Balanced Sample Size and Power Calculation Tools • rashnu

Rashnu is the Zoroastrian deity of truth and justice—the one who weighs souls on a golden scale.
This R package, developed by Zarathu, draws inspiration from Rashnu’s role as the divine judge to offer precision and fairness in sample size determination.

“Where truth is weighed, science begins.”

In clinical trials and research design, every decision matters.
Rashnu helps researchers define the right number of participants for various statistical tests including: - Non-inferiority studies - Superiority comparisons (Lakatos method) - One-arm survival designs with transformation-based inference

This package brings clarity, rigor, and justice to your design process.

Installation

You can install the stable version of rashnu from CRAN with:

install.packages("rashnu")

To access the latest development version, install it from GitHub with:

# install.packages("pak")
pak::pak("zarathucorp/rashnu")

Example

Rstudio Addins

Use rashnuBasic() or Click Interactive Sample Size Calculator Addin

rashnuBasic()

Two sample survival non-inferiority

twoSurvSampleSizeNI(
   syear = 12,
   yrsurv1 = 0.5,
   yrsurv2 = 0.5,
   alloc = 1,
   accrualTime = 24,
   followTime = 24,
   alpha = 0.025,
   power = 0.8,
   margin = 1.3
)

$Sample_size_of_standard_group
[1] 264

$Sample_size_of_test_group
[1] 264

$Total_sample_size
[1] 528

$Expected_event_numbers_of_standard_group
[1] 227.9

$Expected_event_numbers_of_test_group
[1] 227.9

$Total_expected_event_numbers
[1] 455.9

Two sample survival superiority

lakatosSampleSize(
   syear = 12,
   yrsurv1 = 0.3,
   yrsurv2 = 0.5,
   alloc = 1,
   accrualTime = 24,
   followTime = 24,
   alpha = 0.05,
   power = 0.8,
   method = "logrank",
   side = "two.sided"
)

$Sample_size_of_standard_group
[1] 58

$Sample_size_of_test_group
[1] 58

$Total_sample_size
[1] 116

$Expected_event_numbers_of_standard_group
[1] 55.6

$Expected_event_numbers_of_test_group
[1] 49.7

$Total_expected_event_numbers
[1] 105.3

$Actual_power
[1] 0.803

One sample non-parametric survival

oneSurvSampleSize(
   survTime = 12,
   p1 = 0.3,
   p2 = 0.4,
   accrualTime = 24,
   followTime = 24,
   alpha = 0.05,
   power = 0.8,
   side = "two.sided",
   method = "log-log"
)

SampleSize      Power 
   189.000      0.802

Test one mean

# 2-Sided Equality
one_mean_size(mu = 2, mu0 = 1.5, sd = 1, alpha = 0.05, beta = 0.2, test_type = "2-side")
[1] 32
one_mean_size(mu = 2, mu0 = 1.5, sd = 1, alpha = 0.05, n = 32, test_type = "2-side")
[1] 0.8074304

# 1-Sided
one_mean_size(mu = 115, mu0 = 120, sd = 24, alpha = 0.05, beta = 0.2, test_type = "1-side")
[1] 143
one_mean_size(mu = 115, mu0 = 120, sd = 24, alpha = 0.05, n = 143, test_type = "1-side")
[1] 0.8013493

# Non-Inferiority or Superiority
one_mean_size(mu = 2, mu0 = 1.5, delta = -0.5, sd = 1, alpha = 0.05, beta = 0.2, test_type = "non-inferiority")
[1] 7
one_mean_size(mu = 2, mu0 = 1.5, delta = -0.5, sd = 1, alpha = 0.05, n = 7, test_type = "non-inferiority")
[1] 0.8415708

# Equivalence
one_mean_size(mu = 2, mu0 = 2, delta = 0.05, sd = 0.1, alpha = 0.05, beta = 0.2, test_type = "equivalence")
[1] 35
one_mean_size(mu = 2, mu0 = 2, delta = 0.05, sd = 0.1, alpha = 0.05, n = 35, test_type = "equivalence")
[1] 0.810884

Compare two means

# 2-Sided Equality
two_mean_size(muA = 5, muB = 10, kappa = 1, sd = 10, alpha = 0.05, beta = 0.2, test_type = "2-side")
[1] 63
two_mean_size(muA = 5, muB = 10, kappa = 1, sd = 10, alpha = 0.05, nB = 63, test_type = "2-side")
[1] 0.8013024


# 1-Sided
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")
[1] 85
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")
[1] 0.8020669

# Non-Inferiority or Superiority
two_mean_size(muA = 5, muB = 5, delta = 5, kappa = 1, sd = 10, alpha = 0.05, beta = 0.2, test_type = "non-inferiority")
[1] 50
two_mean_size(muA = 5, muB = 5, delta = 5, kappa = 1, sd = 10, alpha = 0.05, nB = 50, test_type = "non-inferiority")
[1] 0.8037819

# Equivalence
two_mean_size(muA = 5, muB = 4, delta = 5, kappa = 1, sd = 10, alpha = 0.05, beta = 0.2, test_type = "equivalence")
[1] 108
two_mean_size(muA = 5, muB = 4, delta = 5, kappa = 1, sd = 10, alpha = 0.05, nB = 108, test_type = "equivalence")
[1] 0.8045235

Compare k Means (1-way ANOVA pairwise)

# 2-Sided Equality
k_mean_size(muA = 5, muB = 10, sd = 10, tau = 1, alpha = 0.05, beta = 0.2, test_type = "2-side")
[1] 63
k_mean_size(muA = 5, muB = 10, sd = 10, tau = 1, alpha = 0.05, n = 63, test_type = "2-side")
[1] 0.8013024

# 1-Sided
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")
[1] 85
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")
[1] 0.8020669

Test one proportion

# 2-Sided Equality
one_prop_size(p = 0.5, p0 = 0.3, alpha = 0.05, beta = 0.2, test_type = "2-side")
[1] 50
one_prop_size(p = 0.5, p0 = 0.3, alpha = 0.05, n = 50, test_type = "2-side")
[1] 0.8074304

# 1-Sided
one_prop_size(p = 0.05, p0 = 0.02, alpha = 0.05, beta = 0.2, test_type = "1-side")
[1] 191
one_prop_size(p = 0.05, p0 = 0.02, alpha = 0.05, n = 191, test_type = "1-side")
[1] 0.8011562

# Non-inferiority or Superiority
one_prop_size(p = 0.5, p0 = 0.3, delta = -0.1 ,alpha = 0.05, beta = 0.2, test_type = "non-inferiority")
[1] 18
one_prop_size(p = 0.5, p0 = 0.3, delta = -0.1, alpha = 0.05, n = 18, test_type = "non-inferiority")

# Equivalence
[1] 0.8161482
one_prop_size(p = 0.6, p0 = 0.6, delta = 0.2, alpha = 0.05, beta = 0.2, test_type = "equivalence")
[1] 52
one_prop_size(p = 0.6, p0 = 0.6, delta = 0.2, alpha = 0.05, n = 52, test_type = "equivalence")
[1] 0.8060834

Compare two proportion

# 2-Sided Equality
two_prop_size(pA = 0.65, pB = 0.85, kappa = 1, alpha = 0.05, beta = 0.2, test_type = "2-side")
[1] 70
two_prop_size(pA = 0.65, pB = 0.85, kappa = 1, alpha = 0.05, nB = 70, test_type = "2-side")
[1] 0.8019139

# 1-Sided
two_prop_size(pA = 0.65, pB = 0.85, kappa = 1, alpha = 0.05, beta = 0.2, test_type = "1-side")
[1] 55
two_prop_size(pA = 0.65, pB = 0.85, kappa = 1, alpha = 0.05, nB = 55, test_type = "1-side")
[1] 0.8008219

# Non-inferiority or Superiority
two_prop_size(pA = 0.85, pB = 0.65, delta = -0.1, kappa = 1, alpha = 0.05, beta = 0.2, test_type = "non-inferiority")
[1] 25
two_prop_size(pA = 0.85, pB = 0.65, delta = -0.1, kappa = 1, alpha = 0.05, nB = 25, test_type = "non-inferiority")
[1] 0.8085998

# Equivalence
two_prop_size(pA = 0.65, pB = 0.85, delta = 0.05, kappa = 1, alpha = 0.05, beta = 0.2, test_type = "equivalence")
[1] 136
two_prop_size(pA = 0.65, pB = 0.85, delta = 0.05, kappa = 1, alpha = 0.05, nB = 136, test_type = "equivalence")
[1] 0.8033294

Compare paired proportions (McNemar’s Z-test)

# 2-Sided Equality
pair_prop_size(p01 = 0.45, p10 = 0.05, alpha = 0.1, beta = 0.1, test_type = "2-side")
[1] 23
pair_prop_size(p01 = 0.45, p10 = 0.05, alpha = 0.1, n = 23, test_type = "2-side")
[1] 0.9023805

# 1-Sided
pair_prop_size(p01 = 0.45, p10 = 0.05, alpha = 0.05, beta = 0.1, test_type = "1-side")
[1] 23
pair_prop_size(p01 = 0.45, p10 = 0.05, alpha = 0.05, n = 23, test_type = "1-side")
[1] 0.9023805

Compare k Proportions (1-way ANOVA pairwise)

k_prop_size(pA = 0.2, pB = 0.4, tau = 2, alpha = 0.05, beta = 0.2)
[1] 96
k_prop_size(pA = 0.2, pB = 0.4, tau = 2, alpha = 0.05, n = 96)
[1] 0.8042732

Test time-to-event data (Cox PH)

# 2-Sided Equaltiy
coxph_size(hr = 2, hr0 = 1, pE = 0.8, pA = 0.5, alpha = 0.05, beta = 0.2, test_type = "2-side")
[1] 82
coxph_size(hr = 2, hr0 = 1, pE = 0.8, pA = 0.5, alpha = 0.05, n = 82, test_type = "2-side")
[1] 0.8015214

# Non-inferiority or Superiority
coxph_size(hr = 2, hr0 = 1, pE = 0.8, pA = 0.5, alpha = 0.025, beta = 0.2, test_type = "non-inferiority")
[1] 82
coxph_size(hr = 2, hr0 = 1, pE = 0.8, pA = 0.5, alpha = 0.025, n = 82, test_type = "non-inferiority")
[1] 0.8015214

# Equivalence
coxph_size(hr = 1, delta = 0.5, pE = 0.8, pA = 0.5, alpha = 0.05, beta = 0.2, test_type = "equivalence")
[1] 172
coxph_size(hr = 1, delta = 0.5, pE = 0.8, pA = 0.5, alpha = 0.05, n = 172, test_type = "equivalence")
[1] 0.8021573

Test odds ratio

# Equality
or_size(pA = 0.4, pB = 0.25, kappa = 1, alpha = 0.05, beta = 0.2, test_type = "equality")
[1] 156
or_size(pA = 0.4, pB = 0.25, kappa = 1, alpha = 0.05, nB = 156, test_type = "equality")
[1] 0.8020239

# Non-inferiority or Superiority
or_size(pA = 0.4, pB = 0.25, delta = 0.2, kappa = 1, alpha = 0.05, beta = 0.2, test_type = "non-inferiority")
[1] 242
or_size(pA = 0.4, pB = 0.25, delta = 0.2, kappa = 1, alpha = 0.05, nB = 242, test_type = "non-inferiority")
[1] 0.8007201

# Equivalence
or_size(pA = 0.25, pB = 0.25, delta = 0.5, kappa = 1, alpha = 0.05, beta = 0.2, test_type = "equivalence")
[1] 366
or_size(pA = 0.25, pB = 0.25, delta = 0.5, kappa = 1, alpha = 0.05, nB = 366, test_type = "equivalence")
[1] 0.8008593

Test relative incidence in self controlled case series studies (SCCS)

# SCCS, Alt-2
sccs_size(p = 3, r = 42/365, alpha = 0.05, beta = 0.2)
[1] 54
sccs_size(p = 3, r = 42/365, alpha = 0.05, n = 54)
[1] 0.8072004

Others

# One Sample Normal
one_norm_size(mu = 2, mu0 = 1.5, sd = 1, alpha = 0.05, beta = 0.2)
[1] 32
one_norm_size(mu = 2, mu0 = 1.5, sd = 1, alpha = 0.05, n = 32)
[1] 0.8074304

# One Sample Binomial
one_bino_size(p = 0.5, p0 = 0.3, alpha = 0.05, beta = 0.2)
[1] 50
one_bino_size(p = 0.5, p0 = 0.3, alpha = 0.05, n = 50)
[1] 0.8074304