Interim power of a replication study

Computes the power of a replication study taking into account data from an interim analysis.

powerSignificanceInterim(
  zo,
  zi,
  c = 1,
  f = 1/2,
  level = 0.025,
  designPrior = c("conditional", "informed predictive", "predictive"),
  analysisPrior = c("flat", "original"),
  alternative = c("one.sided", "two.sided"),
  shrinkage = 0
)

Arguments

zo

Numeric vector of z-values from original studies.

zi

Numeric vector of z-values from interim analyses of replication studies.

c

Numeric vector of variance ratios of the original and replication effect estimates. This is usually the ratio of the sample size of the replication study to the sample size of the original study. Default is 1.

f

Fraction of the replication study already completed. Default is 0.5.

level

Significance level. Default is 0.025.

designPrior

Either "conditional" (default), "informed predictive", or "predictive". "informed predictive" refers to an informative normal prior coming from the original study. "predictive" refers to a flat prior.

analysisPrior

Either "flat" (default) or "original".

alternative

Either "one.sided" (default) or "two.sided". Specifies if the significance level is one-sided or two-sided.

shrinkage

Numeric vector with values in [0,1). Defaults to 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.

Value

The probability of statistical significance in the specified direction at the end of the replication study given the data collected so far in the replication study.

Details

This is an extension of powerSignificance() and adapts the `interim power' from section 6.6.3 of Spiegelhalter et al. (2004) to the setting of replication studies.

powerSignificanceInterim is the vectorized version of .powerSignificanceInterim_. Vectorize is used to vectorize the function.

References

Spiegelhalter, D. J., Abrams, K. R., and Myles, J. P. (2004). Bayesian Approaches to Clinical Trials and Health-Care Evaluation, volume 13. John Wiley & Sons

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

See also

sampleSizeSignificance, powerSignificance

Author

Charlotte Micheloud

Examples

powerSignificanceInterim(zo = 2, zi = 2, c = 1, f = 1/2,
                         designPrior = "conditional",
                         analysisPrior = "flat")
#> [1] 0.7396952

powerSignificanceInterim(zo = 2, zi = 2, c = 1, f = 1/2,
                         designPrior = "informed predictive",
                         analysisPrior = "flat")
#> [1] 0.7659095

powerSignificanceInterim(zo = 2, zi = 2, c = 1, f = 1/2,
                         designPrior = "predictive",
                         analysisPrior = "flat")
#> [1] 0.8074296

powerSignificanceInterim(zo = 2, zi = -2, c = 1, f = 1/2,
                         designPrior = "conditional",
                         analysisPrior = "flat")
#> [1] 0.0003931199

powerSignificanceInterim(zo = 2, zi = 2, c = 1, f = 1/2,
                         designPrior = "conditional",
                         analysisPrior = "flat",
                         shrinkage = 0.25)
#> [1] 0.6136529