Modelling Framework
we extend the current methods for modelling trial-based partitioned survival cost-utility data,
taking advantage of the flexibility of the Bayesian approach, and specify a joint probabilistic model for the
health economic outcomes. We propose a general framework that is able to account for the multiple types of
complexities affecting individual level data (correlation, missingness, skewness and structural values), while
also explicitly modelling the dependence relationships between different types of quality of life and cost components.
Consider a clinical trial in which patient-level information on a set of suitably defined effectiveness and
cost variables is collected at time points on individuals, who have been allocated to intervention groups.
Assume that the primary endpoint of the trial is OS, while secondary endpoints include PFS, a self-reported health-related
quality of life questionnaire (e.g. EQ-5D) and health records on different types of services (e.g. drug frequency and dosage,
hospital visits, etc.). Following standard health economic notation, we denote with and the two
sets of health economic outcomes (effectiveness and costs) collected for the -th individual in treatment of the trial.
For simplicity, we define and based on the variables used in the analysis.
The effectiveness outcomes are represented by pre-progression () and post-progression
() QAS data calculated using survival and utility data collected up to and
beyond progression. We denote the full set of effectiveness variables as ,
formed by the pre and post-progression components. The cost outcomes are represented by a set of variables (, for
) calculated based on different types of health services and associated unit prices. We denote the full set of cost
variables as , formed by the different cost components.
The objective of the economic evaluation is to perform a patient-level partitioned survival cost-utility analysis
by specifying a joint model , where
denotes the full set of model parameters. Among these parameters, interest is in the marginal mean effectiveness and
costs which are used to inform the decision-making process.
Different approaches can be used to specify . Here,
we express the joint distribution as
where is the marginal distribution of the effectiveness
and is the conditional distribution of
the costs given the effectiveness, respectively indexed by and , with
. We specify the model in terms of a marginal distribution for
the effectiveness and a conditional distribution for the costs. A key advantage of using a conditional factorisation, compared to a
multivariate marginal approach, is that univariate models for each variable can be flexibly specified to tackle
the idiosyncrasies of the data (e.g. non-normality ans spikes) while also capturing the potential correlation
between the variables. We now describe how the two factors on the right-hand side of the Equation can be specified.
The Figure provides a visual representation of the proposed modelling framework.
The effectiveness and cost distributions are represented in terms of combined “modules”- the red and blue boxes -
in which the random quantities are linked through logical relationships. Notably, this is general enough to be extended
to any suitable distributional assumption, as well as to handle covariates in each module.
Conclusions
Although our approach may not be applicable to all cases, the data analysed are very much representative of the “typical” data
used in partitioned survival cost-utility analysis alongside clinical trials. Thus, it is highly likely that
the same features apply to other real cases. This is a very important, if somewhat overlooked problem,
as methods that do not take into account the complexities affecting patient-level data, while being easier to
implement and well established among practitioners, may ultimately mislead cost-effectiveness conclusions
and bias the decision-making process.