---
title: "Auto-generated report from BCEA"
header-includes: \usepackage{graphicx} \usepackage{bm}
date: "Version: `r format(Sys.time(), '%d %B, %Y')`"
output:
  word_document: default
  pdf_document:
    fontsize: 11pt
    geometry: margin=1cm
bibliography: biblio.bib
nocite: |
  @Baioetal:2017
---

```{r, echo=FALSE, warning=FALSE, message=FALSE, comment=NA}
options(scipen = 999)

align <- 
  if (params$ext == "pdf") {
    "center"
  } else {
    "default"
  }

# check whether Info-rank should also be computed & shown
eval_IR <- 
  if (!is.null(params$psa_sims)) {
    TRUE
  } else {
    FALSE}
```

## Cost-effectiveness analysis 

The cost-effectiveness analysis is based on the maximisation of the expected utility, defined as the _monetary net benefit_ $nb_t=ke_t-c_t$. Here $t$ indicates one of the interventions (treatments) being assessed, while $(e,c)$ indicate the relevant measures of _effectiveness_ and _cost_. For each intervention, the expected utility is computed as $\mathcal{NB}_t=k\mbox{E}[e_t]-\mbox{E}[c_t]$. When comparing two interventions (say, $t=1$ vs $t=0$), or using a pairwise comparison, we can determine the ``best'' alternative by considering the difference in the expected utilities $\mbox{EIB}=\mathcal{NB}_1-\mathcal{NB}_0$. This can also be expressed in terms of the _population effectiveness and cost differentials_  $\mbox{EIB}=k\mbox{E}[\Delta_e]-\mbox{E}[\Delta_c]$, where $\Delta_e=\mbox{E}[e\mid\bm\theta_1]-\mbox{E}[e\mid\bm\theta_0]$ and $\Delta_c=\mbox{E}[c\mid\bm\theta_1]-\mbox{E}[c\mid\bm\theta_0]$ are the average effectiveness and cost, as function of the relevant model parameters $\bm\theta=(\bm\theta_0,\bm\theta_1)$.

This sub-section presents a summary table reporting basic economic results as well as the optimal decision, given the selected willingness-to-pay threshold $k=$`r params$wtp`. The table below presents a summary of the optimal decision, as well as the values of the Expected Incremental Benefit $\mbox{EIB}=k\mbox{E}[\Delta_e]-\mbox{E}[\Delta_c]$, Cost-Effectiveness Acceptability Curve $\mbox{CEAC}=\Pr(k\Delta_e-\Delta_c)$ and Incremental Cost-Effectiveness Ratio $\mbox{ICER}=\displaystyle\frac{\mbox{E}[\Delta_c]}{\mbox{E}[\Delta_e]}$, for the set willingness-to-pay value.

```{r, echo=echo, warning=FALSE, message=FALSE, comment=NA}
summary(m, wtp = params$wtp)
```

```{r child = 'section_ceplane.Rmd'}
```

```{r child = 'section_EIB.Rmd'}
```

```{r child = 'section_CEAC.Rmd'}
```

```{r child = 'section_CEAF.Rmd'}
```

```{r child = 'section_CEEF.Rmd'}
```

```{r child = 'section_EVPI.Rmd'}
```

```{r child = 'section_InfoRank.Rmd', eval=eval_IR}
```


## References

