Stratified 2x2 Tables: Miettinen-Nurminen and Friends
In sasLM: 'SAS' Linear Model

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:

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:

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:

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:

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:

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:

ORcmh(d1)

Example: aspirin and coronary heart disease

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

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.