sampleSizeSignificance {ReplicationSuccess}

Computes the required relative sample size to achieve significance based on power

Description

The relative sample size to achieve significance of the replication study is computed based on the z-value of the original study, the significance level and the power.

Usage

sampleSizeSignificance(
  zo,
  power = NA,
  level = 0.025,
  alternative = c("one.sided", "two.sided"),
  designPrior = c("conditional", "predictive", "EB"),
  h = 0,
  shrinkage = 0
)

Arguments

zo

A vector of z-values from original studies.

power

The power to achieve replication success.

level

Significance level. Default is 0.025.

alternative

Either "one.sided" (default) or "two.sided". Specifies if the significance level is one-sided or two-sided. If the significance level is one-sided, then sample size calculations are based on a one-sided assessment of significance in the direction of the original effect estimate.

designPrior

Is only taken into account when power is specified. Either "conditional" (default), "predictive", or "EB". If "EB", the power is computed under a predictive distribution where the contribution of the original study is shrunken towards zero based on the evidence in the original study (with an empirical Bayes shrinkage estimator).

h

Is only taken into account when power is specified and designPrior is "predictive" or "EB". The relative between-study heterogeneity, i.e., the ratio of the heterogeneity variance to the variance of the original effect estimate. Default is 0 (no heterogeneity).

shrinkage

Is only taken into account when power is specified. A number in [0,1) with default 0. Specifies the shrinkage of the original effect towards zero (e.g., shrinkage = 0.25 implies shrinkage by a factor of 25%). Is only taken into account when designPrior is "conditional" or "predictive".

Details

sampleSizeSignificance is the vectorized version of .sampleSizeSignificance_. Vectorize is used to vectorize the function.

Value

The relative sample size to achieve significance in the specified direction. If impossible to achieve the desired power for specified inputs NaN is returned.

Author(s)

Leonhard Held, Samuel Pawel, Charlotte Micheloud, Florian Gerber

References

Held, L. (2020). A new standard for the analysis and design of replication studies (with discussion). Journal of the Royal Statistical Society: Series A (Statistics in Society), 183, 431-448. doi:10.1111/rssa.12493

Pawel, S., Held, L. (2020). Probabilistic forecasting of replication studies. PLoS ONE. 15, e0231416. doi:10.1371/journal.pone.0231416

Held, L., Micheloud, C., Pawel, S. (2022). The assessment of replication success based on relative effect size. The Annals of Applied Statistics. 16:706-720. doi:10.1214/21-AOAS1502

Micheloud, C., Held, L. (2022). Power Calculations for Replication Studies. Statistical Science. 37:369-379. doi:10.1214/21-STS828

See Also

powerSignificance

Examples

sampleSizeSignificance(zo = p2z(0.005), power = 0.8)
sampleSizeSignificance(zo = p2z(0.005, alternative = "two.sided"), power = 0.8)
sampleSizeSignificance(zo = p2z(0.005), power = 0.8, designPrior = "predictive")

sampleSizeSignificance(zo = 3, power = 0.8, designPrior = "predictive",
                       shrinkage = 0.5, h = 0.25)
sampleSizeSignificance(zo = 3, power = 0.8, designPrior = "EB",  h = 0.5)

# sample size to achieve  0.8 power as function of original p-value
zo <- p2z(seq(0.0001, 0.05, 0.0001))
oldPar <- par(mfrow = c(1,2))
plot(z2p(zo), sampleSizeSignificance(zo = zo, designPrior = "conditional", power = 0.8),
     type = "l", ylim = c(0.5, 10), log = "y", lwd = 1.5, ylab = "Relative sample size",
     xlab = expression(italic(p)[o]), las = 1)
lines(z2p(zo), sampleSizeSignificance(zo = zo, designPrior = "predictive", power = 0.8),
      lwd = 2, lty = 2)
lines(z2p(zo), sampleSizeSignificance(zo = zo, designPrior = "EB", power = 0.8),
      lwd = 1.5, lty = 3)
legend("topleft", legend = c("conditional", "predictive", "EB"),
       title = "Design prior", lty = c(1, 2, 3), lwd = 1.5, bty = "n")

par(oldPar)