---
title: "Biostatistics III in R"
author:
- Code by Mark Clements
output:
  prettydoc::html_pretty:
    theme:cayman
    highlight: github
---

# Exercise 23. Calculating SMRs/SIRs #

-----------

```{r setup, cache=FALSE, message=FALSE, echo=FALSE}
library('knitr')
read_chunk('../q23.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. Restrict the data to the localised status of the melanoma and to the 10 firts years of follow-up. Use the time-on-study as the timescale. define the event as death from cancer.

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


The standardized mortality ratio (SMR) is the ratio of the observed
    number of deaths in the study population to the number that would be
    expected if the study population experienced the same mortality as
    the standard population. It is an indirectly standardized rate. When
    studying disease incidence the corresponding quantity is called a
    standardized incidence ratio (SIR). These measures are typically
    used when the entire study population is considered ‘exposed’.
    Rather than following-up both the exposed study population and an
    unexposed control population and comparing the two estimated rates
    we instead only estimate the rate (or number of events) in the study
    population and compare this to the expected rate (expected number
    of events) for the standard population. For example, we might study
    disease incidence or mortality among individuals with a certain
    occupation (farmers, painters, airline cabin crew) or cancer
    incidence in a cohort exposed to ionising radiation.

In the analysis of cancer patient survival we typically estimate
    _excess mortality_ (observed - expected deaths). The
    SMR (observed/expected deaths) is a measure of _relative
    mortality_. The estimation of observed and expected numbers
    of deaths are performed in an identical manner for each measure but
    with the SMR we assume that the effect of exposure is multiplicative
    to the baseline rate whereas with excess mortality we assume it
    is additive. Which measure, relative mortality or excess mortality,
    do you think is more homogeneous across age?

    The following example illustrates the approach to estimating
    SMRs/SIRs using R. Specifically, we will estimate SMRs for the
    melanoma data using the general population mortality rates
    stratified by age and calendar period (derived from
    `popmort`) to estimate the expected number of deaths.
    The expected mortality rates depend on current age and current year
    so the approach is as follows

    -   Split follow-up into 1-year age bands

    -   Split the resulting data into 1-year calendar period bands

    -   For each age-period band, merge with <span>popmort.dta</span> to
        obtain the expected mortality rates

    -   Sum the observed and expected numbers of deaths and calculate
        the SMR (observed/expected) and a 95% CI

## (a) ##

Start by splitting the follow-up into 1 year age bands. We do not have
        a date of birth available, so we can make a mid-point
        approximation for the age at diagnosis.

```{r 23.a, results='hide'}
```

## (b) ##

Now split these new records into 1 year calendar period bands. 

```{r 23.b, results='hide'}
```

## (c) ##

Each subject’s follow–up is now divided into small pieces
corresponding to the agebands and calendar periods the subject passes
through. We can make tables of deaths and person-years by age and
calendar period with

```{r 23.c, results='hide'}
```

As the data have been split in 1-year intervals on both time
        scales the table created above is not so informative. Grouped
        variables will provide a better overview.


## (d) ##

To make a table of rates by age and calendar period, try

```{r 23.d, results='hide'}
```

## (e) ##

To calculate the expected cases for a cohort, using reference
        mortality rates classified by age and calendar period, it is
        first necessary to merge the population rates with the
        observed person-time.  Then the expected number of cases are
        calculated by multiplying the follow-up time for each record
        by the reference rate for that record. The SMR is the ratio of
        the total observed cases to the total number expected.
		
```{r 23.e, results='hide'}
```

## (f) ##

We can then model the observed outcomes using Poisson regression with an offset of the log of the expected counts, or using `poisson.test` with the expected counts as the exposure time.

```{r 23.f, results='hide', fig.show='hide'}
```
