The Gold Standard of Experimental Design | Multi-State Models, Transition Hazards and State Occupancy

1. Draw the states before fitting a model

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A state should represent a scientifically meaningful condition with an observable entry rule. Arrows define possible transitions. Death is often absorbing; recovery or relapse may be reversible. The time origin, entry criteria and handling of simultaneous events must be prespecified. Splitting every measurement into a state can create a model too sparse to estimate.

Use the smallest diagram that answers the question. If only first events matter, competing-risks methods may be enough. If events after relapse or discharge matter, a multi-state representation preserves them rather than discarding everything after the first transition.

2. Distinguish a transition hazard from a probability

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The hazard from state h to state j is the instantaneous rate of that move among people currently in h. A state-occupancy probability is the probability of being in a particular state at a given time. Occupancy depends on all routes into and out of that state, not only one transition hazard.

A covariate can increase entry to recovery and also increase exit from recovery, producing a small net change in occupancy. Hazard ratios should not be described as probabilities. Report transition-specific effects beside absolute transition or occupancy probabilities at times relevant to readers.

3. Choose the clock that matches the mechanism

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Clock-forward models use time since study origin for each transition. Clock-reset models use time since entry into the current state. The first can represent calendar or disease-course time; the second can represent duration-dependent risk after relapse or discharge. Semi-Markov models allow dependence on time already spent in a state.

The choice changes the estimand and data layout. State it explicitly. If readmission risk is highest just after discharge, a clock-reset transition may be more interpretable than using time since initial hospital admission. A convenient software default is not a biological argument.

4. Understand Markov and history assumptions

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A Markov model conditions future movement on current state and current time, not the full path used to arrive there. That may be plausible for some processes and implausible when prior episodes, duration or treatment history matter. Adding covariates or expanded states can carry relevant history, but every expansion costs information.

Check whether transition risk varies with time since entry or number of previous episodes. Landmarking, semi-Markov models or history variables can test alternatives. Do not claim that Aalen–Johansen state occupancy always requires a perfect Markov process; the exact interpretation depends on target, sampling and censoring assumptions.

5. Align observation with state definitions

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Exact transition times may be known for death or admission but interval-censored for disease status assessed at visits. Participants can move through unobserved states between visits. Misclassification may be differential across treatment arms or centres. Censoring can depend on health trajectory.

Define visit windows, adjudication, impossible sequences and how ties are ordered. Sensitivity analyses should vary uncertain transition times or use methods for panel-observed processes when needed. Treating the visit date as the exact biological transition creates precision the design never collected.

6. Worked example: treatment, relapse and death

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In an invented trial, participants begin disease-free. By year two, estimated occupancy is 0.62 disease-free, 0.18 alive after relapse and 0.20 dead. A treatment reduces the disease-free-to-relapse hazard but increases survival after relapse. The relapse occupancy can therefore be higher under treatment because more relapsed participants remain alive, even though relapse onset is less frequent.

That is not a contradiction. Occupancy integrates every inflow and outflow. Reporting only the relapse hazard or only the proportion currently relapsed would tell different partial stories. The design should prespecify which pathway quantities answer benefit and burden.

7. Translate intensities into patient-facing outcomes

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Transition hazards are useful for modelling mechanisms and covariate effects. Decision makers may need probabilities of being alive without relapse, alive after relapse or dead at specified times, expected time spent in each state and probabilities of particular pathways. These are nonlinear functions of all relevant transition intensities.

Present uncertainty for derived outcomes, not only coefficients. Standardise over a target population when covariate distributions matter. Avoid a hypothetical “average patient” whose combination of attributes does not occur. Absolute outcomes make competing pathways visible and support interpretation of trade-offs.

8. Changed-context transfer check: school pathways

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Move from a clinical trial to students transitioning among enrolled, temporarily absent, returned and permanently withdrawn states. Absence can recur, administrative records may lag and school transfers can look like withdrawal. Calendar terms and time since absence both matter.

The transferable method is to define observable states and meaningful clocks. Treatment assignment may be replaced by a support programme with non-random uptake, so causal claims require stronger design. The multi-state model describes pathways; it does not by itself remove confounding or repair misclassified transfers.

9. Know the limits and common misconceptions

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More states do not automatically create more insight. Rare transitions yield unstable hazards, and proportional-hazards assumptions can fail differently by arrow. Occupancy probabilities can be estimated while individual paths remain unpredictable. A Markov model is not memoryless in ordinary language when time-dependent covariates and baseline time are included, but it still restricts how past history enters.

Multi-state modelling is not automatically causal. Randomisation helps for treatment strategies, yet post-randomisation states and transition-specific contrasts require careful estimands. Conditioning on entering an intermediate state can destroy the original treatment comparison.

10. Audit the pathway from data to estimand

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Publish the state diagram, allowed transitions, time origin, clocks, event definitions, simultaneous-event rules, observation schedule, censoring, covariates and analysis code. Report counts and person-time for every transition, sparse cells, model convergence and assumption checks.

Compare plausible state aggregations, Markov versus duration-sensitive models and alternative timing of interval-censored events. Plot observed and fitted transition or occupancy summaries where possible. Preserve all causes of entry and exit. A reader should see how each person contributes to each risk set and derived probability.

11. Frequently asked questions

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Is a multi-state model just survival analysis with more outcomes? It generalises time-to-event analysis by representing intermediate states and multiple transitions. Is a transition hazard the chance of moving? It is an instantaneous rate, not a probability. Can someone revisit a state? Yes, if the diagram and data allow recurrent transitions.

Does Aalen–Johansen show individual prognosis? It estimates population transition probabilities under stated conditions. Must the process be Markov? Some targets and estimators can be robust, but history assumptions still need examination. Does randomisation make every state comparison causal? No.

12. The gold standard reports both movement and presence

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Multi-state models make complex longitudinal pathways visible. Transition hazards describe movement out of the state currently occupied; state probabilities describe where the study population is likely to be after all routes operate. Confusing them can reverse the practical interpretation of an intervention.

The gold standard starts from a defensible state system, selects clocks and history assumptions deliberately, preserves observation uncertainty and reports absolute pathway outcomes. It uses the model to clarify the process, not to turn every recorded status into a causal mechanism.