次群分析

用次群分層設計

事先決定要分析的少數次群

人數至少需要主要終點的 4-16 倍

校正多重比較

校正事先決定的共變數

治療效果異質性分析

混合（多層次）模型

貝氏分析

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Bayesian reanalysis of ORBITA

import pymc3 as pm import numpy as np import arviz as az # Percutaneous coronary intervention in stable angina (ORBITA): a double-blind, randomised controlled trial 18 https://www.sciencedirect.com/science/article/abs/pii/S0140673617327149 diff = 16.6 diff_lower = -8.9 diff_upper = 42 # The scale for the Cauchy distribution cauchy_scale = 5 # Model setup with pm.Model() as model:     # Prior distribution for the difference     diff_prior = pm.Cauchy("diff", alpha=0, beta=cauchy_scale)      # Likelihood (normal approximation of the distribution of the difference)     se_diff = (diff_upper - diff_lower) / 3.92     likelihood = pm.Normal("likelihood", mu=diff_prior, sigma=se_diff, observed=np.array([diff]))     # Sample from the posterior distribution     trace = pm.sample(500000, cores=1, tune=200000, chains=4) # Calculate the posterior probability that the difference is negative post_prob_diff_negative = np.mean(t...
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Bayesian reanalysis with pymc3

 # Empagliflozin after Acute Myocardial Infarction 24 https://www.nejm.org/doi/full/10.1056/NEJMoa2314051 Do a Bayesian reanalysis of a RCT for log(hazard ratio) with 500000 samplings with a weakly informative prior, calculate the probability of hazard ratio less than 1 and a sensitivity analysis using pymc3 and only show the results in traditional Chinese instead of the code: A total of 3260 patients were assigned to receive empagliflozin and 3262 to receive placebo. During a median follow-up of 17.9 months, a first hospitalization for heart failure or death from any cause occurred in 267 patients (8.2%) in the empagliflozin group and in 298 patients (9.1%) in the placebo group, with incidence rates of 5.9 and 6.6 events, respectively, per 100 patient-years (hazard ratio, 0.90; 95% confidence interval [CI], 0.76 to 1.06; P=0.21). 使用 pymc3 對一項 RCT 進行貝氏再分析，在弱信息先驗條件下抽樣 500000 次，計算危害比小於 1 的概率，並進行敏感性分析，只用繁體中文顯示結果，而不顯示代碼:  Do a Bayesian reanalysis of a RCT with 500000 samplings wit...
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Bayesian reanalysis of Apolipoprotein A1 Infusions

Apolipoprotein A1 Infusions and Cardiovascular Outcomes after Acute Myocardial Infarction 24 https://www.nejm.org/doi/full/10.1056/NEJMoa2400969 P(θ | D) = (P(D | θ) * P(θ)) / P(D) marginal likelihood P(D) = ∫ P(D | θ) * P(θ) dθ Likelihood: P(D | θ) ~ N(μ_l, σ_l^2) Likelihood ratio: (P(D | θ1))/(P(D | θ2)*) Bayes factor: (P(D | θ1)* P(θ1))/(P(D | θ2)* P(θ2)) Prior: P(θ) ~ N(μ_p, σ_p^2) P(θ | D) ∝ P(D | θ) * P(θ) When we normalize the product of the two PDFs by dividing by the marginal likelihood p(D), the constant term cancels out, and we are left with a normal distribution with mean μ_new and variance σ_new^2. Prior mean 0, sd 0.5 log(HR) = log(0.93) = -0.0726 SE = (log(1.05) - log(0.81)) / (2 * 1.96) = 0.0644 Prior precision = 1 / (0.35^2) = 8.16 Likelihood precision = 1 / (0.0644^2) = 241.18 Posterior precision = 8.16 + 241.18 = 249.34 Posterior mean = (8.16 * 0 + 241.18 * -0.0726) / 249.34 = -0.0701 Posterior SD = sqrt(1 / 249.34) = 0.0634 Posterior 95% credible interval for the lo...
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