# 3A.4 Model transition probabilities or variables, transformation and extrapolation

Page last updated: September 2016

## Information Requests

- Present the transition probabilities and any other modelled variables that are incorporated into the base-case economic model, and identify data sources and any associated translation requirements (Subsection 3A.4.1)
- Justify and describe the transformation of surrogate to target clinical outcomes (Subsection 3A.4.2)
- Derive extrapolations of data where necessary; explain and justify methods used, and prepare alternatives for sensitivity or scenario analyses (Subsection 3A.4.3)

### 3A.4.1 Transition probabilities and variables

Transition probabilities inform the movement of patients between health states in decision trees or state transition models. In a discrete event simulation, time-to-event parameters are analogous to transition probabilities. Transition probabilities or time-to-event parameters may differ by treatment or by how long a patient has been in a particular health state (time-varying probabilities).

Transition probabilities that differ by treatment are generally estimated using the clinical evidence described in Section 2 (with applicability translation in Section 3A.3.2, as appropriate). Cross-reference the relevant subsections for the clinical evidence and note whether further translation studies or extrapolations are required (do these in Subsections 3A.4.2 and 3A.4.3).

Other transition probabilities may be required that describe the progression of a disease or condition following the experience of an intermediate outcome event, and for which the same transition probabilities are applied, regardless of treatment allocation. Where external sources of data (other than the clinical trials from Section 2) are used to inform transition probabilities (or other variables) in the model, assess the applicability of these sources of data with respect to the Australian setting. Note and justify whether the data are applicable, requiring translation (in which case, follow the approach detailed in Subsection 3A.3.2), or is a source of uncertainty within the model.

Detail where the model uses other variables instead of, or in addition to, transition probabilities. Do not include variables associated with the valuation of outcomes or costs; these are described in Subsections 3A.5 and 3A.6, respectively.

Describe and justify the methods used to identify and analyse relevant data to derive transition probabilities and variables.

For each transition probability or variable, present the point estimate and interval
estimates (eg 95% confidence intervals). Follow good-practice guidelines when choosing
the methods to derive interval estimates (eg using probability distributions based
on agreed statistical methods for alternative types of input parameters).^{38} Ensure that values taken from all sources of evidence are appropriately adjusted
to represent the transitions required by the model structure.^{39} For example, translate reported rates or cumulative probabilities to the probabilities
for timeframes associated with a model cycle, if necessary.

Occasionally, secondary outcomes and other trial-derived data (eg adverse event rates) are relevant to outcomes and/or resource use in the economic model, and point estimates are numerically different across the arms, but not statistically significantly different. This may reflect either no ‘real’ difference, or a difference but with insufficient power in the trial to demonstrate it statistically. Explain the approach used to inform the probability in the base-case model (eg whether it has been pooled across arms or differentiated between arms), and explain and justify with supporting evidence, if available. Examine the alternative approach in a sensitivity analysis.

Assess the potential correlation between transition probabilities and/or variables. Correlation between parameters is explored further in Section 3A.9 for uncertainty analysis.

### 3A.4.2 Transformation of surrogate health outcomes to target clinical outcomes

In some cases, the clinical evidence presented in Section 2 provides no data (or underpowered or premature data) on comparative treatment effects for a relevant health outcome that is used in the model (a target clinical outcome). Studies may provide stronger evidence of a comparative treatment effect in a proposed surrogate measure, which is claimed to represent a relevant comparative health outcome. Justify and quantify the claimed relationship between the change in treatment effect in the proposed surrogate measure and the change in treatment effect in the target clinical outcome used for the economic evaluation.

Present a translation study that follows the framework in Appendix 5 for assessing a proposed surrogate measure if the transformation of a change in a proposed surrogate measure predicts a change in a target clinical outcome.

It may not be necessary to detail, in full, the transformation of a proposed surrogate
measure to a target clinical outcome when the PBAC has previously accepted the surrogate
outcome as valid and **all** of the following apply:

- The proposed treatment effect is within the range of the comparative treatment effect identified in the clinical evidence associated with the transformation that was previously accepted by the PBAC.
- The proposed medicine will be used in the same population as the previously accepted transformation.
- The medicines in the evidence used to previously validate the surrogate, the main comparator and the proposed medicine are all in the same class or have a similar mechanism of action.

There is no general principle about the extent to which underpowered or premature treatment effect data for a target clinical outcome justify the transformation of a proposed surrogate measure. However, if a proposed surrogate measure is transformed and direct treatment effect data for the corresponding target clinical outcome are also available, apply the surrogate and direct data separately to populate the model. If both approaches provide similar estimates of the comparative treatment effect on the target clinical outcome in the longer term, this helps validate the model.

If a proposed surrogate measure is transformed, ensure that the sensitivity analyses in Subsection 3A.9 represents the uncertainty in the estimation of the comparative treatment effect on the proposed surrogate measure, and the uncertainty of the transformation. This is more complex than where direct measures of comparative treatment effect for a target clinical outcome are used.

### 3A.4.3 Extrapolation

Extrapolation may be justified when all important differences in costs and outcomes between the intervention and comparator(s) groups are not represented over the time horizon for which observed data are available. Detail any extrapolations of data that are required for the base-case economic model.

Where extrapolation is undertaken, use observed time-to-event data in preference to modelled data up to the time point at which the observed data become unreliable as a result of small numbers of patients remaining event-free.

Describe and justify the selected time point beyond which extrapolated transition probabilities are applied. External data may be used to justify the selected time point – for example, the point at which one or more of the curves fitted to the clinical trial data deviates from a curve fitted to observational data from a similar patient cohort with a larger sample over a longer follow-up period. Test alternative truncation points in the sensitivity analysis.

Derive appropriately estimated parametric survival curves based on the observed data (using individual patient data, if available) to extrapolate transition probabilities beyond the data truncation point.

Detail each of the following:

- Whether an assumption of proportional hazards is appropriate beyond the observed data.
- Fit a range of alternative survival models to the observed data (eg exponential, Weibull,
log-normal, log-logistic, gamma, Gompertz). Include more flexible extrapolation approaches
with multiple points of inflexion (eg piecewise spline models) to better facilitate
extrapolation based on the section of the Kaplan–Meier curve that is most representative
of long-term survival.
^{40} - Assess and discuss goodness of fit using visual inspection, Akaike’s information criterion and Bayesian information criterion. Justify the most appropriate model for the base case and test a number of the best-fitting models in the sensitivity analysis.
- The plausibility of the predictions in the unobserved period (eg the ongoing hazard ratio and/or treatment effect, the point of convergence and/or residual survival in each arm).

The treatment effect resulting from the independent extrapolation of the survival curves should be plotted over the time horizon of the model. If the treatment effect is maintained or increasing, and this is not clinically plausible, apply a hazard ratio such that the intervention and comparator curves converge at a plausible time point. The assessment of plausibility should be linked to the justification of the time horizon (see Subsection 3A.2).

When considering the extrapolated treatment effect, give explicit consideration to clinical decisions regarding the cessation or continuation of treatment. State and justify all assumptions in this regard, and apply them consistently when modelling respective treatment costs.

Numerous sources of advice on extrapolation techniques for economic evaluation are
available in the literature.^{41-46}

#### Other individual patient extrapolation issues

For categorical data that describe the experience of multiple intermediate or outcome events, use a two-stage process of modelling the time to any event, combined with a multinomial logistic model to define the probabilities of the aggregate event being each of the competing events. Include a time covariate in the multinomial logistic model to represent time-varying probabilities, if possible. The other option is to fit independent competing risks time-to-event models for each event, but this approach is likely to overestimate parameter uncertainty as a result of the assumed independence of the multiple events modelled.

For continuous variables, format the data into categories, or use a generalised estimating equation model.

#### Extrapolating published time-to-event data

If individual patient time-to-event data are not available, extrapolate survival probabilities from published Kaplan–Meier curves using graph digitiser software. Fit alternative constant (ie exponential), or monotonically increasing and decreasing (eg Weibull or Gompertz) hazard functions to the extracted survival data beyond the last point of inflexion to the time point at which the observed data become unreliable because of small numbers of patients remaining event-free.

Present tests of the relative and absolute goodness of fit of the alternative curves, and use the best-fitting curve in the base case. Test the alternative models in the sensitivity analyses in Subsection 3A.9.