# Zero to hero

**Gianluca Baio's blog**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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Recently, I’ve been working on a paper, which I think is coming along nicely. The basic problem is like this: in a health economic evaluation, sometimes data are collected on a sample of individuals. Say, for example, that $n_0$ subjects are given a standard treatment $t=0$ and $n_1$ are treated with a new intervention $t=1$. For each subject, we typically observe a measure of clinical benefit $e_i$, which tells us how “good” the treatments are, and a measure of overall cost $c_i$.

Costs (and for that matters benefits) are almost invariably associated with skewed distributions (and thus suitable models are Gamma and log-Normal) and, generally $(e,c)$ are actually correlated. Moreover, sometimes, for some of the patients, $c_i=0$, *ie* some people are observed to accrue no costs to the NHS. For these, you can’t really use a Gamma or a log-Normal.

In the paper, I extend the framework of hurdle models commonly used to tackle the issue of individual patients with observed zero costs, to include a full cost-effectiveness model, accounting for correlation between costs and a suitable measure of clinical effectiveness (eg QALYs). Basically, I do this using a structure consisting of:

- a selection model for the chance of observing a zero cost, typically as a function of some individual covariates (
*eg*age and sex); - a marginal model for the costs, inducing a mixture (of subjects with 0 cost and subjects with positive costs), depending on the selection model;
- a conditional model for the benefits, depending on the costs (so that correlation between $e,c$ is guaranteed).

**B**ayesian

**C**ost-

**E**ffectiveness for

**S**tructural

**0**s) lets you select the distributional assumptions and then builds a model code and runs it in JAGS. The user doesn’t even know how to code JAGS models (provided they’re happy with the relative general model that will be produced automatically). But I’m making R save the model file, so that you can actually see it and modify it as needed.

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**Gianluca Baio's blog**.

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