Working with the R package BCEA

# Working with the R package BCEA

## Gianluca Baio

### [Department of Statistical Science](https://www.ucl.ac.uk/statistics/) | University College London

.title-small[
<svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;top:.1em;fill:#00acee;height:0.8em;">  [ comment ]  <path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"></path></svg>  [g.baio@ucl.ac.uk](mailto:g.baio@ucl.ac.uk)
<svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;top:.1em;fill:#EA7600;height:0.8em;">  [ comment ]  <path d="M503.52,241.48c-.12-1.56-.24-3.12-.24-4.68v-.12l-.36-4.68v-.12a245.86,245.86,0,0,0-7.32-41.15c0-.12,0-.12-.12-.24l-1.08-4c-.12-.24-.12-.48-.24-.6-.36-1.2-.72-2.52-1.08-3.72-.12-.24-.12-.6-.24-.84-.36-1.2-.72-2.4-1.08-3.48-.12-.36-.24-.6-.36-1-.36-1.2-.72-2.28-1.2-3.48l-.36-1.08c-.36-1.08-.84-2.28-1.2-3.36a8.27,8.27,0,0,0-.36-1c-.48-1.08-.84-2.28-1.32-3.36-.12-.24-.24-.6-.36-.84-.48-1.2-1-2.28-1.44-3.48,0-.12-.12-.24-.12-.36-1.56-3.84-3.24-7.68-5-11.4l-.36-.72c-.48-1-.84-1.8-1.32-2.64-.24-.48-.48-1.08-.72-1.56-.36-.84-.84-1.56-1.2-2.4-.36-.6-.6-1.2-1-1.8s-.84-1.44-1.2-2.28c-.36-.6-.72-1.32-1.08-1.92s-.84-1.44-1.2-2.16a18.07,18.07,0,0,0-1.2-2c-.36-.72-.84-1.32-1.2-2s-.84-1.32-1.2-2-.84-1.32-1.2-1.92-.84-1.44-1.32-2.16a15.63,15.63,0,0,0-1.2-1.8L463.2,119a15.63,15.63,0,0,0-1.2-1.8c-.48-.72-1.08-1.56-1.56-2.28-.36-.48-.72-1.08-1.08-1.56l-1.8-2.52c-.36-.48-.6-.84-1-1.32-1-1.32-1.8-2.52-2.76-3.72a248.76,248.76,0,0,0-23.51-26.64A186.82,186.82,0,0,0,412,62.46c-4-3.48-8.16-6.72-12.48-9.84a162.49,162.49,0,0,0-24.6-15.12c-2.4-1.32-4.8-2.52-7.2-3.72a254,254,0,0,0-55.43-19.56c-1.92-.36-3.84-.84-5.64-1.2h-.12c-1-.12-1.8-.36-2.76-.48a236.35,236.35,0,0,0-38-4H255.14a234.62,234.62,0,0,0-45.48,5c-33.59,7.08-63.23,21.24-82.91,39-1.08,1-1.92,1.68-2.4,2.16l-.48.48H124l-.12.12.12-.12a.12.12,0,0,0,.12-.12l-.12.12a.42.42,0,0,1,.24-.12c14.64-8.76,34.92-16,49.44-19.56l5.88-1.44c.36-.12.84-.12,1.2-.24,1.68-.36,3.36-.72,5.16-1.08.24,0,.6-.12.84-.12C250.94,20.94,319.34,40.14,367,85.61a171.49,171.49,0,0,1,26.88,32.76c30.36,49.2,27.48,111.11,3.84,147.59-34.44,53-111.35,71.27-159,24.84a84.19,84.19,0,0,1-25.56-59,74.05,74.05,0,0,1,6.24-31c1.68-3.84,13.08-25.67,18.24-24.59-13.08-2.76-37.55,2.64-54.71,28.19-15.36,22.92-14.52,58.2-5,83.28a132.85,132.85,0,0,1-12.12-39.24c-12.24-82.55,43.31-153,94.31-170.51-27.48-24-96.47-22.31-147.71,15.36-29.88,22-51.23,53.16-62.51,90.36,1.68-20.88,9.6-52.08,25.8-83.88-17.16,8.88-39,37-49.8,62.88-15.6,37.43-21,82.19-16.08,124.79.36,3.24.72,6.36,1.08,9.6,19.92,117.11,122,206.38,244.78,206.38C392.77,503.42,504,392.19,504,255,503.88,250.48,503.76,245.92,503.52,241.48Z"></path></svg>  [http://www.statistica.it/gianluca/](http://www.statistica.it/gianluca/)
<svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;top:.1em;fill:#EA7600;height:0.8em;">  [ comment ]  <path d="M503.52,241.48c-.12-1.56-.24-3.12-.24-4.68v-.12l-.36-4.68v-.12a245.86,245.86,0,0,0-7.32-41.15c0-.12,0-.12-.12-.24l-1.08-4c-.12-.24-.12-.48-.24-.6-.36-1.2-.72-2.52-1.08-3.72-.12-.24-.12-.6-.24-.84-.36-1.2-.72-2.4-1.08-3.48-.12-.36-.24-.6-.36-1-.36-1.2-.72-2.28-1.2-3.48l-.36-1.08c-.36-1.08-.84-2.28-1.2-3.36a8.27,8.27,0,0,0-.36-1c-.48-1.08-.84-2.28-1.32-3.36-.12-.24-.24-.6-.36-.84-.48-1.2-1-2.28-1.44-3.48,0-.12-.12-.24-.12-.36-1.56-3.84-3.24-7.68-5-11.4l-.36-.72c-.48-1-.84-1.8-1.32-2.64-.24-.48-.48-1.08-.72-1.56-.36-.84-.84-1.56-1.2-2.4-.36-.6-.6-1.2-1-1.8s-.84-1.44-1.2-2.28c-.36-.6-.72-1.32-1.08-1.92s-.84-1.44-1.2-2.16a18.07,18.07,0,0,0-1.2-2c-.36-.72-.84-1.32-1.2-2s-.84-1.32-1.2-2-.84-1.32-1.2-1.92-.84-1.44-1.32-2.16a15.63,15.63,0,0,0-1.2-1.8L463.2,119a15.63,15.63,0,0,0-1.2-1.8c-.48-.72-1.08-1.56-1.56-2.28-.36-.48-.72-1.08-1.08-1.56l-1.8-2.52c-.36-.48-.6-.84-1-1.32-1-1.32-1.8-2.52-2.76-3.72a248.76,248.76,0,0,0-23.51-26.64A186.82,186.82,0,0,0,412,62.46c-4-3.48-8.16-6.72-12.48-9.84a162.49,162.49,0,0,0-24.6-15.12c-2.4-1.32-4.8-2.52-7.2-3.72a254,254,0,0,0-55.43-19.56c-1.92-.36-3.84-.84-5.64-1.2h-.12c-1-.12-1.8-.36-2.76-.48a236.35,236.35,0,0,0-38-4H255.14a234.62,234.62,0,0,0-45.48,5c-33.59,7.08-63.23,21.24-82.91,39-1.08,1-1.92,1.68-2.4,2.16l-.48.48H124l-.12.12.12-.12a.12.12,0,0,0,.12-.12l-.12.12a.42.42,0,0,1,.24-.12c14.64-8.76,34.92-16,49.44-19.56l5.88-1.44c.36-.12.84-.12,1.2-.24,1.68-.36,3.36-.72,5.16-1.08.24,0,.6-.12.84-.12C250.94,20.94,319.34,40.14,367,85.61a171.49,171.49,0,0,1,26.88,32.76c30.36,49.2,27.48,111.11,3.84,147.59-34.44,53-111.35,71.27-159,24.84a84.19,84.19,0,0,1-25.56-59,74.05,74.05,0,0,1,6.24-31c1.68-3.84,13.08-25.67,18.24-24.59-13.08-2.76-37.55,2.64-54.71,28.19-15.36,22.92-14.52,58.2-5,83.28a132.85,132.85,0,0,1-12.12-39.24c-12.24-82.55,43.31-153,94.31-170.51-27.48-24-96.47-22.31-147.71,15.36-29.88,22-51.23,53.16-62.51,90.36,1.68-20.88,9.6-52.08,25.8-83.88-17.16,8.88-39,37-49.8,62.88-15.6,37.43-21,82.19-16.08,124.79.36,3.24.72,6.36,1.08,9.6,19.92,117.11,122,206.38,244.78,206.38C392.77,503.42,504,392.19,504,255,503.88,250.48,503.76,245.92,503.52,241.48Z"></path></svg>  [https://egon.stats.ucl.ac.uk/research/statistics-health-economics/](https://egon.stats.ucl.ac.uk/research/statistics-health-economics/)
<svg viewBox="0 0 496 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;top:.1em;fill:black;height:0.8em;">  [ comment ]  <path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"></path></svg>  [https://github.com/giabaio](https://github.com/giabaio)
<svg viewBox="0 0 496 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;top:.1em;fill:black;height:0.8em;">  [ comment ]  <path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"></path></svg>  [https://github.com/StatisticsHealthEconomics](https://github.com/StatisticsHealthEconomics)
<svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;top:.1em;fill:#00acee;height:0.8em;">  [ comment ]  <path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"></path></svg>  [@gianlubaio](https://twitter.com/gianlubaio)     
]

### ISPOR Short courses, Internetville

17 June 2021

.footer-left[
<span><a href="http://www.statistica.it/gianluca/"><img src="assets/logo.png" title="Go home" width="2.0%"></a></span> <span style="position: relative; bottom: 5px; color: #D5D5D5;"> &nbsp; &copy; Gianluca Baio (UCL)</span>
]

---

layout: true
.footer-left[
<span><a href="http://www.statistica.it/gianluca/"><img src="assets/logo.png" title="Go home" width="2.0%"></a></span> <span style="position: relative; bottom: 5px; color: #D5D5D5;"> &nbsp; &copy; Gianluca Baio (UCL)</span>
]

.footer-social[
&nbsp;<a href="https://twitter.com/giabaio"; title="Follow me on Twitter"><svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;top:.1em;fill:#bcc0c4;height:0.8em;bottom:1em;">
  [ comment ]
  <path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"></path>
</svg></a>&nbsp; &nbsp;<a href="mailto:g.baio@ucl.ac.uk"; title="Email me"><svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;top:.1em;fill:#bcc0c4;height:0.8em;">
  [ comment ]
  <path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"></path>
</svg></a>&nbsp; &nbsp;<a href="http://www.statistica.it/gianluca"; title="Visit my website"><svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;top:.1em;fill:#bcc0c4;height:0.8em;">
  [ comment ]
  <path d="M503.52,241.48c-.12-1.56-.24-3.12-.24-4.68v-.12l-.36-4.68v-.12a245.86,245.86,0,0,0-7.32-41.15c0-.12,0-.12-.12-.24l-1.08-4c-.12-.24-.12-.48-.24-.6-.36-1.2-.72-2.52-1.08-3.72-.12-.24-.12-.6-.24-.84-.36-1.2-.72-2.4-1.08-3.48-.12-.36-.24-.6-.36-1-.36-1.2-.72-2.28-1.2-3.48l-.36-1.08c-.36-1.08-.84-2.28-1.2-3.36a8.27,8.27,0,0,0-.36-1c-.48-1.08-.84-2.28-1.32-3.36-.12-.24-.24-.6-.36-.84-.48-1.2-1-2.28-1.44-3.48,0-.12-.12-.24-.12-.36-1.56-3.84-3.24-7.68-5-11.4l-.36-.72c-.48-1-.84-1.8-1.32-2.64-.24-.48-.48-1.08-.72-1.56-.36-.84-.84-1.56-1.2-2.4-.36-.6-.6-1.2-1-1.8s-.84-1.44-1.2-2.28c-.36-.6-.72-1.32-1.08-1.92s-.84-1.44-1.2-2.16a18.07,18.07,0,0,0-1.2-2c-.36-.72-.84-1.32-1.2-2s-.84-1.32-1.2-2-.84-1.32-1.2-1.92-.84-1.44-1.32-2.16a15.63,15.63,0,0,0-1.2-1.8L463.2,119a15.63,15.63,0,0,0-1.2-1.8c-.48-.72-1.08-1.56-1.56-2.28-.36-.48-.72-1.08-1.08-1.56l-1.8-2.52c-.36-.48-.6-.84-1-1.32-1-1.32-1.8-2.52-2.76-3.72a248.76,248.76,0,0,0-23.51-26.64A186.82,186.82,0,0,0,412,62.46c-4-3.48-8.16-6.72-12.48-9.84a162.49,162.49,0,0,0-24.6-15.12c-2.4-1.32-4.8-2.52-7.2-3.72a254,254,0,0,0-55.43-19.56c-1.92-.36-3.84-.84-5.64-1.2h-.12c-1-.12-1.8-.36-2.76-.48a236.35,236.35,0,0,0-38-4H255.14a234.62,234.62,0,0,0-45.48,5c-33.59,7.08-63.23,21.24-82.91,39-1.08,1-1.92,1.68-2.4,2.16l-.48.48H124l-.12.12.12-.12a.12.12,0,0,0,.12-.12l-.12.12a.42.42,0,0,1,.24-.12c14.64-8.76,34.92-16,49.44-19.56l5.88-1.44c.36-.12.84-.12,1.2-.24,1.68-.36,3.36-.72,5.16-1.08.24,0,.6-.12.84-.12C250.94,20.94,319.34,40.14,367,85.61a171.49,171.49,0,0,1,26.88,32.76c30.36,49.2,27.48,111.11,3.84,147.59-34.44,53-111.35,71.27-159,24.84a84.19,84.19,0,0,1-25.56-59,74.05,74.05,0,0,1,6.24-31c1.68-3.84,13.08-25.67,18.24-24.59-13.08-2.76-37.55,2.64-54.71,28.19-15.36,22.92-14.52,58.2-5,83.28a132.85,132.85,0,0,1-12.12-39.24c-12.24-82.55,43.31-153,94.31-170.51-27.48-24-96.47-22.31-147.71,15.36-29.88,22-51.23,53.16-62.51,90.36,1.68-20.88,9.6-52.08,25.8-83.88-17.16,8.88-39,37-49.8,62.88-15.6,37.43-21,82.19-16.08,124.79.36,3.24.72,6.36,1.08,9.6,19.92,117.11,122,206.38,244.78,206.38C392.77,503.42,504,392.19,504,255,503.88,250.48,503.76,245.92,503.52,241.48Z"></path>
</svg></a>&nbsp;
]

.footer-center[
HTA and BCEA
]

.footer-right[
ISPOR Short courses, 17 Jun 2021
]

---

# `BCEA`

## An `R` package for (Bayesian) cost-effectiveness analysis

### What is `BCEA` not?

- `BCEA` is **not** a package to automatically run a Bayesian analysis
   - It cannot build the health economic model for you
   - It does not prepare the data to be used in the model
   - It does not automatically run the MCMC simulations
   - It does not choose the prior distributions for you

### So what *is* it then?

- `BCEA`  provides a set of specific functions to systematically post-process the output of a Bayesian health economic model

- Uses `R` [http://cran.r-project.org/](http://cran.r-project.org/)
   -  Very good at interacting with standard MCMC software
   - `BUGS`: [www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml](www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml)
   - `JAGS`: [www.mcmc-jags.sourceforge.net/](www.mcmc-jags.sourceforge.net/)    
   - `rstan`: [https://mc-stan.org/users/interfaces/rstan](https://mc-stan.org/users/interfaces/rstan)
   - .red[**Free**] and there is a very large community of contributors
   - Specifically designed for statistical analysis and has very good graphical capabilities

---

# `BCEA`

## A `R` package for (Bayesian) cost-effectiveness analysis

### `BCEA` and its use directly in `R` are designed with these objectives in mind

1. Checking the model assumptions

- Do we mean what we mean (eg in terms of PSA simulations)?...
   - Simulation error (especially, **but not only**, for a Bayesian approach)

2. Produce the base-case economic evaluation
   - What’s the most cost-effective intervention, given current evidence?
   - Cost-effectiveness plane, Expected Incremental Benefit (as a function of `$k$`),...

--
 
3. Perform uncertainty analysis
   - Standard PSA (mandatory): Cost-effectiveness Plane, CEAC, ...
   - Fairly easy (but not always used): CEAF
   - More advanced/"too difficult" (rarely used): EVP(P)I/EVSI

4. Standardised reporting
   - Graphical tools (use **excellent** `R` facilities)

---

# `BCEA`

## An `R` package for (Bayesian) cost-effectiveness analysis

<span style="display:block; margin-top: -50px ;"></span>
 
.small[
<svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;">  [ comment ]  <path d="M503.52,241.48c-.12-1.56-.24-3.12-.24-4.68v-.12l-.36-4.68v-.12a245.86,245.86,0,0,0-7.32-41.15c0-.12,0-.12-.12-.24l-1.08-4c-.12-.24-.12-.48-.24-.6-.36-1.2-.72-2.52-1.08-3.72-.12-.24-.12-.6-.24-.84-.36-1.2-.72-2.4-1.08-3.48-.12-.36-.24-.6-.36-1-.36-1.2-.72-2.28-1.2-3.48l-.36-1.08c-.36-1.08-.84-2.28-1.2-3.36a8.27,8.27,0,0,0-.36-1c-.48-1.08-.84-2.28-1.32-3.36-.12-.24-.24-.6-.36-.84-.48-1.2-1-2.28-1.44-3.48,0-.12-.12-.24-.12-.36-1.56-3.84-3.24-7.68-5-11.4l-.36-.72c-.48-1-.84-1.8-1.32-2.64-.24-.48-.48-1.08-.72-1.56-.36-.84-.84-1.56-1.2-2.4-.36-.6-.6-1.2-1-1.8s-.84-1.44-1.2-2.28c-.36-.6-.72-1.32-1.08-1.92s-.84-1.44-1.2-2.16a18.07,18.07,0,0,0-1.2-2c-.36-.72-.84-1.32-1.2-2s-.84-1.32-1.2-2-.84-1.32-1.2-1.92-.84-1.44-1.32-2.16a15.63,15.63,0,0,0-1.2-1.8L463.2,119a15.63,15.63,0,0,0-1.2-1.8c-.48-.72-1.08-1.56-1.56-2.28-.36-.48-.72-1.08-1.08-1.56l-1.8-2.52c-.36-.48-.6-.84-1-1.32-1-1.32-1.8-2.52-2.76-3.72a248.76,248.76,0,0,0-23.51-26.64A186.82,186.82,0,0,0,412,62.46c-4-3.48-8.16-6.72-12.48-9.84a162.49,162.49,0,0,0-24.6-15.12c-2.4-1.32-4.8-2.52-7.2-3.72a254,254,0,0,0-55.43-19.56c-1.92-.36-3.84-.84-5.64-1.2h-.12c-1-.12-1.8-.36-2.76-.48a236.35,236.35,0,0,0-38-4H255.14a234.62,234.62,0,0,0-45.48,5c-33.59,7.08-63.23,21.24-82.91,39-1.08,1-1.92,1.68-2.4,2.16l-.48.48H124l-.12.12.12-.12a.12.12,0,0,0,.12-.12l-.12.12a.42.42,0,0,1,.24-.12c14.64-8.76,34.92-16,49.44-19.56l5.88-1.44c.36-.12.84-.12,1.2-.24,1.68-.36,3.36-.72,5.16-1.08.24,0,.6-.12.84-.12C250.94,20.94,319.34,40.14,367,85.61a171.49,171.49,0,0,1,26.88,32.76c30.36,49.2,27.48,111.11,3.84,147.59-34.44,53-111.35,71.27-159,24.84a84.19,84.19,0,0,1-25.56-59,74.05,74.05,0,0,1,6.24-31c1.68-3.84,13.08-25.67,18.24-24.59-13.08-2.76-37.55,2.64-54.71,28.19-15.36,22.92-14.52,58.2-5,83.28a132.85,132.85,0,0,1-12.12-39.24c-12.24-82.55,43.31-153,94.31-170.51-27.48-24-96.47-22.31-147.71,15.36-29.88,22-51.23,53.16-62.51,90.36,1.68-20.88,9.6-52.08,25.8-83.88-17.16,8.88-39,37-49.8,62.88-15.6,37.43-21,82.19-16.08,124.79.36,3.24.72,6.36,1.08,9.6,19.92,117.11,122,206.38,244.78,206.38C392.77,503.42,504,392.19,504,255,503.88,250.48,503.76,245.92,503.52,241.48Z"></path></svg> [www.statistica.it/gianluca/BCEA](www.statistica.it/gianluca/BCEA)     
<svg viewBox="0 0 496 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;top:.1em;fill:black;height:0.8em;">  [ comment ]  <path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"></path></svg>  [https://github.com/giabaio/BCEA](https://github.com/giabaio/BCEA)
]

---

---

# How does `BCEA` work?

.panelset[
.panel[
.panel-name[Installation]
- `BCEA` is available from [CRAN](https://cran.r-project.org/)
   - Current *stable* version: 2.3-1.1 (26 August 2019)

- But it is also under constant development in the [GitHub repository](https://github.com/giabaio/BCEA)
   - Current *stable* version: 2.3-2 (30 January 2020)
   - Current *development* version: 2.4-1 (5 February 2021) &ndash; **major** update (soon to be released!)

```r
# Install BCEA (only required once and needs an internet connection!).

# You can either get the "official" version from CRAN
install.packages("BCEA")

# Or the development version from the GitHub repository
devtools::install_github("giabaio/BCEA")               # stable version (2.3-2)

devtools::install_github("giabaio/BCEA",ref="devel")   # development version (2.4-1)
```

<span style="display:block; margin-top: 30px ;"></span>
NB: The beauty of the GitHub version is that it can be updated on the fly and be immediately available for users!
]

```r
library(dplyr)  # (Not necessary - helpful for data manipulation!)

library(BCEA)   # Then loads the package (so you can access its functions)
data(Vaccine)   # Loads an example dataset 
```

<span style="display:block; margin-top: 40px ;"></span>
- The "Vaccine" example is a fictional cost-effectiveness model for and influenza vaccine, based on evidence synthesis (and a real case)

- 2 treatment options ("Standard of care" vs "Vaccination") and overall 63 parameters

- Discussed in details in <svg viewBox="0 0 576 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;">  [ comment ]  <path d="M542.22 32.05c-54.8 3.11-163.72 14.43-230.96 55.59-4.64 2.84-7.27 7.89-7.27 13.17v363.87c0 11.55 12.63 18.85 23.28 13.49 69.18-34.82 169.23-44.32 218.7-46.92 16.89-.89 30.02-14.43 30.02-30.66V62.75c.01-17.71-15.35-31.74-33.77-30.7zM264.73 87.64C197.5 46.48 88.58 35.17 33.78 32.05 15.36 31.01 0 45.04 0 62.75V400.6c0 16.24 13.13 29.78 30.02 30.66 49.49 2.6 149.59 12.11 218.77 46.95 10.62 5.35 23.21-1.94 23.21-13.46V100.63c0-5.29-2.62-10.14-7.27-12.99z"></path></svg> [Baio et al, 2017](http://www.statistica.it/gianluca/book/bcea/) and <svg viewBox="0 0 384 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;">  <g label="icon" id="layer6" groupmode="layer">    <path id="path2" d="M 120.19265,177.73779 C 123.18778,77.35076 64.277527,63.999998 64.277527,63.999998 v 31.26245 C 40.834519,83.611374 18.32863,81.929634 18.32863,81.929634 V 337.10903 c 0,0 98.10414,-11.41744 98.10414,84.40952 0,0 36.58424,-153.37442 248.86103,26.48145 0,-61.59342 0.37757,-216.93925 0.37757,-268.28471 C 169.9561,37.131382 120.1931,177.73779 120.1931,177.73779 Z m 187.20631,173.82056 -12.37599,-97.65441 h -0.448 l -40.72819,97.65441 h -17.55994 l -38.9362,-97.65441 h -0.448 l -14.17589,97.65441 h -43.87514 l 28.8015,-169.61925 h 43.42716 l 34.43518,90.6496 36.46566,-90.6496 h 43.87513 l 25.6817,169.61925 h -44.13938 z" style="stroke-width:0.0675239"></path>  </g></svg> [Baio and Dawid, 2011](https://pubmed.ncbi.nlm.nih.gov/21930515/)

- In this case, PSA simulations obtained from a full Bayesian model, but could be done in a spreadsheet and imported into `R`
]

```r
# Creates a matrix with the underlying model simulations
inp = CreateInputs(vaccine, `print.lincom=FALSE`)           `# NB: this option will be slightly different in 2.4-1!`
# Visualise the output
inp$mat `%>% as_tibble()`                                   `# "piping" ('%>%') and formatting nicely`
```

```
# A tibble: 1,000 x 56
   Adverse.events Death.1.1. Death.2.1. Death.2.2. GP.1.1. GP.2.1. GP.2.2. Hospital.1.1. Hospital.2.1. Hospital.2.2. Infected.1.1. Infected.2.1. Infected.2.2. Mild.Compl.1.1. Mild.Compl.2.1. Mild.Compl.2.2. Pneumonia.1.1. Pneumonia.2.1. Pneumonia.2.2. Trt.1.1.1. Trt.2.1.1. Trt.1.2.1. Trt.2.2.1.
            <dbl>      <dbl>      <dbl>      <dbl>   <dbl>   <dbl>   <dbl>         <dbl>         <dbl>         <dbl>         <dbl>         <dbl>         <dbl>           <dbl>           <dbl>           <dbl>          <dbl>          <dbl>          <dbl>      <dbl>      <dbl>      <dbl>      <dbl>
 1           1466          1          0          0    1664     958     230             0             1             0          5992          3401           876             691             405             102             18             15              5        714        565        411        330
 2           5329          1          1          0    1414     748     276             0             0             1          7471          4024          1536             570             308             112             12             15              3        588        463        322        255
 3           5203          1          1          0     809     489      80             0             0             0          6718          4300           788             332             214              40             10              2              4        345        266        211        174
 4           2351          2          0          0    1761    1157     261             1             0             0          4837          3269           702             739             479             109             19             17              5        735        609        505        395
 5           8303          1          2          0    2472     964     432             1             1             0          4749          1894           846            1049             425             177             25             11              2       1048        838        427        337
 6           3607          1          1          0    2224    1342     260             1             0             0          4938          2976           596             915             560             100             35             21              2        962        720        575        455
 7           6304          4          1          1    3478    1107     591             2             1             0         11080          3547          2045            1505             482             247             66             19             10       1437       1258        449        388
 8           4337          1          1          1    1483     799     189             0             0             0          3867          2164           525             622             333              65             22              7              3        630        501        351        259
 9           5482          0          0          0    1587     798     279             0             0             0          5163          2532           910             675             332             115             25             11              4        697        535        338        269
10           3125          2          2          0    2578    1681     243             0             0             0          7265          4766           700            1063             711             102             41             17              3       1082        864        699        577
# … with 990 more rows, and 33 more variables: Trt.1.2.2. <dbl>, Trt.2.2.2. <dbl>, beta.1. <dbl>, beta.2. <dbl>, beta.3. <dbl>, beta.4. <dbl>, beta.5. <dbl>, beta.6. <dbl>, beta.7. <dbl>, delta <dbl>, eta <dbl>, gamma.1. <dbl>, gamma.2. <dbl>, lambda <dbl>, n.1.2. <dbl>, n.2.2. <dbl>, phi <dbl>,
#   pi.1.2. <dbl>, psi.1. <dbl>, psi.2. <dbl>, psi.3. <dbl>, psi.4. <dbl>, psi.5. <dbl>, psi.6. <dbl>, psi.7. <dbl>, psi.8. <dbl>, q.1. <dbl>, q.4. <dbl>, q.5. <dbl>, q.6. <dbl>, q.7. <dbl>, rho.2. <dbl>, xi <dbl>
```
]

```r
# Defines the number of simulations considered
n.sims=`inp$mat %>% nrow()`                             `# applies the function 'nrow' (number of rows) to the object 'inp$mat'`

`# NB: in R 4.1.0, can also use 'native' pipe ('|>')`
                                                       `# (probably a bit quicker, but in most cases, may be immaterial...)`

# Aggregates the model inputs to compute (e,c)
QALYs.inf = QALYs.pne <- QALYs.hosp <- QALYs.adv <- QALYs.death <- matrix(0,n.sims,2)
for (t in 1:2) {
  QALYs.inf[,t] = ((Infected[,t,1] + Infected[,t,2])*omega[,1]/365)/N
  QALYs.pne[,t] = ((Pneumonia[,t,1] + Pneumonia[,t,2])*omega[,4]/365)/N
  QALYs.hosp[,t] = ((Hospital[,t,1] + Hospital[,t,2])*omega[,5]/365)/N
  QALYs.death[,t] = ((Death[,t,1] + Death[,t,2])*omega[,6])/N
}
QALYs.adv[,2] = (Adverse.events*omega[,7]/365)/N
e = -(QALYs.inf + QALYs.pne + QALYs.adv + QALYs.hosp + QALYs.death) + ...
```

<span style="display:block; margin-top: 40px ;"></span>
- NB: The data stored in the `Vaccine` object (built-in in `BCEA`) already contains the objects `e,c` that can be used to run the decision analysis...

- So, this step is actually not needed (but documented in <svg viewBox="0 0 576 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;">  [ comment ]  <path d="M542.22 32.05c-54.8 3.11-163.72 14.43-230.96 55.59-4.64 2.84-7.27 7.89-7.27 13.17v363.87c0 11.55 12.63 18.85 23.28 13.49 69.18-34.82 169.23-44.32 218.7-46.92 16.89-.89 30.02-14.43 30.02-30.66V62.75c.01-17.71-15.35-31.74-33.77-30.7zM264.73 87.64C197.5 46.48 88.58 35.17 33.78 32.05 15.36 31.01 0 45.04 0 62.75V400.6c0 16.24 13.13 29.78 30.02 30.66 49.49 2.6 149.59 12.11 218.77 46.95 10.62 5.35 23.21-1.94 23.21-13.46V100.63c0-5.29-2.62-10.14-7.27-12.99z"></path></svg> [Baio et al, 2017](http://www.statistica.it/gianluca/book/bcea/))
]

```r
cbind(e,c) %>% as_tibble(`.name_repair="universal"`)     `# ensures that the columns are named` 
```

```
# A tibble: 1,000 x 4
   Status.Quo...1 Vaccination...2 Status.Quo...3 Vaccination...4
            <dbl>           <dbl>          <dbl>           <dbl>
 1      -0.00105        -0.000899          10.4            16.3 
 2      -0.000884       -0.000732           5.83            9.37
 3      -0.000890       -0.000698           5.78           15.9 
 4      -0.00164        -0.00114           12.2            18.7 
 5      -0.00135        -0.000957           9.79           16.5 
 6      -0.00143        -0.000936           6.56            9.69
 7      -0.000960       -0.00105            8.45           11.3 
 8      -0.00181        -0.00139            6.76            9.99
 9      -0.000842       -0.000556           3.60           10.1 
10      -0.00168        -0.00105            4.09           11.0 
# … with 990 more rows
```

- These calculations *can* be done also in a spreadsheet (nothing more than algebra, **once you have the simulations**)
]
]

---

- At this point, we are ready to call the function `bcea` that runs the economic analysis, for example something like

```r
treats = c("Status quo","Vaccination")
m = bcea(e=e,c=c,ref=2,interventions=treats,Kmax=50000)
```

- The inputs to the function are
   - `e`: a **matrix** containing the simulations for the clinical benefits (that is `$n_{\rm{sim}}\times n_{\rm{int}}$` values)
   - `c`: a **matrix** containing the simulations for the costs (that is `$n_{\rm{sim}}\times n_{\rm{int}}$` values)
   -  `ref`: an indication of which intervention is to be taken as reference (default: the intervention in the first column of `e` or `c`)
   - `interventions`: a vector of labels for the interventions being compared 
   - `Kmax`: the maximum value of `$k$`, the parameter of willingness to pay

- The output is an object `m` containing several elements

```r
names(m)
```

```
 [1] "n.sim"         "n.comparators" "n.comparisons" "delta.e"       "delta.c"       "ICER"          "Kmax"          "k"             "ceac"          "ib"            "eib"           "kstar"         "best"          "U"             "vi"            "Ustar"         "ol"            "evi"          
[19] "interventions" "ref"           "comp"          "step"          "e"             "c"            
```

---

Can visualise the output in various formats (tables/graphs)

```r
# The 'summary' "method" produces a tabular output
summary(m)
```

```

Cost-effectiveness analysis summary

Reference intervention:  Vaccination
Comparator intervention: Status quo

Optimal decision: choose Status quo for k<20100 and Vaccination for k>=20100

Analysis for willingness to pay parameter k = 25000

Expected utility
Status quo           -36.054
Vaccination          -34.826

EIB  CEAC  ICER
Vaccination vs Status quo 1.2284 0.529 20098

Optimal intervention (max expected utility) for k=25000: Vaccination
           
EVPI 2.4145
```

---

Can visualise the output in various formats (tables/graphs)

```r
# The 'plot' "method" produces a *specific* version of graphical output
plot(m)
```

---

```r
ceplane.plot(m,wtp=20000,xlim=c(-.002,.002),ylim=c(-10,20))
```

---

```r
# Using 'ggplot', you can go crazy with customisation...
ceplane.plot(m,wtp=10000,`graph="gg"`,point_colors="blue",point_sizes=.8,area_color="springgreen3")
```

<span style="display:block; margin-top: -40px ;"></span>
.small[<svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;">  [ comment ]  <path d="M503.52,241.48c-.12-1.56-.24-3.12-.24-4.68v-.12l-.36-4.68v-.12a245.86,245.86,0,0,0-7.32-41.15c0-.12,0-.12-.12-.24l-1.08-4c-.12-.24-.12-.48-.24-.6-.36-1.2-.72-2.52-1.08-3.72-.12-.24-.12-.6-.24-.84-.36-1.2-.72-2.4-1.08-3.48-.12-.36-.24-.6-.36-1-.36-1.2-.72-2.28-1.2-3.48l-.36-1.08c-.36-1.08-.84-2.28-1.2-3.36a8.27,8.27,0,0,0-.36-1c-.48-1.08-.84-2.28-1.32-3.36-.12-.24-.24-.6-.36-.84-.48-1.2-1-2.28-1.44-3.48,0-.12-.12-.24-.12-.36-1.56-3.84-3.24-7.68-5-11.4l-.36-.72c-.48-1-.84-1.8-1.32-2.64-.24-.48-.48-1.08-.72-1.56-.36-.84-.84-1.56-1.2-2.4-.36-.6-.6-1.2-1-1.8s-.84-1.44-1.2-2.28c-.36-.6-.72-1.32-1.08-1.92s-.84-1.44-1.2-2.16a18.07,18.07,0,0,0-1.2-2c-.36-.72-.84-1.32-1.2-2s-.84-1.32-1.2-2-.84-1.32-1.2-1.92-.84-1.44-1.32-2.16a15.63,15.63,0,0,0-1.2-1.8L463.2,119a15.63,15.63,0,0,0-1.2-1.8c-.48-.72-1.08-1.56-1.56-2.28-.36-.48-.72-1.08-1.08-1.56l-1.8-2.52c-.36-.48-.6-.84-1-1.32-1-1.32-1.8-2.52-2.76-3.72a248.76,248.76,0,0,0-23.51-26.64A186.82,186.82,0,0,0,412,62.46c-4-3.48-8.16-6.72-12.48-9.84a162.49,162.49,0,0,0-24.6-15.12c-2.4-1.32-4.8-2.52-7.2-3.72a254,254,0,0,0-55.43-19.56c-1.92-.36-3.84-.84-5.64-1.2h-.12c-1-.12-1.8-.36-2.76-.48a236.35,236.35,0,0,0-38-4H255.14a234.62,234.62,0,0,0-45.48,5c-33.59,7.08-63.23,21.24-82.91,39-1.08,1-1.92,1.68-2.4,2.16l-.48.48H124l-.12.12.12-.12a.12.12,0,0,0,.12-.12l-.12.12a.42.42,0,0,1,.24-.12c14.64-8.76,34.92-16,49.44-19.56l5.88-1.44c.36-.12.84-.12,1.2-.24,1.68-.36,3.36-.72,5.16-1.08.24,0,.6-.12.84-.12C250.94,20.94,319.34,40.14,367,85.61a171.49,171.49,0,0,1,26.88,32.76c30.36,49.2,27.48,111.11,3.84,147.59-34.44,53-111.35,71.27-159,24.84a84.19,84.19,0,0,1-25.56-59,74.05,74.05,0,0,1,6.24-31c1.68-3.84,13.08-25.67,18.24-24.59-13.08-2.76-37.55,2.64-54.71,28.19-15.36,22.92-14.52,58.2-5,83.28a132.85,132.85,0,0,1-12.12-39.24c-12.24-82.55,43.31-153,94.31-170.51-27.48-24-96.47-22.31-147.71,15.36-29.88,22-51.23,53.16-62.51,90.36,1.68-20.88,9.6-52.08,25.8-83.88-17.16,8.88-39,37-49.8,62.88-15.6,37.43-21,82.19-16.08,124.79.36,3.24.72,6.36,1.08,9.6,19.92,117.11,122,206.38,244.78,206.38C392.77,503.42,504,392.19,504,255,503.88,250.48,503.76,245.92,503.52,241.48Z"></path></svg> [https://ggplot2.tidyverse.org/](https://ggplot2.tidyverse.org/)]

---

```r
# Plots the Cost-Effectiveness Acceptability Curve
ceac.plot(m)
```

---

```r
# Plots the Expected Value of Partial Information (EVPI)
evi.plot(m)
```

---

# Specialised plots

- Can generate a *contour* plot of the cost-effectiveness plane and estimate the proportion of points in each quadrant

```r
# "Basic" contourplot
contour(m)
```
]

.right-column[
<img src="./img/howwork18-1.png" style="display: block; margin: auto;" title="" width="65%">
]

---

- The specialised function `contour2` also shows the **sustainability area**

```r
contour2(m)
```

<img src="./img/howwork19-1.png" style="display: block; margin: auto;" title="" width="80%">
]

```r
contour2(m,wtp=100)
```

<img src="./img/howwork20-1.png" style="display: block; margin: auto;" title="" width="80%">
]
---

```r
ceef.plot(m,print.plot=FALSE)
```

```

Cost-effectiveness efficiency frontier summary

Interventions on the efficiency frontier:
            Effectiveness   Costs Increase slope Increase angle
Status quo    -0.00105595  9.6555             NA             NA
Vaccination   -0.00080537 14.6914          20098         1.5707
```
]

```r
ceef.plot(m,print.summary=FALSE)
```

<img src="./img/howwork20tris-1.png" style="display: block; margin: auto;" title="" width="80%">
]---

# Exporting graphical output

- `R` has excellent graphical facilities and the graphs produced by `BCEA` can be easily exported to many different formats

```r
# "Opens" the graphical device
pdf("NAME_OF_THE_FILE",width=`8`,height=`8`)      `# for 'pdf', units are in inches`
# Makes the plot
ceplane.plot(`BCEA_OBJECT`)                     `# of course, specify whatever name you've chosen when creating the object...`
# "Closes" the graphical device
dev.off()

# "Open" the graphical device"
jpeg("NAME_OF_FILE.jpg",width=`480`,height=`480`)  `# for 'jpeg' units are in px`
# Makes the plot
ceplane.plot(BCEA_OBJECT)
# "Closes" the graphical device
dev.off()
```

<span style="display:block; margin-top: 30px ;"></span>
**NB**: `Rstudio` and [`rmarkdown`](https://rmarkdown.rstudio.com/) can do even more &ndash; that's for another time...
---

---

# Multiple treatment comparisons
## Probabilistic "depression model"

- Fictional model comparing antidepressants to cognitive behaviour therapy (CBT) and no treatment in people with depression

- Statistical modelling based on evidence synthesis
   - Benefits: based on QALYs
   - Costs: associated with treatments and various resources use
   
- Economic modelling: two matrices with relevant population summaries
   - `effects`
   - `costs`
   
<span style="display:block; margin-top: 30px ;"></span>
- NB: The details of the actual modelling are *not* important for the purposes of demonstrating the example...
   
---

count: false
# Multiple treatment comparisons
## Probabilistic "depression model"

```r
# Intervention labels
t.names<-c("No treatment","CBT","Antidepressant")

# "Standard" analysis: pairwise comparisons
depression.bcea = bcea(effects,costs,
                       interventions=t.names,`ref=3`)  
# `the third intervention is the reference`

# Plots the results
plot(depression.bcea)
```
]
.pull-right[
<img src="./img/depression3-1.png" style="display: block; margin: auto;" width="90%">

]

---

count: false
# Multiple treatment comparisons
## Probabilistic "depression model"

```r
# For `multiple treatment comparison`
depression.multi.ce = `multi.ce`(depression.bcea)

# Specialised plot method
`mce.plot`(depression.multi.ce,pos=c(1,0.8),
           graph=c("base","ggplot2"))
```
]
.pull-right[
<img src="./img/depression5-1.png" style="display: block; margin: auto;" width="90%">

]

---

count: false
# Multiple treatment comparisons
## Probabilistic "depression model"

.pull-left[
<span style="display:block; margin-top: 20px ;"></span>
- Can use `ggplot` to customise the graph

```r
mce.plot(depression.multi.ce,pos=c(1,1),graph="ggplot2") + 
  ggplot2::stat_summary(fun=max, geom="line", 
                        colour="grey25", alpha=.3, lwd=2.5)
```
]
.pull-right[
<img src="./img/depression7-1.png" style="display: block; margin: auto;" width="90%">
]

---

count: false
# Multiple treatment comparisons
## Probabilistic "depression model"

.pull-left[
<span style="display:block; margin-top: 20px ;"></span>
- Can use a specialised plotting method for the *cost-effectiveness acceptability **frontier***

```r
# Specialised plot
ceaf.plot(depression.multi.ce)
```
]
.pull-right[
<img src="./img/depression9-1.png" style="display: block; margin: auto;" width="90%">
]

---

# `BCEAweb`

-  Inspired by similar projects &ndash; eg [SAVI](http://savi.shef.ac.uk/SAVI/)

- Create a web interface to use BCEA without even opening R (or even having it installed on your computer!)
<span style="display:block; margin-top: 40px ;"></span>

- Typical work flow
   1. Design the economic model (eg Markov model, decision tree, ...)
   2. Run the statistical analysis to estimate the quantities of interest (eg survival analysis, evidence synthesis, ...)
   3. Run the economic model and obtain "PSA samples"

--
<span style="display:block; margin-top: 40px ;"></span>
  
   4. Upload "PSA samples", including values for `$(e,c)$` to `BCEAweb`
   5. Use `BCEA` in the background to do **all** the economic analysis
   6. Create reports that can be used as the basis for papers, reimbursement files, ...

---

```r
# Creates a matrix with the underlying model simulations
inp = CreateInputs(vaccine, print.lincom=FALSE)

# Runs BCEAweb
BCEAweb(e=e,                 # matrix of simulations for the effectiveness
        c=c,                 # matrix of simulations for the costs
        parameters=inp$mat   # matrix of simulations for all the model parameters
       )
```

- `BCEAweb` exists as a standalone webapp
   
   - Can access it <svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;">  [ comment ]  <path d="M503.52,241.48c-.12-1.56-.24-3.12-.24-4.68v-.12l-.36-4.68v-.12a245.86,245.86,0,0,0-7.32-41.15c0-.12,0-.12-.12-.24l-1.08-4c-.12-.24-.12-.48-.24-.6-.36-1.2-.72-2.52-1.08-3.72-.12-.24-.12-.6-.24-.84-.36-1.2-.72-2.4-1.08-3.48-.12-.36-.24-.6-.36-1-.36-1.2-.72-2.28-1.2-3.48l-.36-1.08c-.36-1.08-.84-2.28-1.2-3.36a8.27,8.27,0,0,0-.36-1c-.48-1.08-.84-2.28-1.32-3.36-.12-.24-.24-.6-.36-.84-.48-1.2-1-2.28-1.44-3.48,0-.12-.12-.24-.12-.36-1.56-3.84-3.24-7.68-5-11.4l-.36-.72c-.48-1-.84-1.8-1.32-2.64-.24-.48-.48-1.08-.72-1.56-.36-.84-.84-1.56-1.2-2.4-.36-.6-.6-1.2-1-1.8s-.84-1.44-1.2-2.28c-.36-.6-.72-1.32-1.08-1.92s-.84-1.44-1.2-2.16a18.07,18.07,0,0,0-1.2-2c-.36-.72-.84-1.32-1.2-2s-.84-1.32-1.2-2-.84-1.32-1.2-1.92-.84-1.44-1.32-2.16a15.63,15.63,0,0,0-1.2-1.8L463.2,119a15.63,15.63,0,0,0-1.2-1.8c-.48-.72-1.08-1.56-1.56-2.28-.36-.48-.72-1.08-1.08-1.56l-1.8-2.52c-.36-.48-.6-.84-1-1.32-1-1.32-1.8-2.52-2.76-3.72a248.76,248.76,0,0,0-23.51-26.64A186.82,186.82,0,0,0,412,62.46c-4-3.48-8.16-6.72-12.48-9.84a162.49,162.49,0,0,0-24.6-15.12c-2.4-1.32-4.8-2.52-7.2-3.72a254,254,0,0,0-55.43-19.56c-1.92-.36-3.84-.84-5.64-1.2h-.12c-1-.12-1.8-.36-2.76-.48a236.35,236.35,0,0,0-38-4H255.14a234.62,234.62,0,0,0-45.48,5c-33.59,7.08-63.23,21.24-82.91,39-1.08,1-1.92,1.68-2.4,2.16l-.48.48H124l-.12.12.12-.12a.12.12,0,0,0,.12-.12l-.12.12a.42.42,0,0,1,.24-.12c14.64-8.76,34.92-16,49.44-19.56l5.88-1.44c.36-.12.84-.12,1.2-.24,1.68-.36,3.36-.72,5.16-1.08.24,0,.6-.12.84-.12C250.94,20.94,319.34,40.14,367,85.61a171.49,171.49,0,0,1,26.88,32.76c30.36,49.2,27.48,111.11,3.84,147.59-34.44,53-111.35,71.27-159,24.84a84.19,84.19,0,0,1-25.56-59,74.05,74.05,0,0,1,6.24-31c1.68-3.84,13.08-25.67,18.24-24.59-13.08-2.76-37.55,2.64-54.71,28.19-15.36,22.92-14.52,58.2-5,83.28a132.85,132.85,0,0,1-12.12-39.24c-12.24-82.55,43.31-153,94.31-170.51-27.48-24-96.47-22.31-147.71,15.36-29.88,22-51.23,53.16-62.51,90.36,1.68-20.88,9.6-52.08,25.8-83.88-17.16,8.88-39,37-49.8,62.88-15.6,37.43-21,82.19-16.08,124.79.36,3.24.72,6.36,1.08,9.6,19.92,117.11,122,206.38,244.78,206.38C392.77,503.42,504,392.19,504,255,503.88,250.48,503.76,245.92,503.52,241.48Z"></path></svg>  [here](https://egon.stats.ucl.ac.uk/projects/BCEAweb/) 
   
- **Or**, you can launch your own "local" version from the `BCEA` package (as in the code above)!
   
   - This will launch a web page from which you can manipulate your output (<svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;">  [ comment ]  <path d="M256 8c137 0 248 111 248 248S393 504 256 504 8 393 8 256 119 8 256 8zm-28.9 143.6l75.5 72.4H120c-13.3 0-24 10.7-24 24v16c0 13.3 10.7 24 24 24h182.6l-75.5 72.4c-9.7 9.3-9.9 24.8-.4 34.3l11 10.9c9.4 9.4 24.6 9.4 33.9 0L404.3 273c9.4-9.4 9.4-24.6 0-33.9L271.6 106.3c-9.4-9.4-24.6-9.4-33.9 0l-11 10.9c-9.5 9.6-9.3 25.1.4 34.4z"></path></svg> Live Demo)

---
class: thankyou-michelle