difference as clinical evidence. Cycle length is a modelling choice, not a treatment effect or a synonym for the full time horizon.