驗統出

以獨算與系較證統析果。

用

• 驗管呈之主次端點析→用
• 行雙編（R vs SAS、或獨 R 實）→用
• 證析碼生正果→用
• 碼或境變後重驗→用

入

• 必：主析碼與果
• 必：參果（獨算、刊值、已知試數）
• 必：數較容差
• 可：管呈境

行

一：定較框

# Define tolerance levels for different statistics
tolerances <- list(
  counts = 0,           # Exact match for integers
  proportions = 1e-4,   # 0.01% for proportions
  means = 1e-6,         # Numeric precision for means
  p_values = 1e-4,      # 4 decimal places for p-values
  confidence_limits = 1e-3  # 3 decimal places for CIs
)

得：諸統類定容差，整計嚴（精配）、浮點寬（p 值、信限）。

敗：容差有爭→錄各值理據、續前得統頭簽。參 ICH E9 於管呈。

二：建較函

#' Compare two result sets with tolerance-based matching
#'
#' @param primary Results from the primary analysis
#' @param reference Results from the independent calculation
#' @param tolerances Named list of tolerance values
#' @return Data frame with comparison results
compare_results <- function(primary, reference, tolerances) {
  stopifnot(names(primary) == names(reference))

  comparison <- data.frame(
    statistic = names(primary),
    primary_value = unlist(primary),
    reference_value = unlist(reference),
    stringsAsFactors = FALSE
  )

  comparison$absolute_diff <- abs(comparison$primary_value - comparison$reference_value)
  comparison$tolerance <- sapply(comparison$statistic, function(s) {
    # Match to tolerance category or use default
    tol <- tolerances[[s]]
    if (is.null(tol)) tolerances$means  # default tolerance
    else tol
  })

  comparison$pass <- comparison$absolute_diff <= comparison$tolerance

  comparison
}

得：compare_results() 返附統名、主值、參值、絕差、容差、過/敗欄之數據框。

敗：函於名不配誤→驗二果列用同名。容差對應失→加默容差於未知名。

三：行雙編

書獨實，以異碼達同果：

# PRIMARY ANALYSIS (in R/primary_analysis.R)
primary_analysis <- function(data) {
  model <- lm(endpoint ~ treatment + baseline + sex, data = data)
  coefs <- summary(model)$coefficients

  list(
    treatment_estimate = coefs["treatmentActive", "Estimate"],
    treatment_se = coefs["treatmentActive", "Std. Error"],
    treatment_p = coefs["treatmentActive", "Pr(>|t|)"],
    n_subjects = nobs(model),
    r_squared = summary(model)$r.squared
  )
}

# INDEPENDENT VERIFICATION (in validation/independent_analysis.R)
# Written by a different analyst or using different methodology
independent_analysis <- function(data) {
  # Using matrix algebra instead of lm()
  X <- model.matrix(~ treatment + baseline + sex, data = data)
  y <- data$endpoint

  beta <- solve(t(X) %*% X) %*% t(X) %*% y
  residuals <- y - X %*% beta
  sigma2 <- sum(residuals^2) / (nrow(X) - ncol(X))
  var_beta <- sigma2 * solve(t(X) %*% X)
  se <- sqrt(diag(var_beta))

  t_stat <- beta["treatmentActive"] / se["treatmentActive"]
  p_value <- 2 * pt(-abs(t_stat), df = nrow(X) - ncol(X))

  list(
    treatment_estimate = as.numeric(beta["treatmentActive"]),
    treatment_se = se["treatmentActive"],
    treatment_p = as.numeric(p_value),
    n_subjects = nrow(data),
    r_squared = 1 - sum(residuals^2) / sum((y - mean(y))^2)
  )
}

得：二獨實存，用異碼路（如 lm() vs 矩陣代數）達同統果。實由異析者書、或用根本異法。

敗：獨實生異果→先驗二用同入數（較 digest::digest(data)）。次察 NA 處、對比編、自由度算之異。

四：行較

# Execute both analyses
primary_results <- primary_analysis(study_data)
independent_results <- independent_analysis(study_data)

# Compare
comparison <- compare_results(primary_results, independent_results, tolerances)

# Report
cat("Validation Comparison Report\n")
cat("============================\n")
cat(sprintf("Date: %s\n", Sys.time()))
cat(sprintf("Overall: %s\n\n",
  ifelse(all(comparison$pass), "ALL PASS", "DISCREPANCIES FOUND")))

print(comparison)

得：較報示諸統於容差。Overall 行讀「ALL PASS」。

敗：覓差→勿即假主析誤。察二實：察中算、驗同入數、較缺值與邊例之處。

五：較外參（SAS）

R 與 SAS 較：

# Load SAS results (exported as CSV or from .sas7bdat)
sas_results <- list(
  treatment_estimate = 1.2345,  # From SAS PROC GLM output
  treatment_se = 0.3456,
  treatment_p = 0.0004,
  n_subjects = 200,
  r_squared = 0.4567
)

comparison <- compare_results(primary_results, sas_results, tolerances)

# Known sources of difference between R and SAS:
# - Default contrasts (R: treatment, SAS: GLM parameterization)
# - Rounding of intermediate calculations
# - Handling of missing values (na.rm vs listwise deletion)

得：R vs SAS 較果於容差，已知系統異（對比編、捨入）錄釋。

敗：R 與 SAS 異超容差→察三常分歧源：默對比編（R 用處理對比、SAS 用 GLM 參化）、缺值處、中算捨入。各異錄根因。

六：錄果

建驗報：

# validation/output_comparison_report.R
sink("validation/output_comparison_report.txt")

cat("OUTPUT VALIDATION REPORT\n")
cat("========================\n")
cat(sprintf("Project: %s\n", project_name))
cat(sprintf("Date: %s\n", format(Sys.time())))
cat(sprintf("Primary Analyst: %s\n", primary_analyst))
cat(sprintf("Independent Analyst: %s\n", independent_analyst))
cat(sprintf("R Version: %s\n\n", R.version.string))

cat("COMPARISON RESULTS\n")
cat("------------------\n")
print(comparison, row.names = FALSE)

cat(sprintf("\nOVERALL VERDICT: %s\n",
  ifelse(all(comparison$pass), "VALIDATED", "DISCREPANCIES - INVESTIGATION REQUIRED")))

cat("\nSESSION INFO\n")
print(sessionInfo())

sink()

得：完驗報檔存於 validation/output_comparison_report.txt，含案元、較果、總判、會信。

敗：sink() 敗或生空檔→察出目存（dir.create("validation", showWarnings = FALSE)）、無前 sink() 仍活（sink.number() 察）。

七：理差

果不配時：

1. 驗二實用同入數（雜湊較）
2. 察 NA 處異
3. 步步較中算
4. 錄根因
5. 定差可受（容差內）或須改碼

得：諸差究、根因辨、各歸可受（容差內附錄因）或須改碼。

敗：差不能釋→升予統頭。勿略未釋差，或示一實真誤。

驗

• 獨析果於容差
• 諸較統錄
• 差（若有）究而解
• 入數完整驗（雜湊配）
• 容差預定且有理
• 驗報完且簽

忌

• 同析者書二實：雙編須獨析者方為真驗
• 實間共碼：獨版不可由主版抄
• 容差不宜：寬掩真誤；嚴標浮點噪
• 忽系統差：小恒偏或示真誤雖於容差
• 不驗驗：以已知入察較碼自身正

參

• setup-gxp-r-project - 驗工之案構
• write-validation-documentation - 綱與報模
• implement-audit-trail - 跡驗過程自身
• write-testthat-tests - 持驗之自動試套