TOST Power for Tests of Two Proportions

Power analysis for TOST for difference between two proportions using Z-test (pooled)

powerTOSTtwo.prop(
  alpha,
  statistical_power,
  prop1,
  prop2,
  N,
  low_eqbound_prop,
  high_eqbound_prop
)

power_twoprop(
  p1,
  p2,
  n = NULL,
  null = 0,
  alpha = NULL,
  power = NULL,
  alternative = c("two.sided", "one.sided", "equivalence")
)

Arguments

alpha

a priori alpha-level (i.e., significance level).

statistical_power

Deprecated. desired power (e.g., 0.8)

prop1

Deprecated. expected proportion in group 1.

prop2

Deprecated. expected proportion in group 2.

N

Deprecated. sample size (e.g., 108)

low_eqbound_prop

Deprecated. lower equivalence bounds (e.g., -0.05) expressed in proportion

high_eqbound_prop

Deprecated. upper equivalence bounds (e.g., 0.05) expressed in proportion

p1, p2

Proportions in each respective group.

n

Sample size per group.

null

the null hypothesis value.

power

statistical power (1-beta).

alternative

equivalence, one-sided, or two-sided test. Can be abbreviated.

Value

Calculate either achieved power, equivalence bounds, or required N, assuming a true effect size of 0. Returns a string summarizing the power analysis, and a numeric variable for number of observations, equivalence bounds, or power.

References

Silva, G. T. da, Logan, B. R., & Klein, J. P. (2008). Methods for Equivalence and Noninferiority Testing. Biology of Blood and Marrow Transplantation: Journal of the American Society for Blood and Marrow Transplantation, 15(1 Suppl), 120-127. https://doi.org/10.1016/j.bbmt.2008.10.004

Julious, S. A. & Campell, M. J. (2012). Tutorial in biostatistics: sample sizes for parallel group clinical trials with binary data. Statistics in Medicine, 31:2904-2936.

Chow, S.-C., Wang, H., & Shao, J. (2007). Sample Size Calculations in Clinical Research, Second Edition (2 edition). Boca Raton: Chapman and Hall/CRC.

Examples

## Sample size for alpha = 0.05, 90% power, assuming true effect prop1 = prop 2 = 0.5,
## equivalence bounds of 0.4 and 0.6 (so low_eqbound_prop = -0.1 and high_eqbound_prop = 0.1)

#powerTOSTtwo.prop(alpha = 0.05, statistical_power = 0.9, prop1 = 0.5, prop2 = 0.5,
#    low_eqbound_prop = -0.1, high_eqbound_prop = 0.1)

   power_twoprop(alpha = 0.05, power = 0.9, p1 = 0.5, p2 = 0.5,
   null = 0.1, alternative = "e")
#> 
#>      Power for Test of Differences in Two Proportions (z-test) 
#> 
#>               n = 541.1074
#>     proportions = 0.5, 0.5
#>           alpha = 0.05
#>            beta = 0.1
#>           power = 0.9
#>            null = 0.1, -0.1
#>     alternative = equivalence
#>            NOTE = Sample sizes for EACH group
#> 

## Power for alpha = 0.05, N 542 , assuming true effect prop1 = prop 2 = 0.5,
## equivalence bounds of 0.4 and 0.6 (so low_eqbound_prop = -0.1 and high_eqbound_prop = 0.1)

#powerTOSTtwo.prop(alpha = 0.05, N = 542, prop1 = 0.5, prop2 = 0.5,
#    low_eqbound_prop = -0.1, high_eqbound_prop = 0.1)

power_twoprop(alpha = 0.05, n = 542, p1 = 0.5, p2 = 0.5,
   null = 0.1, alternative = "e")
#> 
#>      Power for Test of Differences in Two Proportions (z-test) 
#> 
#>               n = 542
#>     proportions = 0.5, 0.5
#>           alpha = 0.05
#>            beta = 0.09944181
#>           power = 0.9005582
#>            null = 0.1, -0.1
#>     alternative = equivalence
#>            NOTE = Sample sizes for EACH group
#> 


#Example 4.2.4 from Chow, Wang, & Shao (2007, p. 93)
#powerTOSTtwo.prop(alpha=0.05, statistical_power=0.8, prop1 = 0.75, prop2 = 0.8,
#    low_eqbound_prop = -0.2, high_eqbound_prop = 0.2)

power_twoprop(alpha = 0.05, power = 0.8, p1 = 0.75, p2 = 0.8,
   null = 0.2, alternative = "e")
#> 
#>      Power for Test of Differences in Two Proportions (z-test) 
#> 
#>               n = 132.2626
#>     proportions = 0.75, 0.80
#>           alpha = 0.05
#>            beta = 0.2
#>           power = 0.8
#>            null = 0.2, -0.2
#>     alternative = equivalence
#>            NOTE = Sample sizes for EACH group
#> 

# Example 5 from Julious & Campbell (2012, p. 2932)
#powerTOSTtwo.prop(alpha=0.025, statistical_power=0.9, prop1 = 0.8, prop2 = 0.8,
#    low_eqbound_prop=-0.1, high_eqbound_prop=0.1)
 power_twoprop(alpha = 0.025, power = 0.9, p1 = 0.8, p2 = 0.8,
   null = 0.1, alternative = "e")
#> 
#>      Power for Test of Differences in Two Proportions (z-test) 
#> 
#>               n = 415.8307
#>     proportions = 0.8, 0.8
#>           alpha = 0.025
#>            beta = 0.1
#>           power = 0.9
#>            null = 0.1, -0.1
#>     alternative = equivalence
#>            NOTE = Sample sizes for EACH group
#> 
# From Machin, D. (Ed.). (2008). Sample size tables for clinical studies (3rd ed).

# Example 9.4b equivalence of two proportions (p. 113) #
# powerTOSTtwo.prop(alpha=0.010, statistical_power=0.8, prop1 = 0.5, prop2 = 0.5,
#    low_eqbound_prop = -0.2, high_eqbound_prop = 0.2)/2
power_twoprop(alpha = 0.01, power = 0.8, p1 = 0.5, p2 = 0.5,
   null = 0.2, alternative = "e")
#> 
#>      Power for Test of Differences in Two Proportions (z-test) 
#> 
#>               n = 162.7117
#>     proportions = 0.5, 0.5
#>           alpha = 0.01
#>            beta = 0.2
#>           power = 0.8
#>            null = 0.2, -0.2
#>     alternative = equivalence
#>            NOTE = Sample sizes for EACH group
#>