Sample Size Calculator for Clinical Research • sampleSizeCalc

Sample Size Calculator for Clinical Research

A comprehensive R package for sample size determination across 39 design combinations: experimental trials (superiority / non-inferiority / equivalence), observational studies (cohort, case-control, cross-sectional), diagnostic accuracy studies (estimation, testing, comparison, AUC), and complex designs (cluster RCT, Simon two-stage, bioequivalence, ordered outcomes, prediction models, interrupted time series).

Every result displays the formula in plain text and LaTeX, a calculation process, and literature references in the default R console output. Parameter roles and methodological hints are included where available.

Installation

devtools::install_github("portos-wang/Sample_Size_Calc")
# or from a local source
devtools::install_local("path/to/Sample_Size_Calc")

Quick start: clinical study planning

These are teaching protocols with illustrative clinical inputs. In a real study, document compatible evidence for the expected effects, variability, prevalence, and margins; a citation for the formula does not establish those clinical assumptions. The English and Chinese guides expand 52 scenarios into population, endpoint, parameter, design, and recruitment decisions.

Scenario 1 — Antihypertensive RCT (continuous endpoint). A blinded, 1:1 parallel trial enrolls adults aged 40–75 with stable background therapy. The primary endpoint is baseline minus week-12 systolic BP, using the same averaged seated-reading protocol at both visits. Assume mean reductions of 10 mmHg with placebo and 12 mmHg with study treatment, with change-score SD 3 mmHg, two-sided alpha 0.05, and power 80%. The relevant SD is for the change score, not baseline BP. The decision is how many independent patients with complete endpoints are required.

library(sampleSizeCalc)

# design x task x outcome
trial_mean <- calculate("rct", "test", "mean",
  mean1 = 10, mean2 = 12, sd = 3
)
trial_mean
#> ────────────────────────────────────────────────────────────────────────────────
#> ✔ Sample Size Calculation Results
#> • Design type: "Two independent samples, mean comparison"
#> • Sample size per group: 37
#> • Total sample size: 74
#> Formula (plain text):
#> `n = 2 * ((Z_alpha/2 + Z_beta) * sd / (mean1 - mean2))^2`
#> Formula (LaTeX):
#> $$n = 2\left(\frac{Z_{\alpha/2} + Z_{\beta}}{\delta}\right)^2 = 2\left(\frac{(Z_{\alpha/2} + Z_{\beta}) \cdot \sigma}{\mu_1 - \mu_2}\right)^2$$
#> Calculation process:
#> 
#> • Step 1: State hypotheses: H0: mu1 = mu2 vs H1: mu1 != mu2 (two-sided alpha =
#> 0.05, power = 0.80).
#> • Step 2: Calculate mean difference delta = |mu1 - mu2| = |10 - 12| = 2; common
#> SD sigma = 3.
#> • Step 3: Determine critical values: Z_(alpha/2) = 1.96 (for two-sided alpha =
#> 0.05), Z_beta = 0.8416 (for power = 0.80).
#> • Step 4: Compute initial sample size via normal approximation: n0 = 2 *
#> ((Z_(alpha/2) + Z_beta) * sigma / delta)^2 = 2 * ((1.96 + 0.8416) * 3 / 2)^2 =
#> 35.32.
#> • Step 5: Refine via exact two-sample Student's t-test power iteration
#> (accounting for degrees of freedom df = 2n - 2).
#> • Step 6: Round up to integer: n = 37 per group, total sample size N = 74.
#> Reference:
#> Chow, S. C., Shao, J., Wang, H., & Lokhnygina, Y. (2017). *Sample size calculations in clinical research* (3rd ed.). CRC Press.
#> ────────────────────────────────────────────────────────────────────────────────
#>

This requires 37 complete patients per arm. If 10% are expected to lack the primary endpoint, plan 42 recruits per arm (84 total); this additional allowance is not included in the displayed RCT result.

Scenario 2 — H. pylori eradication RCT (binary endpoint). Adults with confirmed infection are randomized to two 14-day regimens. Define eradication by a standardized post-treatment breath test in a fixed follow-up window, with prespecified rules for invalid tests, rescue treatment, and missing assessments. Assume cure rates of 85% and 70%, with independent groups, two-sided alpha 0.05, and power 80%. Evidence for these rates should match treatment history and local resistance patterns; symptomatic improvement is not the eradication endpoint.

trial_prop <- calculate("rct", "test", "proportion",
  p1 = 0.85, p2 = 0.70
)
trial_prop
#> ────────────────────────────────────────────────────────────────────────────────
#> ✔ Sample Size Calculation Results
#> • Design type: "Two independent proportions"
#> • Sample size per group: 121
#> • Total sample size: 242
#> Formula (plain text):
#> `n = (Z_a/2 * sqrt(2*p_bar*(1-p_bar)) + Z_b * sqrt(p1*(1-p1)+p2*(1-p2)))^2 /
#> (p1-p2)^2`
#> Formula (LaTeX):
#> $$n = \frac{\left[Z_{\alpha/2}\sqrt{2\bar{p}(1-\bar{p})} + Z_{\beta}\sqrt{p_1(1-p_1) + p_2(1-p_2)}\right]^2}{(p_1 - p_2)^2}$$
#> Calculation process:
#> 
#> • Step 1: State hypotheses: H0: p1 = p2 vs H1: p1 != p2 (two-sided alpha =
#> 0.05, power = 0.80).
#> • Step 2: Compute pooled proportion: p_bar = (p1 + p2) / 2 = (0.85 + 0.70) / 2
#> = 0.775.
#> • Step 3: Determine critical values: Z_(alpha/2) = 1.96, Z_beta = 0.8416.
#> • Step 4: Compute Fleiss formula numerator components:
#> Z_(alpha/2)*sqrt(2*p_bar*(1-p_bar)) = 1.1575; Z_beta*sqrt(p1(1-p1)+p2(1-p2)) =
#> 0.4889.
#> • Step 5: Calculate unrounded sample size per group: n = (1.1575 + 0.4889)^2 /
#> (0.85 - 0.70)^2 = 120.47.
#> • Step 6: Round up to integer: n = 121 per group, total sample size N = 242.
#> Reference:
#> Primary (formula as implemented, without continuity correction): Fleiss, J. L., Tytun, A., & Ury, H. K. (1980). A simple approximation for calculating sample sizes for comparing independent proportions. Biometrics, 36(2), 343-346.
#> 
#> With continuity correction: Casagrande, J. T., Pike, M. C., & Smith, P. G. (1978). An improved approximate formula for calculating sample sizes for comparing two binomial distributions. Biometrics, 34(3), 483-494.
#> 
#> Book: Fleiss, J. L., Levin, B., & Paik, M. C. (2003). Statistical methods for rates and proportions (3rd ed.). Wiley.
#> ────────────────────────────────────────────────────────────────────────────────
#>

The result is 121 patients per arm, 242 total. Endpoint completeness of 90% would require 135 recruits per arm, alongside the prespecified analysis and missing-data strategy.

Scenario 3 — Test versus reference formulation (bioequivalence). Eligible healthy adults are randomized to AB or BA in a two-period crossover study. Evaluate one prespecified log-transformed PK endpoint, such as AUC, with standardized sampling and a justified washout period. Assume within-subject CV 25%, expected geometric mean ratio 1.0, acceptance limits 0.80–1.25, one-sided alpha 0.05, and target power 80%. CV should come from compatible crossover data for the same PK endpoint; additional co-primary PK endpoints require their own planning.

be_trial <- calculate("bioequivalence", "equivalence", "mean", cv = 0.25)
be_trial
#> ────────────────────────────────────────────────────────────────────────────────
#> ✔ Sample Size Calculation Results
#> • Design type: "Bioequivalence (2x2 crossover, exact TOST noncentral t)"
#> • Required sample size: 12
#> • Total sample size: 24
#> • Power achieved: 0.8372
#> Parameter roles
#> 
#> • cv = intra-subject coefficient of variation (log scale implied)
#> • theta0 = anticipated geometric mean ratio (true ratio, default 1.0)
#> • margin = [0.80, 1.25] average BE criteria
#> • n is per sequence; total subjects = 2n
#> Formula (plain text):
#> `exact TOST (Phillips 1990): power = pt(-t, df, ncp=d2) - pt(t, df, ncp=d1)`
#> Formula (LaTeX):
#> $$\text{Power} = F_t(-t_{1-\alpha,\, \nu};\, \nu,\, \delta_2) - F_t(t_{1-\alpha,\, \nu};\, \nu,\, \delta_1), \quad \nu = N-2$$
#> Calculation process:
#> 
#> • Step 1: Intra-subject variance on log scale: sigma_w = sqrt(ln(1 + CV^2)) =
#> sqrt(ln(1 + 0.25^2)) = 0.2462.
#> • Step 2: Standard BE log-scale boundaries: [ln(0.80), ln(1.25)] = [-0.2231,
#> 0.2231].
#> • Step 3: Two One-Sided Tests (TOST) under assumed geometric mean ratio theta0
#> = 1.
#> • Step 4: Search sequence sample size n by evaluating the difference of
#> noncentral t distribution probabilities (Phillips 1990; df = 2n - 2).
#> • Step 5: Required sample size: n = 12 per sequence (achieved power = 0.8372,
#> Total N = 24).
#> Reference:
#> Primary: Phillips, K. F. (1990). Power of the two one-sided tests procedure in bioequivalence. Journal of Pharmacokinetics and Biopharmaceutics, 18(2), 137-144.
#> 
#>  Also: Julious, S. A. (2004). Tutorial in biostatistics: sample sizes for clinical trials with normal data. Statistics in Medicine, 23, 1921-1986 (Eq 13, p. 1941);
#>  Schuirmann, D. J. (1987). J Pharmacokinet Biopharm, 15(6), 657-680;
#>  Chow & Liu (2009). Design and Analysis of Bioavailability and Bioequivalence Studies.
#> ────────────────────────────────────────────────────────────────────────────────
#>

This needs 12 complete subjects per sequence, 24 total, each completing both periods. With 10% incomplete follow-up, a balanced recruitment plan is 28 subjects.

Scenario 4 — Diagnostic sensitivity in a colorectal referral clinic. Consecutively enroll symptomatic or high-risk patients referred for colonoscopy, collect the index-test specimen before reference assessment, and keep the positive threshold fixed. Assume sensitivity 85%, a 95% CI half-width of 0.05, and disease prevalence 20% in this referral setting. Prevalence converts confirmed-case requirements into screening capacity; it is not the test sensitivity and need not match community prevalence. Plan specificity separately if it is also a primary objective.

diag_precision <- calculate("diagAccuracy", "estimate", "proportion",
  prob = 0.85, d = 0.05, prevalence = 0.2
)
diag_precision
#> ────────────────────────────────────────────────────────────────────────────────
#> ✔ Sample Size Calculation Results
#> • Design type: "Diagnostic accuracy (single)"
#> • Cases needed: 196
#> • Total subjects to screen: 980
#> • Total subjects: 980
#> Formula (plain text):
#> `N_cases = (Z_1-a/2)^2 * P*(1-P)/d^2`
#> Formula (LaTeX):
#> $$n_{{{cases}}} = \frac{Z_{1-\alpha/2}^2 \cdot p(1-p)}{d^2}$$
#> Calculation process:
#> 
#> • Step 1: Specify diagnostic accuracy prob (Se or Sp) = 0.85, margin of error d
#> = 0.05, prevalence = 0.20 (alpha = 0.05).
#> • Step 2: Determine critical value: Z_(1-alpha/2) = 1.96 (confidence level =
#> 95%).
#> • Step 3: Calculate target cases required: n_cases = Z_sum^2 * prob * (1 -
#> prob) / d^2 = (1.96)^2 * 0.85 * 0.15 / (0.05)^2 = 195.91.
#> • Step 4: Adjust for disease prevalence: total subjects to screen = n_cases /
#> prevalence = 195.91 / 0.20 = 979.57.
#> • Step 5: Round up to integer: Target cases needed = 196, Total subjects to
#> screen = 980.
#> Reference:
#> Primary: Hanley, J. A., & McNeil, B. J. (1982). The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology, 143(1), 29-36.
#> 
#> Review: Hajian-Tilaki, K. (2014). Sample size estimation in diagnostic test studies of biomedical informatics. Journal of Biomedical Informatics, 48, 193-204.
#> ────────────────────────────────────────────────────────────────────────────────
#>

The requirement is 196 confirmed cases, with an expectation-based screening total of 980. A 90% probability of enough cases instead requires 1061 complete participants under the binomial prevalence assumption. Incomplete reference examinations need additional operational allowance.

Scenario 5 — Diabetes prevalence in a defined older population. A district survey samples eligible residents aged 65 years or older from an explicit population frame. Apply the same disease-ascertainment protocol to each participant. For teaching, assume prevalence 30% and seek a 95% CI absolute half-width of 5 percentage points; this is precision estimation, so no between-group difference or target power is specified. Cluster sampling and nonresponse require separate adjustments.

survey <- calculate("singleProportion", p = 0.30, precision = 0.05)
survey
#> ────────────────────────────────────────────────────────────────────────────────
#> ✔ Sample Size Calculation Results
#> • Design type: "Single proportion estimation (precision)"
#> • Required sample size: 323
#> Parameter roles
#> 
#> • p = expected proportion (e.g. prevalence)
#> • precision = margin of error d (half-width of the CI)
#> • confidence level = 95%
#> Formula (plain text):
#> `n = Z^2 * p(1-p) / d^2`
#> Formula (LaTeX):
#> $$n = \frac{Z_{1-\alpha/2}^2 \cdot p(1-p)}{d^2}$$
#> Calculation process:
#> 
#> • Step 1: Specify anticipated proportion p = 0.30, margin of error d = 0.05
#> (absolute precision), alpha = 0.05.
#> • Step 2: Determine critical value: Z_(1-alpha/2) = 1.96 (confidence level =
#> 95%).
#> • Step 3: Compute variance component: p * (1 - p) = 0.30 * 0.70 = 0.21.
#> • Step 4: Calculate unrounded sample size: n = Z_(1-alpha/2)^2 * p * (1 - p) /
#> d^2 = (1.96)^2 * 0.21 / (0.05)^2 = 322.68.
#> • Step 5: Round up to integer: Required sample size n = 323.
#> Reference:
#> Bhardwaj et al. (2024). Determination of sample size for various study designs in medical research: A practical primer. Journal of Family Medicine and Primary Care, 13(7), 2555-2561 (p. 2558).
#> 
#> Also: Lwanga, S. K., & Lemeshow, S. (1991). Sample size determination in health studies: A practical manual. World Health Organization.
#> ────────────────────────────────────────────────────────────────────────────────
#>

Obtain 323 valid records; at a 90% response rate, invite about 359 people before any design-effect adjustment.

Scenario 6 — Precision of a continuous biomarker’s AUC. Select reference-confirmed cases and clinically comparable non-cases in equal numbers, using a frozen score and one observation per patient. Assume AUC 0.80 and a 95% CI half-width of 0.10 under a binormal variance model. The quota sample estimates discrimination; it does not directly estimate population prevalence. Because this design is unambiguous, task and outcome can be omitted:

auc_precision <- calculate("diagAUC", auc = 0.80, d = 0.10,
  ratio = 1, var_method = "binormal"
)
auc_precision
#> ────────────────────────────────────────────────────────────────────────────────
#> ✔ Sample Size Calculation Results
#> • Design type: "Single-group AUC CI precision"
#> • Cases needed: 46
#> • Total subjects to screen: 92
#> • Total subjects: 92
#> Parameter roles
#> 
#> • auc = anticipated area under the ROC curve
#> • precision = desired CI half-width L
#> • ratio = case:control ratio R (cases:non-cases; default 1)
#> • var_method = binormal variance function
#> Formula (plain text):
#> `N_cases = (Z_1-a/2 / d)^2 * V(AUC)`
#> Formula (LaTeX):
#> $$n_{cases} = \left(\frac{Z_{1-\alpha/2}}{d}\right)^2 \cdot V(AUC)$$
#> Calculation process:
#> 
#> • Step 1: Anticipated AUC = 0.80, precision d = 0.10, supplied allocation R =
#> 1, alpha = 0.05.
#> • Step 2: Use the binormal variance model with the supplied allocation: V(AUC)
#> = 0.1195.
#> • Step 3: Calculate cases: n_cases = (Z_(1-alpha/2)/d)^2 * V(AUC) =
#> (1.96/0.10)^2 * 0.1195 = 45.89.
#> • Step 4: Convert using the supplied allocation: total = n_cases*(1+R) =
#> 45.89*(1+1) = 91.78.
#> • Step 5: Round up: Target cases needed = 46, Total subjects to screen = 92.
#> Reference:
#> Primary: Zhou, X.-H., Obuchowski, N. A., & McClish, D. K. (2011). Statistical Methods in Diagnostic Medicine (2nd ed.). Wiley. Section 6.1.2, pp. 196-199 (Eq 6.4/6.5/6.6; CTC worked example).
#> 
#>  Original variance: Hanley, J. A., & McNeil, B. J. (1982). Radiology, 143(1), 29-36.
#>  Binormal variance: Obuchowski, N. A. (1994). Medical Decision Making, 14(2), 154-162.
#> ────────────────────────────────────────────────────────────────────────────────
#>

Plan 46 cases and the same number of non-cases, each contributing a complete score and reference result.

Illegal combinations error with the list of legal ones. The English guide and Chinese guide cover design choices, parameters, formulas, and worked clinical examples. The regression tests check sample sizes against published examples.

Legacy API (silently compatible)

All 17 pre-3.0 keywords keep working with identical results:

sample_size_calculator("twoMeans", mean1 = 10, mean2 = 12, sd = 3)  # 37/group
#> ────────────────────────────────────────────────────────────────────────────────
#> ✔ Sample Size Calculation Results
#> • Design type: "Two independent samples, mean comparison"
#> • Sample size per group: 37
#> • Total sample size: 74
#> Formula (plain text):
#> `n = 2 * ((Z_alpha/2 + Z_beta) * sd / (mean1 - mean2))^2`
#> Formula (LaTeX):
#> $$n = 2\left(\frac{Z_{\alpha/2} + Z_{\beta}}{\delta}\right)^2 = 2\left(\frac{(Z_{\alpha/2} + Z_{\beta}) \cdot \sigma}{\mu_1 - \mu_2}\right)^2$$
#> Calculation process:
#> 
#> • Step 1: State hypotheses: H0: mu1 = mu2 vs H1: mu1 != mu2 (two-sided alpha =
#> 0.05, power = 0.80).
#> • Step 2: Calculate mean difference delta = |mu1 - mu2| = |10 - 12| = 2; common
#> SD sigma = 3.
#> • Step 3: Determine critical values: Z_(alpha/2) = 1.96 (for two-sided alpha =
#> 0.05), Z_beta = 0.8416 (for power = 0.80).
#> • Step 4: Compute initial sample size via normal approximation: n0 = 2 *
#> ((Z_(alpha/2) + Z_beta) * sigma / delta)^2 = 2 * ((1.96 + 0.8416) * 3 / 2)^2 =
#> 35.32.
#> • Step 5: Refine via exact two-sample Student's t-test power iteration
#> (accounting for degrees of freedom df = 2n - 2).
#> • Step 6: Round up to integer: n = 37 per group, total sample size N = 74.
#> Reference:
#> Chow, S. C., Shao, J., Wang, H., & Lokhnygina, Y. (2017). *Sample size calculations in clinical research* (3rd ed.). CRC Press.
#> ────────────────────────────────────────────────────────────────────────────────
#> 
sample_size_calculator("survival", hr = 0.7)                        # 247 events
#> ────────────────────────────────────────────────────────────────────────────────
#> ✔ Sample Size Calculation Results
#> • Design type: "Survival (log-rank)"
#> • Events needed: 247
#> Formula (plain text):
#> `E = (Z_a/2 + Z_b)^2 / (pE*(1-pE)*log(HR)^2)`
#> Formula (LaTeX):
#> $$E = \frac{(Z_{\alpha/2} + Z_{\beta})^2}{p_E(1-p_E)[\ln(HR)]^2}$$
#> Calculation process:
#> 
#> • Step 1: State survival parameters: Hazard Ratio HR = 0.70, experimental arm
#> allocation pE = 0.50 (alpha = 0.05, power = 0.80).
#> • Step 2: Compute log hazard ratio: ln(HR) = ln(0.70) = -0.3567.
#> • Step 3: Determine critical values: Z_(alpha/2) = 1.96, Z_beta = 0.8416.
#> • Step 4: Apply Schoenfeld formula: E = (Z_(alpha/2) + Z_beta)^2 / [pE * (1 -
#> pE) * (ln HR)^2] = (1.96 + 0.8416)^2 / [0.50 * 0.50 * (-0.3567)^2] = 246.79.
#> • Step 5: Round up to integer: Target events needed E = 247.
#> Reference:
#> Primary: Schoenfeld, D. A. (1983). Sample-size formula for the proportional-hazards regression model. Biometrics, 39(2), 499-503.
#> 
#> Extensions:
#> - Hsieh, F. Y., & Lavori, P. W. (2000). Sample-size calculations for the Cox proportional hazards regression model with nonbinary covariates. Controlled Clinical Trials, 21(6), 552-560.
#> - Rubinstein, L. V., Gail, M. H., & Santner, T. J. (1981). Planning the duration of a comparative clinical trial with loss to follow-up and a period of continued observation. Journal of Chronic Diseases, 34(9-10), 469-479.
#> ────────────────────────────────────────────────────────────────────────────────
#>

Result object

calculate() returns a sample_size_result S3 object. Printing the object (or calling print()) displays the design, sample size, and all four report components:

Report component	Console label	Result field
Plain-text formula	`Formula (plain text)`	`formula`
LaTeX source	`Formula (LaTeX)`	`formula_latex`
Calculation process	`Calculation process`	`calculation_steps` (also `calculation`)
Literature sources	`Reference`	`reference`

The same reporting components are available through sample_size_calculator(). Assigning a result to a variable stores it; print that variable to display the report. summary() additionally shows all input parameters, classification axes, and recorded adjustments. plot() provides the supported visual diagnostics.

res <- calculate("rct", "test", "mean", mean1 = 10, mean2 = 12, sd = 3)
summary(res)
#> ────────────────────────────────────────────────────────────────────────────────
#> ✔ Sample Size Calculation Summary
#> ────────────────────────────────────────────────────────────────────────────────
#> 
#> ── Study Design
#> • Type: "Two independent samples, mean comparison"
#> • Design: "rct"
#> • Task: "test" | Outcome: "mean"
#> 
#> ── Parameters
#> • mean1: 10
#> • mean2: 12
#> • sd: 3
#> • alpha: 0.05
#> • power: 0.8
#> 
#> ── Sample Size Results
#> • Sample size per group: 37
#> • Total sample size: 74
#> 
#> ── Formula
#> Plain text:
#> `n = 2 * ((Z_alpha/2 + Z_beta) * sd / (mean1 - mean2))^2`
#> LaTeX:
#> $$n = 2\left(\frac{Z_{\alpha/2} + Z_{\beta}}{\delta}\right)^2 = 2\left(\frac{(Z_{\alpha/2} + Z_{\beta}) \cdot \sigma}{\mu_1 - \mu_2}\right)^2$$
#> 
#> ── Calculation Process
#> • Step 1: State hypotheses: H0: mu1 = mu2 vs H1: mu1 != mu2 (two-sided alpha =
#> 0.05, power = 0.80).
#> • Step 2: Calculate mean difference delta = |mu1 - mu2| = |10 - 12| = 2; common
#> SD sigma = 3.
#> • Step 3: Determine critical values: Z_(alpha/2) = 1.96 (for two-sided alpha =
#> 0.05), Z_beta = 0.8416 (for power = 0.80).
#> • Step 4: Compute initial sample size via normal approximation: n0 = 2 *
#> ((Z_(alpha/2) + Z_beta) * sigma / delta)^2 = 2 * ((1.96 + 0.8416) * 3 / 2)^2 =
#> 35.32.
#> • Step 5: Refine via exact two-sample Student's t-test power iteration
#> (accounting for degrees of freedom df = 2n - 2).
#> • Step 6: Round up to integer: n = 37 per group, total sample size N = 74.
#> 
#> ── Reference
#> Chow, S. C., Shao, J., Wang, H., & Lokhnygina, Y. (2017). *Sample size calculations in clinical research* (3rd ed.). CRC Press.
#> ────────────────────────────────────────────────────────────────────────────────

You can also extract the report components for a protocol or manuscript:

res$formula
cat(res$formula_latex)
cat(res$calculation_steps, sep = "\n")
cat(res$reference)

The R console displays LaTeX as copyable source. In an R Markdown document, use cat(res$formula_latex) in a chunk with results = "asis" to typeset it. See the reporting guide for an executed example and instructions in English and Chinese.

Study designs (family overview)

Family	Designs
Trials	`rct` (test/NI/superiority/equivalence x mean/proportion/survival), `paired` (mean/proportion), `rctSingleArm`, `crossover`, `bioequivalence`, `singleArmPhaseII` (Simon optimal/minimax, A’Hern)
Observational	`cohort` (proportion/rate), `caseControl`, `caseControlMatched`, `crosstab`
Diagnostic	`diagAccuracy` (estimate/test/dual-endpoint), `diagAccuracyCompare` (test/NI/equivalence), `diagAUC`, `diagAUCCompare` (test/NI/equivalence), `diagLR`
Estimation	`singleProportion`, `singleMean`, `singleCorrelation`
Complex	`clusterRCT`, `steppedWedge`, `kappa`, `twoOrdinal`, `predictiveModel`, `its` (experimental)

Literature

Methods are anchored to primary sources, with worked examples from the reference literature used as automated numeric test benchmarks:

Zhou, Obuchowski & McClish (2011). Statistical Methods in Diagnostic Medicine (2nd ed.), Wiley - diagnostic module.
Machin, Campbell, Tan & Tan (2018). Sample Sizes for Clinical, Laboratory and Epidemiology Studies (4th ed.), Wiley - trial/complex designs.
Hajian-Tilaki (2014). J Biomed Informatics 48:193-204 - diagnostic formulas.
Akoglu (2022). Turkish J Emergency Medicine 22(4):177-185 - diagnostic comparisons and dual-endpoint strategy.
Bhardwaj et al. (2024). J Family Med Prim Care 13(7):2555-2561 - prevalence studies and dropout adjustment.
Plus the original methods: Schoenfeld (1983), Fleiss et al. (1980), Casagrande et al. (1978), Schlesselman (1982), Dupont (1988), Connor (1987), Hanley & McNeil (1982/1983), Buderer (1996), Simon (1989), A’Hern (2001), Whitehead (1993), Peduzzi et al. (1996), Schuirmann (1987).

Citation

If you use the package in research, please cite the original methodology papers for each design (listed in every result’s reference field) along with the package:

@software{sampleSizeCalc,
  title = {sampleSizeCalc: Sample Size Calculator for Clinical Research},
  author = {Portos (Yishan) Wang and Bingxin Cai},
  organization = {Gansu Provincial Maternity and Child-care Hospital (Gansu Provincial Central Hospital)},
  year = {2026},
  version = {3.1.1},
  url = {https://github.com/portos-wang/Sample_Size_Calc}
}

License

MIT (see LICENSE).