---
title: "Stratified 2x2 Tables: Miettinen-Nurminen and Friends"
author: "Kyun-Seop Bae"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Stratified 2x2 Tables: Miettinen-Nurminen and Friends}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(comment = NA)
options(width = 100)
library(sasLM)
```

## A single 2x2 table

For one 2x2 table, `RD`, `RR`, and `OR` give the risk difference, relative risk,
and odds ratio with their score confidence intervals:

```{r}
RD(7, 10, 3, 10) # y1, n1, y2, n2
RR(7, 10, 3, 10)
OR(7, 10, 3, 10)
```

The Miettinen-Nurminen (MN) score intervals for a single stratum are
`RDmn1`, `RRmn1`, and `ORmn1`:

```{r}
RDmn1(7, 10, 3, 10)
RRmn1(7, 10, 3, 10)
ORmn1(7, 10, 3, 10)
```

These intervals perform well even in extreme cases such as zero cells:

```{r}
RDmn1(10, 10, 0, 10)
RRmn1(10, 10, 1, 10)
```

## Stratified analysis by the MN score method

When the data have strata (centers, studies, subgroups), provide a `data.frame`
with columns `y1, n1, y2, n2`, one row per stratum:

```{r}
d0 = data.frame(y1=c(25, 23), n1=c(339, 370), y2=c(28, 40), n2=c(335, 364))
RDmn(d0)
RRmn(d0)
ORmn(d0)
```

The `Strata` part shows the per-stratum MN intervals, and the `Common` part shows
the common (pooled) estimate with its stratified score confidence interval.

Since version 1.0.0:

* `RDmn` and `RRmn` agree with `ratesci::scoreci(weighting="MN", skew=FALSE)` by
  Pete Laud to 8 decimal places, including zero-cell strata.
* `ORmn` uses the inverse variance weighted score statistic with the score bias
  correction following Laud, and agrees with
  `ratesci::scoreci(contrast="OR", stratified=TRUE, skew=FALSE)` to at least
  7 significant digits.

## Inverse variance (meta-analysis) and CMH methods

The `*inv` functions pool by the inverse variance method and report both the
fixed effect and DerSimonian-Laird random effects results with Cochran's Q test -
the standard meta-analysis summary:

```{r}
d1 = data.frame(y1=c(25, 23), n1=c(339, 370), y2=c(28, 40), n2=c(335, 364))
RRinv(d1)
```

The Cochran-Mantel-Haenszel common odds ratio:

```{r}
ORcmh(d1)
```

## Example: aspirin and coronary heart disease

`aspirinCHD` contains six trials of aspirin versus placebo for post-myocardial
infarction mortality:

```{r}
aspirinCHD
ORmn(aspirinCHD)$Common
ORinv(aspirinCHD)$Common
```

## Choosing a method

* **MN score (`RDmn`, `RRmn`, `ORmn`)**: recommended for clinical trials with strata;
  asymmetric intervals with excellent small-sample coverage; no standard error reported.
* **Inverse variance (`RDinv`, `RRinv`, `ORinv`)**: the classical meta-analysis
  approach with fixed and random effects and a heterogeneity test.
* **CMH (`ORcmh`)**: the familiar Cochran-Mantel-Haenszel common odds ratio.