12 方法学比较

12.1 分析目的

方法学比较（method comparison）评价候选方法（candidate）与参考方法（reference）在相同样本上测得结果的一致性，对应 CLSI EP09。ivdtools 的 mcr() 提供一个渐进式 S3 工作流：描述统计 → 相关分析 → 回归（OLS、WLS、Deming、加权 Deming、Passing–Bablok）→ Bland–Altman → 异常值 → 医学决定水平偏倚，并提供绘图、预测与汇总。本文以一个包含不同批次与样本类型的完整示例演示全流程，并演示按批次/样本类型拆分后的子组比较。

示例数据为确定性的教学数据，其中人为加入了一个离群点以演示异常值检测；统计结果不自动构成合格判定，接受标准应在分析前确定。

代码

library(ivdtools)
library(readr)

12.2 函数概述

函数	主要用途	关键输入或输出
`mcr()`	创建方法学比较对象	`id`、`candidate`、`reference`、`weights`
`describe()`	描述统计	候选/参考/差值及额外列
`correlation()`	相关分析	pearson/spearman/kendall
`regression()`	回归拟合	ols/wls/deming/wdeming/pb、`lambda`、`weights`
`bland_altman()`	一致性限	difference/ratio/percent、`x_axis`
`outlier()`	差值异常值	grubbs/esd/dixon/iqr、`type`
`bias()`	医学决定水平偏倚	`mdl`、`interval`
`predict()`	正向/逆向预测	需先回归
`plot()` / `summary()`	图形与汇总	`type` 选择图形

12.3 示例：完整的单示例分析

12.3.1 读取和核验数据

数据包含 40 例，每例有编号 id、候选方法结果 candidate、参考方法结果 reference，以及批次 batch（B1/B2）与样本类型 sample_type（serum/plasma/urine）：

代码

mc_dat <- read_csv("./data/method-comparison.csv", show_col_types = FALSE)
mc_dat <- as.data.frame(mc_dat)
str(mc_dat)

'data.frame':   40 obs. of  5 variables:
 $ id         : num  1 2 3 4 5 6 7 8 9 10 ...
 $ batch      : chr  "B1" "B1" "B1" "B1" ...
 $ sample_type: chr  "serum" "plasma" "urine" "serum" ...
 $ reference  : num  10 14.9 19.7 24.6 29.5 34.4 39.2 44.1 49 53.8 ...
 $ candidate  : num  11.6 16.6 20.9 30.4 34 ...

代码

dim(mc_dat)

[1] 40  5

代码

knitr::kable(table(mc_dat$batch), caption = "批次分布")

批次分布
Var1	Freq
B1	20
B2	20

代码

knitr::kable(table(mc_dat$sample_type), caption = "样本类型分布")

样本类型分布
Var1	Freq
plasma	13
serum	14
urine	13

12.3.2 创建对象与描述统计

代码

mc <- mcr(mc_dat, id = "id", candidate = "candidate", reference = "reference")

代码

mc <- describe(mc, cols = c("batch", "sample_type"))


Descriptive Statistics
  Variable               n     Mean       SD      Min       Q1   Median       Q3      Max  NA
  --------------------------------------------------------------------------- 
    candidate (X)       40 112.4977  59.2513  11.5900  63.1075 112.5750 159.5925 209.9000  
    reference (Y)       40 105.0000  56.9555  10.0000  57.4750 105.0000 152.5250 200.0000  
    Diff (X-Y)          40   7.4977   3.9583   1.2000   5.2725   6.6100   9.7950  22.1000  

  batch
  Level                Count  Percent
   -------------------------------------- 
  B1                      20    50.0%
  B2                      20    50.0%

  sample_type
  Level                Count  Percent
   -------------------------------------- 
  plasma                  13    32.5%
  serum                   14    35.0%
  urine                   13    32.5%

代码

mc


Method Comparison
  Data class:        data.frame
  Total rows:        40
  Complete pairs:    40
  ID variable:       id
  Test method (X):   candidate
  Reference (Y):     reference
  Duplicate IDs:     none

Analysis slots:
    [x] Describe
    [ ] Correlation
    [ ] Regression
    [ ] Outlier
    [ ] Bland-Altman
    [ ] Bias

describe() 的 cols 指定纳入描述的分类/数值附加列，支持 - 前缀排除。

12.3.3 相关分析

代码

mc <- correlation(mc, method = "pearson")


Correlation
  Method: pearson
  r = 0.9985, 95% CI [0.9971, 0.9992]
  p-value: < 2.2e-16
  n = 40

参数说明： correlation() 的 method 可选 "pearson"、"spearman"、"kendall"。相关反映两变量共同变化的程度，不等于一致性，不能替代 Bland–Altman 或回归偏差评价。

12.3.4 回归分析

依次比较 OLS、Deming、Passing–Bablok 与 WLS。由于 regression() 会更新对象内的回归结果，多种方法分别存入不同对象以便比较：

代码

mc_ols <- regression(mc, method = "ols")


Regression
  Method: OLS
  Intercept = -2.9723  (SE = 1.0971)
  Slope     = 0.9598  (SE = 0.0087)
  Intercept 95% CI: [-5.1933, -0.7513]
  Slope     95% CI: [0.9423, 0.9773]
    H0: slope = 1 -> t = -4.6494, p = 3.944e-05
    slope significantly different from 1 (CI excludes 1)
  R-squared = 0.9969
  Sigma     = 3.2015
  n = 40

代码

mc_dem <- regression(mc, method = "deming")


Regression
  Method: Deming
  Intercept = -3.1323  (SE = 1.4133)
  Slope     = 0.9612  (SE = 0.0092)
  Intercept 95% CI: [-5.9934, -0.2712]
  Slope     95% CI: [0.9426, 0.9798]
    H0: slope = 1 -> t = -4.2313, p = 0.0001413
    slope significantly different from 1 (CI excludes 1)
  Sigma     = 3.2026
  n = 40

代码

mc_pb  <- regression(mc, method = "pb")


Regression
  Method: Passing-Bablok
  Intercept = -2.1674  (SE =    NA)
  Slope     = 0.9556  (SE =    NA)
  Intercept 95% CI: [-3.1487, -0.9828]
  Slope     95% CI: [0.9444, 0.9669]
  Sigma     = 3.2299
  n = 40

代码

mc_wls <- regression(mc, method = "wls", weights = "1/y")


Regression
  Method: WLS
  Weights: 1/y
  Intercept = -2.2924  (SE = 0.9153)
  Slope     = 0.9518  (SE = 0.0108)
  Intercept 95% CI: [-4.1452, -0.4396]
  Slope     95% CI: [0.9299, 0.9736]
    H0: slope = 1 -> t = -4.4712, p = 6.818e-05
    slope significantly different from 1 (CI excludes 1)
  R-squared = 0.9951
  Sigma     = 0.4819
  n = 40

代码

knitr::kable(
  data.frame(
    方法 = c("OLS", "Deming", "Passing-Bablok", "WLS(1/y)"),
    截距 = c(mc_ols$regression$intercept, mc_dem$regression$intercept,
             mc_pb$regression$intercept, mc_wls$regression$intercept),
    斜率 = c(mc_ols$regression$slope, mc_dem$regression$slope,
             mc_pb$regression$slope, mc_wls$regression$slope)
  ),
  digits = 4,
  caption = "四种回归方法截距与斜率比较"
)

四种回归方法截距与斜率比较
方法	截距	斜率
OLS	-2.9723	0.9598
Deming	-3.1323	0.9612
Passing-Bablok	-2.1674	0.9556
WLS(1/y)	-2.2924	0.9518

代码

print(mc_ols)


Method Comparison
  Data class:        data.frame
  Total rows:        40
  Complete pairs:    40
  ID variable:       id
  Test method (X):   candidate
  Reference (Y):     reference
  Duplicate IDs:     none

Analysis slots:
    [x] Describe
    [x] Correlation (pearson)
    [x] Regression (OLS)
    [ ] Outlier
    [ ] Bland-Altman
    [ ] Bias

本例 OLS 斜率 ≈ 0.96，95% CI 不含 1，说明候选方法存在约 4% 的比例偏差（数据真实偏差即为 5%）。

参数说明： regression() 的 method 可选 "ols"、"wls"、"deming"、"wdeming"、"pb"。 Deming 用 lambda 指定方差比（ref/cand，默认 1）；wls/wdeming 必须提供 weights（内置方案或数据列名）；conf.level 控制参数置信区间。

12.3.5 医学决定水平的偏倚

用 bias() 评价在医学决定水平（MDL）处的预测偏倚：

代码

mc_ols <- bias(mc_ols, mdl = c(30, 80, 150), interval = "both")


Bias
  Method: OLS
  Interval: both (95%)
  MDL points: 3
  Bias range: [4.1791, 9.0064]

 mdl     bias ci_lower  ci_upper  pi_lower pi_upper 
--------------------------------------------------- 
  30 4.179112 2.407658  5.950566 -2.539698 10.89792
  80 6.190463 5.018240  7.362685 -0.395770 12.77670
 150 9.006354 7.789153 10.223554  2.411967 15.60074

代码

mc_ols$bias

代码

plot(mc_ols, type = "bias", mdl = c(30, 80, 150))

参数说明： bias(mdl, level, interval) 中 mdl 为医学决定水平向量；interval 可选 ""、"confidence"、"prediction"、"both"。偏倚定义参考候选方法 mdl 处的拟合值与 mdl 之差，解释时应结合回归方向和方案规定的允许偏倚。

12.3.6 Bland–Altman 分析

代码

mc_ols <- bland_altman(mc_ols, type = "difference")


Bland-Altman
  Type:        difference
  Y-axis:      candidate - reference
  X-axis:      Mean of candidate and reference
  n = 40

  Mean diff:       7.4977
  SD diff:         3.9583
  95% LoA: [-0.2603, 15.2558]

  95% CI for LoA:
    Lower LoA: [-2.4419, 1.9213]
    Upper LoA: [13.0742, 17.4374]

代码

plot(mc_ols, type = "bland_altman")

代码

mc_ols$bland_altman[c("mean_diff", "sd_diff", "loa")]

$mean_diff
[1] 7.49775

$sd_diff
[1] 3.958259

$loa
     lower      upper 
-0.2602947 15.2557947

参数说明： bland_altman() 的 type 可选 "difference"、"ratio"、"percent"（Y 轴度量）， x_axis 可选 "mean"、"candidate"、"reference"（X 轴）；agree.level 控制 LoA 宽度， conf.level 控制 LoA 置信区间。

12.3.7 异常值检测

对配对差值检测异常值：

代码

mc_ols <- outlier(mc_ols, method = "grubbs", type = "difference")


Outlier
  Method: grubbs
  Data:   Difference (candidate - reference)
  Alpha:  0.05

  1 outlier(s) found:
  Row                Value   Statistic  Critical
   -------------------------------------------------- 
  7                22.1000      3.6891  3.0361

代码

mc_ols$outlier


Outlier
  Method: grubbs
  Data:   Difference (candidate - reference)
  Alpha:  0.05

  1 outlier(s) found:
  Row                Value   Statistic  Critical
   -------------------------------------------------- 
  7                22.1000      3.6891  3.0361

代码

mc_ols$outlier$indices

[1] 7

检测到第 7 号样本的差值明显偏大。检出异常值不等于应删除——应回查原始记录、实验过程，并在有充分理由时进行包含/不包含的敏感性分析。

12.3.8 预测

代码

predict(mc_ols, candidate = c(40, 100))

代码

predict(mc_ols, reference = c(50, 120), inverse = TRUE)

12.3.9 子组比较

不同批次或样本类型的方法表现可能不同。先按批次拆分，再对子组重跑回归与 Bland–Altman：

代码

for (b in c("B1", "B2")) {
  sub <- mc_dat[mc_dat$batch == b, ]
  mcs <- mcr(sub, id = "id", candidate = "candidate", reference = "reference")
  mcs <- regression(mcs, method = "ols")
  mcs <- bland_altman(mcs, type = "difference")
  cat(b, ": slope =", round(mcs$regression$slope, 4),
      ", mean diff =", round(mcs$bland_altman$mean_diff, 3), "\n")
}


Regression
  Method: OLS
  Intercept = -2.9704  (SE = 2.2333)
  Slope     = 0.9582  (SE = 0.0327)
  Intercept 95% CI: [-7.6623, 1.7215]
  Slope     95% CI: [0.8895, 1.0269]
    H0: slope = 1 -> t = -1.2784, p = 0.2173
    slope not significantly different from 1 (CI contains 1)
  R-squared = 0.9795
  Sigma     = 4.2427
  n = 20

Bland-Altman
  Type:        difference
  Y-axis:      candidate - reference
  X-axis:      Mean of candidate and reference
  n = 20

  Mean diff:       5.5550
  SD diff:         4.3129
  95% LoA: [-2.8981, 14.0081]

  95% CI for LoA:
    Lower LoA: [-6.4069, 0.6107]
    Upper LoA: [10.4993, 17.5169]
B1 : slope = 0.9582 , mean diff = 5.555 

Regression
  Method: OLS
  Intercept = -1.3159  (SE = 2.3598)
  Slope     = 0.9502  (SE = 0.0142)
  Intercept 95% CI: [-6.2736, 3.6419]
  Slope     95% CI: [0.9203, 0.9801]
    H0: slope = 1 -> t = -3.4988, p = 0.002564
    slope significantly different from 1 (CI excludes 1)
  R-squared = 0.9960
  Sigma     = 1.8780
  n = 20

Bland-Altman
  Type:        difference
  Y-axis:      candidate - reference
  X-axis:      Mean of candidate and reference
  n = 20

  Mean diff:       9.4405
  SD diff:         2.3693
  95% LoA: [4.7968, 14.0842]

  95% CI for LoA:
    Lower LoA: [2.8693, 6.7244]
    Upper LoA: [12.1566, 16.0117]
B2 : slope = 0.9502 , mean diff = 9.44

按样本类型同理 split() 后分别分析。子组比较的结论用于判断方法表现是否受批次/样本类型影响，只有预先定义的接受标准才能支撑可接受性结论。

12.3.10 汇总

代码

summary(mc_ols)


Method Comparison Regression (mcr)
-----------------------------------------------------

Method Comparison
  Data class:        data.frame
  Total rows:        40
  Complete pairs:    40
  ID variable:       id
  Test method (X):   candidate
  Reference (Y):     reference
  Duplicate IDs:     none

Analysis slots:
    [x] Describe
    [x] Correlation (pearson)
    [x] Regression (OLS)
    [x] Outlier (grubbs)
    [x] Bland-Altman (difference)
    [x] Bias

Descriptive Statistics
  Variable               n     Mean       SD      Min       Q1   Median       Q3      Max  NA
  --------------------------------------------------------------------------- 
    candidate (X)       40 112.4977  59.2513  11.5900  63.1075 112.5750 159.5925 209.9000  
    reference (Y)       40 105.0000  56.9555  10.0000  57.4750 105.0000 152.5250 200.0000  
    Diff (X-Y)          40   7.4977   3.9583   1.2000   5.2725   6.6100   9.7950  22.1000  

  batch
  Level                Count  Percent
   -------------------------------------- 
  B1                      20    50.0%
  B2                      20    50.0%

  sample_type
  Level                Count  Percent
   -------------------------------------- 
  plasma                  13    32.5%
  serum                   14    35.0%
  urine                   13    32.5%

Correlation
  Method: pearson
  r = 0.9985, 95% CI [0.9971, 0.9992]
  p-value: < 2.2e-16
  n = 40

Regression
  Method: OLS
  Intercept = -2.9723  (SE = 1.0971)
  Slope     = 0.9598  (SE = 0.0087)
  Intercept 95% CI: [-5.1933, -0.7513]
  Slope     95% CI: [0.9423, 0.9773]
    H0: slope = 1 -> t = -4.6494, p = 3.944e-05
    slope significantly different from 1 (CI excludes 1)
  R-squared = 0.9969
  Sigma     = 3.2015
  n = 40

Outlier
  Method: grubbs
  Data:   Difference (candidate - reference)
  Alpha:  0.05

  1 outlier(s) found:
  Row                Value   Statistic  Critical
   -------------------------------------------------- 
  7                22.1000      3.6891  3.0361

Bland-Altman
  Type:        difference
  Y-axis:      candidate - reference
  X-axis:      Mean of candidate and reference
  n = 40

  Mean diff:       7.4977
  SD diff:         3.9583
  95% LoA: [-0.2603, 15.2558]

  95% CI for LoA:
    Lower LoA: [-2.4419, 1.9213]
    Upper LoA: [13.0742, 17.4374]

Bias
  Method: OLS
  Interval: both (95%)
  MDL points: 3
  Bias range: [4.1791, 9.0064]

 mdl     bias ci_lower  ci_upper  pi_lower pi_upper 
--------------------------------------------------- 
  30 4.179112 2.407658  5.950566 -2.539698 10.89792
  80 6.190463 5.018240  7.362685 -0.395770 12.77670
 150 9.006354 7.789153 10.223554  2.411967 15.60074

12.4 结果判读要点

方向核对：回归与 Bland–Altman 均需确认候选相对参考的方向与偏差符号。
相关≠一致：相关系数高不等于方法一致，重点看回归斜率和 Bland–Altman LoA。
方法选择：OLS 假设参考无误差；参考有误差时用 Deming/PB；方差不齐时考虑 WLS/WDeming。
离群处理：检出离群值后回查并做敏感性分析，不自动删除。
子组解释：批次/样本类型拆分后分别判断，避免均值掩盖子组差异。
接受标准：偏差、LoA、MDL 偏倚都必须与预先规定的允许限比较才能作出可接受性结论。