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<!DOCTYPE html>
<html lang="zh-CN">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width,initial-scale=1.0">
<title>医学统计与生物信息学习平台 | Abel医研统计</title>
<style>
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<tr><td>独立t</td><td>t</td><td>t=(x̄₁-x̄₂)/√(s²(1/n₁+1/n₂))</td><td>正态+方差齐</td></tr>
<tr><td>配对t</td><td>t</td><td>t=d̄/(sd/√n)</td><td>差值正态</td></tr>
<tr><td>卡方</td><td>χ²</td><td>χ²=Σ(O-E)²/E</td><td>期望≥5</td></tr>
<tr><td>Pearson r</td><td>r</td><td>r=Cov(X,Y)/(sx·sy)</td><td>双变量正态</td></tr>
<tr><td>线性回归F</td><td>F</td><td>F=MSR/MSE</td><td>线性+正态</td></tr>
<tr><td>Logistic OR</td><td>OR</td><td>OR=exp(β)</td><td>二分类Y</td></tr>
<tr><td>灵敏度Se</td><td>Se</td><td>Se=TP/(TP+FN)</td><td>金标准</td></tr>
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<div class="cg">
<div class="cd" id="cd-pvalue"><h3>P 值解读</h3><div class="ds"><strong>定义：</strong>P值：原假设H₀为真时，观察到当前或更极端结果的概率。需结合效应量和置信区间解读。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'pvalue-t0')">方法介绍</button><button class="tab" onclick="swT(this,'pvalue-t1')">SPSS操作</button><button class="tab" onclick="swT(this,'pvalue-t2')">R代码</button><button class="tab" onclick="swT(this,'pvalue-t3')">Python代码</button><button class="tab" onclick="swT(this,'pvalue-t4')">案例解读</button></div><div class="tp on" id="pvalue-t0"><p>P值是统计学中最常用的概念。它衡量在原假设为真的条件下，观察到当前结果或更极端结果的概率。P<0.05常被视为统计学显落，但这只是约定俗成的阈值。ASA发布的官方声明强调，P值不能代表效应大小或结果重要性。</p></div><div class="tp" id="pvalue-t1"><ol><li>分析 -> 描述统计 -> 交叉表（分类变量）或 分析 -> 比较均值 -> T检验（连续变量）</li><li>在输出结果中查看Sig.列即为P值</li><li>注意: SPSS默认输出双侧P值</li></ol></div><div class="tp" id="pvalue-t2"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># P值计算示例
set.seed(123)
g1 <- rnorm(30, mean=100, sd=15)
g2 <- rnorm(30, mean=110, sd=15)
result <- t.test(g1, g2)
print(result)
cat("P:", result$p.value, "\n")
# P值取决于: 效应量 + 样本量 + 变异度</div></div></div><div class="tp" id="pvalue-t3"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from scipy import stats
g1 = np.random.normal(100,15,30)
g2 = np.random.normal(110,15,30)
t, p = stats.ttest_ind(g1, g2)
print(f't={t:.3f}, p={p:.4f}')
# 多重比较校正
from scipy.stats import multipletests
_, corr, _, _ = multipletests([0.012,0.043,0.210,0.003], method='bonferroni')
print(f'Corr: {corr}')</div></div></div><div class="tp" id="pvalue-t4"><div class="res-box"><div class="res-title">📋 P值案例</div><div class="res-body"><strong>情景：</strong>比较两种降压药的疗效<br><strong>结果：</strong>t=2.45, df=58, <span class=sig>P=0.017</span><br><strong>解读：</strong>P<0.05显示组间差异显著。但需关注效应量(Cohen d=0.63)和95%CI[1.2,11.8]</div></div></div></div></div></div>
<div class="cd" id="cd-ci"><h3>置信区间 (CI)</h3><div class="ds"><strong>定义：</strong>参数估计的区间范围，同时展示效应大小与精度。95%CI不含无效值=统计显著。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'ci-t0')">方法介绍</button><button class="tab" onclick="swT(this,'ci-t1')">SPSS操作</button><button class="tab" onclick="swT(this,'ci-t2')">R代码</button><button class="tab" onclick="swT(this,'ci-t3')">Python代码</button><button class="tab" onclick="swT(this,'ci-t4')">案例解读</button></div><div class="tp on" id="ci-t0"><p>CI是参数估计的区间范围。95%CI含义: 重复抽样100次，约95次区间会包含总体真实值。CI展示效应大小和精度，比P值提供更多临床相关信息。</p></div><div class="tp" id="ci-t1"><ol><li>分析 -> 比较均值 -> 独立样本T检验</li><li>在选项中设置置信区间百分比(默认95%)</li><li>查看差值的95%置信区间</li></ol></div><div class="tp" id="ci-t2"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># CI
set.seed(123)
data <- rnorm(50, 100, 15)
t.test(data, conf.level=0.95)
n <- length(data); se <- sd(data)/sqrt(n)
ci <- mean(data)+c(-1,1)*qt(0.975,n-1)*se
cat("95%CI:", round(ci,2))
g1 <- rnorm(30,130,10); g2 <- rnorm(30,140,12)
t.test(g1,g2,conf.level=0.95)</div></div></div><div class="tp" id="ci-t3"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from scipy import stats
data = np.random.normal(100,15,50)
ci = stats.t.interval(0.95, len(data)-1,
loc=np.mean(data), scale=stats.sem(data))
print(f'95%CI: {ci}')</div></div></div><div class="tp" id="ci-t4"><div class="res-box"><div class="res-title">📋 CI案例</div><div class="res-body"><strong>结果：</strong>均值差=-8.5, <span class=sig>95%CI[-12.3,-4.7]</span><br><strong>解读：</strong>不包含0→显著。最保守估计(-4.7)也有临床意义。</div></div></div></div></div></div>
<div class="cd" id="cd-normality"><h3>正态性检验</h3><div class="ds"><strong>方法：</strong>Shapiro-Wilk(n<50)、K-S(n≥50)。参数检验的前提。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'normality-t0')">方法介绍</button><button class="tab" onclick="swT(this,'normality-t1')">SPSS操作</button><button class="tab" onclick="swT(this,'normality-t2')">R代码</button><button class="tab" onclick="swT(this,'normality-t3')">Python代码</button><button class="tab" onclick="swT(this,'normality-t4')">案例解读</button></div><div class="tp on" id="normality-t0"><p>正态性检验判断数据是否服从正态分布，是t检验、ANOVA、线性回归的前提。Shapiro-Wilk适用于小样本(n<50)，K-S适用于大样本。大样本时微小偏离也会显著，建议结合Q-Q图和偏度/峰度综合判断。</p></div><div class="tp" id="normality-t1"><ol><li>分析 -> 描述统计 -> 探索</li><li>因变量列表选入待检验变量</li><li>点击绘制，勾选带检验的正态图</li><li>p>0.05服从正态分布；结合Q-Q图辅助判断</li></ol></div><div class="tp" id="normality-t2"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># 正态性检验
set.seed(123)
data <- rnorm(50, 100, 15)
shapiro.test(data)
# 偏态数据对比
rexp(50, 0.1) |> shapiro.test()
# Q-Q图
qqnorm(data); qqline(data, col="red")</div></div></div><div class="tp" id="normality-t3"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from scipy import stats
data = np.random.normal(100, 15, 50)
stat, p = stats.shapiro(data)
print(f'W={stat:.3f}, p={p:.4f}')
import matplotlib.pyplot as plt
stats.probplot(data, dist="norm", plot=plt); plt.show()</div></div></div><div class="tp" id="normality-t4"><div class="res-box"><div class="res-title">📋 正态性案例</div><div class="res-body"><strong>数据：</strong>50名患者收缩压<br><strong>结果：</strong>W=0.982, <span class=sig>P=0.234</span><br><strong>解读：</strong>P>0.05，不拒绝正态性。如不满足，可用非参数检验</div></div></div></div></div></div>
<div class="cd" id="cd-homogeneity"><h3>方差齐性检验</h3><div class="ds"><strong>方法：</strong>Levene检验、Bartlett检验。t检验和ANOVA的前提。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'homogeneity-t0')">方法介绍</button><button class="tab" onclick="swT(this,'homogeneity-t1')">SPSS操作</button><button class="tab" onclick="swT(this,'homogeneity-t2')">R代码</button><button class="tab" onclick="swT(this,'homogeneity-t3')">Python代码</button><button class="tab" onclick="swT(this,'homogeneity-t4')">案例解读</button></div><div class="tp on" id="homogeneity-t0"><p>方差齐性指各组总体方差相等。Levene检验对非正态数据较稳健；Bartlett对正态敏感。ANOVA方差不齐时可用Welch校正或非参数替代。</p></div><div class="tp" id="homogeneity-t1"><ol><li>分析 -> 比较均值 -> 独立样本T检验</li><li>在结果中查看Levene方差齐性检验</li><li>P>0.05示方差齐，看第一行t结果</li><li>ANOVA中: 在选项勾选方差齐性检验</li></ol></div><div class="tp" id="homogeneity-t2"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># 方差齐性
set.seed(123)
g1 <- rnorm(30,100,10); g2 <- rnorm(30,110,15); g3 <- rnorm(30,105,12)
var.test(g1,g2)
library(car)
leveneTest(c(g1,g2,g3), factor(rep(1:3,each=30)))
t.test(g1,g2,var.equal=FALSE) # Welch</div></div></div><div class="tp" id="homogeneity-t3"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from scipy import stats
g1 = np.random.normal(100,10,30)
g2 = np.random.normal(110,15,30)
g3 = np.random.normal(105,12,30)
stat, p = stats.levene(g1, g2, g3)
print(f'Levene: stat={stat:.3f}, p={p:.4f}')</div></div></div><div class="tp" id="homogeneity-t4"><div class="res-box"><div class="res-title">📋 方差齐性案例</div><div class="res-body"><strong>结果：</strong>Levene F=2.34, <span class=sig>P=0.102</span><br><strong>解读：</strong>P>0.05，方差齐，满足ANOVA前提。</div></div></div></div></div></div>
<div class="cd" id="cd-ind-ttest"><h3>独立样本t检验</h3><div class="ds"><strong>用途：</strong>比较两组独立样本的均值差异。前提：正态性+方差齐。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'ind-ttest-t0')">方法介绍</button><button class="tab" onclick="swT(this,'ind-ttest-t1')">SPSS操作</button><button class="tab" onclick="swT(this,'ind-ttest-t2')">R代码</button><button class="tab" onclick="swT(this,'ind-ttest-t3')">Python代码</button><button class="tab" onclick="swT(this,'ind-ttest-t4')">案例解读</button></div><div class="tp on" id="ind-ttest-t0"><p>独立样本t检验比较两组独立(不配对)样本的均值差异。要求数据近似正态且方差齐。不满足可用Welch校正或Mann-Whitney U检验。</p></div><div class="tp" id="ind-ttest-t1"><ol><li>分析 -> 比较均值 -> 独立样本T检验</li><li>检验变量和分组变量选入</li><li>定义组别名称(如 1=试验组, 2=对照组)</li><li>查看Levene检验判断方差齐性，阅读对应行t检验结果</li></ol></div><div class="tp" id="ind-ttest-t2"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># 独立样本t检验
set.seed(123)
treatment <- rnorm(35, 125, 10)
control <- rnorm(35, 135, 12)
t_result <- t.test(treatment, control, var.equal=TRUE)
print(t_result)
library(effsize); cohen.d(treatment, control)</div></div></div><div class="tp" id="ind-ttest-t3"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from scipy import stats
treatment = np.random.normal(125,10,35)
control = np.random.normal(135,12,35)
t, p = stats.ttest_ind(treatment, control)
print(f't={t:.3f}, p={p:.4f}')
d = (np.mean(treatment)-np.mean(control)) / np.sqrt(
(np.var(treatment,ddof=1)+np.var(control,ddof=1))/2)
print(f"Cohen's d={d:.3f}")</div></div></div><div class="tp" id="ind-ttest-t4"><div class="res-box"><div class="res-title">📋 独立t检验案例</div><div class="res-body"><strong>结果：</strong>试验组125.3±10.2 vs 对照组135.8±12.1<br><span class=sig>t=-3.87, df=68, P<0.001, 95%CI[-15.8,-5.2]</span><br><strong>解读：</strong>新药显著降低SBP，Cohen d=0.93(大效应)。</div></div></div></div></div></div>
<div class="cd" id="cd-paired-ttest"><h3>配对t检验</h3><div class="ds"><strong>用途：</strong>比较配对样本的均值差异(如治疗前后、配对病例对照)。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'paired-ttest-t0')">方法介绍</button><button class="tab" onclick="swT(this,'paired-ttest-t1')">SPSS操作</button><button class="tab" onclick="swT(this,'paired-ttest-t2')">R代码</button><button class="tab" onclick="swT(this,'paired-ttest-t3')">Python代码</button><button class="tab" onclick="swT(this,'paired-ttest-t4')">案例解读</button></div><div class="tp on" id="paired-ttest-t0"><p>配对t检验用于同一组受试者在两个时间点或匹配条件下的均值比较。本质是对差值进行单样本t检验。优点: 消除个体间变异，统计效能更高。</p></div><div class="tp" id="paired-ttest-t1"><ol><li>分析 -> 比较均值 -> 成对样本T检验</li><li>将治疗前和治疗后变量选入成对变量</li><li>查看均值差、t值、df、P值、95%CI</li></ol></div><div class="tp" id="paired-ttest-t2"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># 配对t检验
set.seed(123)
before <- rnorm(25, 140, 15)
after <- before - rnorm(25, 10, 5)
t.test(before, after, paired=TRUE)
# 效应量
diff <- before - after
cat("Cohen's d:", mean(diff)/sd(diff), "\n")</div></div></div><div class="tp" id="paired-ttest-t3"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from scipy import stats
before = np.random.normal(140,15,25)
after = before - np.random.normal(10,5,25)
t, p = stats.ttest_rel(before, after)
print(f'Paired t: t={t:.3f}, p={p:.4f}')
d = np.mean(before-after)/np.std(before-after, ddof=1)
print(f"d={d:.3f}")</div></div></div><div class="tp" id="paired-ttest-t4"><div class="res-box"><div class="res-title">📋 配对t案例</div><div class="res-body"><strong>结果：</strong>治疗前142.3→131.8<br><span class=sig>均值差=10.5, t=6.82, df=24, P<0.001</span></div></div></div></div></div></div>
<div class="cd" id="cd-oneway-anova"><h3>单因素ANOVA</h3><div class="ds"><strong>用途：</strong>比较三组及以上独立样本的均值差异。事后检验：Tukey、LSD、Bonferroni。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'oneway-anova-t0')">方法介绍</button><button class="tab" onclick="swT(this,'oneway-anova-t1')">SPSS操作</button><button class="tab" onclick="swT(this,'oneway-anova-t2')">R代码</button><button class="tab" onclick="swT(this,'oneway-anova-t3')">Python代码</button><button class="tab" onclick="swT(this,'oneway-anova-t4')">案例解读</button></div><div class="tp on" id="oneway-anova-t0"><p>ANOVA用于比较三个或以上组的均值差异。F统计量=组间方差/组内方差。ANOVA显著只表明至少有一组不同，需要事后检验进行两两比较。</p></div><div class="tp" id="oneway-anova-t1"><ol><li>分析 -> 比较均值 -> 单因素ANOVA</li><li>因变量和因子选入</li><li>事后多重比较：方差齐选Tukey，不齐选Games-Howell</li><li>选项 -> 描述性 + 方差齐性检验</li><li>读取F值和P值，再看事后比较</li></ol></div><div class="tp" id="oneway-anova-t2"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># ANOVA
set.seed(123)
value <- c(rnorm(25,100,10), rnorm(25,110,10), rnorm(25,95,10))
group <- factor(rep(c("A","B","C"), each=25))
aov_model <- aov(value ~ group)
summary(aov_model)
TukeyHSD(aov_model)
library(lsr); etaSquared(aov_model)</div></div></div><div class="tp" id="oneway-anova-t3"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">import pandas as pd
import statsmodels.api as sm
from statsmodels.formula.api import ols
df = pd.DataFrame({
'value': np.concatenate([np.random.normal(100,10,25),
np.random.normal(110,10,25),
np.random.normal(95,10,25)]),
'group': ['A']*25+['B']*25+['C']*25
})
print(sm.stats.anova_lm(ols('value~group',data=df).fit(), typ=2))
from statsmodels.stats.multicomp import pairwise_tukeyhsd
print(pairwise_tukeyhsd(df['value'], df['group']))</div></div></div><div class="tp" id="oneway-anova-t4"><div class="res-box"><div class="res-title">📋 ANOVA案例</div><div class="res-body"><strong>结果：</strong><span class=sig>F=4.82, df=2,72, P=0.011</span><br><strong>事后：</strong>A vs C差异显著(P=0.008)。</div></div></div></div></div></div>
<div class="cd" id="cd-rm-anova"><h3>重复测量ANOVA</h3><div class="ds"><strong>用途：</strong>同一组受试者多个时间点的测量比较。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'rm-anova-t0')">方法介绍</button><button class="tab" onclick="swT(this,'rm-anova-t1')">R代码</button><button class="tab" onclick="swT(this,'rm-anova-t2')">Python代码</button><button class="tab" onclick="swT(this,'rm-anova-t3')">案例解读</button></div><div class="tp on" id="rm-anova-t0"><p>重复测量ANOVA用于同一组受试者在三个或以上时间点的测量数据。需满足球形假设(Mauchly检验)。不满足时用Greenhouse-Geisser校正。</p></div><div class="tp" id="rm-anova-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># 重复测量ANOVA
library(ez)
set.seed(123)
id <- factor(rep(1:20, each=3))
time <- factor(rep(c("T0","T1","T2"), 20))
value <- c(rnorm(20,140,10), rnorm(20,130,10), rnorm(20,125,10))
rm_data <- data.frame(id, time, value)
ezANOVA(data=rm_data, dv=value, wid=id, within=time, detailed=TRUE)</div></div></div><div class="tp" id="rm-anova-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">import pandas as pd
from statsmodels.stats.anova import AnovaRM
df = pd.DataFrame({
'id': np.repeat(range(20), 3),
'time': np.tile(['T0','T1','T2'], 20),
'value': np.concatenate([np.random.normal(140,10,20),
np.random.normal(130,10,20),
np.random.normal(125,10,20)])
})
print(AnovaRM(df, 'value', 'id', within=['time']).fit())</div></div></div><div class="tp" id="rm-anova-t3"><div class="res-box"><div class="res-title">📋 重复测量案例</div><div class="res-body"><strong>结果：</strong><span class=sig>F=12.45, P<0.001</span><br><strong>解读：</strong>血压随时间显著下降(140→130→125mmHg)。</div></div></div></div></div></div>
<div class="cd" id="cd-mannwhitney"><h3>Mann-Whitney U检验</h3><div class="ds"><strong>用途：</strong>两组独立样本的非参数检验。t检验的非参数替代，不要求正态性。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'mannwhitney-t0')">方法介绍</button><button class="tab" onclick="swT(this,'mannwhitney-t1')">SPSS操作</button><button class="tab" onclick="swT(this,'mannwhitney-t2')">R代码</button><button class="tab" onclick="swT(this,'mannwhitney-t3')">Python代码</button><button class="tab" onclick="swT(this,'mannwhitney-t4')">案例解读</button></div><div class="tp on" id="mannwhitney-t0"><p>Mann-Whitney U检验是独立t检验的非参数替代。基于秩次而非原始值，不要求正态分布。适用于有序分类变量或偏态连续变量。</p></div><div class="tp" id="mannwhitney-t1"><ol><li>分析 -> 非参数检验 -> 旧对话框 -> 2个独立样本</li><li>检验变量和分组变量选入</li><li>检验类型勾选Mann-Whitney U</li><li>查看U统计量和精确P值</li></ol></div><div class="tp" id="mannwhitney-t2"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># Mann-Whitney U检验
set.seed(123)
g1 <- rexp(25, 0.1); g2 <- rexp(25, 0.05)
wilcox.test(g1, g2)
cat("Median G1:", median(g1), "\nMedian G2:", median(g2), "\n")</div></div></div><div class="tp" id="mannwhitney-t3"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from scipy import stats
g1 = np.random.exponential(10, 25)
g2 = np.random.exponential(20, 25)
stat, p = stats.mannwhitneyu(g1, g2)
print(f'U={stat:.0f}, p={p:.4f}')</div></div></div><div class="tp" id="mannwhitney-t4"><div class="res-box"><div class="res-title">📋 Mann-Whitney案例</div><div class="res-body"><strong>结果：</strong>A组中位8天(IQR:5-12)，B组12天(IQR:7-18)<br><span class=sig>U=185.5, P=0.003</span></div></div></div></div></div></div>
<div class="cd" id="cd-wilcoxon-sr"><h3>Wilcoxon符号秩检验</h3><div class="ds"><strong>用途：</strong>配对数据的非参数检验。配对t检验的非参数替代。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'wilcoxon-sr-t0')">方法介绍</button><button class="tab" onclick="swT(this,'wilcoxon-sr-t1')">R代码</button><button class="tab" onclick="swT(this,'wilcoxon-sr-t2')">Python代码</button><button class="tab" onclick="swT(this,'wilcoxon-sr-t3')">案例解读</button></div><div class="tp on" id="wilcoxon-sr-t0"><p>Wilcoxon符号秩检验是配对t检验的非参数替代。计算差值的绝对值排序后比较正负秩和。不要求差值正态。</p></div><div class="tp" id="wilcoxon-sr-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># Wilcoxon符号秩检验
set.seed(123)
before <- runif(20, 50, 100)
after <- before - runif(20, 5, 20)
wilcox.test(before, after, paired=TRUE)
cat("Median diff:", median(before-after), "\n")</div></div></div><div class="tp" id="wilcoxon-sr-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from scipy import stats
before = np.random.uniform(50,100,20)
after = before - np.random.uniform(5,20,20)
stat, p = stats.wilcoxon(before, after)
print(f'W={stat:.0f}, p={p:.4f}')</div></div></div><div class="tp" id="wilcoxon-sr-t3"><div class="res-box"><div class="res-title">📋 Wilcoxon案例</div><div class="res-body"><strong>结果：</strong>治疗前VAS 7(IQR:5-8) → 3(IQR:2-5)<br><span class=sig>V=66.5, P=0.002</span></div></div></div></div></div></div>
<div class="cd" id="cd-kruskal-wallis"><h3>Kruskal-Wallis检验</h3><div class="ds"><strong>用途：</strong>三组及以上独立样本的非参数ANOVA。事后：Dunn检验。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'kruskal-wallis-t0')">方法介绍</button><button class="tab" onclick="swT(this,'kruskal-wallis-t1')">R代码</button><button class="tab" onclick="swT(this,'kruskal-wallis-t2')">Python代码</button><button class="tab" onclick="swT(this,'kruskal-wallis-t3')">案例解读</button></div><div class="tp on" id="kruskal-wallis-t0"><p>Kruskal-Wallis检验是ANOVA的非参数替代。基于秩次比较分布差异。显著后需Dunn检验进行事后两两比较。</p></div><div class="tp" id="kruskal-wallis-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># Kruskal-Wallis
set.seed(123)
value <- c(rexp(20,0.1), rexp(20,0.08), rexp(20,0.05))
group <- factor(rep(c("A","B","C"), each=20))
kruskal.test(value ~ group)
library(FSA); dunnTest(value ~ group, method="bonferroni")</div></div></div><div class="tp" id="kruskal-wallis-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from scipy import stats
g1, g2, g3 = [np.random.exponential(r,20) for r in [10,12.5,20]]
stat, p = stats.kruskal(g1, g2, g3)
print(f'H={stat:.3f}, p={p:.4f}')</div></div></div><div class="tp" id="kruskal-wallis-t3"><div class="res-box"><div class="res-title">📋 Kruskal-Wallis案例</div><div class="res-body"><strong>结果：</strong><span class=sig>H=8.92, df=2, P=0.012</span><br>三种化疗方案的恶心评分存在显著差异。</div></div></div></div></div></div>
<div class="cd" id="cd-chisq-test"><h3>卡方检验</h3><div class="ds"><strong>用途：</strong>检验分类变量间关联性。条件：期望频数≥5。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'chisq-test-t0')">方法介绍</button><button class="tab" onclick="swT(this,'chisq-test-t1')">SPSS操作</button><button class="tab" onclick="swT(this,'chisq-test-t2')">R代码</button><button class="tab" onclick="swT(this,'chisq-test-t3')">Python代码</button><button class="tab" onclick="swT(this,'chisq-test-t4')">案例解读</button></div><div class="tp on" id="chisq-test-t0"><p>卡方检验检验两个分类变量间的关联性。基本思想是比较观测频数与期望频数的差异。公式χ²=Σ(O-E)²/E。条件: 总样本≥40且所有期望频数≥5。</p></div><div class="tp" id="chisq-test-t1"><ol><li>分析 -> 描述统计 -> 交叉表</li><li>行变量和列变量选入</li><li>统计 -> 卡方</li><li>单元格 -> 期望频数和百分比</li><li>查看Pearson卡方值和P值</li></ol></div><div class="tp" id="chisq-test-t2"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># 卡方检验
data <- matrix(c(45,30,20,50), nrow=2,
dimnames=list(Treatment=c("Drug","Placebo"), Outcome=c("有效","无效")))
chi <- chisq.test(data)
print(chi)
cat("chi2 =", round(chi$statistic,3), ", P =", round(chi$p.value,4))
library(rstatix); cramer_v(data)</div></div></div><div class="tp" id="chisq-test-t3"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from scipy.stats import chi2_contingency
table = np.array([[45,30],[20,50]])
chi2, p, dof, exp = chi2_contingency(table)
print(f'chi2={chi2:.3f}, p={p:.4f}')
n = table.sum()
v = np.sqrt(chi2/(n*(min(table.shape)-1)))
print(f"V={v:.3f}")</div></div></div><div class="tp" id="chisq-test-t4"><div class="res-box"><div class="res-title">📋 卡方案例</div><div class="res-body"><strong>结果：</strong><span class=sig>χ²=12.45, df=1, P<0.001</span>, V=0.35<br>吸烟组肺癌比例显著高于非吸烟组。</div></div></div></div></div></div>
<div class="cd" id="cd-fisher-exact"><h3>Fisher精确检验</h3><div class="ds"><strong>用途：</strong>小样本或期望频数<5时分类变量的关联性检验。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'fisher-exact-t0')">方法介绍</button><button class="tab" onclick="swT(this,'fisher-exact-t1')">R代码</button><button class="tab" onclick="swT(this,'fisher-exact-t2')">Python代码</button><button class="tab" onclick="swT(this,'fisher-exact-t3')">案例解读</button></div><div class="tp on" id="fisher-exact-t0"><p>Fisher精确检验适用于2×2表期望频数<5时。基于超几何分布精确计算P值。提供OR值和精确置信区间。</p></div><div class="tp" id="fisher-exact-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># Fisher
data <- matrix(c(4,10,12,25), nrow=2)
f <- fisher.test(data)
print(f)
cat("OR =", round(f$estimate,3), ", P =", round(f$p.value,4))</div></div></div><div class="tp" id="fisher-exact-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from scipy.stats import fisher_exact
table = np.array([[4,10],[12,25]])
or_, p = fisher_exact(table)
print(f'OR={or_:.3f}, p={p:.4f}')</div></div></div><div class="tp" id="fisher-exact-t3"><div class="res-box"><div class="res-title">📋 Fisher案例</div><div class="res-body"><strong>结果：</strong><span class=sig>P=0.039, OR=8.33</span><br>治疗组有效比例显著高于对照组，但样本量小。</div></div></div></div></div></div>
<div class="cd" id="cd-linear-reg"><h3>线性回归</h3><div class="ds"><strong>用途：</strong>多个自变量对连续因变量的影响。前提：线性、独立、正态、方差齐。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'linear-reg-t0')">方法介绍</button><button class="tab" onclick="swT(this,'linear-reg-t1')">SPSS操作</button><button class="tab" onclick="swT(this,'linear-reg-t2')">R代码</button><button class="tab" onclick="swT(this,'linear-reg-t3')">Python代码</button><button class="tab" onclick="swT(this,'linear-reg-t4')">案例解读</button></div><div class="tp on" id="linear-reg-t0"><p>线性回归建模连续因变量与自变量的线性关系。Y=β₀+β₁X₁+...+ε。核心前提: 线性关系、残差独立、残差正态、方差齐。R²解释模型拟合度。</p></div><div class="tp" id="linear-reg-t1"><ol><li>分析 -> 回归 -> 线性</li><li>因变量和自变量选入</li><li>统计 -> 估计、模型拟合、Durbin-Watson</li><li>绘制 -> 残差图检查方差齐性</li></ol></div><div class="tp" id="linear-reg-t2"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># 线性回归
set.seed(123)
data <- data.frame(age=rnorm(100,60,10), bmi=rnorm(100,25,3))
data$sbp <- 80 + 0.5*data$age + 1.2*data$bmi + rnorm(100,0,8)
lm_model <- lm(sbp ~ age + bmi, data=data)
summary(lm_model)
confint(lm_model)
par(mfrow=c(2,2)); plot(lm_model)</div></div></div><div class="tp" id="linear-reg-t3"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">import statsmodels.api as sm
X = sm.add_constant(df[['age','bmi']])
model = sm.OLS(df['sbp'], X).fit()
print(model.summary())
print(f'R2 = {model.rsquared:.3f}')</div></div></div><div class="tp" id="linear-reg-t4"><div class="res-box"><div class="res-title">📋 线性回归案例</div><div class="res-body"><strong>结果：</strong>年龄β=0.48(P<0.001), BMI β=1.15(P=0.002)<br><span class=sig>R²=0.42, 调整R²=0.41</span><br>年龄和BMI解释SBP变异的42%。</div></div></div></div></div></div>
<div class="cd" id="cd-logistic-reg"><h3>Logistic回归</h3><div class="ds"><strong>用途：</strong>二分类因变量建模(发病/未发病)。输出OR值。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'logistic-reg-t0')">方法介绍</button><button class="tab" onclick="swT(this,'logistic-reg-t1')">SPSS操作</button><button class="tab" onclick="swT(this,'logistic-reg-t2')">R代码</button><button class="tab" onclick="swT(this,'logistic-reg-t3')">Python代码</button><button class="tab" onclick="swT(this,'logistic-reg-t4')">案例解读</button></div><div class="tp on" id="logistic-reg-t0"><p>Logistic回归用于二分类因变量建模。自变量对log-odds线性影响，指数化转为OR。最大似然估计参数。似然比检验用于模型比较。</p></div><div class="tp" id="logistic-reg-t1"><ol><li>分析 -> 回归 -> 二元Logistic</li><li>因变量和协变量选入</li><li>分类变量点击分类指定</li><li>选项 -> HL检验、CI for exp(B)</li><li>读取B、OR、95%CI、P值</li></ol></div><div class="tp" id="logistic-reg-t2"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># Logistic
set.seed(123)
age <- rnorm(200,60,10); bmi <- rnorm(200,25,3)
smoking <- rbinom(200,1,0.3)
logit <- -3+0.05*age+0.08*bmi+0.8*smoking
disease <- rbinom(200,1,plogis(logit))
model <- glm(disease~age+bmi+smoking, family=binomial())
summary(model)
OR <- exp(cbind(OR=coef(model), confint(model)))
print(round(OR,3))</div></div></div><div class="tp" id="logistic-reg-t3"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">X = sm.add_constant(df[['age','bmi','smoking']])
model = sm.Logit(df['disease'], X).fit()
print('OR:', np.exp(model.params))
print('95%CI:', np.exp(model.conf_int()))</div></div></div><div class="tp" id="logistic-reg-t4"><div class="res-box"><div class="res-title">📋 Logistic案例</div><div class="res-body"><strong>结果：</strong>吸烟 OR=2.24(95%CI:1.42-3.56, P<0.001)<br><strong>解读：</strong>调整年龄和BMI后，吸烟者冠心病风险是非吸烟者的2.24倍。</div></div></div></div></div></div>
<div class="cd" id="cd-poisson-reg"><h3>Poisson回归</h3><div class="ds"><strong>用途：</strong>计数数据建模(发病率、死亡率)。偏移量处理人年数据。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'poisson-reg-t0')">方法介绍</button><button class="tab" onclick="swT(this,'poisson-reg-t1')">R代码</button><button class="tab" onclick="swT(this,'poisson-reg-t2')">Python代码</button><button class="tab" onclick="swT(this,'poisson-reg-t3')">案例解读</button></div><div class="tp on" id="poisson-reg-t0"><p>Poisson回归用于计数数据建模。连接函数为log，系数指数化为发生率比(IRR)。要求均值=方差(等离散)。过离散时用负二项回归。</p></div><div class="tp" id="poisson-reg-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># Poisson
set.seed(123)
age <- rnorm(100,50,12); smoking <- rbinom(100,1,0.3)
pyears <- rep(1000,100)
lam <- exp(-3+0.03*age+0.5*smoking)
events <- rpois(100, lam*pyears/1000)
model <- glm(events~age+smoking+offset(log(pyears)), family=poisson())
summary(model)
IRR <- exp(cbind(IRR=coef(model), confint(model)))
print(round(IRR,3))</div></div></div><div class="tp" id="poisson-reg-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">model = sm.GLM(df['events'], X, family=sm.families.Poisson()).fit()
print('IRR:', np.exp(model.params))</div></div></div><div class="tp" id="poisson-reg-t3"><div class="res-box"><div class="res-title">📋 Poisson案例</div><div class="res-body"><strong>结果：</strong>吸烟 IRR=1.85(95%CI:1.42-2.41, P<0.001)<br><strong>解读：</strong>调整年龄后，吸烟者肺癌发病率是非吸烟者的1.85倍。</div></div></div></div></div></div>
<div class="cd" id="cd-pearson-corr"><h3>Pearson相关</h3><div class="ds"><strong>用途：</strong>两个连续变量的线性相关。前提：双变量正态。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'pearson-corr-t0')">方法介绍</button><button class="tab" onclick="swT(this,'pearson-corr-t1')">SPSS操作</button><button class="tab" onclick="swT(this,'pearson-corr-t2')">R代码</button><button class="tab" onclick="swT(this,'pearson-corr-t3')">Python代码</button><button class="tab" onclick="swT(this,'pearson-corr-t4')">案例解读</button></div><div class="tp on" id="pearson-corr-t0"><p>Pearson相关系数r衡量线性相关强度。|r|<0.3弱，0.3-0.7中等，>0.7强相关。前提: 两变量近似正态且关系呈线性。</p></div><div class="tp" id="pearson-corr-t1"><ol><li>分析 -> 相关 -> 双变量</li><li>变量选入，勾选Pearson</li><li>查看r值和P值</li></ol></div><div class="tp" id="pearson-corr-t2"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># Pearson
set.seed(123)
x <- rnorm(50,100,15); y <- 0.6*x + rnorm(50,0,10)
cor.test(x, y, method="pearson")
plot(x,y,col="#0d9488"); abline(lm(y~x),col="red")</div></div></div><div class="tp" id="pearson-corr-t3"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from scipy import stats
r, p = stats.pearsonr(x, y)
print(f'r={r:.3f}, p={p:.4f}')
z = np.arctanh(r); se = 1/np.sqrt(len(x)-3)
ci = np.tanh(z + np.array([-1,1])*1.96*se)
print(f'95%CI: [{ci[0]:.3f}, {ci[1]:.3f}]')</div></div></div><div class="tp" id="pearson-corr-t4"><div class="res-box"><div class="res-title">📋 Pearson案例</div><div class="res-body"><strong>结果：</strong><span class=sig>r=0.52, P<0.001</span>, 95%CI[0.35,0.68]<br>BMI与SBP呈中等正相关。</div></div></div></div></div></div>
<div class="cd" id="cd-spearman-corr"><h3>Spearman相关</h3><div class="ds"><strong>用途：</strong>非参数相关。适用于偏态或有序数据。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'spearman-corr-t0')">方法介绍</button><button class="tab" onclick="swT(this,'spearman-corr-t1')">R代码</button><button class="tab" onclick="swT(this,'spearman-corr-t2')">Python代码</button><button class="tab" onclick="swT(this,'spearman-corr-t3')">案例解读</button></div><div class="tp on" id="spearman-corr-t0"><p>Spearman秩相关是Pearson的非参数替代。基于秩次，衡量单调相关。对异常值不敏感，适用于有序变量或偏态分布。</p></div><div class="tp" id="spearman-corr-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># Spearman
set.seed(123)
x <- rexp(30,0.1); y <- x^2 + runif(30,0,50)
cor.test(x, y, method="spearman")</div></div></div><div class="tp" id="spearman-corr-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from scipy import stats
rho, p = stats.spearmanr(x, y)
print(f'rho={rho:.3f}, p={p:.4f}')</div></div></div><div class="tp" id="spearman-corr-t3"><div class="res-box"><div class="res-title">📋 Spearman案例</div><div class="res-body"><strong>结果：</strong><span class=sig>ρ=-0.38, P=0.008</span><br>住院天数与满意度呈弱负相关。</div></div></div></div></div></div>
<div class="cd" id="cd-icc"><h3>ICC组内相关系数</h3><div class="ds"><strong>用途：</strong>评价连续变量测量的一致性/信度。>0.75良好，>0.9优秀。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'icc-t0')">方法介绍</button><button class="tab" onclick="swT(this,'icc-t1')">R代码</button><button class="tab" onclick="swT(this,'icc-t2')">Python代码</button><button class="tab" onclick="swT(this,'icc-t3')">案例解读</button></div><div class="tp on" id="icc-t0"><p>ICC用于评价连续变量测量一致性。不同类型对应不同设计: ICC(1,1)随机选评价者; ICC(2,1)固定评价者; ICC(3,1)一致性测量。</p></div><div class="tp" id="icc-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># ICC
library(irr)
r1 <- rnorm(20,50,10); r2 <- r1 + rnorm(20,0,3)
icc(data.frame(r1,r2), model="twoway", type="consistency")
library(psych)
multi <- data.frame(r1=rnorm(20,50,10), r2=rnorm(20,50,10)+rnorm(20,0,3), r3=rnorm(20,50,10)+rnorm(20,0,4))
ICC(multi)</div></div></div><div class="tp" id="icc-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">import pingouin as pg
df = pd.DataFrame({
'target': np.repeat(range(20),2),
'rater': np.tile(['A','B'],20),
'score': np.concatenate([r1, r2])
})
print(pg.intraclass_corr(df, 'target', 'rater', 'score'))</div></div></div><div class="tp" id="icc-t3"><div class="res-box"><div class="res-title">📋 ICC案例</div><div class="res-body"><strong>结果：</strong><span class=sig>ICC(2,1)=0.87, 95%CI[0.78-0.93]</span><br>评分者间一致性良好。</div></div></div></div></div></div>
<div class="cd" id="cd-kappa"><h3>Kappa一致性</h3><div class="ds"><strong>用途：</strong>分类变量的一致性评价。加权Kappa用于有序分类。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'kappa-t0')">方法介绍</button><button class="tab" onclick="swT(this,'kappa-t1')">R代码</button><button class="tab" onclick="swT(this,'kappa-t2')">Python代码</button><button class="tab" onclick="swT(this,'kappa-t3')">案例解读</button></div><div class="tp on" id="kappa-t0"><p>Kappa系数评价两个评价者对分类变量的一致性，校正了随机一致。Kappa≥0.75一致性好，0.4-0.75中等，<0.4差。加权Kappa用于有序分类。</p></div><div class="tp" id="kappa-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># Kappa
library(irr)
r1 <- c(1,1,1,0,1,0,0,0,1,1)
r2 <- c(1,1,1,1,1,0,0,0,0,0)
kappa2(cbind(r1, r2))
# 加权Kappa
ord1 <- c(1,2,3,2,1,2,3,3,2,1)
ord2 <- c(1,2,3,2,2,2,3,2,2,1)
kappa2(cbind(ord1, ord2), weight="squared")</div></div></div><div class="tp" id="kappa-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from sklearn.metrics import cohen_kappa_score
r1 = [1,1,1,0,1,0,0,0,1,1]
r2 = [1,1,1,1,1,0,0,0,0,0]
kappa = cohen_kappa_score(r1, r2)
print(f'Kappa = {kappa:.3f}')
wkappa = cohen_kappa_score(r1, r2, weights='linear')
print(f'Weighted Kappa = {wkappa:.3f}')</div></div></div><div class="tp" id="kappa-t3"><div class="res-box"><div class="res-title">📋 Kappa案例</div><div class="res-body"><strong>结果：</strong><span class=sig>Kappa=0.78, P<0.001</span><br>两名诊断医生的判断一致性良好。</div></div></div></div></div></div>
<div class="cd" id="cd-dx-indices"><h3>诊断试验指标</h3><div class="ds"><strong>核心：</strong>灵敏度(Se)、特异度(Sp)、PPV、NPV、似然比(LR)、约登指数。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'dx-indices-t0')">方法介绍</button><button class="tab" onclick="swT(this,'dx-indices-t1')">R代码</button><button class="tab" onclick="swT(this,'dx-indices-t2')">Python代码</button><button class="tab" onclick="swT(this,'dx-indices-t3')">案例解读</button></div><div class="tp on" id="dx-indices-t0"><p>诊断试验指标评价诊断方法的准确性。Se=TP/(TP+FN)，Sp=TN/(TN+FP)。PPV为阳性预测值，NPV为阴性预测值。LR+=Se/(1-Sp)，LR-=(1-Se)/Sp。约登指数=Se+Sp-1。</p></div><div class="tp" id="dx-indices-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># 诊断指标
set.seed(123)
gold <- rbinom(200,1,0.3)
test <- ifelse(gold==1, rbinom(200,1,0.85), rbinom(200,1,0.15))
TP=sum(test==1&gold==1); FP=sum(test==1&gold==0)
FN=sum(test==0&gold==1); TN=sum(test==0&gold==0)
cat("Se:", round(TP/(TP+FN),3), "\nSp:", round(TN/(TN+FP),3))
cat("PPV:", round(TP/(TP+FP),3), "\nNPV:", round(TN/(TN+FN),3))
cat("LR+:", round((TP/(TP+FN))/(1-TN/(TN+FP)),2))
cat("\nLR-:", round((1-TP/(TP+FN))/(TN/(TN+FP)),2))
library(epiR); epi.tests(data.frame(TP,FP,FN,TN))</div></div></div><div class="tp" id="dx-indices-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from sklearn.metrics import confusion_matrix
gold = np.random.binomial(1,0.3,200)
test = np.where(gold==1, np.random.binomial(1,0.85,200), np.random.binomial(1,0.15,200))
cm = confusion_matrix(gold, test)
TP, FP, FN, TN = cm[1,1], cm[0,1], cm[1,0], cm[0,0]
se=TP/(TP+FN); sp=TN/(TN+FP)
ppv=TP/(TP+FP); npv=TN/(TN+FN)
print(f'Se={se:.3f}, Sp={sp:.3f}, PPV={ppv:.3f}, NPV={npv:.3f}')
print(f'LR+={se/(1-sp):.2f}, LR-={(1-se)/sp:.2f}')</div></div></div><div class="tp" id="dx-indices-t3"><div class="res-box"><div class="res-title">📋 诊断指标案例</div><div class="res-body"><strong>结果：</strong>Se=0.85, Sp=0.85, LR+=5.67<br><span class=sig>PPV=0.71, NPV=0.93</span><br>阴性预测值高，阴性结果可较好排除疾病。</div></div></div></div></div></div>
<div class="cd" id="cd-roc-curve"><h3>ROC曲线</h3><div class="ds"><strong>用途：</strong>评价诊断试验/预测模型的判别能力。AUC、最佳切点、Se、Sp。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'roc-curve-t0')">方法介绍</button><button class="tab" onclick="swT(this,'roc-curve-t1')">SPSS操作</button><button class="tab" onclick="swT(this,'roc-curve-t2')">R代码</button><button class="tab" onclick="swT(this,'roc-curve-t3')">Python代码</button><button class="tab" onclick="swT(this,'roc-curve-t4')">案例解读</button></div><div class="tp on" id="roc-curve-t0"><p>ROC曲线以1-特异度为横轴、灵敏度为纵轴绘制。AUC综合评价: 0.5无判别，0.7-0.8可接受，0.8-0.9优秀。最佳切点用约登指数确定。DeLong检验比较两个AUC。</p></div><div class="tp" id="roc-curve-t1"><ol><li>分析 -> ROC曲线</li><li>检验变量选入预测概率，状态变量选入金标准</li><li>状态变量值设为1(阳性)</li><li>选项 -> AUC置信区间和坐标点</li></ol></div><div class="tp" id="roc-curve-t2"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># ROC
library(pROC)
set.seed(123)
score <- c(rnorm(50,70,15), rnorm(50,50,15))
true <- c(rep(1,50), rep(0,50))
roc_obj <- roc(true, score)
cat("AUC:", round(auc(roc_obj),3), "\n95%CI:", round(ci.auc(roc_obj),3))
best <- coords(roc_obj, "best", best.method="youden")
print(best)
plot(roc_obj, col="#0d9488", lwd=2)</div></div></div><div class="tp" id="roc-curve-t3"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from sklearn.metrics import roc_curve, auc
fpr, tpr, thr = roc_curve(true, score)
roc_auc = auc(fpr, tpr)
print(f'AUC={roc_auc:.3f}')
youden = tpr - fpr
best = thr[np.argmax(youden)]
print(f'Best threshold={best:.2f}')</div></div></div><div class="tp" id="roc-curve-t4"><div class="res-box"><div class="res-title">📋 ROC案例</div><div class="res-body"><strong>结果：</strong><span class=sig>AUC=0.87, 95%CI[0.82-0.92]</span><br>最佳切点NT-proBNP>450pg/mL: Se=0.82, Sp=0.79</div></div></div></div></div></div>
<div class="cd" id="cd-calibration"><h3>校准曲线</h3><div class="ds"><strong>用途：</strong>评价预测模型的校准度—预测概率与实际概率的一致性。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'calibration-t0')">方法介绍</button><button class="tab" onclick="swT(this,'calibration-t1')">R代码</button><button class="tab" onclick="swT(this,'calibration-t2')">Python代码</button><button class="tab" onclick="swT(this,'calibration-t3')">案例解读</button></div><div class="tp on" id="calibration-t0"><p>校准曲线展示预测概率与实际观测概率的一致性。完美校准沿45°对角线。HL检验不显著=校准良好。Brier Score综合评估判别和校准。</p></div><div class="tp" id="calibration-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># 校准曲线
library(rms)
set.seed(123)
n <- 300
data <- data.frame(age=rnorm(n,60,10), bmi=rnorm(n,25,3), smoking=rbinom(n,1,0.3))
logit <- -3+0.05*data$age+0.08*data$bmi+0.8*data$smoking
data$disease <- rbinom(n, 1, plogis(logit))
dd <- datadist(data); options(datadist="dd")
model <- lrm(disease~age+bmi+smoking, data=data, x=TRUE, y=TRUE)
cal <- calibrate(model, B=200)
plot(cal, xlab="Predicted", ylab="Actual")</div></div></div><div class="tp" id="calibration-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from sklearn.calibration import calibration_curve
import matplotlib.pyplot as plt
prob_pred, prob_true = calibration_curve(y_true, y_pred, n_bins=10)
plt.plot(prob_pred, prob_true, marker='o')
plt.plot([0,1],[0,1], 'k--'); plt.show()
from sklearn.metrics import brier_score_loss
print(f'Brier Score = {brier_score_loss(y_true, y_pred):.4f}')</div></div></div><div class="tp" id="calibration-t3"><div class="res-box"><div class="res-title">📋 校准案例</div><div class="res-body"><strong>结果：</strong>校准曲线接近45°对角线<br>HL检验P=0.342(>0.05，校准良好)<br>Brier Score=0.12<0.25(有临床价值)</div></div></div></div></div></div>
<div class="cd" id="cd-pca"><h3>PCA主成分分析</h3><div class="ds"><strong>用途：</strong>降维、多重共线性处理、高维数据可视化。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'pca-t0')">方法介绍</button><button class="tab" onclick="swT(this,'pca-t1')">R代码</button><button class="tab" onclick="swT(this,'pca-t2')">Python代码</button><button class="tab" onclick="swT(this,'pca-t3')">案例解读</button></div><div class="tp on" id="pca-t0"><p>PCA将多个相关变量转为不相关主成分(原始变量的线性组合)。第一主成分方差最大。需对变量标准化。用于降维、去共线性、探索数据结构。</p></div><div class="tp" id="pca-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># PCA
set.seed(123)
data <- data.frame(x1=rnorm(100,50,10), x2=0.7*x1+rnorm(100,0,5),
x3=0.5*x1+0.3*x2+rnorm(100,0,4), x4=rnorm(100,30,8))
pca <- prcomp(data, scale=TRUE)
summary(pca)
print(pca$rotation[,1:2])
screeplot(pca, type="lines"); abline(h=1,lty=2,col="red")
biplot(pca)</div></div></div><div class="tp" id="pca-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
pca = PCA(n_components=2)
X_pca = pca.fit_transform(StandardScaler().fit_transform(df))
print(f'Explained variance: {pca.explained_variance_ratio_}')
print(f'Cumulative: {np.cumsum(pca.explained_variance_ratio_)}')</div></div></div><div class="tp" id="pca-t3"><div class="res-box"><div class="res-title">📋 PCA案例</div><div class="res-body"><strong>结果：</strong>前2个主成分解释68%方差<br>PC1=代谢负荷(BMI+血糖+血脂), PC2=炎症因子</div></div></div></div></div></div>
<div class="cd" id="cd-efa"><h3>EFA探索性因子分析</h3><div class="ds"><strong>用途：</strong>探索变量背后的潜在结构/因子。旋转：Varimax(正交)、Promax(斜交)。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'efa-t0')">方法介绍</button><button class="tab" onclick="swT(this,'efa-t1')">R代码</button><button class="tab" onclick="swT(this,'efa-t2')">Python代码</button><button class="tab" onclick="swT(this,'efa-t3')">案例解读</button></div><div class="tp on" id="efa-t0"><p>EFA假设观测变量由潜在因子决定，用于问卷结构效度评价。与PCA不同，因子分析有测量误差模型。旋转使因子载荷更清晰。KMO>0.6且Bartlett P<0.05表示适合做EFA。</p></div><div class="tp" id="efa-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># EFA
library(psych)
set.seed(123)
data <- data.frame(q1=rnorm(200,3,1), q2=0.6*q1+rnorm(200,0,0.8),
q3=0.7*q1+rnorm(200,0,0.7), q4=rnorm(200,3,1),
q5=0.5*q4+rnorm(200,0,0.9), q6=0.6*q4+rnorm(200,0,0.8))
KMO(cor(data))
cortest.bartlett(cor(data), n=200)
fa <- fa(data, nfactors=2, rotate="varimax")
print(fa$loadings, cutoff=0.3)</div></div></div><div class="tp" id="efa-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from factor_analyzer import FactorAnalyzer, calculate_kmo
from factor_analyzer.factor_analyzer import calculate_bartlett_sphericity
kmo_all, kmo = calculate_kmo(df)
print(f'KMO = {kmo:.3f}')
chi2, p = calculate_bartlett_sphericity(df)
print(f'Bartlett: p={p:.4f}')
fa = FactorAnalyzer(n_factors=2, rotation='varimax')
fa.fit(df)
print('Loadings:', fa.loadings_)</div></div></div><div class="tp" id="efa-t3"><div class="res-box"><div class="res-title">📋 EFA案例</div><div class="res-body"><strong>结果：</strong>KMO=0.82, Bartlett P<0.001<br>2个因子解释58%方差: 因子1=躯体症状, 因子2=心理症状<br>问卷结构效度良好。</div></div></div></div></div></div>
<div class="cd" id="cd-kmeans"><h3>K-means聚类</h3><div class="ds"><strong>用途：</strong>将样本划分为K个簇。基于距离的硬聚类。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'kmeans-t0')">方法介绍</button><button class="tab" onclick="swT(this,'kmeans-t1')">R代码</button><button class="tab" onclick="swT(this,'kmeans-t2')">Python代码</button><button class="tab" onclick="swT(this,'kmeans-t3')">案例解读</button></div><div class="tp on" id="kmeans-t0"><p>K-means将数据划分为K个簇，每个样本属于最近的质心。需指定K值。最佳K可通过肘部法则(降低曲线)或轮廓系数选择。</p></div><div class="tp" id="kmeans-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># K-means
set.seed(123)
data <- data.frame(x1=rnorm(150,c(0,5,10),1.5), x2=rnorm(150,c(0,5,10),1.5))
wss <- sapply(1:8, function(k) kmeans(data,k,nstart=25)$tot.withinss)
plot(1:8,wss,type="b",xlab="K",ylab="WSS")
km <- kmeans(data, centers=3, nstart=25)
plot(data$x1, data$x2, col=km$cluster, pch=19)
points(km$centers, col=1:3, pch=8, cex=2)</div></div></div><div class="tp" id="kmeans-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score
kmeans = KMeans(n_clusters=3, random_state=123, n_init=25)
df['cluster'] = kmeans.fit_predict(X)
sil = silhouette_score(X, df['cluster'])
print(f'Silhouette = {sil:.3f}')</div></div></div><div class="tp" id="kmeans-t3"><div class="res-box"><div class="res-title">📋 K-means案例</div><div class="res-body"><strong>结果：</strong>K=3最优(轮廓系数0.62)<br>簇1: 年轻+轻度代谢异常 | 簇2: 中年+中重度 | 簇3: 老年+多并发症</div></div></div></div></div></div>
<div class="cd" id="cd-hclust"><h3>层次聚类</h3><div class="ds"><strong>用途：</strong>无需预设K的聚类。输出树状图。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'hclust-t0')">方法介绍</button><button class="tab" onclick="swT(this,'hclust-t1')">R代码</button><button class="tab" onclick="swT(this,'hclust-t2')">Python代码</button><button class="tab" onclick="swT(this,'hclust-t3')">案例解读</button></div><div class="tp on" id="hclust-t0"><p>层次聚类按层次聚合(自底向上)或分裂(自顶向下)。不需预指定K，树状图直观展示聚类层次。常见连接法: ward.D2、complete、average。</p></div><div class="tp" id="hclust-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># 层次聚类
set.seed(123)
data <- data.frame(x1=rnorm(50,c(0,5,10),1.5), x2=rnorm(50,c(0,5,10),1.5))
dist_m <- dist(data, method="euclidean")
hc <- hclust(dist_m, method="ward.D2")
plot(hc, main="Dendrogram", xlab="", sub="")
rect.hclust(hc, k=3, border=1:3)
groups <- cutree(hc, k=3)
print(table(groups))</div></div></div><div class="tp" id="hclust-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from scipy.cluster.hierarchy import dendrogram, linkage, fcluster
Z = linkage(df_scaled, method='ward')
dendrogram(Z); plt.show()
clusters = fcluster(Z, t=3, criterion='maxclust')
print(pd.Series(clusters).value_counts())</div></div></div><div class="tp" id="hclust-t3"><div class="res-box"><div class="res-title">📋 层次聚类案例</div><div class="res-body"><strong>结果：</strong>树状图显示3个主要腐瘤亚型，与临床预后相关<br>发现新的疾病亚型。</div></div></div></div></div></div>
<div class="cd" id="cd-mediation"><h3>中介分析</h3><div class="ds"><strong>用途：</strong>检验X通过M影响Y的间接路径(中介效应)。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'mediation-t0')">方法介绍</button><button class="tab" onclick="swT(this,'mediation-t1')">R代码</button><button class="tab" onclick="swT(this,'mediation-t2')">Python代码</button><button class="tab" onclick="swT(this,'mediation-t3')">案例解读</button></div><div class="tp on" id="mediation-t0"><p>中介分析检验X是否通过M影响Y。总效应=直接效应(c')+间接效应(a×b)。Bootstrap法检验间接效应(不要求正态)。</p></div><div class="tp" id="mediation-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># 中介分析
library(mediation)
set.seed(123)
n <- 200
data <- data.frame(X=rnorm(n), M=0.5*X+rnorm(n), Y=0.3*M+0.2*X+rnorm(n))
model_M <- lm(M ~ X, data=data)
model_Y <- lm(Y ~ X + M, data=data)
med <- mediate(model_M, model_Y, treat="X", mediator="M", boot=TRUE, sims=1000)
summary(med)
cat("ACME:", med$d0, "\nDirect:", med$z0, "\nProp:", med$n.avg)</div></div></div><div class="tp" id="mediation-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">a_m = sm.OLS(df['M'], sm.add_constant(df['X'])).fit()
b_m = sm.OLS(df['Y'], sm.add_constant(df[['X','M']])).fit()
indirect = a_m.params['X'] * b_m.params['M']
direct = b_m.params['X']
total = indirect + direct
print(f'Indirect={indirect:.3f}, Direct={direct:.3f}')
print(f'Mediation ratio={indirect/total:.1%}')</div></div></div><div class="tp" id="mediation-t3"><div class="res-box"><div class="res-title">📋 中介案例</div><div class="res-body"><strong>结果：</strong>间接效应=0.12(P=0.002), 直接效应=0.08(P=0.124)<br><strong>解读：</strong>健康素养完全中介SES对健康的影响(中介比例~60%)。</div></div></div></div></div></div>
<div class="cd" id="cd-moderation"><h3>调节效应</h3><div class="ds"><strong>用途：</strong>检验调节变量W是否改变X对Y的影响方向/强度(交互作用)。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'moderation-t0')">方法介绍</button><button class="tab" onclick="swT(this,'moderation-t1')">R代码</button><button class="tab" onclick="swT(this,'moderation-t2')">Python代码</button><button class="tab" onclick="swT(this,'moderation-t3')">案例解读</button></div><div class="tp on" id="moderation-t0"><p>调节效应检验X对Y的效应是否依赖于调节变量W。核心是交互项X×W的回归系数。交互项显著即存在调节效应。连续变量需中心化。</p></div><div class="tp" id="moderation-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r"># 调节效应
set.seed(123)
n <- 200; X <- rnorm(n); W <- rnorm(n)
Y <- 0.3*X + 0.2*W + 0.4*X*W + rnorm(n)
data <- data.frame(X, W, Y)
data$X_c <- scale(data$X, scale=FALSE)
data$W_c <- scale(data$W, scale=FALSE)
data$XW <- data$X_c * data$W_c
mod <- lm(Y ~ X_c + W_c + XW, data=data)
summary(mod)
library(interactions); sim_slopes(mod, pred=X_c, modx=W_c)</div></div></div><div class="tp" id="moderation-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">df['X_c'] = df['X']-df['X'].mean()
df['W_c'] = df['W']-df['W'].mean()
df['XW'] = df['X_c']*df['W_c']
X = sm.add_constant(df[['X_c','W_c','XW']])
model = sm.OLS(df['Y'], X).fit()
print(model.summary())
# 交互项显著→存在调节效应</div></div></div><div class="tp" id="moderation-t3"><div class="res-box"><div class="res-title">📋 调节效应案例</div><div class="res-body"><strong>结果：</strong>运动×年龄交互项β=0.03, <span class=sig>P=0.008</span><br><strong>解读：</strong>年龄调节了运动对血压的效果—年轻人运动降压效果更明显。</div></div></div></div></div></div>
</div><!-- end stats -->
<!-- ============ 生存分析 ============ -->
<div id="survival" style="margin-bottom:1.5rem">
<div class="tl"><a href="https://cran.r-project.org/web/packages/survival/index.html" target="_blank" rel="noopener">⏳ survival R包文档</a></div>
<h3 style="margin-bottom:.6rem;font-size:1.1rem">⏳ 生存分析</h3>
<div class="cg">
<div class="cd"><h3>Kaplan-Meier分析</h3><div class="ds">生存曲线估计，组间比较<button class="mb" onclick="togM(this)">查看代码</button>
<div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'kmr')">R代码</button></div>
<div class="tp on" id="kmr"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r">library(survival)
library(survminer)
# 使用内置肺癌数据
data(lung)
lung$sex <- factor(lung$sex, labels=c("男","女"))
# KM估计
km_fit <- survfit(Surv(time, status) ~ sex,
data=lung)
summary(km_fit)
# Log-rank检验
survdiff(Surv(time, status) ~ sex, data=lung)
# 生存曲线
ggsurvplot(km_fit, data=lung,
pval=TRUE, conf.int=TRUE,
risk.table=TRUE,
xlab="时间(天)", ylab="生存概率")</div></div></div>
</div></div></div>
<div class="cd"><h3>Cox回归</h3><div class="ds">多因素生存分析<button class="mb" onclick="togM(this)">查看代码</button>
<div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'coxr')">R代码</button></div>
<div class="tp on" id="coxr"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r">library(survival)
# Cox回归
cox <- coxph(Surv(time, status) ~ sex + age + ph.ecog,
data=lung)
summary(cox)
# PH假设检验
cox.zph(cox)
# 森林图
library(survminer)
ggforest(cox, data=lung)
# 校准曲线
library(riskRegression)
score <- Score(list("Cox"=cox),
formula=Surv(time,status)~1,
data=lung, times=365)
plotCalibration(score, times=365)</div></div></div>
</div></div></div>
<div class="cd"><h3>竞争风险模型</h3><div class="ds">Fine-Gray模型，累积发生率<button class="mb" onclick="togM(this)">查看代码</button>
<div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'cpr')">R代码</button></div>
<div class="tp on" id="cpr"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r">library(cmprsk)
# 模拟竞争风险数据
set.seed(123)
time <- rexp(200, rate=0.1)
status <- sample(0:2, 200, replace=TRUE,
prob=c(0.3,0.5,0.2))
group <- sample(0:1, 200, replace=TRUE)
# 累积发生率
ci <- cuminc(time, status, group)
plot(ci, xlab="时间", ylab="累积发生率")
# Fine-Gray检验
print(ci$Tests)
# 竞争风险回归
fg <- crr(time, status, covariate=as.matrix(group))
summary(fg)</div></div></div>
</div></div></div>
</div></div>
<!-- ============ 缺失数据处理 ============ -->
<div id="missing-data" style="margin-bottom:1.5rem">
<h3 style="margin-bottom:.6rem;font-size:1.1rem">🔧 缺失数据处理</h3>
<div class="cg">
<div class="cd"><h3>缺失机制</h3><p class="ds"><strong>MCAR：</strong>完全随机缺失，与数据值无关<br><strong>MAR：</strong>随机缺失，与其他观测变量有关<br><strong>MNAR：</strong>非随机缺失，与缺失值本身有关</p></div>
<div class="cd"><h3>多重插补MICE</h3><div class="ds">推荐方法<button class="mb" onclick="togM(this)">查看代码</button>
<div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'micer')">R代码</button><button class="tab" onclick="swT(this,'micep')">Python代码</button></div>
<div class="tp on" id="micer"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r">library(mice)
set.seed(123)
data <- data.frame(age=rnorm(100,60,10),
bmi=rnorm(100,25,3), sbp=rnorm(100,130,15))
data$bmi[sample(1:100,20)] <- NA
data$sbp[sample(1:100,15)] <- NA
md.pattern(data)
imp <- mice(data, m=5, method="pmm", seed=123)
complete_data <- complete(imp,1)
fit <- with(imp, lm(sbp~age+bmi))
summary(pool(fit))</div></div></div>
<div class="tp" id="micep"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from sklearn.impute import IterativeImputer
import pandas as pd, numpy as np
imp = IterativeImputer(max_iter=10, random_state=123)
df_imp = pd.DataFrame(imp.fit_transform(df), columns=df.columns)</div></div></div>
</div></div></div>
</div></div>
<!-- ============ ROC曲线深度分析 ============ -->
<div id="roc" style="margin-bottom:1.5rem">
<div class="tl"><a href="https://cran.r-project.org/web/packages/pROC/index.html" target="_blank" rel="noopener">📈 pROC R包</a></div>
<h3 style="margin-bottom:.6rem;font-size:1.1rem">📈 ROC曲线与预测模型评价</h3>
<div class="cg">
<div class="cd"><h3>ROC曲线基础</h3><p class="ds"><strong>AUC：</strong>0.5=无区分，0.7-0.8可接受，0.8+优秀<br><strong>最佳切点：</strong>约登指数(灵敏度+特异度-1)<br><strong>多模型比较：</strong>DeLong检验<br><strong>校准曲线：</strong>预测概率vs实际概率</p></div>
<div class="cd"><h3>ROC比较与校准</h3><div class="ds">多模型AUC对比<button class="mb" onclick="togM(this)">查看R代码</button>
<div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'rocr2')">R代码</button></div>
<div class="tp on" id="rocr2"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r">library(pROC)
# 比较两个模型AUC
set.seed(123)
true <- rbinom(100, 1, 0.5)
pred1 <- rnorm(100) + true*1.5
pred2 <- rnorm(100) + true*1.0
roc1 <- roc(true, pred1)
roc2 <- roc(true, pred2)
# DeLong检验
roc.test(roc1, roc2, method="delong")
# 校准曲线
library(rms)
cal <- calibrate(lrm(true ~ pred1), B=200)
plot(cal)
# DCA决策曲线
library(rmda)
dca <- decision_curve(true ~ pred1,
data=data.frame(true, pred1),
bootstraps=50)
plot_decision_curve(dca)</div></div></div>
</div></div></div>
</div></div>
<!-- ============ 时间序列分析 ============ -->
<div id="time-series" style="margin-bottom:1.5rem">
<h3 style="margin-bottom:.6rem;font-size:1.1rem">📈 时间序列分析</h3>
<div class="cg">
<div class="cd"><h3>ARIMA模型</h3><div class="ds">自回归移动平均，预测未来趋势<button class="mb" onclick="togM(this)">查看详细操作</button>
<div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'arimar')">R代码</button><button class="tab" onclick="swT(this,'arimap')">Python代码</button></div>
<div class="tp on" id="arimar"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r">library(forecast)
set.seed(123)
ts_data <- ts(rpois(120,10)+5*sin(2*pi*1:120/12),
start=c(2020,1), frequency=12)
model <- auto.arima(ts_data)
fc <- forecast(model, h=12)
plot(fc)
accuracy(fc)</div></div></div>
<div class="tp" id="arimap"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">from statsmodels.tsa.arima.model import ARIMA
import numpy as np, pandas as pd
ts = np.random.poisson(10,120)+5*np.sin(2*np.pi*np.arange(120)/12)
model = ARIMA(ts, order=(1,1,1)).fit()
fc = model.forecast(steps=12)
print(fc)</div></div></div>
</div></div></div>
<div class="cd" id="cd-ets"><h3>ETS指数平滑</h3><div class="ds">用途：处理时间序列的趋势和季节性，适合单变量预测。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'ets-t0')">方法介绍</button><button class="tab" onclick="swT(this,'ets-t1')">R代码</button><button class="tab" onclick="swT(this,'ets-t2')">Python代码</button><button class="tab" onclick="swT(this,'ets-t3')">案例解读</button></div><div class="tp on" id="ets-t0"><p>ETS（Error Trend Seasonal）是指数平滑方法的统一框架，用于处理时间序列的误差、趋势和季节性。ETS(A,N,N)表示可加性误差、无趋势、无季节；ETS(A,A,A)表示可加性误差、可加性趋势、可加性季节。通过拟合优度选择最优模型。</p></div><div class="tp" id="ets-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r">library(forecast)
set.seed(123)
ts_data <- ts(rpois(120,10)+5*sin(2*pi*1:120/12),
start=c(2020,1), frequency=12)
fit <- ets(ts_data)
summary(fit)
fc <- forecast(fit, h=12)
plot(fc)
accuracy(fc)</div></div></div><div class="tp" id="ets-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">import numpy as np, pandas as pd
from statsmodels.tsa.holtwinters import ExponentialSmoothing
np.random.seed(123)
ts = np.random.poisson(10,120)+5*np.sin(2*np.pi*np.arange(120)/12)
df = pd.DataFrame({'y':ts}, index=pd.date_range('2020-01',periods=120,freq='M'))
model = ExponentialSmoothing(df['y'], seasonal_periods=12,
trend='add', seasonal='add').fit()
fc = model.forecast(12)
print(fc)</div></div></div><div class="tp" id="ets-t3"><div class="res-box"><div class="res-title">📋 ETS案例</div><div class="res-body">数据：2019-2024月度呼吸道感染病登记例数<br>结果：ETS(A,N,A)模型最优，RMSE=15.3<br>解读：去季节后套合良好，2025年预测值呈现稳定季节性波动。</div></div></div></div></div></div>
<div class="cd" id="cd-prophet"><h3>Prophet时间序列预测</h3><div class="ds">用途：Facebook开源的时间序列预测框架，自动处理节假日效应和变点。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'prophet-t0')">方法介绍</button><button class="tab" onclick="swT(this,'prophet-t1')">R代码</button><button class="tab" onclick="swT(this,'prophet-t2')">Python代码</button><button class="tab" onclick="swT(this,'prophet-t3')">案例解读</button></div><div class="tp on" id="prophet-t0"><p>Prophet由Facebook于2017年开源，基于可分解时间序列模型：趋势 + 季节性 + 节假日效应。Prophet能自动处理缺失值、异常值和变点，且对非专业用户友好。适合具有明显季节性和多年历史数据的预测场景。</p></div><div class="tp" id="prophet-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r">library(prophet)
library(dplyr)
# 模拟月度数据
set.seed(123)
ds <- seq(as.Date("2020-01-01"), as.Date("2024-12-01"), by="month")
trend <- 10 + 0.05*1:60
seasonal <- 3*sin(2*pi*1:60/12)
y <- trend + seasonal + rnorm(60, 0, 1)
df <- data.frame(ds, y)
# Prophet模型
m <- prophet(df, yearly.seasonality=TRUE)
future <- make_future_dataframe(m, periods=12, freq="month")
fc <- predict(m, future)
plot(m, fc)
prophet_plot_components(m, fc)</div></div></div><div class="tp" id="prophet-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">import numpy as np, pandas as pd
from prophet import Prophet
np.random.seed(123)
ds = pd.date_range("2020-01-01", periods=60, freq="M")
trend = 10 + 0.05*np.arange(60)
seasonal = 3*np.sin(2*np.pi*np.arange(60)/12)
y = trend + seasonal + np.random.normal(0, 1, 60)
df = pd.DataFrame({"ds": ds, "y": y})
model = Prophet(yearly_seasonality=True)
model.fit(df)
future = model.make_future_dataframe(periods=12, freq="M")
fc = model.predict(future)
model.plot(fc).show()
model.plot_components(fc).show()</div></div></div><div class="tp" id="prophet-t3"><div class="res-box"><div class="res-title">📋 Prophet案例</div><div class="res-body">数据：2020-2024年某医院月度门诊量<br>结果：模型拟合良好，周期性波动被成功捕捉<br>解读：2025年门诊量预计保持上升趋势，季节性高峰出现在冬季呼吸道疾病高发期。</div></div></div></div></div></div>
<div class="cd" id="cd-lstm-ts"><h3>LSTM时间序列预测</h3><div class="ds">用途：深度学习方法，适合复杂模式和长期依赖的时间序列。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'lstm-ts-t0')">方法介绍</button><button class="tab" onclick="swT(this,'lstm-ts-t1')">R代码</button><button class="tab" onclick="swT(this,'lstm-ts-t2')">Python代码</button><button class="tab" onclick="swT(this,'lstm-ts-t3')">案例解读</button></div><div class="tp on" id="lstm-ts-t0"><p>LSTM（Long Short-Term Memory）是循环神经网络的变种，通过徘徊门机制解决了传统RNN的梯度消失问题。LSTM能捕捉时间序列中的长期依赖关系，适合复杂模式的时间序列预测。需要注意：需要先处理数据创建观测窗口，通常比统计方法需要更多数据。</p></div><div class="tp" id="lstm-ts-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r">library(keras)
# 生成模拟数据
set.seed(123)
n <- 300
x <- seq(0, 10*pi, length.out=n)
y <- sin(x) + rnorm(n, 0, 0.1)
# 创建时间窗口
create_seq <- function(data, lookback=10){
X <- t(sapply(lookback:n, function(i) data[(i-lookback+1):i]))
Y <- data[(lookback+1):(n+1)]
list(X=array(X, dim=c(nrow(X), lookback, 1)), Y=Y)
}
lookback <- 10
data <- create_seq(y, lookback)
# LSTM模型
model <- keras_model_sequential() |>
layer_lstm(units=50, input_shape=c(lookback,1)) |>
layer_dense(units=1)
model |> compile(optimizer='adam', loss='mse')
history <- model |> fit(data$X[1:200,,], data$Y[1:200],
epochs=50, batch_size=16, validation_split=0.2, verbose=0)
# 预测
pred <- model |> predict(data$X[201:290,,])
plot(data$Y[201:290], type='l', col='blue')
lines(pred, col='red')
legend('topright', c('True','Pred'), col=c('blue','red'), lty=1)</div></div></div><div class="tp" id="lstm-ts-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">import numpy as np
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import LSTM, Dense
np.random.seed(123)
n = 300; x = np.linspace(0, 10*np.pi, n)
y = np.sin(x) + np.random.normal(0, 0.1, n)
lookback = 10
X, Y = [], []
for i in range(lookback, n-1):
X.append(y[i-lookback+1:i+1])
Y.append(y[i+1])
X = np.array(X).reshape(-1, lookback, 1)
Y = np.array(Y)
# LSTM模型
model = Sequential([
LSTM(50, input_shape=(lookback, 1)),
Dense(1)
])
model.compile(optimizer="adam", loss="mse")
model.fit(X[:200], Y[:200], epochs=50, batch_size=16,
validation_split=0.2, verbose=0)
pred = model.predict(X[200:290], verbose=0)
print("Prediction shape:", pred.shape)</div></div></div><div class="tp" id="lstm-ts-t3"><div class="res-box"><div class="res-title">📋 LSTM案例</div><div class="res-body">数据：模拟的周期性生物标志物测定时间序列<br>结果：LSTM成功学习了波形模式，MSE=0.015<br>解读：深度学习方法在捕捉复杂循环模式方面优于传统统计方法，但需要较多数据和调参。</div></div></div></div></div></div>
<div class="cd" id="cd-var"><h3>VAR向量自回归</h3><div class="ds">用途：多变量时间序列分析，同时预测多个相互关联的变量。<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button><div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'var-t0')">方法介绍</button><button class="tab" onclick="swT(this,'var-t1')">R代码</button><button class="tab" onclick="swT(this,'var-t2')">Python代码</button><button class="tab" onclick="swT(this,'var-t3')">案例解读</button></div><div class="tp on" id="var-t0"><p>VAR（Vector Autoregression）是多变量时间序列的经典模型，同时建模多个时间序列的动态关系。VAR(p)表示包含P阶滞后项。核心优势：无需区分内生和外生变量，所有变量均等待处。通常用于宏观经济和卫生政策评估。</p></div><div class="tp" id="var-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r">library(vars)
set.seed(123)
n <- 200
# 双变量VAR(1)模拟
e1 <- rnorm(n); e2 <- rnorm(n)
y1 <- 0.5*e1[1]; y2 <- 0.3*e2[1]
for(i in 2:n){
y1[i] <- 1 + 0.6*y1[i-1] + 0.2*y2[i-1] + e1[i]
y2[i] <- 2 + 0.1*y1[i-1] + 0.5*y2[i-1] + e2[i]
}
data <- cbind(y1, y2)
# VAR模型
var_select <- VARselect(data, lag.max=8)
print(var_select$selection)
model <- VAR(data, p=2)
summary(model)
# 脉冲响应
irf <- irf(model, n.ahead=10)
plot(irf)
# 预测
fc <- predict(model, n.ahead=6)
plot(fc)</div></div></div><div class="tp" id="var-t2"><div class="cb"><div class="ch"><span class="cl2">Python</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="python">import numpy as np, pandas as pd
from statsmodels.tsa.api import VAR
np.random.seed(123)
n = 200; e1 = np.random.normal(0, 1, n)
e2 = np.random.normal(0, 1, n)
y1 = np.zeros(n); y2 = np.zeros(n)
y1[0] = 0.5*e1[0]; y2[0] = 0.3*e2[0]
for i in range(1, n):
y1[i] = 1 + 0.6*y1[i-1] + 0.2*y2[i-1] + e1[i]
y2[i] = 2 + 0.1*y1[i-1] + 0.5*y2[i-1] + e2[i]
df = pd.DataFrame({"y1": y1, "y2": y2})
model = VAR(df)
lag_order = model.select_order(maxlags=8)
print(lag_order.selected_orders)
result = model.fit(2)
print(result.summary())
# 脉冲响应
irf = result.irf(10)
irf.plot()
# 预测
fc = result.forecast(df.values[-2:], steps=6)
print("Forecast:", fc)</div></div></div><div class="tp" id="var-t3"><div class="res-box"><div class="res-title">📋 VAR案例</div><div class="res-body">数据：某地区每月流感发病率和气温数据<br>结果：VAR(2)模型最优，气温对流感有显著滞后影响<br>解读：气温下降后2周流感发病率上升，为预防提供了时间窗口。</div></div></div></div></div></div>
</div>
</div>
<!-- ============ 样本量计算 ============ -->
<div id="sample-size" style="margin-bottom:1.5rem">
<h3 style="margin-bottom:.6rem;font-size:1.1rem">🧮 样本量计算（含R代码）</h3>
<div class="cg">
<div class="cd"><h3>核心参数</h3><p class="ds"><strong>α值：</strong>一类错误，通常0.05<br><strong>β值：</strong>二类错误，通常0.2，效能80%<br><strong>效应量：</strong>组间预期差异<br><strong>脱落率：</strong>10–20%</p></div>
<div class="cd" id="cd-ss-anova"><h3>ANOVA样本量</h3><div class="ds">多组均值比较的方差分析样本量<button class="mb" onclick="togM(this)" data-i18n="view-details">查看详细操作</button>
<div class="mx mx-col"><div class="tabs"><button class="tab on" onclick="swT(this,'anova-t0')">方法介绍</button><button class="tab" onclick="swT(this,'anova-t1')">R代码</button><button class="tab" onclick="swT(this,'anova-t2')">Python代码</button><button class="tab" onclick="swT(this,'anova-t3')">案例解读</button></div>
<div class="tp on" id="anova-t0"><p><strong>ANOVA样本量计算</strong>基于Cohen's f效应量。f = σ<sub>m</sub>/σ（组间标准差/组内标准差）。小效应f=0.10，中等f=0.25，大效应f=0.40。需设定组数k、检验效能(通常0.80)、显著性水平α。</p></div>
<div class="tp" id="anova-t1"><div class="cb"><div class="ch"><span class="cl2">R</span><button class="cp" onclick="cpC(this)">复制</button></div><div class="cy" data-lang="r">library(pwr)
# ANOVA样本量 k=3组, 中等效应f=0.25
pwr.anova.test(k=3, f=0.25, power=0.8, sig.level=0.05)