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

In ReplicationSuccess: Design and Analysis of Replication Studies

Computes the required relative sample size to achieve replication success with the sceptical p-value

Description

The relative sample size to achieve replication success is computed based on the z-value of the original study, the type of recalibration, the power and the design prior.

Usage

sampleSizeReplicationSuccess(
  zo,
  power = NA,
  level = 0.025,
  alternative = c("one.sided", "two.sided"),
  type = c("golden", "nominal", "controlled"),
  designPrior = c("conditional", "predictive", "EB"),
  shrinkage = 0,
  h = 0
)

Arguments

zo	Numeric vector of z-values from original studies.
power	The power to achieve replication success.
level	Threshold for the calibrated sceptical p-value. Default is 0.025.
alternative	Specifies if level is "one.sided" (default) or "two.sided". If "one.sided" then sample size calculations are based on a one-sided assessment of replication success in the direction of the original effect estimates.
type	Type of recalibration. Can be either "golden" (default), "nominal" (no recalibration), or "controlled". "golden" ensures that for an original study just significant at the specified level, replication success is only possible for replication effect estimates larger than the original one. "controlled" ensures exact overall Type-I error control at level level^2.
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).
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 estimate towards zero (e.g., the effect is shrunken by a factor of 25% for shrinkage = 0.25). Is only taken into account when the designPrior is "conditional" or "predictive".
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).

Details

sampleSizeReplicationSuccess is the vectorized version of the internal function .sampleSizeReplicationSuccess_. Vectorize is used to vectorize the function.

Value

The relative sample size for replication success. If impossible to achieve the desired power for specified inputs NaN is returned.

Author(s)

Leonhard Held, Charlotte Micheloud, Samuel Pawel, 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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/rssa.12493")}

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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/21-AOAS1502")}

Micheloud, C., Balabdaoui, F., Held, L. (2023). Beyond the two-trials rule: Type-I error control and sample size planning with the sceptical p-value. https://arxiv.org/abs/2207.00464

See Also

pSceptical, powerReplicationSuccess, levelSceptical

Examples

## based on power
sampleSizeReplicationSuccess(zo = p2z(0.0025), power = 0.8, level = 0.025,
                             type = "golden")
sampleSizeReplicationSuccess(zo = p2z(0.0025), power = 0.8, level = 0.025,
                             type = "golden", designPrior = "predictive")

ReplicationSuccess documentation built on April 3, 2023, 5:11 p.m.