Package 'rashnu'

Title: Balanced Sample Size and Power Calculation Tools
Description: Implements sample size and power calculation methods with a focus on balance and fairness in study design, inspired by the Zoroastrian deity Rashnu, the judge who weighs truth. Supports survival analysis and various hypothesis testing frameworks.
Authors: Sungho Choi [aut], Gyeom Hwangbo [ctb, cre], Zarathu [cph, fnd]
Maintainer: Gyeom Hwangbo <[email protected]>
License: MIT + file LICENSE
Version: 0.1.2
Built: 2026-05-29 10:00:22 UTC
Source: https://github.com/zarathucorp/rashnu

Help Index

Sample Size or Power for Cox Proportional Hazards

Description

Calculates sample size or power for a cox proportional hazards model.

Usage

coxph_size(
  hr,
  hr0 = NULL,
  delta = NULL,
  pE,
  pA,
  alpha,
  beta = NULL,
  n = NULL,
  test_type = "2-side"
)

Arguments

hr

Numeric. True hazard ratio.
hr0

Numeric (optional). Null hypothesis hazard ratio. Required for "2-side", "non-inferiority" test.
delta

Numeric (optional). Margin for "equivalence test". Required for "equivalence" test.
pE

Numeric. Overall event probability.
pA

Numeric. Proportion of group A.
alpha

Numeric. Type I error rate.
beta

Numeric (optional). Type II error rate. Required for sample size calculation.
n

Integer (optional). Sample size. Required for power calculation.
test_type

Character. "2-side", "non-inferiority", or "equivalence". Default is "2-side".

Value

Numeric. Returns sample size (if beta is given), or power (if n is given).

Note

Only one of beta (for sample size calculation) or n (for power calculation) should be specified.

Required arguments by test_type:

  • "2-side"/⁠"non-inferiority⁠:

    • For sample size: hr, hr0, pE, pA, alpha, beta

    • For power: hr, hr0, pE, pA, alpha, n

  • "equivalence":

    • For sample size: hr, delta, pE, pA, alpha, beta

    • For power: hr, delta, pE, pA, alpha, n

Examples

# Sample size for a `"2-side"` test
coxph_size(hr = 2, hr0 = 1, pE = 0.8, pA = 0.5,
           alpha = 0.05, beta = 0.2, test_type = "2-side")

# Power of `"2-side"` test
coxph_size(hr = 2, hr0 = 1, pE = 0.8, pA = 0.5,
           alpha = 0.05, n = 82, test_type = "2-side")

# Sample size for `"non-inferiority"` test
coxph_size(hr = 2, hr0 = 1, pE = 0.8, pA = 0.5,
           alpha = 0.025, beta = 0.2, test_type = "non-inferiority")

# Power of `"non-inferiority"` test
coxph_size(hr = 2, hr0 = 1, pE = 0.8, pA = 0.5,
           alpha = 0.025, n = 82, test_type = "non-inferiority")

# Sample size for `"equivalence"` test
coxph_size(hr = 1, delta = 0.5, pE = 0.8, pA = 0.5,
           alpha = 0.05, beta = 0.2, test_type = "equivalence")

# Power of `"equivalence"` test
coxph_size(hr = 1, delta = 0.5, pE = 0.8, pA = 0.5,
           alpha = 0.05, n = 172, test_type = "equivalence")

Sample Size or Power Calculation for K Means

Description

Calculates sample size or power for a multiple-sample mean test.

Usage

k_mean_size(
  muA,
  muB,
  kappa = 1,
  sd = NULL,
  sdA = NULL,
  sdB = NULL,
  tau = 1,
  alpha,
  beta = NULL,
  n = NULL,
  nA = NULL,
  test_type = "2-side"
)

Arguments

muA

Numeric. True mean of group A.
muB

Numeric. True mean of group B.
kappa

Numeric. Ratio of sample sizes (nA/nB). Default is 1.
sd

Numeric (optional). Standard deviation. Required for "2-side" test.
sdA

Numeric (optional). Standard deviation of group A. Required for "1-side" test.
sdB

Numeric (optional). Standard deviation of group B. Required for "1-side" test.
tau

Integer. Number of comparisons.
alpha

Numeric. Type I error rate.
beta

Numeric (optional). Type II error rate (1 - power). Required for sample size calculation.
n

Integer (optional). Sample size. Required for power calculation of "2-side" test.
nA

Integer (optional). Sample size of group A. Required for power calculation of "1-side" test.
test_type

Character. "2-side" or "1-side". Default is "2-side"

Value

Numeric. Returns sample size (if beta is given), or power (if n/nA is given).

Note

Only one of beta (for sample size calculation) or n/nA (for power calculation) should be specified.

Required arguments by test_type:

  • "2-side":

    • For sample size: muA, muB, sd, tau, alpha, beta

    • For power: muA, muB, sd, tau, alpha, n

-"1-side":

  • For sample size: muA, muB, sdA, sdB, tau, alpha, beta

  • For power: muA, muB, sdA, sdB, tau, alpha, nA

Examples

# Sample size for `"2-side"` test
k_mean_size(muA = 5, muB = 10, sd = 10, tau = 1,
            alpha = 0.05, beta = 0.2, test_type = "2-side")

# Power of `"2-side"` test
k_mean_size(muA = 5, muB = 10, sd = 10, tau = 1,
            alpha = 0.05, n = 63, test_type = "2-side")

# Sample size for `"1-side"` test
k_mean_size(muA = 132.86, muB = 127.44, kappa = 2, sdA = 15.34, sdB = 18.23, tau = 1,
            alpha = 0.05, beta = 0.2, test_type = "1-side")

# Power of `"1-side"` test
k_mean_size(muA = 132.86, muB = 127.44, kappa = 2, sdA = 15.34, sdB = 18.23, tau = 1,
            alpha = 0.05, nA = 85, test_type = "1-side")

Sample Size or Power Calculation for K proportion

Description

Calculates sample size or power for a multiple-sample proportion test.

Usage

k_prop_size(pA, pB, tau, alpha, beta = NULL, n = NULL)

Arguments

pA

Numeric. True proportion of group A.
pB

Numeric. True proportion of group B.
tau

Integer. Number of comparisons.
alpha

Numeric. Type I error rate.
beta

Numeric (optional). Type II error rate. Required for sample size calculation.
n

Integer (optional). Sample size. Required when calculating power.

Value

Returns sample size (if beta is given), or power (if n is given).

Note

Only one of beta (for sample size calculation) or n (for power calculation) should be specified.

Required arguments:

  • For sample size: pA, pB, tau, alpha, beta

  • For power: pA, pB, tau, alpha, n

Examples

# Sample size
k_prop_size(pA = 0.2, pB = 0.4, tau = 2,
            alpha = 0.05, beta = 0.2)

# Power
k_prop_size(pA = 0.2, pB = 0.4, tau = 2,
            alpha = 0.05, n = 96)

Sample Size Calculation Using Lakatos Method for Survival Analysis

Description

Computes the required sample size and expected event numbers for two-group survival analysis using Lakatos' method under exponential survival assumptions and varying weight functions (log-rank, Gehan, Tarone-Ware).

Usage

lakatosSampleSize(
  syear,
  yrsurv1,
  yrsurv2,
  alloc,
  accrualTime,
  followTime,
  alpha,
  power,
  method = c("logrank", "gehan", "tarone-ware"),
  side = c("two.sided", "one.sided"),
  b = 24
)

Arguments

syear

Survival time horizon in years.
yrsurv1

Survival probability of the standard group at syear.
yrsurv2

Survival probability of the test group at syear.
alloc

Allocation ratio (Test / Standard). For equal allocation, use 1.
accrualTime

Accrual period duration.
followTime

Additional follow-up time after last patient is accrued.
alpha

Significance level (e.g., 0.05 for two-sided tests).
power

Desired statistical power (e.g., 0.8).
method

Weighting method for test statistic. One of "logrank", "gehan", or "tarone-ware".
side

Type of test: "two.sided" or "one.sided".
b

Number of time divisions per year for numerical integration (default = 24).

Value

A list containing:

Sample_size_of_standard_group

Required sample size in the standard group.

Sample_size_of_test_group

Required sample size in the test group.

Total_sample_size

Total sample size.

Expected_event_numbers_of_standard_group

Expected number of events in the standard group.

Expected_event_numbers_of_test_group

Expected number of events in the test group.

Total_expected_event_numbers

Total number of expected events.

Actual_power

Achieved power given the calculated sample size.

error

(Optional) Error message when sample size cannot be calculated.

References

Lakatos E. (1988). Sample sizes based on the log-rank statistic in complex clinical trials. Biometrics, 44, 229–241.

Lakatos E, Lan KK. (1992). A comparison of sample size methods for the logrank statistic. Statistics in Medicine, 11(2), 179–191.

Web calculator (Superiority): https://nshi.jp/en/js/twosurvyr/

Examples

lakatosSampleSize(
  syear = 2,
  yrsurv1 = 0.7,
  yrsurv2 = 0.6,
  alloc = 1,
  accrualTime = 1,
  followTime = 1,
  alpha = 0.05,
  power = 0.8,
  method = "logrank",
  side = "two.sided"
)

Sample Size or Power for One-Sample Binomial Proportion Test

Description

Calculates sample size or power for a two-sample binomial proportion test.

Usage

one_bino_size(p, p0, alpha, beta = NULL, n = NULL)

Arguments

p

Numeric. True proportion.
p0

Numeric. Null hypothesis proportion.
alpha

Numeric. Type I error rate.
beta

Numeric (optional). Type II error rate. Required for sample size calculation.
n

Integer (optional). Sample size. Required for power calculation.

Value

Numeric. Returns sample size (if beta is given), or power (if n is given).

Note

Only one of beta (for sample size calculation) or n (for power calculation) should be specified.

Required arguments:

  • For sample size: "p", "p0", "alpha", "beta"

  • For power: "p", "p0", "alpha", "n"

Examples

# Required sample size
one_bino_size(p = 0.5, p0 = 0.3,
              alpha = 0.05, beta = 0.2)

# Power
one_bino_size(p = 0.5, p0 = 0.3,
              alpha = 0.05, n = 50)

Sample Size or Power for One-Sample Mean Test

Description

Calculates sample size or power for a one-sample mean test.

Usage

one_mean_size(
  mu,
  mu0,
  delta = NULL,
  sd,
  alpha,
  beta = NULL,
  n = NULL,
  test_type = "2-side"
)

Arguments

mu

Numeric. True mean.
mu0

Numeric. Null hypothesis mean.
delta

Numeric (optional). Margin for "non-inferiority" or "equivalence" test. Required for "non-inferiority" or "equivalence" test.
sd

Numeric. Standard deviation.
alpha

Numeric. Type I error rate.
beta

Numeric (optional). Type II error rate. Required for sample size calculation.
n

Integer (optional). Sample size. Required for power calculation.
test_type

Character. "2-side", "1-side", "non-inferiority", or "equivalence". Default is "2-side".

Value

Numeric. Returns sample size (if beta is given), or power (if n is given).

Note

Only one of beta (for sample size calculation) or n (for power calculation) should be specified.

Required arguments by test_type:

  • "2-side" / "1-side":

    • For sample size: mu, mu0, sd, alpha, beta

    • For power: mu, mu0, sd, alpha, n

  • "non-inferiority" / "equivalence":

    • For sample size: mu, mu0, delta, sd, alpha, beta

    • For power: mu, mu0, delta, sd, alpha, n

Examples

# Sample size for `"2-side"` test
one_mean_size(mu = 2, mu0 = 1.5, sd = 1,
              alpha = 0.05, beta = 0.2, test_type = "2-side")

# Power of `"2-side"` test
one_mean_size(mu = 2, mu0 = 1.5, sd = 1,
              alpha = 0.05, n = 32, test_type = "2-side")

# Sample size for `"1-side"` test
one_mean_size(mu = 115, mu0 = 120, sd = 24,
              alpha = 0.05, beta = 0.2, test_type = "1-side")

# Power of `"1-side"` test
one_mean_size(mu = 115, mu0 = 120, sd = 24,
              alpha = 0.05, n = 143, test_type = "1-side")

# Sample size for `"non-inferiority"` test
one_mean_size(mu = 2, mu0 = 1.5, delta = -0.5, sd = 1,
              alpha = 0.05, beta = 0.2, test_type = "non-inferiority")

# Power of `"non-inferiority"` test
one_mean_size(mu = 2, mu0 = 1.5, delta = -0.5, sd = 1,
              alpha = 0.05, n = 7, test_type = "non-inferiority")

# Sample size for `"equivalence"` test
one_mean_size(mu = 2, mu0 = 2, delta = 0.05, sd = 0.1,
              alpha = 0.05, beta = 0.2, test_type = "equivalence")

# Power of `"equivalence"` test
one_mean_size(mu = 2, mu0 = 2, delta = 0.05, sd = 0.1,
              alpha = 0.05, n = 35, test_type = "equivalence")

Sample Size or Power Calculation for One-Sample Normal Mean Test

Description

Calculates sample size or power for a two-sample normal mean test.

Usage

one_norm_size(mu, mu0, sd, alpha, beta = NULL, n = NULL)

Arguments

mu

Numeric. True mean.
mu0

Numeric. Null hypothesis mean.
sd

Numeric. Standard deviation.
alpha

Numeric. Type I error rate.
beta

Numeric (optional). Type II error rate. Required for sample size calculation.
n

Integer (optional). Sample size. Required for power calculation.

Value

Numeric. Returns sample size (if beta is given), or power (if n is given).

Note

Only one of beta (for sample size calculation) or n (for power calculation) should be specified.

Required arguments:

  • For sample size: "mu", "mu0", "sd", "alpha", "beta"

  • For power: "mu", "mu0", "sd", "alpha", "n"

Examples

# Sample size
one_norm_size(mu = 2, mu0 = 1.5, sd = 1,
              alpha = 0.05, beta = 0.2)

# Power
one_norm_size(mu = 2, mu0 = 1.5, sd = 1,
              alpha = 0.05, n = 32)

Sample Size or Power for One-Sample Proportion Test

Description

Calculates sample size or power for a one-sample proportion test.

Usage

one_prop_size(
  p,
  p0,
  delta = NULL,
  alpha,
  beta = NULL,
  n = NULL,
  test_type = "2-side"
)

Arguments

p

Numeric. True proportion.
p0

Numeric. Null hypothesis proportion.
delta

Numeric (optional). Margin for "non-inferiority" or "equivalence" test. Required for "non-inferiority" or "equivalence" test.
alpha

Numeric. Type I error rate.
beta

Numeric (optional). Type II error rate. Required for sample size calculation.
n

Integer (optional). Sample size. Required for power calculation.
test_type

Character. "2-side", "1-side", "non-inferiority", or "equivalence". Default is "2-side".

Value

Numeric. Returns sample size (if beta is given), or power (if n is given).

Note

Only one of beta (for sample size calculation) or n (for power calculation) should be specified.

Required arguments by test_type:

  • "2-side"/⁠"1-side⁠:

    • For sample size: p, p0, alpha, beta

    • For power: p, p0, alpha, n

  • "non-inferiority"/"equivalence":

    • For sample size: p, p0, delta, alpha, beta

    • For power: p, p0, sdA, delta, alpha, n

Examples

# Sample size for `"2-side"` test
one_prop_size(p = 0.5, p0 = 0.3,
              alpha = 0.05, beta = 0.2, test_type = "2-side")

# Power of `"2-side"` test
one_prop_size(p = 0.5, p0 = 0.3,
              alpha = 0.05, n = 50, test_type = "2-side")

# Sample size for `"1-side"` test
one_prop_size(p = 0.05, p0 = 0.02,
              alpha = 0.05, beta = 0.2, test_type = "1-side")

# Power of `"1-sided"` test
one_prop_size(p = 0.05, p0 = 0.02,
              alpha = 0.05, n = 191, test_type = "1-side")

# Sample size for `"non-inferiority"` test
one_prop_size(p = 0.5, p0 = 0.3, delta = -0.1,
              alpha = 0.05, beta = 0.2, test_type = "non-inferiority")

# Power of `"non-inferiority"` test
one_prop_size(p = 0.5, p0 = 0.3, delta = -0.1,
              alpha = 0.05, n = 18, test_type = "non-inferiority")

# Sample size for `"equivalence"` test
one_prop_size(p = 0.6, p0 = 0.6, delta = 0.2,
              alpha = 0.05, beta = 0.2, test_type = "equivalence")

# Power of `"equivalence"` test
one_prop_size(p = 0.6, p0 = 0.6, delta = 0.2,
              alpha = 0.05, n = 52, test_type = "equivalence")

One-Sample Survival Study Sample Size or Power Calculation

Description

Calculates the required sample size or power for a single-arm survival study using various transformation-based methods, including arcsine-square root, log-log, logit, and others. This function assumes an exponential survival model.

Usage

oneSurvSampleSize(
  survTime,
  p1,
  p2,
  accrualTime,
  followTime,
  alpha,
  power,
  side = c("two.sided", "one.sided"),
  method = c("arcsin", "log-log", "logit", "log", "log-swog", "identity")
)

Arguments

survTime

Time point at which survival is evaluated (e.g., median follow-up time).
p1

Expected survival probability under the alternative hypothesis.
p2

Survival probability under the null hypothesis.
accrualTime

Patient accrual period.
followTime

Additional follow-up period after accrual ends.
alpha

Significance level (e.g., 0.05).
power

Desired statistical power (e.g., 0.8).
side

Type of hypothesis test. Either "two.sided" (default) or "one.sided".
method

Transformation method for comparison. One of "arcsin", "log-log", "logit", "log", "log-swog", "identity".

Value

A named numeric vector with:

SampleSize

Calculated required sample size.

Power

Achieved power with the calculated sample size.

References

Fleming TR, Harrington DP. (1991). Counting Processes and Survival Analysis. New York: Wiley, pp. 236–237, Example 6.3.1.

Andersen PK, Borgan O, Gill RD, Keiding N. (1993). Statistical Models Based on Counting Processes. New York: Springer-Verlag, pp. 176–287, Section IV.1–3.

Bie O, Borgan O, Liestol K. (1987). Confidence intervals and confidence bands for the cumulative hazard rate function and their small sample properties. Scandinavian Journal of Statistics, 14(3), 221–233.

Borgan O, Liestol K. (1990). A note on confidence intervals and bands for the survival function based on transformations. Scandinavian Journal of Statistics, 17(1), 35–41.

Nagashima K, Noma H, Sato Y, Gosho M. (2020). Sample size calculations for single-arm survival studies using transformations of the Kaplan–Meier estimator. Pharmaceutical Statistics. https://doi.org/10.1002/pst.2090 Available at: https://arxiv.org/abs/2012.03355

Web calculator (One-sample): https://nshi.jp/en/js/onesurvyr/

Examples

oneSurvSampleSize(
  survTime = 2,
  p1 = 0.75,
  p2 = 0.6,
  accrualTime = 1,
  followTime = 1,
  alpha = 0.05,
  power = 0.8,
  side = "two.sided",
  method = "log-log"
)

Sample Size or Power for Odds Ratio Test

Description

Calculates sample size or power for odds ratio test.

Usage

or_size(
  pA,
  pB,
  delta = NULL,
  kappa = 1,
  alpha,
  beta = NULL,
  nB = NULL,
  test_type = "equality"
)

Arguments

pA

Numeric. True proportion of group A.
pB

Numeric. True proportion of group B.
delta

Numeric (optional). Margin for "non-inferiority" or "equivalence" test. Required for "non-inferiority" or "equivalence" test.
kappa

Numeric. Ratio of sample sizes (nA/nB). Default is 1.
alpha

Numeric. Type I error rate.
beta

Numeric (optional). Type II error rate. Required for sample size calculation.
nB

Integer (optional). Sample size for group B. Required for power calculation.
test_type

Character. "equality", "non-inferiority", or "equivalence". Default is "2-side".

Value

Numeric. Returns sample size (if beta is given), or power (if nB is given).

Note

Only one of beta (for sample size calculation) or nB (for power calculation) should be specified.

Required arguments by test_type:

  • "equality":

    • For sample size: pA, pB, alpha, beta

    • For power: pA, pB, alpha, nB

  • "non-inferiority"/"equivalence":

    • For sample size: pA, pB, delta, alpha, beta

    • For power: pA, pB, delta, alpha, nB

Examples

# Sample size for `"equality"` test
or_size(pA = 0.4, pB = 0.25, kappa = 1,
        alpha = 0.05, beta = 0.2, test_type = "equality")

# Power of `"equality"` test
or_size(pA = 0.4, pB = 0.25, kappa = 1,
        alpha = 0.05, nB = 156, test_type = "equality")

# Sample size for `"non-inferiority"` test
or_size(pA = 0.4, pB = 0.25, delta = 0.2, kappa = 1,
        alpha = 0.05, beta = 0.2, test_type = "non-inferiority")

# Power of `"non-inferiority"` test
or_size(pA = 0.4, pB = 0.25, delta = 0.2, kappa = 1,
        alpha = 0.05, nB = 242, test_type = "non-inferiority")

# Sample size for `"equivalence"` test
or_size(pA = 0.25, pB = 0.25, delta = 0.5, kappa = 1,
        alpha = 0.05, beta = 0.2, test_type = "equivalence")

# Power of `"equivalence"` test
or_size(pA = 0.25, pB = 0.25, delta = 0.5, kappa = 1,
        alpha = 0.05, nB = 366, test_type = "equivalence")

Sample Size or Power for Paired-Sample Proportion Test

Description

Calculates sample size or power for a paired-sample proportion test.

Usage

pair_prop_size(p01, p10, alpha, beta = NULL, n = NULL, test_type = "2-side")

Arguments

p01

Numeric. Proportion of discordant pairs with (before = 1, after = 0).
p10

Numeric. Proportion of discordant pairs with (before = 0, after = 1).
alpha

Numeric. Type I error rate.
beta

Numeric (optional). Type II error rate. Required for sample size calculation.
n

Integer (optional). Sample size. Required for power calculation.
test_type

Character. "2-side" or "1-side". Default is "2-side".

Value

Numeric. Returns sample size (if beta is given), or power (if n is given).

Note

Only one of beta (for sample size calculation) or n (for power calculation) should be specified.

Required arguments:

  • For sample size: p01, p10, alpha, beta

  • For power: p01, p10, alpha, n

Examples

# Sample size for `"2-side"` test
pair_prop_size(p01 = 0.45, p10 = 0.05,
               alpha = 0.1, beta = 0.1, test_type = "2-side")

# Power of `"2-side"` test
pair_prop_size(p01 = 0.45, p10 = 0.05,
               alpha = 0.1, n = 23, test_type = "2-side")

# Sample size for `"1-side"` test
pair_prop_size(p01 = 0.45, p10 = 0.05,
               alpha = 0.05, beta = 0.1, test_type = "1-side")

# Power of `"1-side"` test
pair_prop_size(p01 = 0.45, p10 = 0.05,
               alpha = 0.05, n = 23, test_type = "1-side")

Interactive Sample Size Calculator for Survival Studies (Shiny App)

Description

Launches a Shiny web application that calculates required sample sizes and expected event numbers for different types of survival analysis designs:

  • Two-group Non-Inferiority

  • Two-group Superiority (Lakatos method)

  • One-sample survival test (with transformation methods)

Usage

rashnuBasic()

Details

Users can specify survival probabilities, accrual and follow-up durations, allocation ratios, non-inferiority margins, transformation methods, and test types. The app dynamically adjusts input UI based on the selected design and displays results in a data table format.

Test Types:

  • "ni" - Non-Inferiority (two-group exponential survival comparison)

  • "sup" - Superiority (Lakatos method with logrank/Gehan/Tarone-Ware weighting)

  • "one" - One-sample survival test with multiple transformation options

Included References:

  • Jung SH, Chow SC. Journal of Biopharmaceutical Statistics, 2012.

  • Lakatos E. Biometrics, 1988.

  • Lakatos & Lan. Statistics in Medicine, 1992.

  • Fleming & Harrington. Counting Processes and Survival Analysis, 1991.

  • Borgan 0, Andersen PK et al. Springer-Verlag, 1993.

  • Nagashima et al. Pharmaceutical Statistics, 2020.

Value

Launches a Shiny app in the default browser.

Note

Requires associated functions twoSurvSampleSizeNI(), lakatosSampleSize(), and oneSurvSampleSize() to be defined in the environment. Assumes a CSS file is available at "www/style.css" for custom styling.

Examples

if (interactive()) {
  rashnuBasic()
}

Sample Size or Power for Self-Controlled Case Series (SCCS)

Description

Calculates sample size or power for self-controlled case series studies.

Usage

sccs_size(p, r, alpha, beta = NULL, n = NULL)

Arguments

p

Numeric. True relative incidence (risk period vs baseline).
r

Numeric. Proportion of observation time that is risk period.
alpha

Numeric. Type I error rate.
beta

Numeric (optional). Type II error rate. Required for sample size calculation.
n

Integer (optional). Sample size. Required for power calculation.

Value

Numeric. Returns sample size (if beta is given), or power (if n is given).

Note

Only one of beta (for sample size calculation) or n (for power calculation) should be specified.

Required arguments:

  • For sample size: p, r, alpha, beta

  • For power: p, r, alpha, n

Examples

# Sample size
sccs_size(p = 3, r = 42/365,
          alpha = 0.05, beta = 0.2)

# Power
sccs_size(p = 3, r = 42/365,
          alpha = 0.05, n = 54)

Sample Size or Power for Two-Sample Mean Test

Description

Calculates sample size or power for a two-sample mean test.

Usage

two_mean_size(
  muA,
  muB,
  delta = NULL,
  kappa = 1,
  sd = NULL,
  sdA = NULL,
  sdB = NULL,
  alpha,
  beta = NULL,
  nA = NULL,
  nB = NULL,
  test_type = "2-side"
)

Arguments

muA

Numeric. True mean of group A.
muB

Numeric. True mean of group B.
delta

Numeric (optional). Margin for "non-inferiority" or "equivalence test". Required for "non-inferiority" or "equivalence" test.
kappa

Numeric. Ratio of sample sizes (nA/nB). Default is 1.
sd

Numeric (optional). Standard deviation. Required for "2-side", "non-inferiority" or "equivalence" test.
sdA

Numeric (optional). Standard deviation of group A. Required for "1-side" test.
sdB

Numeric (optional). Standard deviation of group B. Required for "1-side" test.
alpha

Numeric. Type I error rate.
beta

Numeric (optional). Type II error rate. Required for sample size calculation.
nA

Integer (optional). Sample size for group A. Required for power calculation of "1-side" test.
nB

Integer (optional). Sample size for group B. Required for power calculation of "2-side", "non-inferiority" or "equivalence" test.
test_type

Character. "2-side", "1-side", "non-inferiority", or "equivalence". Default is "2-side".

Value

Numeric. Returns sample size (if beta is given), or power (if nA/nB is given).

Note

Only one of beta (for sample size calculation) or nA/nB (for power calculation) should be specified.

Required arguments by test_type:

  • "2-side":

    • For sample size: muA, muB, sd, alpha, beta

    • For power: muA, muB, sd, alpha, nB

  • "1-side":

    • For sample size: muA, muB, sdA, sdB, alpha, beta

    • For power: muA, muB, sdA, sdB, alpha, nA

  • "non-inferiority"/"equivalence":

    • For sample size: muA, muB, delta, sd, alpha, beta

    • For power: muA, muB, delta, sd, alpha, nB

Examples

# Sample size for `"2-side"` test
two_mean_size(muA = 5, muB = 10, kappa = 1, sd = 10,
              alpha = 0.05, beta = 0.2, test_type = "2-side")

# Power of `"2-side"` test
two_mean_size(muA = 5, muB = 10, kappa = 1, sd = 10,
              alpha = 0.05, nB = 63, test_type = "2-side")

# Sample size for `"1-side"` test
two_mean_size(muA = 132.86, muB = 127.44, kappa = 2, sdA = 15.34, sdB = 18.23,
              alpha = 0.05, beta = 0.2, test_type = "1-side")

# Power of `"1-sided"` test
two_mean_size(muA = 132.86, muB = 127.44, kappa = 2, sdA = 15.34, sdB = 18.23,
              alpha = 0.05, nA = 85, test_type = "1-side")

# Sample size for `"non-inferiority"` test
two_mean_size(muA = 5, muB = 5, delta = 5, kappa = 1, sd = 10,
              alpha = 0.05, beta = 0.2, test_type = "non-inferiority")

# Power of `"non-inferiority"` test
two_mean_size(muA = 5, muB = 5, delta = 5, kappa = 1, sd = 10,
              alpha = 0.05, nB = 50, test_type = "non-inferiority")

# Sample size for `"equivalence"` test
two_mean_size(muA = 5, muB = 4, delta = 5, kappa = 1, sd = 10,
              alpha = 0.05, beta = 0.2, test_type = "equivalence")

# Power of `"equivalence"` test
two_mean_size(muA = 5, muB = 4, delta = 5, kappa = 1, sd = 10,
              alpha = 0.05, nB = 108, test_type = "equivalence")

Sample Size or Power for Two-Sample Proportion Test

Description

Calculates sample size or power for a two-sample proportion test.

Usage

two_prop_size(
  pA,
  pB,
  delta = NULL,
  kappa = 1,
  alpha,
  beta = NULL,
  nB = NULL,
  test_type = "2-side"
)

Arguments

pA

Numeric. True proportion of group A.
pB

Numeric. True proportion of group B.
delta

Numeric (optional). Margin for "non-inferiority" or "equivalence" test. Required for "non-inferiority" or "equivalence" test.
kappa

Numeric. Ratio of sample sizes (nA/nB). Default is 1.
alpha

Numeric. Type I error rate.
beta

Numeric (optional). Type II error rate. Required for sample size calculation.
nB

Integer (optional). Sample size for group B. Required for power calculation.
test_type

Character. "2-side", "1-side", "non-inferiority", or "equivalence". Default is "2-side".

Value

Numeric. Returns sample size (if beta is given), or power (if nB is given).

Note

Only one of beta (for sample size calculation) or nA/nB (for power calculation) should be specified.

Required arguments by test_type:

  • "2-side"/"1-side":

    • For sample size: pA, pB, alpha, beta

    • For power: pA, pB, alpha, nB

  • "non-inferiority"/"equivalence":

    • For sample size: pA, pB, delta, alpha, beta

    • For power: pA, pB, delta, alpha, nB

Examples

# Sample size for `"2-side"` test
two_prop_size(pA = 0.65, pB = 0.85, kappa = 1,
              alpha = 0.05, beta = 0.2, test_type = "2-side")

# Power of `"2-side"` test
two_prop_size(pA = 0.65, pB = 0.85, kappa = 1,
              alpha = 0.05, nB = 70, test_type = "2-side")

# Sample size for `"1-side"` test
two_prop_size(pA = 0.65, pB = 0.85, kappa = 1,
              alpha = 0.05, beta = 0.2, test_type = "1-side")

# Power of `"1-sided"` test
two_prop_size(pA = 0.65, pB = 0.85, kappa = 1,
              alpha = 0.05, nB = 55, test_type = "1-side")

# Sample size for `"non-inferiority"` test
two_prop_size(pA = 0.85, pB = 0.65, delta = -0.1, kappa = 1,
              alpha = 0.05, beta = 0.2, test_type = "non-inferiority")

# Power of `"non-inferiority"` test
two_prop_size(pA = 0.85, pB = 0.65, delta = -0.1, kappa = 1,
              alpha = 0.05, nB = 25, test_type = "non-inferiority")

# Sample size for `"equivalence"` test
two_prop_size(pA = 0.65, pB = 0.85, delta = 0.05, kappa = 1,
              alpha = 0.05, beta = 0.2, test_type = "equivalence")

# Power of `"equivalence"` test
two_prop_size(pA = 0.65, pB = 0.85, delta = 0.05, kappa = 1,
              alpha = 0.05, nB = 136, test_type = "equivalence")

Sample Size Calculation for Two-Group Non-Inferiority Survival Study

Description

Calculates the required sample size and expected event numbers for a non-inferiority trial with two survival curves, using piecewise integration of hazard functions under exponential survival assumptions.

Usage

twoSurvSampleSizeNI(
  syear,
  yrsurv1,
  yrsurv2,
  alloc,
  accrualTime,
  followTime,
  alpha,
  power,
  margin
)

Arguments

syear

Survival time horizon (e.g., median survival time) in years.
yrsurv1

Survival probability of the standard group at syear.
yrsurv2

Survival probability of the test group at syear.
alloc

Allocation ratio (Test / Standard), e.g., 1 means equal allocation.
accrualTime

Duration of patient accrual period.
followTime

Follow-up period after last patient is accrued.
alpha

One-sided significance level (e.g., 0.025).
power

Desired statistical power (e.g., 0.8).
margin

Non-inferiority margin for hazard ratio (HR).

Value

A list containing:

Sample_size_of_standard_group

Required sample size in the standard group.

Sample_size_of_test_group

Required sample size in the test group.

Total_sample_size

Total sample size.

Expected_event_numbers_of_standard_group

Expected number of events in the standard group.

Expected_event_numbers_of_test_group

Expected number of events in the test group.

Total_expected_event_numbers

Total number of expected events across both groups.

References

Jung SH, Chow SC. (2012). On sample size calculation for comparing survival curves under general hypothesis testing. Journal of Biopharmaceutical Statistics, 22(3), 485–495.

Web calculator (Non-Inferiority): https://nshi.jp/en/js/twosurvyrni/

Examples

twoSurvSampleSizeNI(
  syear = 2,
  yrsurv1 = 0.7,
  yrsurv2 = 0.65,
  alloc = 1,
  accrualTime = 1,
  followTime = 1,
  alpha = 0.025,
  power = 0.8,
  margin = 1.3
)