驗統計之出

以獨計與系較，驗統計析之果。

用時

• 為監管呈驗主與次端點析
• 行雙編程（R 對 SAS、或獨 R 之施）
• 驗析碼生正果
• 碼或境變後重驗

入

• 必要：主析之碼與果
• 必要：參果（獨計、已發值、或已知試數）
• 必要：數較之容差準
• 可選：監管呈之脈絡

法

第一步：定較之框

# 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：每統計類之容差已定，整計嚴（精配）、浮點統計（p 值、信區）寬。

敗則：容差爭者，記每閾之理而前進前得統計領之准。監管呈查 ICH E9 之囑。

第二步：立較之函

#' 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() 返數框，含統計名、主值、參值、絕差、容差、過敗狀。

敗則：函於名不配時訛者，驗兩果列用同統計名。容差映敗者，加默容差為未識統計名。

第三步：施雙編程

書獨之施，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：兩獨施存，用異碼徑（如 lm() 對矩陣代數）達同統計果。其由異析者書或用根本異法。

敗則：獨施生異果者，先驗兩用同入數（較 digest::digest(data)）。次察 NA 處、對比編、自由度計之差。

第四步：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：較報示諸統計皆於容差內。Overall 行讀「ALL PASS」。

敗則：見差者，勿即假主析誤。察兩施：察中計、驗同入數、較缺值與邊例之處。

第五步：對外參較（SAS）

R 出對 SAS 較時：

# 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 對 SAS 較果於容差內，已知系差（對比編、舍入）已記已釋。

敗則：R 與 SAS 異超容者，察三常分歧之源：默對比編（R 用處理對比、SAS 用 GLM 參化）、缺值處、中計舍入。每差記其根因。

第六步：記其果

立驗報：

# 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：完驗報文存於 validation/output_comparison_report.txt，含項目元、較果、總判、會信。

敗則：sink() 敗或生空文者，察出域存（dir.create("validation", showWarnings = FALSE)）且無前 sink() 仍活（用 sink.number() 察）。

第七步：處差

果不配時：

1. 驗兩施用同入數（雜湊較）
2. 察 NA 處之異
3. 逐步較中計
4. 記根因
5. 定其差可受（容內）抑需碼修

得：諸差皆已究、根因已識，各分為可受（容內並有理）抑需碼修。

敗則：差不能釋者，升至統計領。勿輕忽未釋之差，蓋或示一施有真訛。

驗

• 獨析生於容差內之果
• 諸較統計已記
• 差（若有）已究而解
• 入數整已驗（雜湊配）
• 容差準已預定且有理
• 驗報全且簽

陷

• 同析者書兩施：雙編程需獨析者方為真驗
• 施間共碼：獨版不可抄主版
• 不宜容差：過寬掩真訛；過嚴標浮點噪
• 忽系差：小恆偏或示真訛雖在容內
• 不驗驗：以已知入察較碼自正

參

• setup-gxp-r-project - 已驗工作之項目結構
• write-validation-documentation - 程與報之模
• implement-audit-trail - 追驗過自身
• write-testthat-tests - 持驗之自試套