1' Excel 公式从斜率计算 qPCR 效率
2' 如果斜率在单元格 A2 中，则放在单元格 B2 中
3=10^(-1/A2)-1
4
5' Excel 公式将效率转换为百分比
6' 如果效率小数在单元格 B2 中，则放在单元格 C2 中
7=B2*100
8
9' 计算效率的函数，基于 Ct 值和稀释因子
10Function qPCR_Efficiency(CtValues As Range, DilutionFactor As Double) As Double
11    Dim i As Integer
12    Dim n As Integer
13    Dim sumX As Double, sumY As Double, sumXY As Double, sumXX As Double
14    Dim logDilution As Double, slope As Double
15    
16    n = CtValues.Count
17    
18    ' 计算线性回归
19    For i = 1 To n
20        logDilution = (i - 1) * WorksheetFunction.Log10(DilutionFactor)
21        sumX = sumX + logDilution
22        sumY = sumY + CtValues(i)
23        sumXY = sumXY + (logDilution * CtValues(i))
24        sumXX = sumXX + (logDilution * logDilution)
25    Next i
26    
27    ' 计算斜率
28    slope = (n * sumXY - sumX * sumY) / (n * sumXX - sumX * sumX)
29    
30    ' 计算效率
31    qPCR_Efficiency = (10 ^ (-1 / slope) - 1) * 100
32End Function
33

1# R 函数从 Ct 值和稀释因子计算 qPCR 效率
2calculate_qpcr_efficiency <- function(ct_values, dilution_factor) {
3  # 创建对数稀释值
4  log_dilutions <- log10(dilution_factor) * seq(0, length(ct_values) - 1)
5  
6  # 执行线性回归
7  model <- lm(ct_values ~ log_dilutions)
8  
9  # 提取斜率和 R 平方
10  slope <- coef(model)[2]
11  r_squared <- summary(model)$r.squared
12  
13  # 计算效率
14  efficiency <- (10^(-1/slope) - 1) * 100
15  
16  # 返回结果
17  return(list(
18    efficiency = efficiency,
19    slope = slope,
20    r_squared = r_squared,
21    intercept = coef(model)[1]
22  ))
23}
24
25# 示例用法
26ct_values <- c(15.0, 18.5, 22.0, 25.5, 29.0)
27dilution_factor <- 10
28results <- calculate_qpcr_efficiency(ct_values, dilution_factor)
29cat(sprintf("效率: %.2f%%\n", results$efficiency))
30cat(sprintf("斜率: %.4f\n", results$slope))
31cat(sprintf("R 平方: %.4f\n", results$r_squared))
32

1import numpy as np
2from scipy import stats
3import matplotlib.pyplot as plt
4
5def calculate_qpcr_efficiency(ct_values, dilution_factor):
6    """
7    从 Ct 值和稀释因子计算 qPCR 效率。
8    
9    参数：
10    ct_values (list): Ct 值列表
11    dilution_factor (float): 连续样本之间的稀释因子
12    
13    返回：
14    dict: 包含效率、斜率、r_squared 和截距的字典
15    """
16    # 创建对数稀释值
17    log_dilutions = np.log10(dilution_factor) * np.arange(len(ct_values))
18    
19    # 执行线性回归
20    slope, intercept, r_value, p_value, std_err = stats.linregress(log_dilutions, ct_values)
21    
22    # 计算效率
23    efficiency = (10 ** (-1 / slope) - 1) * 100
24    r_squared = r_value ** 2
25    
26    return {
27        'efficiency': efficiency,
28        'slope': slope,
29        'r_squared': r_squared,
30        'intercept': intercept
31    }
32
33def plot_standard_curve(ct_values, dilution_factor, results):
34    """
35    绘制带有回归线的标准曲线。
36    """
37    log_dilutions = np.log10(dilution_factor) * np.arange(len(ct_values))
38    
39    plt.figure(figsize=(10, 6))
40    plt.scatter(log_dilutions, ct_values, color='blue', s=50)
41    
42    # 为回归线生成点
43    x_line = np.linspace(min(log_dilutions) - 0.5, max(log_dilutions) + 0.5, 100)
44    y_line = results['slope'] * x_line + results['intercept']
45    plt.plot(x_line, y_line, 'r-', linewidth=2)
46    
47    plt.xlabel('对数稀释')
48    plt.ylabel('Ct 值')
49    plt.title('qPCR 标准曲线')
50    
51    # 将方程和 R² 添加到图中
52    equation = f"y = {results['slope']:.4f}x + {results['intercept']:.4f}"
53    r_squared = f"R² = {results['r_squared']:.4f}"
54    efficiency = f"效率 = {results['efficiency']:.2f}%"
55    
56    plt.annotate(equation, xy=(0.05, 0.95), xycoords='axes fraction')
57    plt.annotate(r_squared, xy=(0.05, 0.90), xycoords='axes fraction')
58    plt.annotate(efficiency, xy=(0.05, 0.85), xycoords='axes fraction')
59    
60    plt.grid(True, linestyle='--', alpha=0.7)
61    plt.tight_layout()
62    plt.show()
63
64# 示例用法
65ct_values = [15.0, 18.5, 22.0, 25.5, 29.0]
66dilution_factor = 10
67results = calculate_qpcr_efficiency(ct_values, dilution_factor)
68
69print(f"效率: {results['efficiency']:.2f}%")
70print(f"斜率: {results['slope']:.4f}")
71print(f"R 平方: {results['r_squared']:.4f}")
72print(f"截距: {results['intercept']:.4f}")
73
74# 绘制标准曲线
75plot_standard_curve(ct_values, dilution_factor, results)
76

1/**
2 * 从 Ct 值和稀释因子计算 qPCR 效率
3 * @param {Array<number>} ctValues - Ct 值数组
4 * @param {number} dilutionFactor - 连续样本之间的稀释因子
5 * @returns {Object} 包含效率、斜率、rSquared 和截距的对象
6 */
7function calculateQPCREfficiency(ctValues, dilutionFactor) {
8  // 创建对数稀释值
9  const logDilutions = ctValues.map((_, index) => index * Math.log10(dilutionFactor));
10  
11  // 计算线性回归的均值
12  const n = ctValues.length;
13  let sumX = 0, sumY = 0, sumXY = 0, sumXX = 0, sumYY = 0;
14  
15  for (let i = 0; i < n; i++) {
16    sumX += logDilutions[i];
17    sumY += ctValues[i];
18    sumXY += logDilutions[i] * ctValues[i];
19    sumXX += logDilutions[i] * logDilutions[i];
20    sumYY += ctValues[i] * ctValues[i];
21  }
22  
23  // 计算斜率和截距
24  const slope = (n * sumXY - sumX * sumY) / (n * sumXX - sumX * sumX);
25  const intercept = (sumY - slope * sumX) / n;
26  
27  // 计算 R 平方
28  const yMean = sumY / n;
29  let totalVariation = 0;
30  let explainedVariation = 0;
31  
32  for (let i = 0; i < n; i++) {
33    const yPredicted = slope * logDilutions[i] + intercept;
34    totalVariation += Math.pow(ctValues[i] - yMean, 2);
35    explainedVariation += Math.pow(yPredicted - yMean, 2);
36  }
37  
38  const rSquared = explainedVariation / totalVariation;
39  
40  // 计算效率
41  const efficiency = (Math.pow(10, -1 / slope) - 1) * 100;
42  
43  return {
44    efficiency,
45    slope,
46    rSquared,
47    intercept
48  };
49}
50
51// 示例用法
52const ctValues = [15.0, 18.5, 22.0, 25.5, 29.0];
53const dilutionFactor = 10;
54const results = calculateQPCREfficiency(ctValues, dilutionFactor);
55
56console.log(`效率: ${results.efficiency.toFixed(2)}%`);
57console.log(`斜率: ${results.slope.toFixed(4)}`);
58console.log(`R 平方: ${results.rSquared.toFixed(4)}`);
59console.log(`截距: ${results.intercept.toFixed(4)}`);
60