Treatment Sequence Model

How a treatment sequence model follows care over time

A treatment sequence model represents an ordered strategy in which patients receive one treatment and may move to later options after non-response, loss of response, toxicity, intolerance, or another stopping event. It connects outcomes across lines because earlier choices affect who reaches later treatment, when they arrive, and what benefit remains possible. This page explains how sequences are specified, simulated, compared, validated, and interpreted for economic decisions.

The decision concerns complete strategies

The relevant alternatives are treatment sequences rather than individual medicines viewed in isolation. A first-line option can appear attractive because of strong initial response yet produce poorer lifetime value if it delays a more effective later therapy, causes irreversible harm, or changes eligibility for subsequent care. Every comparator should therefore be written as a complete and clinically feasible strategy.

Sequence element	Question the model must answer	Example representation
Entry	Who starts the sequence and in what condition?	Treatment-naive patients with active disease
Line of therapy	Which treatment is used at each position?	A then B then C
Assessment	When and how is success judged?	Response assessed at 12 weeks
Continuation	Who remains on current treatment?	Responders without unacceptable toxicity
Switching	What triggers movement to the next line?	Primary failure, loss of response, or adverse event
Exit	What happens after the modelled options are exhausted?	Best supportive care, surgery, or death

Sequence position can change treatment effects

The effect of a medicine may differ when used first, second, or later because the patient population, disease duration, prior exposure, resistance, and prognosis have changed. Applying one treatment effect at every line can overstate or understate benefit. Line-specific evidence should be used when available, and any assumed constancy should be tested.

Important sources of history dependence include:

• Prior response or failure to a medicine with a related mechanism.
• Cumulative toxicity or organ damage.
• Disease progression while earlier treatment is attempted.
• Treatment-induced resistance or sensitisation.
• Changes in severity, functional status, or biomarker profile.
• Selection of patients who tolerate and survive earlier lines.

Patients move for different reasons

Treatment failure is not a single event. Primary non-response, secondary loss of response, adverse events, patient preference, poor adherence, administrative restrictions, and planned completion have different implications for prognosis and later care. Combining them into one discontinuation rate can erase clinically important pathways.

The model should distinguish, when material:

• Primary failure before meaningful benefit is achieved.
• Loss of response after an initial benefit.
• Discontinuation because of an adverse event or intolerance.
• Discontinuation for non-clinical reasons such as access or preference.
• Planned stopping after a defined course.
• Death or another event that prevents further treatment.

The model structure must preserve relevant history

A cohort state-transition model can represent sequences when future outcomes depend mainly on the current line and response state. Patient-level simulation is often more appropriate when previous treatments, individual characteristics, event timing, or multiple competing rules affect later outcomes. The structure should be chosen for the decision problem rather than for programming convenience.

Common structures include:

• Decision trees for short sequences with fixed assessment points.
• Markov models with states defined by treatment line, response, or disease status.
• Semi-Markov models when risks depend on time spent in a state.
• Partitioned survival models when progression and survival curves define occupancy.
• Discrete-event simulation when individual histories and event timing drive complex pathways.
• Microsimulation when patient heterogeneity and treatment-history interactions are material.

Treatment-line states require clear definitions

States such as first-line treatment or second-line treatment are incomplete unless they specify response, disease status, or time since initiation when those features affect outcomes. Two patients on the same line can have different costs and prognosis if one is responding and another is awaiting assessment. State definitions should be mutually exclusive, collectively exhaustive, and aligned with the available evidence.

A state set might distinguish induction, response, non-response, maintenance, adverse-event interruption, subsequent treatment, supportive care, and death. More detail is justified only when it changes outcomes or decisions and can be parameterised credibly.

Transition probabilities govern movement through the sequence

At each model step, patients can remain on treatment, respond, discontinue, switch, progress, experience an adverse event, or die. Transition probabilities must refer to the same time interval and sum consistently across mutually exclusive destinations. Competing events should not be calculated independently when doing so can create impossible totals.

For a cohort state-transition model with state vector (\mathbf{s}_t) and transition matrix (\mathbf{P}_t):

$$ \mathbf{s}_{t+1} = \mathbf{s}_t\mathbf{P}_t $$

For each origin state (i):

$$ \sum_{j=1}^{J}p_{ij,t}=1 $$

Time-varying matrices can represent changing response, discontinuation, mortality, or waning. The model must also prevent transitions that are clinically impossible or inconsistent with the sequence rules.

Converting rates and risks requires compatible timing

Clinical studies may report hazards, cumulative risks, median time to discontinuation, or proportions remaining on treatment. These quantities should not be inserted interchangeably. Conversion requires an assumption about the event process and must match the model cycle length.

Under a constant hazard assumption, a rate (r) can be converted to a probability over cycle length (\Delta t):

$$ p = 1-\exp(-r\Delta t) $$

The constant-hazard assumption should be checked because discontinuation and failure frequently vary after initiation. Survival curves, flexible parametric models, or piecewise rates may better represent observed timing.

Response rules determine who continues

Many sequences use an induction or trial period followed by an assessment. Responders may continue treatment, while non-responders move to the next option. The model should define the response measure, threshold, assessment time, missing-data rule, and whether partial response changes care.

Misclassification matters because an imperfect assessment can retain patients on ineffective treatment or switch patients who would have benefited. Scenario analysis can test alternative response definitions, timing, and adherence to stopping rules.

Discontinuation and loss of response are time-dependent

Persistence often falls over time, and the reasons for stopping can change after the early treatment period. A single annual discontinuation probability may distort both duration and the timing of later-line entry. Time-to-discontinuation evidence should be used when it is available and applicable.

If (S_k(t)) is the probability of remaining on treatment (k) at time (t), expected time on treatment over horizon (T) is:

$$ E[T_k] = \int_0^T S_k(t),dt $$

This duration affects acquisition costs, monitoring, accumulated benefit, and the number of patients reaching the next line.

Washout, bridging, and switching costs can be material

Movement between treatments may require tapering, washout, testing, vaccination, bridging therapy, or waiting for authorisation. These intervals can cause cost, reduced quality of life, disease worsening, or safety risk. Treating switching as instantaneous can favour sequences with frequent transitions.

The model should include clinically relevant delays, one-off switching costs, temporary outcomes, and mortality risk. The same assumptions should be applied consistently across sequences unless evidence supports a difference.

Adverse events affect current and later treatment

Adverse events can add short-term costs and disutility, cause permanent harm, trigger discontinuation, or restrict future choices. Sequence models should not represent them only as a one-cycle decrement when the consequences persist. The relationship between event risk, treatment duration, dose, and previous exposure should be considered.

An adverse event can influence:

• Immediate treatment and monitoring costs.
• Temporary or permanent quality-of-life loss.
• Probability and timing of discontinuation.
• Eligibility for the next treatment.
• Future mortality or morbidity.
• Patient willingness to continue or restart therapy.

Mortality must follow the treatment pathway

Mortality can depend on age, disease state, response, treatment, adverse events, and accumulated history. Background mortality and disease-specific mortality should be combined without double counting. Patients who die must be removed from all later treatment lines and costs.

If independent background and disease-specific survival components are justified, overall survival can be expressed as:

$$ S_{overall}(t)=S_{background}(t)\times S_{disease}(t) $$

Independence may not hold, and disease evidence can already include background mortality. The model should document the approach and test plausible alternatives.

Costs follow treatment, events, and time

Each line can generate acquisition, administration, monitoring, adverse-event, switching, disease-management, and subsequent-care costs. Dosing may depend on weight, body surface area, vial size, dose intensity, wastage, or adherence. Prices and resource use should match the relevant jurisdiction and year.

For treatment (k), a simplified expected line cost is:

$$ E[C_k]=E[T_k]\times C_{routine,k}+C_{initiation,k}+E[C_{events,k}] $$

The calculation should distinguish recurring and one-off costs and should not multiply an annual price by a nominal line duration when discontinuation occurs continuously.

Health outcomes accumulate across the sequence

Quality-adjusted life-years depend on time spent in each health and treatment state, adjusted for quality of life. Treatment-specific convenience, adverse events, response, disease severity, and caregiver effects may matter when supported by the perspective and evidence. Utilities should avoid double counting effects already captured by disease-state values.

For state (h) over cycle (t), discounted QALYs can be accumulated as:

$$ QALY = \sum_t\sum_h s_{h,t}u_{h,t}\Delta t(1+d_E)^{-t} $$

where (s_{h,t}) is state occupancy, (u_{h,t}) is utility, (\Delta t) is cycle length, and (d_E) is the applicable outcome discount rate expressed consistently with time.

Evidence for later lines is often sparse

Randomised evidence frequently focuses on one treatment position and may not report outcomes conditional on prior histories. Later-line parameters may come from observational data, subgroup analyses, registries, or assumptions. These sources require careful adjustment and transparent assessment of transportability.

Naive indirect comparison can be misleading when patients receiving later lines differ in prognosis or when treatment choice is confounded by previous response. The model should separate observed evidence from extrapolation and show how uncertainty in later lines affects the decision.

Treatment comparators can create combinatorial complexity

With many available treatments, the number of possible sequences grows rapidly. It is rarely useful or clinically credible to model every permutation. Candidate sequences should reflect guidelines, practice, contraindications, mechanism, prior use, and genuine decision alternatives.

Dominance screening may remove strategies that cost more and produce less health, but screening should occur after the model correctly represents all outcomes. Structural constraints should also exclude sequences that repeat ineffective mechanisms or violate clinical eligibility.

Comparing complete sequences

Costs and outcomes should be compared across the full horizon for each strategy. An incremental analysis orders non-dominated sequences by cost and calculates incremental cost-effectiveness between adjacent efficient options. Comparing every sequence only with current care can conceal extended dominance.

For strategy (a) versus (b), incremental net monetary benefit is:

$$ INMB_{a,b}=\lambda(E_a-E_b)-(C_a-C_b) $$

Positive INMB favours sequence (a) at threshold (\lambda), conditional on the model and evidence. The result should be accompanied by uncertainty and by a description of which line-specific assumptions drive the difference.

Structural uncertainty is central

Sequence models contain structural choices about switching, stopping, waning, re-treatment, mortality, and post-sequence care. These cannot always be represented by probability distributions around one structure. Alternative credible structures should be tested explicitly.

High-value scenarios include:

• Equal versus line-specific treatment effects.
• Different stopping and response-assessment rules.
• Alternative treatment-waning assumptions.
• Instantaneous versus delayed switching.
• Different rules for subsequent treatment and supportive care.
• Alternative survival extrapolations.
• Exclusion or inclusion of history-dependent effects.
• Alternative adherence, persistence, and real-world implementation assumptions.

Patient heterogeneity can change the preferred sequence

The best sequence for an average cohort may not be best for every patient. Biomarkers, severity, age, comorbidity, contraindications, previous treatment, preferences, and risk tolerance can modify benefit, harm, or feasibility. Subgroup analysis should be prespecified and supported by credible effect-modification evidence.

Patient-level models can apply eligibility and switching rules dynamically. They also require more data, stronger validation, and enough simulated patients to control Monte Carlo error.

Worked two-line example

Suppose 1,000 patients start treatment A. At the first assessment, 60% respond and continue A, 30% do not respond and move to B, 5% stop because of an adverse event and move to B, and 5% leave the active sequence for other reasons. The number entering B is therefore 350, assuming the two switching groups are mutually exclusive and all are eligible.

$$ N_B=1{,}000\times(0.30+0.05)=350 $$

If 40% of patients entering B respond, 140 achieve response on B:

$$ Responders_B=350\times0.40=140 $$

This simple calculation illustrates flow but omits timing, mortality, later loss of response, costs, utilities, and uncertainty. A full model must preserve those consequences and avoid applying the 40% response rate if the evidence came from a materially different prior-treatment population.

Validation should test pathways and totals

Validation should examine both the mechanics of patient flow and the plausibility of outcomes. A model can reproduce overall survival while sending implausible numbers through individual lines, or it can match line-specific use while misrepresenting long-term outcomes. Both pathway and aggregate checks are needed.

Useful checks include:

• Every patient occupies one allowable state at each time.
• Transition probabilities and competing events reconcile.
• Numbers starting each later line match preceding exits and eligibility.
• Treatment duration matches observed persistence when comparable data exist.
• Predicted response, discontinuation, survival, and utilisation match internal and external evidence.
• Extreme inputs produce clinically logical behaviour.
• Independent calculations reproduce key flow, cost, and outcome results.

Common mistakes

Sequence models can look realistic because they contain named lines of treatment, yet still lose the history that makes sequencing important. The following errors commonly create false precision or bias comparisons. Each should be checked explicitly before the model informs a decision.

• Comparing drugs rather than complete feasible sequences.
• Applying first-line efficacy unchanged to every later line without justification.
• Treating all discontinuation as lack of efficacy.
• Switching patients instantly with no washout, delay, cost, or health consequence.
• Allowing dead or ineligible patients to enter later treatment.
• Double counting disease progression, adverse events, or mortality.
• Using later-line observational outcomes without addressing selection and confounding.
• Assuming every patient receives all planned treatments.
• Ignoring sequences that are clinically relevant because they are inconvenient to model.
• Reporting a preferred sequence without identifying the line-specific assumptions driving it.

Reporting a treatment sequence model

Transparent reporting should allow readers to reconstruct every strategy and follow patients from entry to exit. Each line's evidence and assumptions should be visible rather than hidden in aggregate results. The report should also distinguish clinical policy from modelled simplification.

• List every comparator sequence, line, stopping rule, and exit pathway.
• Define states, cycle length, assessment timing, and transition rules.
• Report line-specific efficacy, discontinuation, adverse events, mortality, costs, and utilities.
• Identify which parameters depend on treatment history or patient characteristics.
• Show patient flow and the proportion reaching, responding to, and stopping each line.
• Report structural, parameter, methodological, and heterogeneity uncertainty.
• Provide verification, validation, version, and reproducibility records.
• State which sequences, populations, and settings the conclusions support.

The decision standard

A credible treatment sequence model shows how today's choice changes tomorrow's options, timing, outcomes, and costs. It compares complete clinically feasible strategies, preserves material treatment history, and carries uncertainty through every line of care. The preferred sequence is therefore a conditional decision result—not a universal ranking of individual treatments—and should be revised when evidence, prices, practice, or available options change.