# L_efficacy: Likelihood Support for Efficacy In likelihoodR: Likelihood Analyses for Common Statistical Tests

 L_efficacy R Documentation

## Likelihood Support for Efficacy

### Description

This function calculates the support for the efficacy, the likelihood interval and the likelihood-based confidence interval. It uses the optimize function to locate desired limits and their error.

### Usage

``````L_efficacy(a, n, null=0, exp.eff=NULL, L.int=2,
alpha=0.05, toler=0.0001, logplot=FALSE, supplot=-10, verb=TRUE)
``````

### Arguments

 `a` the number of affected in control group. `n` total number of participants. `null` the null value for efficacy, if no effect then it would be 0, default = 0. `exp.eff` the expected or hypothesized efficacy, default = NULL. `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. `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 the observed efficacy versus the null value.

\$obs.eff - the observed efficacy.

\$null - the null efficacy.

\$exp.eff - expected efficacy as specified.

\$S.exp.vsObs - support for expected efficacy versus observed.

\$S.exp.versus.null - support for the expected efficacy versus the null.

\$L.int - the likelihood interval for the observed efficacy.

\$S_int - the specified likelihood interval.

\$observed - observed numbers affected in control and intervention groups.

\$expected - expected numbers according to the null.

\$chi.sq - chi-squared statistic.

\$p.value - p value associated with chi-squared statistic.

\$df - degrees of freedom for chi-squared.

\$residuals - the Pearson residuals.

\$conf.int - likelihood-based confidence interval according to specified alpha.

\$alpha - specified alpha for confidence interval.

\$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

### Examples

``````# pfizer covid-19 efficacy 2020
m = L_efficacy(a = 86, n = 94, null=0.8, exp.eff=0.95, L.int=2,
alpha=0.05, toler=0.0001, logplot=FALSE, supplot=-10, verb=TRUE)
m

``````

likelihoodR documentation built on Sept. 14, 2023, 9:08 a.m.