Treatment Sequence Model

Treatment Sequence Model in Health Technology Assessment

A treatment sequence model is a health economic model in which each option compared is an ordered pathway of therapies, such as drug A, then drug B, then best supportive care, and patients move down the pathway when a treatment fails or has to stop. Costs and QALYs are added up over every line, so the value of a new medicine depends on where it sits in the pathway and on what patients receive after it. Published sequence models concentrate in chronic conditions with several treatment options, above all inflammatory arthritis and cancer. The hardest part is usually the evidence, because trials test single treatments at one point in the pathway and seldom report how a drug performs after another has failed.

Why the comparison is between whole sequences

Zheng and colleagues observe that as the number of interventions in a therapeutic area grows, the decision questions in health technology assessment expand to compare treatment sequences instead of discrete treatments, and to find the best position for a treatment within a sequence. The NICE manual (PMG36, section 2.2.14) states that when the technology and the comparator or standard care are both part of a sequence in the care pathway, the evaluation may compare alternative sequences. A drug with a high first-line response can still give poorer value over a lifetime if it pushes a more effective option later, where fewer patients reach it.

Lewis and colleagues coded the decision problems found in published sequence models. In their notation A, B, C and D are existing treatments and X is the new one.

Lewis and colleagues note that the number of unique sequences increases geometrically as treatments are added, which makes randomised trials of every sequence impractical. With no drug repeated, the count of possible orderings is

$$N = \frac{n!}{(n-k)!}$$

where $N$ is the number of ordered sequences, $n$ is the number of treatments available and $k$ is the number of lines modelled. Five treatments used in three lines give 5 × 4 × 3 = 60 sequences, so most models compare a few predefined sequences that reflect clinical practice or trial design.

Lewis and colleagues recommend that every evaluation starts at the point of divergence, where the compared sequences first differ. When sequences share the same opening lines, some patients die before the options differ, so incremental results per patient are spread over too large a denominator and understate the true effects.

Model structures that can carry treatment history

A sequence model has to remember what each patient has already received, because earlier treatment can change how well later treatment works. Siebert and colleagues, in the ISPOR-SMDM report on state-transition models, explain that cohort models assume transition probabilities depend neither on past states nor on time spent in the current state, the Markov assumption. A cohort model can hold memory by adding states that include history, at the cost of a large rise in the number of states, while individual-level models keep track of each person's history with tracker variables.

Zheng and colleagues identified 40 treatment sequence models in NICE assessments. Most (28) were cohort state-transition models with tracking states, followed by discrete event simulation (6), individual state-transition models (3) and decision trees (3). Lewis and colleagues set out how each structure handles sequences.

Moving patients through the lines

In a cohort version the sequence is a set of states, each tied to a line of therapy and often to response. The cohort is redistributed among those states each cycle.

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

where $\mathbf{s}_t$ is the row vector of the proportion of the cohort in each state at cycle $t$ and $\mathbf{P}_t$ is the matrix of transition probabilities for that cycle, whose rows each sum to one. Lewis and colleagues describe tunnel states used to make the probability of continuing treatment vary with time on a drug, and to carry cross-resistance from a previous treatment. They also note that a cohort model built only from treatment-specific states cannot separate different reasons for stopping.

The reason for leaving a line carries weight. Lewis and colleagues conclude that discontinuation for lack of effect, loss of effect or intolerance has a differential effect on the effectiveness and choice of the next treatment, and that primary studies report it poorly. A model that pools all stopping into one probability sends every patient onward with the same prognosis.

Assumptions about how well later lines work

Trials of whole sequences are rare, so most models apply simplifying assumptions to evidence on single treatments at one point in the pathway. Lewis and colleagues built a taxonomy of these assumptions and counted their use in 68 modelling studies. The commonest was that a treatment's effect does not depend on its position in the sequence, used for some or all later treatments in 49 studies (72%), and only 6 studies (9%) tested it in sensitivity analysis.

Lewis and colleagues warn that such assumptions can misrepresent the true level of uncertainty, bias estimates of effectiveness and cost-effectiveness, and lead to the wrong decision. In rheumatoid arthritis models, later-line evidence has come from a national registry and an uncontrolled open-label study, which are open to confounding, and a network meta-analysis that mixes trials from different points in the pathway may also be biased. Tosh and colleagues, reviewing rheumatoid arthritis models, found reporting of the evidence for downstream treatments generally poor and methods applied inconsistently, giving varied estimates of cost-effectiveness.

Waning benefit and gains that come from fast cycling

Many treatments for chronic conditions give an initial improvement that then wanes. Lewis and colleagues point out that when simulated patients move quickly through a sequence, for example after early stopping for adverse effects, they can collect several short-term benefits in a row and gain an additive effect. Some arthritis models counter this with a rebound that returns the patient to the starting severity on stopping.

The same artefact affects the adding problem, since a sequence with one extra drug offers one more short-term benefit and can look better simply because it has more lines. Rebound and waning assumptions are therefore part of the structural uncertainty of the model and suit explicit scenario analysis.

Continuation rules inside a sequence

Many sequences assess response after a trial period and continue the drug only in responders. The NICE manual (PMG36, section 4.9.13) says a treatment continuation rule should not be analysed as a separate subgroup, and should instead be treated as an additional strategy alongside the base-case interventions and comparators so that costs such as extra monitoring are included. Its listed considerations include the time at which response is measured and whether the rule can be incorporated into routine practice.

Worked example with two orderings of two drugs

All numbers here are illustrative. Drug A has a response probability of 0.6, an initiation cost of GBP 2,000, and responders gain 1.0 QALY at a maintenance cost of GBP 15,000. Drug B has a response probability of 0.4, an initiation cost of GBP 1,000, and responders gain 0.8 QALY at a maintenance cost of GBP 10,000. Non-responders move to the second drug, and those who respond to neither receive supportive care, taken as the zero point. For a sequence of drug X followed by drug Y, expected QALYs and costs per patient are

$$E_{XY} = r_X Q_X + (1 - r_X)\, m\, r_Y Q_Y, \quad C_{XY} = i_X + r_X M_X + (1 - r_X)\,(i_Y + m\, r_Y M_Y)$$

where $r$ is a drug's response probability when used first, $Q$ is the QALY gain per responder, $i$ is the initiation cost, $M$ is the maintenance cost per responder, and $m$ is a multiplier on second-line response, equal to 1 when effects are independent of position.

1. Position-independent effects. With $m$ = 1, A then B gives 0.6 × 1.0 + 0.4 × 0.4 × 0.8 = 0.728 QALYs and costs of 2,000 + 0.6 × 15,000 + 0.4 × 1,000 + 0.4 × 0.4 × 10,000 = 13,000. B then A gives 0.4 × 0.8 + 0.6 × 0.6 × 1.0 = 0.68 QALYs and 1,000 + 0.4 × 10,000 + 0.6 × 2,000 + 0.6 × 0.6 × 15,000 = 11,600 in costs.

2. Compare the orderings. Starting with A adds 0.728 − 0.68 = 0.048 QALYs and 13,000 − 11,600 = GBP 1,400. At an illustrative threshold of GBP 25,000 per QALY, the incremental net monetary benefit of A first is

$$\text{INMB} = 25000 \times 0.048 - 1400 = -200$$

where 25,000 is the threshold in GBP per QALY, 0.048 is the QALY difference and 1,400 is the cost difference in GBP. The ICER is 1,400 / 0.048 = 29,167, so starting with the cheaper drug B is preferred.

3. Halve second-line response. With $m$ = 0.5, A then B gives 0.6 × 1.0 + 0.4 × 0.5 × 0.4 × 0.8 = 0.664 QALYs and 2,000 + 9,000 + 400 + 0.4 × 0.5 × 0.4 × 10,000 = 12,200 in costs. B then A gives 0.32 + 0.6 × 0.5 × 0.6 × 1.0 = 0.50 QALYs and 1,000 + 4,000 + 1,200 + 0.6 × 0.5 × 0.6 × 15,000 = 8,900 in costs.

4. Compare again. A first now adds 0.664 − 0.50 = 0.164 QALYs and 12,200 − 8,900 = GBP 3,300.

$$\text{INMB} = 25000 \times 0.164 - 3300 = 800$$

where the terms are as in step 2. The ICER falls to 3,300 / 0.164 = 20,122, and starting with A becomes the preferred sequence.

5. Interpretation. The ordering reverses on one assumption about later-line effectiveness, the assumption Lewis and colleagues found was rarely tested. When drugs lose effect at later lines, putting the more effective drug first protects its benefit. A real model would add time on treatment, mortality, adverse events and discounting at 3.5% a year (PMG36, section 4.5.1). PMG36 (section 4.7.22) gives GBP 25,000 and GBP 35,000 per QALY gained as example thresholds, and the position-independent ICER of 29,167 lies between them, so at GBP 35,000 A first is preferred under both assumptions. With several sequences, PMG36 (section 4.10.8) asks for a fully incremental analysis that removes dominated and extendedly dominated options.

Treatment sequence models and neighbouring ideas

A treatment sequence model makes the sequence itself the comparator. Lewis and colleagues note that many economic evaluations instead compare single treatments at one decision point and attach the downstream costs of later treatments. The treatment switching page covers a different problem, where control patients in a trial start the new drug and survival estimates need adjustment.

Where treatment sequence models mislead

The recurring errors come from evidence gaps filled by untested assumptions. Each can change which sequence looks best.

1. Assuming effects are the same at every line. Most models do so and few test it, though the worked example shows it can reverse the order.
2. Ignoring displacement. Models usually give a drug pushed later by a new entrant its earlier effect, although randomised evidence after the new drug is seldom available.
3. Pooling all reasons for stopping. Intolerance and loss of response lead to different next steps.
4. Rewarding fast cycling. Without waning or rebound, sequences with more lines collect extra short-term benefit.
5. Starting before the point of divergence. Shared opening lines dilute incremental costs and QALYs.

Sources

• Lewis RA, Hughes D, Sutton AJ, Wilkinson C. Quantitative evidence synthesis methods for the assessment of the effectiveness of treatment sequences for clinical and economic decision making: a review and taxonomy of simplifying assumptions. PharmacoEconomics. 2021;39(1):25-61. https://doi.org/10.1007/s40273-020-00980-w
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 13 October 2026. Sections 2.2.14, 4.5.1, 4.7.22, 4.9.13 and 4.10.8. https://www.nice.org.uk/process/pmg36
• Siebert U, Alagoz O, Bayoumi AM, Jahn B, Owens DK, Cohen DJ, Kuntz KM. State-transition modeling: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-3. Value in Health. 2012;15(6):812-820. https://doi.org/10.1016/j.jval.2012.06.014
• Tosh J, Stevenson M, Akehurst R. Health economic modelling of treatment sequences for rheumatoid arthritis: a systematic review. Current Rheumatology Reports. 2014;16(10):447. https://doi.org/10.1007/s11926-014-0447-2
• Zheng Y, Pan F, Sorensen S. Modeling treatment sequences in pharmacoeconomic models. PharmacoEconomics. 2017;35(1):15-24. https://doi.org/10.1007/s40273-016-0455-3