L_RR {likelihoodR}

Likelihood Support for Relative Risk (RR)

Description

This function calculates the support for an RR from a 2 x 2 categorical data table. An expected RR can be specified and the support calculated for this relative to the observed and null (which is assumed to be 1, but can also be specified) values. A likelihood function is plotted for the obtained RR with a likelihood interval, and expected RR, if specified. The log likelihood plot can optionally be given instead. Chi-squared statistics are also provided and a likelihood-based % confidence interval. It uses the optimize function to locate desired limits for both intervals and other support calculations.

Usage

L_RR(table, null=1, exp.RR=NULL, L.int=2, alpha=0.05,
cc=FALSE, toler=0.0001, logplot=FALSE, supplot=-10, verb=TRUE)

Arguments

table

a 2 x 2 matrix or contingency table containing counts.

null

the value against which the obtained RR is tested, default = 1.

exp.RR

an expected or hypothetical RR.

L.int

likelihood interval given as support values, e.g. 2 or 3, default = 2.

alpha

the significance level used, 1 - alpha interval calculated, default = 0.05.

cc

logical indicating whether to apply continuity correction, default = FALSE.

toler

the desired accuracy using optimise, default = 0.0001.

logplot

plot vertical axis as log likelihood, default = FALSE

supplot

set minimum likelihood display value in plot, default = -10

verb

show output, default = TRUE.

Value

$S.val - support for observed RR from expected.

$df - degrees of freedom.

$exp.RR - expected RR.

$S.exp.RRvsObs - support for expected RR versus observed.

$S.exp.RRvsNull - support for expected RR versus the null.

$L.int - likelihood interval of observed RR for specified level of support.

$S_int - specified likelihood interval in units of support.

$observed - observed frequencies.

$expected - the expected values for null hypothesis of no interaction.

$chi.sq - chi-squared statistic.

$corrected - whether chi-squared was corrected, default = FALSE.

$p.value - p value.

$residuals - the Pearson residuals.

$alpha - specified significance level.

$conf.int - likelihood-based confidence interval for observed RR.

$all.err.acc - error accuracy for each application of the optimize function.

References

Aitkin, M. et al (1989) Statistical Modelling in GLIM, Clarendon Press, ISBN : 978-0198522041

Cahusac, P.M.B. (2020) Evidence-Based Statistics, Wiley, ISBN : 978-1119549802

Royall, R. M. (1997). Statistical evidence: A likelihood paradigm. London: Chapman & Hall, ISBN : 978-0412044113

Edwards, A.W.F. (1992) Likelihood, Johns Hopkins Press, ISBN : 978-0801844430

Dienes, Z. (2008) Understanding Psychology as a Science: An Introduction to Scientific and Statistical Inference, Palgrave, MacMillan, ISBN : 978-0230542303

Examples

# for folic acid and neural tube defects example
tab <- as.table(rbind(c(6,587),c(21,581)))
dimnames(tab) <- list(Treatment=c("Folic acid","None"),Defect=c("Yes","No"))
L_RR(tab, exp.RR = 0.5, L.int = 2, alpha=0.05, cc=FALSE,
toler=0.0001, logplot=FALSE, supplot=-10, verb=TRUE)

# S. Korea COVID-19 patient mortality
tabcor <- as.table(rbind(c(41,3095),c(34,4992)))
dimnames(tabcor) <- list(Sex=c("Male","Female"),Status=c("Dead","Alive"))
L_RR(tabcor, exp.RR = 0.5, L.int = 2, alpha=0.05, cc=FALSE, toler=0.0001,
logplot=FALSE, supplot=-10, verb=TRUE)