RCT 的分期

 第一期臨床試驗（小規模， 2-100 人）：為了在正常人或病人找出沒有藥物副作用的最大劑量


第二期臨床試驗（中規模， 100-300 人）：為了探索藥物是否有效或有生物活性、副作用


第三期臨床試驗（大規模， 300-3000 人）：為了確定藥物是否有效以及有什麼副作用


第四期臨床試驗（上市後追蹤）：為了確認藥物是否有什麼副作用

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Bayesian reanalysis of ORBITA

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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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