p_value_functions: _p_-value functions

In felix-hof/hMean: Confidence Curves and P-Value Functions for Meta-Analysis

p-value functions

Description

These functions combine individual effect estimates and the corresponding
standard errors into a single \emph{p}-value. Under the hood, all of the
functions transform the estimates and standard errors into \emph{z}, and
subsequently into \emph{p}-values. The resulting \emph{p}-values are
combined into the chosen statistic and an appropriate distribution is
used to derive the combined \emph{p}-value.

All of the \emph{p}-value functions are vectorized over the \code{mu}
argument.

Usage

p_edgington(
  estimates,
  SEs,
  mu = 0,
  heterogeneity = "none",
  phi = NULL,
  tau2 = NULL,
  alternative = "two.sided",
  check_inputs = TRUE,
  approx = TRUE,
  input_p = "greater"
)

p_fisher(
  estimates,
  SEs,
  mu = 0,
  phi = NULL,
  tau2 = NULL,
  heterogeneity = "none",
  check_inputs = TRUE,
  input_p = "greater"
)

p_hmean(
  estimates,
  SEs,
  mu = 0,
  phi = NULL,
  tau2 = NULL,
  heterogeneity = "none",
  alternative = "none",
  check_inputs = TRUE,
  w = rep(1, length(estimates)),
  distr = "chisq"
)

p_wilkinson(
  estimates,
  SEs,
  mu,
  phi = NULL,
  tau2 = NULL,
  heterogeneity = "none",
  alternative = "none",
  check_inputs = TRUE,
  input_p = "greater"
)

p_pearson(
  estimates,
  SEs,
  mu = 0,
  phi = NULL,
  tau2 = NULL,
  heterogeneity = "none",
  check_inputs = TRUE,
  input_p = "greater"
)

p_tippett(
  estimates,
  SEs,
  mu = 0,
  phi = NULL,
  tau2 = NULL,
  heterogeneity = "none",
  check_inputs = TRUE,
  input_p = "greater"
)

p_stouffer(
  estimates,
  SEs,
  mu = 0,
  phi = NULL,
  tau2 = NULL,
  heterogeneity = "none",
  alternative = "two.sided",
  check_inputs = TRUE,
  w = NULL
)

Arguments

estimates	Numeric vector of effect estimates.
SEs	Numeric vector containing the standard errors of the effect estimates.
mu	A numeric vector containing null hypothesis value(s).
heterogeneity	One of c("none", "additive", "multiplicative"). If heterogeneity = "none" p-values are returned for the passed se without any adaption. If heterogeneity = "additive", the standard errors se are reassigned the value of sqrt(se^2 + tau2) before computation of the p-values. If heterogeneity = "multiplicative", the standard errors se are multiplied with the value of phi before computation of the p-values. Defaults to "none".
phi	A numeric vector of length 1. Must be finite and larger than 0. The square root of the argument is used to scale the standard errors.
tau2	A numeric vector of length 1.
alternative	Either "greater", "less", "two.sided", or "none" (default). Specifies the alternative to be considered in the computation of the p-value.
check_inputs	Either TRUE (default) or FALSE. Indicates whether or not to check the input arguments. The idea of this argument is that if the function is called a large amount of times in an automated manner as for example in simulations, performance might be increased by not checking inputs in every single iteration. However, setting the argument to FALSE might be dangerous.
approx	Must be either TRUE (default) or FALSE. If TRUE, the p-value is computed using the normal approximation of the Irwin-Hall distribution whenever length(estimates) >= 12. This avoids issues that can lead to overflow of the double precision floating point numbers R uses for numeric vectors.
input_p	Either "two.sided", "less", or "greater" (default). Specifies whether two-sided or one-sided p-values are used as inputs for a p-value combination method.
w	Numeric vector of weights.
distr	The distribution to use for the calculation of the p-value. Currently, the options are "f" (F-distribution) and "chisq" (Chi-squared distribution). Defaults to "chisq".

Value

The corresponding p-values given mu under the null-hypothesis.

Note

Add references to p-value statistics.

Examples

    # Simulating estimates and standard errors
    n <- 15
    estimates <- rnorm(n)
    SEs <- rgamma(n, 5, 5)

    # Calculate the between-study variance tau2
    tau2 <- estimate_tau2(estimates = estimates, SEs = SEs)
    phi <- estimate_phi(estimates = estimates, SEs = SEs)

    # Set up a vector of means under the null hypothesis
    mu <- seq(
      min(estimates) - 0.5 * max(SEs),
      max(estimates) + 0.5 * max(SEs),
      length.out = 1e5
    )

    # Using Edgington's method to calculate the combined p-value
    # for each of the means with additive adjustement for SEs
    p_edgington(
        estimates = estimates,
        SEs = SEs,
        mu = mu,
        heterogeneity = "additive",
        tau2 = tau2
    )
    # Using Fisher's method to calculate the combined \emph{p}-value
    # for each of the means with multiplicative adjustement for SEs
    p_fisher(
        estimates = estimates,
        SEs = SEs,
        mu = mu,
        heterogeneity = "multiplicative",
        phi = phi
    )

    # Using the harmonic mean method to calculate the combined p-value
    # for each of the means with additive adjustment for SEs.
    p_hmean(
        estimates = estimates,
        SEs = SEs,
        mu = mu,
        heterogeneity = "additive",
        tau2 = tau2,
        distr = "chisq"
    )

# Using Wilkinson's method to calculate the combined p-value
# for each of the means with multiplicative adjustement for SEs
p_wilkinson(
    estimates = estimates,
    SEs = SEs,
    mu = mu,
    heterogeneity = "multiplicative",
    phi = phi
)
# Using Pearson's method to calculate the combined p-value
# for each of the means with multiplicative adjustement for SEs
p_pearson(
    estimates = estimates,
    SEs = SEs,
    mu = mu,
    heterogeneity = "multiplicative",
    phi = phi
)
# Using Tippett's method to calculate the combined p-value
# for each of the means with multiplicative adjustement for SEs
p_tippett(
    estimates = estimates,
    SEs = SEs,
    mu = mu,
    heterogeneity = "multiplicative",
    phi = phi
)
# Using weighted Stouffer's method to calculate the combined p-value for
# each of the means with multiplicative adjustement for SEs
p_stouffer(
    estimates = estimates,
    SEs = SEs,
    mu = mu,
    heterogeneity = "multiplicative",
    phi = phi
)

felix-hof/hMean documentation built on Jan. 26, 2025, 4:59 p.m.