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flowchart LR
A{"输入数据层级"} -->|逐例判定| B["raw_to_table()"]
A -->|TP/FP/TN/FN| C["counts_to_table()"]
B --> D["diagnostics() / kappa()<br/>mcnemar()"]
C --> D
A -->|连续内部响应| E["continuous_to_binary()<br/>或 c5_c95()"]
D --> F["临床性能或<br/>观察者一致性"]
E --> G["阈值附近检出概率<br/>或声明验证"]
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classDef process fill:#EAF7E6,stroke:#3FB618,color:#212529
classDef decision fill:#FFF4E8,stroke:#FF7518,color:#212529
classDef output fill:#F4EEFB,stroke:#9954BB,color:#212529
class A decision
class B,C,D,E process
class F,G output
15 定性分析与 C5/C95
本文回答三个层次不同的问题：候选方法与参考方法的二分类结果是否一致、阳性/阴性判定的一致程度有多大，以及连续响应在临界浓度附近达到指定检出概率的位置。前两类问题使用配对四格表，后一类问题使用 c5_c95()。
重要使用边界
分析前必须固定阳性方向、参考方法或临床状态定义、重复测量的合并规则和置信区间方法。若一个受试者有多次结果，应先按方案确定“受试者级”判定，不能把重复结果直接当作独立样本扩大样本量。
分析流程：从判定结果到定性性能结论
定性（qualitative）分析评价候选方法与参考方法在阳性/阴性判定上的一致程度，对应 CLSI EP12。ivdtools 提供 raw_to_table() 从原始配对数据构建四格表，counts_to_table() 从已有的 TP/FP/TN/FN 计数直接构建，并配套 diagnostics()（灵敏度、特异度、PPV、NPV、似然比等）、kappa()（Kappa 与 PABAK）与 mcnemar()（配对差异检验）三个分析方法。定量结果需转定性时可用 continuous_to_binary()。
代码
library(ivdtools)
library(readr)15.1 主要函数
| 函数 | 主要用途 | 关键输入或输出 |
|---|---|---|
raw_to_table() |
原始配对数据构建四格表 | candidate、reference、 positive、 na.rm |
counts_to_table() |
由 TP/FP/TN/FN 构建四格表 | candidate/reference 命名 |
continuous_to_binary() |
定量转定性 | cutoff（≥ cutoff 为 1） |
describe() |
原始数据描述 | 仅 raw_to_table() 来源可用 |
diagnostics() |
诊断准确性指标 | ci.method、prevalence |
kappa() |
Kappa / PABAK | prevalence 切换 |
mcnemar() |
配对差异检验 | 不一致对 <25 用精确检验 |
c5_c95() |
内部连续响应的 C5/C95 | cutoff、direction、精密度剖面 |
选择函数时，先看数据处于哪一个层级：已有 TP/FP/TN/FN 时使用 counts_to_table()；有逐受试者配对判定时使用 raw_to_table()；只有连续信号和参考浓度时，先确认能否建立 c5_c95() 所需的重复性/精密度关系。diagnostics()、kappa() 和 mcnemar() 的统计对象都来自同一张四格表，报告时应保持分母一致。
15.1.1 四格表指标与检验公式
代码
raw_to_table(data, candidate, reference, id = NULL,
na.rm = TRUE, positive = NULL)
counts_to_table(tp, fp, tn, fn,
candidate = "candidate", reference = "reference")
diagnostics(object, conf.level = 0.95,
ci.method = "wilson", prevalence = NULL)
kappa(x, prevalence = NULL, conf.level = 0.95)
mcnemar(x, conf.level = 0.95)约定四格表为 \(a=TP,b=FP,c=FN,d=TN\)。主要指标为
\[ Se=\frac{a}{a+c},\quad Sp=\frac{d}{b+d},\quad PPV=\frac{a}{a+b},\quad NPV=\frac{d}{c+d}, \]
\[ LR^+=\frac{Se}{1-Sp},\qquad LR^-=\frac{1-Se}{Sp}. \]
diagnostics() 的比例区间可选 Wilson、Wald、连续性校正 Wald/Wilson、Agresti–Coull、Jeffreys 或 Clopper–Pearson。给出目标人群患病率 \(\pi\) 时，PPV/NPV 用贝叶斯关系重算；其余指标仍来自原四格表。零格时 LR 或 OR 的对数近似区间可能为 NA，函数不自动作 0.5 校正。
Cohen Kappa 使用
\[ \kappa=\frac{P_o-P_e}{1-P_e},\qquad P_o=\frac{a+d}{n}, \]
其中 \(P_e\) 由两种判定的边际比例计算。向 kappa() 传入 prevalence 时，当前实现切换为 \(PABAK=2P_o-1\)；该数值参数只触发 PABAK 并记录标签，不进入公式。McNemar 只使用不一致对 \(b,c\)：\(b+c<25\) 时做双侧精确二项检验，否则使用连续性校正统计量
\[ \chi^2=\frac{(|b-c|-1)^2}{b+c}. \]
raw_to_table() 和 counts_to_table() 返回四格表对象；continuous_to_binary() 返回新增二分类列的数据框；describe() 返回描述统计表；diagnostics()、kappa() 和 mcnemar() 返回统计量、区间和检验结果
15.1.2 C5/C95 的概率模型
代码
c5_c95(data, result = NULL, sample = NULL, cutoff,
direction = c("geq", "leq"),
probabilities = c(0.05, 0.95), component = NULL,
model.no = 1:10, K = 2, search_range = NULL)对内部连续响应均值 \(\mu\) 和精密度轮廓 \(\sigma(\mu)\)，direction="geq" 时
\[ P(\text{阳性}\mid\mu) =1-\Phi\left(\frac{c-\mu}{\sigma(\mu)}\right). \]
C5/C95 是分别令该概率等于 0.05 和 0.95 时求得的 \(\mu\)。输入可为原始重复数据，也可为已经执行 variance() 的 precision 对象。若存在多个根，函数选取最接近 cutoff 的根；无根、多根或超出观测均值范围都会记录在 issues，不应静默忽略。
c5_c95() 返回 C5/C95、拟合模型和 issues。
15.2 分析案例
15.2.1 示例一：原始配对数据的完整分析
代码
qual <- read_csv("./data/015-定性分析与C5C95/qualitative-raw.csv", show_col_types = FALSE)
qual <- as.data.frame(qual)
qa <- raw_to_table(
qual,
candidate = "new",
reference = "gold",
id = "id",
positive = "positive"
)
qa
Fourfold Table
Source : raw data
Total n : 60
Duplicate IDs : none
Candidate : new
Reference : gold
2x2 Contingency Table
----------------------------------------
gold
positive negative Sum
----------------------------------------
new positive 23 1 24
negative 1 35 36
sum 24 36 60
---------------------------------------- raw_to_table() 要求候选与参考列都恰好有 2 个水平；positive 指定阳性水平（用于因子/字符列的水平映射）；na.rm 控制是否删除缺失行。id 可选，用于重复样本检测。
代码
qa <- describe(qa)
Data Summary
Rows: 60
Columns: 5
ID: 60 unique, no duplicates
new
negative 36 ( 60.0%)
positive 24 ( 40.0%)
gold
negative 36 ( 60.0%)
positive 24 ( 40.0%)
age
Mean (SD): 51.05 (13.45)
Median (Q1-Q3): 48.90 (42.15 - 57.28)
Range: 24.30 - 90.10
gender
F 32 ( 53.3%)
M 28 ( 46.7%)describe() 仅对 raw_to_table() 来源可用，输出行数、ID 重复、各列摘要与缺失情况。
代码
qa <- diagnostics(qa, ci.method = "wilson")
Diagnostic Performance Summary
Sensitivity 0.958 (0.798, 0.993)
Specificity 0.972 (0.858, 0.995)
PPV 0.958 (0.798, 0.993)
NPV 0.972 (0.858, 0.995)
Accuracy 0.967 (0.886, 0.991)
Prevalence 0.400 (0.286, 0.526)
LR+ 34.500 (4.986, 238.724)
LR- 0.043 (0.006, 0.292)
Odds Ratio 805.000 (47.921, 13522.837)
# PPV & NPV are based on data prevalence of 0.400.
# Confidence intervals for proportions use 'wilson' method.本例灵敏度 0.958、特异度 0.972。若已知目标人群患病率，可用 prevalence 重算 PPV/NPV：
代码
qa <- diagnostics(qa, prevalence = 0.4)
Diagnostic Performance Summary
Sensitivity 0.958 (0.798, 0.993)
Specificity 0.972 (0.858, 0.995)
PPV 0.958 (0.790, 0.993)
NPV 0.972 (0.864, 0.995)
Accuracy 0.967 (0.886, 0.991)
Prevalence 0.400
LR+ 34.500 (4.986, 238.724)
LR- 0.043 (0.006, 0.292)
Odds Ratio 805.000 (47.921, 13522.837)
# PPV & NPV are based on user-specified prevalence of 0.400.
# Confidence intervals for proportions use 'wilson' method.diagnostics() 的 ci.method 可选 7 种比例置信区间方法（默认 "wilson"）；给出 prevalence 时 PPV/NPV 按贝叶斯公式重算，否则基于数据患病率。
代码
qa <- kappa(qa)
Cohen's Kappa
new vs gold
n = 60
Kappa 0.9306
SE 0.0483
95% CI (0.8359, 1.0000)
Observed agreement 0.9667
Expected agreement 0.5200代码
qa <- kappa(qa, prevalence = 0.5)
PABAK
new vs gold
n = 60
Kappa 0.9333
SE 0.0463
95% CI (0.8425, 1.0000)
Observed agreement 0.9667
Expected agreement 0.5000
# PABAK (prevalence = 0.500): 2 * p_obs - 1, assumes expected agreement = 0.5kappa() 给出 Cohen’s Kappa；当给出 prevalence 时改为计算 PABAK（2·p_obs − 1）。两者对患病率偏倚的处理不同，报告时应注明方法。
代码
qa <- mcnemar(qa)
McNemar Test
new vs gold
Discordant pairs: b (pos, neg) = 1, c (neg, pos) = 1
n (b + c) = 2
Method: Exact binomial test
P-value: 1.0000
Conclusion: Not significant at 95% confidence level不一致对 b+c = 2 < 25，函数自动使用精确二项检验。
代码
summary(qa)
Qualitative Analysis - summary
-------------------------------------------------
Fourfold Table
Source : raw data
Total n : 60
Duplicate IDs : none
Candidate : new
Reference : gold
2x2 Contingency Table
----------------------------------------
gold
positive negative Sum
----------------------------------------
new positive 23 1 24
negative 1 35 36
sum 24 36 60
----------------------------------------
Analyses performed:
[x] Describe
[x] Diagnostics
[x] Kappa
[x] McNemar
Data Summary
Rows: 60
Columns: 5
ID: 60 unique, no duplicates
new
negative 36 ( 60.0%)
positive 24 ( 40.0%)
gold
negative 36 ( 60.0%)
positive 24 ( 40.0%)
age
Mean (SD): 51.05 (13.45)
Median (Q1-Q3): 48.90 (42.15 - 57.28)
Range: 24.30 - 90.10
gender
F 32 ( 53.3%)
M 28 ( 46.7%)
Diagnostic Performance Summary
Sensitivity 0.958 (0.798, 0.993)
Specificity 0.972 (0.858, 0.995)
PPV 0.958 (0.790, 0.993)
NPV 0.972 (0.864, 0.995)
Accuracy 0.967 (0.886, 0.991)
Prevalence 0.400
LR+ 34.500 (4.986, 238.724)
LR- 0.043 (0.006, 0.292)
Odds Ratio 805.000 (47.921, 13522.837)
# PPV & NPV are based on user-specified prevalence of 0.400.
# Confidence intervals for proportions use 'wilson' method.
PABAK
new vs gold
n = 60
Kappa 0.9333
SE 0.0463
95% CI (0.8425, 1.0000)
Observed agreement 0.9667
Expected agreement 0.5000
# PABAK (prevalence = 0.500): 2 * p_obs - 1, assumes expected agreement = 0.5
McNemar Test
new vs gold
Discordant pairs: b (pos, neg) = 1, c (neg, pos) = 1
n (b + c) = 2
Method: Exact binomial test
P-value: 1.0000
Conclusion: Not significant at 95% confidence level15.2.2 示例二：由 TP/FP/TN/FN 直接构建
代码
tab <- counts_to_table(
tp = 80, fp = 5, tn = 120, fn = 3,
candidate = "new method",
reference = "gold standard"
)
tab
Fourfold Table
Source : counts
Total n : 208
Candidate : new method
Reference : gold standard
2x2 Contingency Table
-----------------------------------------------
gold standard
positive negative Sum
-----------------------------------------------
new method positive 80 5 85
negative 3 120 123
sum 83 125 208
----------------------------------------------- 代码
tab <- diagnostics(tab)
Diagnostic Performance Summary
Sensitivity 0.964 (0.899, 0.988)
Specificity 0.960 (0.910, 0.983)
PPV 0.941 (0.870, 0.975)
NPV 0.976 (0.931, 0.992)
Accuracy 0.962 (0.926, 0.980)
Prevalence 0.399 (0.335, 0.467)
LR+ 24.096 (10.198, 56.934)
LR- 0.038 (0.012, 0.114)
Odds Ratio 640.000 (148.773, 2753.180)
# PPV & NPV are based on data prevalence of 0.399.
# Confidence intervals for proportions use 'wilson' method.代码
tab <- kappa(tab)
Cohen's Kappa
new method vs gold standard
n = 208
Kappa 0.9201
SE 0.0277
95% CI (0.8659, 0.9744)
Observed agreement 0.9615
Expected agreement 0.5184代码
tab <- mcnemar(tab)
McNemar Test
new method vs gold standard
Discordant pairs: b (pos, neg) = 5, c (neg, pos) = 3
n (b + c) = 8
Method: Exact binomial test
P-value: 0.7266
Conclusion: Not significant at 95% confidence level代码
describe(tab) # counts 来源无原始数据，describe() 不可用counts_to_table() 构建的对象没有原始数据，因此 describe() 不可用；diagnostics()、kappa()、 mcnemar() 均正常。
15.2.3 示例三：定量数据转定性
候选方法为定量结果 result，参考为定性 gold：
代码
cont <- read_csv("./data/015-定性分析与C5C95/qualitative-continuous.csv", show_col_types = FALSE)
cont <- as.data.frame(cont)
head(cont, 6) id result gold
1 S001 10.111087 positive
2 S002 13.057209 positive
3 S003 1.534680 negative
4 S004 7.782787 negative
5 S005 4.982424 negative
6 S006 9.443399 negative按 cutoff = 8 转二分类：
代码
cont_bin <- continuous_to_binary(cont, cols = "result", cutoff = 8)
head(cont_bin, 6) id result gold result_binary
1 S001 10.111087 positive 1
2 S002 13.057209 positive 1
3 S003 1.534680 negative 0
4 S004 7.782787 negative 0
5 S005 4.982424 negative 0
6 S006 9.443399 negative 1continuous_to_binary() 生成 result_binary 列（≥ cutoff 为 1，否则 0）。为满足 raw_to_table() 的 positive 映射要求，先重标为与参考一致的标签：
代码
cont_bin$result_binary_lab <- ifelse(cont_bin$result_binary == 1, "positive", "negative")代码
qa3 <- raw_to_table(
cont_bin,
candidate = "result_binary_lab",
reference = "gold",
id = "id",
positive = "positive"
)
qa3 <- diagnostics(qa3)
Diagnostic Performance Summary
Sensitivity 0.952 (0.773, 0.992)
Specificity 0.897 (0.736, 0.964)
PPV 0.870 (0.679, 0.955)
NPV 0.963 (0.817, 0.993)
Accuracy 0.920 (0.812, 0.968)
Prevalence 0.420 (0.294, 0.558)
LR+ 9.206 (3.140, 26.994)
LR- 0.053 (0.008, 0.361)
Odds Ratio 173.333 (16.746, 1794.100)
# PPV & NPV are based on data prevalence of 0.420.
# Confidence intervals for proportions use 'wilson' method.positive 指定的水平必须同时存在于两列中，因此先把二值列重标为 positive/negative。若不指定 positive，函数可能按排序水平把阳性/阴性方向颠倒，导致 TP/FP 翻转，务必核对。
15.2.4 示例四：由内部连续响应估计 C5/C95
当定性判定来自内部连续信号与固定 cutoff 时，可用重复测量建立 SD-均值精密度剖面，再求达到指定阳性概率时的平均响应。下面以 result >= 40 定义目标事件：
代码
head(c5_data, 6) level response
1 L1 35.14000
2 L1 35.29636
3 L1 35.45273
4 L1 35.60909
5 L1 35.76545
6 L1 35.92182代码
c5_result <- c5_c95(
c5_data,
result = "response",
sample = "level",
cutoff = 40,
direction = "geq",
probabilities = c(0.05, 0.95),
model.no = 1
)
c5_resultC5/C95 estimation from an internal continuous response
Source: raw data
Precision component: repeatability
Event: response >= cutoff
cutoff label probability mean_response SD actual_probability extrapolated
------------------------------------------------------------------------------
40 C5 0.05 39.0291 0.5903 0.05 FALSE
40 C95 0.95 40.9709 0.5903 0.95 FALSE 代码
plot(c5_result, type = "probability")
direction = "geq" 表示响应大于等于 cutoff 为目标事件，"leq" 表示小于等于 cutoff。若根超出实测均值范围，对象会标记外推；精密度剖面的模型选择与覆盖范围应纳入结果解释。