sampleSizeSignificance: Computes the required relative sample size to achieve...

In ReplicationSuccess: Design and Analysis of Replication Studies

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 either the power or the minimum relative effect size. When the approach based on power is used, the arguments design prior, shrinkage, and relative heterogeneity also have to be specified.

Usage

sampleSizeSignificance(zo, 
                       power, 
                       d, 
                       level = 0.025, 
                       alternative = "one.sided",
                       designPrior = "conditional", 
                       h = 0, 
                       shrinkage = 0)

Arguments

zo	A vector of z-values from original studies.
power	The power to achieve replication success.
d	The minimum relative effect size (ratio of the effect estimate from the replication study to the effect estimate from the original study)
level	Significance level. Default is 0.025.
alternative	Either "two.sided", "one.sided", "less", or "greater". Specifies direction of the alternative. Defaults to "one.sided", the same direction as the original estimate.
designPrior	Is only taken into account when "power" is specified. Either "conditional", "predictive", or "EB". Defaults to "conditional". 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. 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). Is only taken into account when designPrior = "predictive" or designPrior = "EB".
shrinkage	Is only taken into account when "power" is specified. A number in [0,1]. Defaults to 0. Specifies how much the original effect estimate is shrunken towards zero (e.g. the effect is shrunken by a factor of 25% for shrinkage = 0.25). Is only taken into account when designPrior = "conditional" or designPrior = "predictive".

Value

The relative sample size to achieve significance in the specified direction. If larger than 1000 then NA is returned.

Author(s)

Leonhard Held, Samuel Pawel, Charlotte Micheloud

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. https://doi.org/10.1111/rssa.12493

Pawel, S., Held, L. (2020). Probabilistic forecasting of replication studies. PLoS ONE 15(4):e0231416. https://doi.org/10.1371/journal.pone.0231416

Held, L., Micheloud, C. & Pawel, S. (2020). The assessment of replication success based on relative effect size. https://arxiv.org/abs/2009.07782

See Also

powerSignificance

Examples

par(mfrow = c(1,2))
sampleSizeSignificance(zo = p2z(0.005), power = 0.8)
sampleSizeSignificance(zo = p2z(0.005, alternative = "greater"), 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)
                       
# required relative sample size for 0.8 power as function of original p-value
zo <- p2z(seq(0.0001, 0.05, 0.0001))
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")
       
sampleSizeSignificance(zo = p2z(0.005), d = 1)
sampleSizeSignificance(zo = p2z(0.005), d = 0.5)
# required relative effect size of 0.8 power as function of original p-value
zo <- p2z(seq(0.0001, 0.05, 0.0001))
plot(z2p(zo), sampleSizeSignificance(zo = zo, d = 0.8, level = 0.025),
     type = "l", ylim = c(0.5, 10), log = "y", lwd = 1.5, ylab = "Relative sample size",
     xlab = expression(italic(p)[o]), las = 1)

ReplicationSuccess documentation built on Dec. 2, 2020, 3 p.m.