hMeanChiSq: p-values and confidence intervals from the harmonic mean...

In florafauna/RStest: Design and Analysis of Replication Studies

Description

p-values and confidence intervals from the harmonic mean chi-squared test

Usage

hMeanChiSq(
  z,
  w = rep(1, length(z)),
  alternative = c("greater", "less", "two.sided", "none"),
  bound = FALSE
)

hMeanChiSqMu(
  thetahat,
  se,
  w = rep(1, length(thetahat)),
  mu = 0,
  alternative = c("greater", "less", "two.sided", "none"),
  bound = FALSE
)

hMeanChiSqCI(
  thetahat,
  se,
  w = rep(1, length(thetahat)),
  alternative = c("two.sided", "greater", "less", "none"),
  level = 0.95
)

Arguments

z	Numeric vector of z-values.
w	Numeric vector of weights.
alternative	Either "greater" (default), "less", "two.sided", or "none". Specifies the alternative to be considered in the computation of the p-value.
bound	If FALSE (default), p-values that cannot be computed are reported as NaN. If TRUE, they are reported as "> bound".
thetahat	Numeric vector of parameter estimates.
se	Numeric vector of standard errors.
mu	The null hypothesis value. Defaults to 0.
level	Numeric vector specifying the level of the confidence interval. Defaults to 0.95.

Value

hMeanChiSq returns the p-values from the harmonic mean chi-squared test based on the study-specific z-values.

hMeanChiSqMu returns the p-value from the harmonic mean chi-squared test based on study-specific estimates and standard errors.

hMeanChiSqCI returns confidence interval(s) from inverting the harmonic mean chi-squared test based on study-specific estimates and standard errors. If alternative is "none", the return value may be a set of (non-overlapping) confidence intervals. In that case, the output is a vector of length 2n, where n is the number of confidence intervals.

Author(s)

Leonhard Held

References

Held, L. (2020). The harmonic mean chi-squared test to substantiate scientific findings. Journal of the Royal Statistical Society: Series C (Applied Statistics), 69, 697-708. doi: 10.1111/rssc.12410

Examples

## Example from Fisher (1999) as discussed in Held (2020)
pvalues <- c(0.0245, 0.1305, 0.00025, 0.2575, 0.128)
lower <- c(0.04, 0.21, 0.12, 0.07, 0.41)
upper <- c(1.14, 1.54, 0.60, 3.75, 1.27)
se <- ci2se(lower, upper, ratio=TRUE)
estimate <- ci2estimate(lower, upper, ratio=TRUE)

## hMeanChiSq() --------
hMeanChiSq(p2z(pvalues, alternative="less"), alternative="less")
hMeanChiSq(p2z(pvalues, alternative="less"), alternative="two.sided")
hMeanChiSq(p2z(pvalues, alternative="less"), alternative="none")

hMeanChiSq(p2z(pvalues, alternative="less"),  w=1/se^2, alternative="less")
hMeanChiSq(p2z(pvalues, alternative="less"),  w=1/se^2, alternative="two.sided")
hMeanChiSq(p2z(pvalues, alternative="less"),  w=1/se^2, alternative="none")


## hMeanChiSqMu() --------
hMeanChiSqMu(thetahat=estimate, se=se, alternative="two.sided")
hMeanChiSqMu(thetahat=estimate, se=se, w=1/se^2, alternative="two.sided")
hMeanChiSqMu(thetahat=estimate, se=se, alternative="two.sided", mu=-0.1)


## hMeanChiSqCI() --------
## two-sided
CI1 <- hMeanChiSqCI(thetahat=estimate, se=se, w=1/se^2, alternative="two.sided")
CI2 <- hMeanChiSqCI(thetahat=estimate, se=se, w=1/se^2, alternative="two.sided", level=0.99875)
## one-sided
CI1b <- hMeanChiSqCI(thetahat=estimate, se=se, w=1/se^2, alternative="less", level=0.975)
CI2b <- hMeanChiSqCI(thetahat=estimate, se=se, w=1/se^2, alternative="less", level=1-0.025^2)
## confidence intervals on hazard ratio scale
print(round(exp(CI1),2))
print(round(exp(CI2),2))
print(round(exp(CI1b),2))
print(round(exp(CI2b),2))

florafauna/RStest documentation built on Dec. 20, 2021, 8:44 a.m.