Why Remission and Relapse Need Careful State Definitions
A clinical record may use “remission,” “relapse,” and “death” as if they were self-explanatory categories. A model needs more: it needs criteria for assigning each patient to exactly one state at a time, and a specification of which changes count as transitions. The distinction matters because “has relapsed at least once” is an event-history description, whereas “currently has active disease” describes a present condition. A patient can have relapsed, returned to remission, and relapsed again; those histories cannot all be represented by the same simple state label.
The study question determines the structure. If the endpoint is time to first relapse after remission, a model may record whether that first relapse has occurred. If the aim is to describe the ongoing clinical course, the model must allow movement from remission to active disease and back again. In both cases, death is an absorbing state: once entered, it cannot be left.
Before drawing arrows, specify the disease criteria, how remission and relapse are confirmed, how deaths are ascertained, and the time origin (for example, treatment initiation). The rules should be sufficiently precise that two reviewers would classify the same clinical history the same way. States should be exhaustive for the population and period under study: a patient who has not yet reached remission, for example, cannot be left unclassified.
Two Different Structures for Relapse
One structure records the first relapse as a milestone. Let \(A_0\) denote active disease before remission, \(R_0\) remission before any relapse, \(L\) the state “first relapse has occurred,” and \(D\) death. A suitable diagram for a cohort entering with active disease is:
Here \(L\) means that the person has experienced a first relapse; it does not necessarily mean that the person is currently in active disease. The diagram records the first relapse and permits death afterward. It does not record later remission or additional relapses. If everyone enters the study in remission, \(A_0\) is unnecessary: \(R_0\) is the initial state.
A different structure describes the current disease course. Let \(A\) mean active disease, \(R\) remission, and \(D\) death. Permit transitions in both directions between \(A\) and \(R\), as well as death from either living state:
The cycle \(A \to R \to A \to R\) is allowed, so the model can represent repeated remission-relapse episodes. The names and arrows must match the protocol: if a relapse is possible only after a documented remission, the relapse transition is \(R \to A\), not a transition from a state that the patient never occupied.
Worked Example: Drawing a First-Relapse Structure From a Protocol
Hypothetical protocol. Twelve patients enter a study with active disease. During 12 months, nine achieve protocol-defined remission, two die before remission, and one remains alive with active disease. Of the nine who enter remission, three have a documented first relapse, two die while still in remission, and four remain in remission at month 12. One of the three patients who relapses later dies.
Start with \(A_0\) because all 12 patients enter with active disease. The counts of observed outcomes from this state are \(9\) to \(R_0\), \(2\) to \(D\), and \(1\) remaining in \(A_0\). The accounting is \(9+2+1=12\), so all entrants are classified.
Among the nine who enter \(R_0\), the observed counts are \(3\) to \(L\), \(2\) to \(D\), and \(4\) still in \(R_0\). Again, \(3+2+4=9\). The three first relapses are therefore represented by \(R_0 \to L\), and the later death among them by \(L \to D\). The other two deaths after remission use \(R_0 \to D\).
This structure answers questions about whether and when a first relapse occurred, and it retains death after relapse. It cannot say whether a patient in \(L\) later returned to remission: the state means “ever had first relapse,” not “currently active.” The simple observed fraction \(3/9=0.333\), or 33.3%, is the proportion of these nine patients with a recorded first relapse during the stated observation period; it is not, by itself, a time-to-event estimate that accounts for differing follow-up.
Allowing Repeated Remission-Relapse Cycles
For a model of current clinical status, use \(A\), \(R\), and \(D\), with \(A \leftrightarrow R\) and death reachable from both living states. This structure preserves whether a patient is currently in remission or active disease. It also permits a sequence with more than one relapse, provided that the observed clinical definitions support each \(R \to A\) transition. The initial state is assigned from the patient’s status at the study time origin.
Worked Example: Translating Patient Histories Into Recurrent Transitions
Hypothetical histories. Four patients enter with active disease. Their observed paths are: patient 1, \(A \to R \to A \to R\); patient 2, \(A \to R \to D\); patient 3, \(A \to D\); and patient 4, \(A \to R \to A \to D\). Each arrow represents a documented change; the records end at the last listed state.
Count the transitions under the recurrent structure. There are four \(A \to R\) transitions: patient 1 has two, patient 2 has one, and patient 4 has one, giving \(2+1+1=4\). There are two \(R \to A\) transitions, one each for patients 1 and 4. There is one \(R \to D\) transition, for patient 2. There are two \(A \to D\) transitions, for patients 3 and 4. Thus the total is \(4+2+1+2=9\) observed transitions.
Under the first-relapse structure, patients 1 and 4 move from \(R_0\) to \(L\) at their first \(R \to A\) change. Patient 2 instead moves from \(R_0\) to \(D\), and patient 3 moves from \(A_0\) to \(D\). Patient 4 can then move from \(L\) to \(D\). Patient 1 remains classified as \(L\) in that structure, even after the later return to remission. The recurrent model distinguishes patient 1’s subsequent states; the first-relapse model deliberately does not.
Choosing States and Checking the Assumptions
A state diagram is a specification of what histories the model can represent. It does not, on its own, establish a Markov model. The Markov property requires that, conditional on the present state (and any specified time variables), the future state distribution does not depend on additional past history. The earlier material on the Markov property distinguishes that assumption from simply drawing a diagram.
For example, if relapse risk depends on how long a patient has been in remission, a model using only \(R\) may not have enough information in its current state for a time-homogeneous Markov description. The structure may need remission duration or another relevant history feature represented, or the model may need to allow dependence on time. Similarly, an \(L\) state that combines patients currently in remission with patients currently active can be unsuitable for modeling their future disease transitions: those clinical conditions may have different possible next changes.
Use the protocol and the study question to check the structure before analyzing data:
- Mutual exclusivity: Can a person be classified in two listed states at once? “Currently active” and “ever relapsed” overlap, so they cannot be treated as mutually exclusive states without further definition.
- Exhaustiveness: Does every patient have a state at every relevant time, including before first remission and after relapse?
- Feasible arrows: Does each permitted transition correspond to a clinically possible, observable change? Is a transition missing that the protocol allows?
- Death: Is death absorbing, with no outgoing arrows? A living state after death is not a permissible transition.
- History needed: Does the state preserve the information required for the target question, such as whether a first relapse has occurred or the patient’s current disease status?
Worked Example: When “Ever Relapsed” Is Not Current Disease Status
Hypothetical history. A patient enters remission at month 2, has a confirmed relapse at month 7, returns to remission at month 10, and remains alive and in remission at month 14.
For a first-relapse endpoint, the path is \(A_0 \to R_0 \to L\). At month 14 the patient is still classified as \(L\), because the first-relapse event has occurred. This is correct if the question is whether the patient ever had a first relapse.
For current disease status with recurrent cycles, the path is \(A \to R \to A \to R\). At month 14 the patient is in \(R\). If the study records the person only as \(L\), it cannot distinguish this patient from someone currently in active disease after a relapse. The correct choice depends on the target: use the first-relapse structure for a first-event history, and the recurrent structure when subsequent current states matter.
Comparison, Limitations, and Common Pitfalls
| Feature | First-relapse structure | Repeated-cycle structure |
|---|---|---|
| Main state meaning | Whether first relapse has occurred | Current active-disease or remission status |
| Relapse transitions | One recorded transition from \(R_0\) to \(L\) | Any permitted number of \(R \to A\) transitions |
| After relapse | Later clinical status is not distinguished unless states are added | Later remission and relapse remain representable |
| Best suited to | A question focused on first relapse | A question about ongoing disease-state history |
Neither structure is universally preferable. A first-relapse model simplifies the event history but discards post-relapse status unless it is expanded. A recurrent model retains more clinical detail, but requires reliable recording of repeated transitions and well-defined criteria for every remission and relapse. More states can also leave few observations in some categories; fewer states can conceal clinically relevant distinctions. State choice is therefore a trade-off between the question, the protocol, and the information actually collected.
Common mistake: treating \(L\), “first relapse has occurred,” as though it meant “currently has active disease.” This incorrectly classifies a person who relapsed and later returned to remission. Correct the interpretation by either retaining \(L\) explicitly as an event-history state or using a recurrent structure that records current status. Do not infer repeated cycles from a first-relapse record that never collected them.
Another pitfall is assuming that every \(A \to R\) transition is followed by a relapse. Patients may remain in remission or die there, so both \(R \to A\) and \(R \to D\) may be possible, as may continued residence in \(R\) over an observation interval. A state diagram describes permitted changes; it does not claim that every patient follows every arrow. Finally, a clinically sensible diagram does not prove that the Markov assumption holds. Check whether relevant past duration or event history still predicts the future after conditioning on the proposed state and time scale.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- A study begins with patients in remission and asks whether they experience a first relapse or die before relapse. What initial state and transitions are needed?
- A patient follows \(A \to R \to A \to R\). How many relapse transitions are represented in the recurrent model, and what does the first-relapse model retain?
- Why is a state called “ever relapsed” not necessarily a valid substitute for “currently active disease” in a recurrent model?
- A proposed diagram has \(D \to R\). What is wrong with this structure?
- What should be considered if future relapse depends on time already spent in remission?
Solutions. (1) Use \(R_0\) as the initial state, with \(R_0 \to L\) for first relapse and \(R_0 \to D\) for death; \(L\) can also lead to \(D\) if post-relapse death is represented. (2) There is one \(R \to A\) relapse transition. The first-relapse model records that this first relapse occurred, but does not retain the later return to remission as current status. (3) Someone can have relapsed before and later be in remission, so “ever relapsed” does not identify current disease status. (4) Death is absorbing, so a transition from death to remission is impossible. (5) Consider whether remission duration or another time variable must be represented, and assess whether the proposed Markov assumption is appropriate; a state diagram alone does not guarantee it.