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

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.

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).

Value

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

Details

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

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

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., Balabdaoui, F., Held, L. (2023). Assessing replicability with the sceptical p-value: Type-I error control and sample size planning. Statistica Neerlandica. doi:10.1111/stan.12312

Author

Leonhard Held, Charlotte Micheloud, Samuel Pawel, Florian Gerber

Examples

## based on power
sampleSizeReplicationSuccess(zo = p2z(0.0025), power = 0.8, level = 0.025,
                             type = "golden")
#> [1] 0.72048
sampleSizeReplicationSuccess(zo = p2z(0.0025), power = 0.8, level = 0.025,
                             type = "golden", designPrior = "predictive")
#> [1] 0.9575662