---
title: "Biostatistics III in R"
author:
- Code by Johan Zetterqvist and Mark Clements
output:
  prettydoc::html_pretty:
    mathjax: https://biostat3.net/js/mathjax/tex-chtml.js
    theme: cayman
    highlight: github
---


# Exercise 13. Modelling the diet data using Cox regression #

-----------

Now fit a model to the localised melanoma data where the outcome is observed survival (i.e. all deaths are considered to be events).

```{r setup, cache=FALSE, message=FALSE, echo=FALSE}
library('knitr')
read_chunk('../q13.R')
opts_chunk$set(cache=FALSE)
```

You may have to install the required packages the first time you use them. You can install a package by `install.packages("package_of_interest")` for each package you require.

```{r loadDependencies, message=FALSE}
```
Load the melanoma data and explore it.

```{r loadPreprocess, results='hide'}
```

## (a) ## 

```{r 13.a, warning=FALSE, message=FALSE}
```

These two models are conceptually different since the Cox model
adjusts for ‘time’ even though this is not explicit in the
`coxph` function. In this example, ‘time’ refers to ‘time on
study’ (time since entry) which we do not expect to be a
strong confounder. That is, we would expect the estimates of the
effect of high energy to be similar for the two models, which
they are.

## (b) ## 

If we use a different timescale then this amounts to adjusting
for a different factor. As such, we would not expect the
estimates to be identical. Attained age, unlike time since
entry, is expected to be a confounder but we see that it is not
a strong confounder.
		
```{r 13.b, warning=FALSE, message=FALSE}
```
