---
title: "dsrTest - examples"
author: "Michael Nelson"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{dsrTest - example}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

To demonstrate the functionality of `dsrTest` the various methods to
construct confidence interval are demonstrated on the example data drawn from Table 14.4 in Fleiss (1981) (also used in Fay and Feuer (1997)).

The example data come from a study of Down Syndrome and maternal age 
(Stark and Mantell, 1966).

```{r example-data}
library(dsrTest)
# the data are in `downs.mi`
data("downs.mi", package = "dsrTest")
# Birth order 5 +
b5 <- downs.mi[downs.mi$BirthOrder == 5, ]
# Gamma Method
with(b5, dsrTest(Cases, Births, Standard, mult = 1e5, method = "gamma"))
# Gamma Mid-p
with(b5, dsrTest(Cases, Births, Standard, mult = 1e5, method = "gamma",
                 control = list(midp = TRUE)))
# Dobson (exact)
with(b5, dsrTest(Cases, Births, Standard, mult = 1e5, method = "dobson"))
# Dobson (Mid-p)
with(b5, dsrTest(Cases, Births, Standard, mult = 1e5, method = "dobson",
                 control = list(midp = TRUE)))
# Asymptotic (no transformation)
with(b5, dsrTest(Cases, Births, Standard, mult = 1e5, method = "asymptotic"))
# Asymptotic (log transformation)
with(b5, dsrTest(Cases, Births, Standard, mult = 1e5, method = "asymptotic",
                 control = list(trans = "log")))
# Beta Method
with(b5, dsrTest(Cases, Births, Standard, mult = 1e5, method = "beta"))
# Approximate Bootstrap Method
with(b5, dsrTest(Cases, Births, Standard, mult = 1e5, method = "bootstrap"))
```

## Summaries

```{r summaries}
# A list of methods to implement
methods_list <- list(
  gamma = list(
    list(wmtype = "max"),
    list(midp = TRUE),
    list(wmtype = "tcz"),
    list(wmtype = "mean"),
    list(wmtype = "minmaxavg")),
  asymptotic = list(
    list(trans = "none"),
    list(trans = "log"),
    list(trans = "loglog"),
    list(trans = "logit")),
  dobson = list(
    list(midp = FALSE),
    list(midp = TRUE)),
  beta = list(
    list(wmtype = "none"),
    list(wmtype = "tcz"),
    list(wmtype = "mean"),
    list(wmtype = "minmaxavg"),
    list(wmtype = "max")),
  bootstrap = list(list())
)
# split out to allow call to mapply
methods <-rep(names(methods_list), times = lengths(methods_list))
controls <- do.call(c, unname(methods_list))
all_methods <- mapply(dsrTest,
  method = methods, control = controls,
  MoreArgs = list(mult = 1e5, x = b5$Cases, n = b5$Births, w = b5$Standard),
  SIMPLIFY = FALSE)
# create some "short" names
control_types <- unlist(controls)
control_names <- c(gsub("midp=FALSE", "Exact CI",
  gsub("=TRUE", "",
       sprintf("[%s=%s]", names(control_types), control_types))), "")
names(all_methods) <- paste(methods, control_names)
# combine CI into one data.frame
results <- do.call(rbind,lapply(all_methods,
  function(data) data.frame(
    estimate = data$estimate,
    lci = data$conf.int[1], 
    uci = data$conf.int[2])))
# and display
knitr::kable(results, digits = 3)
```



# References

Fleiss, JL (1981) *Statistical Methods for Rates and Proportions*, 
Wiley, New York.

Stark CR and Mantel N (1966) 'Effects of maternal age and birth order 
on the risk of mongolism and leukemia' *J Natl Cancer Inst* 
**37** (5) 687--698. https://doi.org/10.1093/jnci/37.5.687

Fay MP & Feuer EJ (1997). 'Confidence intervals for directly
standardized rates: a method based on the gamma distribution.
 *Statistics in Medicine*. **16**: 791--801.
 [https://doi.org/10.1002/(SICI)1097-0258(19970415)16:7<791::AID-SIM500>3.0.CO;2-%23](https://doi.org/10.1002/(SICI)1097-0258(19970415)16:7<791::AID-SIM500>3.0.CO;2-%23)