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

# Exercise 25. Localised melanoma : generating and analysing a nested case-control (NCC) study #

-----------

```{r setup, cache=FALSE, message=FALSE, echo=FALSE}
library('knitr')
read_chunk('../q25.R')
opts_chunk$set(cache=FALSE)
```


```{r loadDependencies, message=FALSE}
```

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

```{r ex_25_coxph,  message=FALSE, warning=FALSE}
```

## (a) ## 

There are 5318 individuals in the study that we would need to
        collect data for if we were to use the complete cohort
        of patients.
		
```{r  n_ind,  message=FALSE, warning=FALSE}
```

## (b) ## 
960 cancer patients die from melanoma during the first 10 years
        of follow-up.

```{r  n_event,  message=FALSE, warning=FALSE}
```

## (c1) ## 

```{r gen_ncc,  message=FALSE, warning=FALSE, results='asis'}
```

## (c2) ## 

```{r clogit,  message=FALSE, warning=FALSE}
```

## (d) ## 

```{r n_unique_ncc,  message=FALSE, warning=FALSE}
```

## (e) ## 
Note that, since every nested case-control study is different,
        the parameter estimates you obtain will not be identical to
        those above. However, the hazard ratios from the two models
        should be very similar. The standard errors are slightly larger
        for the nested case-control study since the estimates are based
        on a sample from the full cohort. Loss of precision is the
        trade-off we have to make when designing a nested
        case-control study. The precision can be improved by adding more
        controls to each case.

```{r compare_coh_ncc,  message=FALSE, warning=FALSE}
```

## (f) ## 
We see that there is sampling variation in
        the parameter estimates from the five nested case-control
        studies but they are centered on the full cohort estimate. We
        see that the standard errors of the estimates from the nested
        case-control studies are larger than for the full cohort but
        there is some sampling variation.
		
```{r loop_ncc,  message=FALSE, warning=FALSE, results='hide'}
```

