seed <- 2023
prob_arm1 <- 0.333
library(bssd)df <- read.csv("small_historic.csv")
map_small <- stan_map_patient_data(
y = df$y, trial = df$trial, time = df$time,
a_alpha = 1 / 3, a_beta = 1 / 3,
b_alpha = 5, b_beta = 5,
refresh = 0, seed = seed
)
map_small## Prob(Event): Mean 0.168 (HPDI 0.079, 0.253)
## MAP Prob(Event): Mean 0.168 (HPDI 0.038, 0.299)map_small$fit## Inference for Stan model: map_prior_patient_data.
## 4 chains, each with iter=2000; warmup=1000; thin=1;
## post-warmup draws per chain=1000, total post-warmup draws=4000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff
## a 0.17 0.00 0.04 0.09 0.14 0.17 0.20 0.26 1448
## b 0.51 0.00 0.15 0.24 0.41 0.51 0.62 0.79 2155
## pi_h[1] 0.15 0.00 0.06 0.05 0.11 0.14 0.19 0.28 2058
## pi_h[2] 0.20 0.00 0.06 0.11 0.16 0.20 0.24 0.33 2239
## pi_h[3] 0.15 0.00 0.05 0.06 0.11 0.15 0.18 0.27 2284
## pi_h[4] 0.15 0.00 0.05 0.06 0.12 0.15 0.19 0.26 2266
## pi_h[5] 0.17 0.00 0.06 0.08 0.13 0.17 0.21 0.30 2345
## pi_star 0.17 0.00 0.07 0.05 0.12 0.16 0.21 0.32 2162
## pi_star_alpha 8.62 0.08 3.31 3.18 6.15 8.28 10.71 15.98 1528
## pi_star_beta 42.81 0.26 12.35 20.12 33.84 42.63 51.40 66.81 2269
## avg 0.17 0.00 0.04 0.09 0.14 0.17 0.20 0.26 1448
## ess 51.43 0.31 14.51 24.49 40.97 51.46 61.73 78.65 2155
## lp__ -52.57 0.08 2.37 -58.23 -53.83 -52.17 -50.85 -49.18 965
## Rhat
## a 1
## b 1
## pi_h[1] 1
## pi_h[2] 1
## pi_h[3] 1
## pi_h[4] 1
## pi_h[5] 1
## pi_star 1
## pi_star_alpha 1
## pi_star_beta 1
## avg 1
## ess 1
## lp__ 1
##
## Samples were drawn using NUTS(diag_e) at Wed Nov 15 12:39:23 2023.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).mix_small <- fit_mixture(map_small)
mix_small## EM for Beta Mixture Model
## Log-Likelihood = 5124.374
##
## Univariate beta mixture
## Mixture Components:
## comp1 comp2
## w 0.579896 0.420104
## a 6.820920 3.890079
## b 29.176607 24.198249df <- read.csv("large_historic.csv")
map_large <- stan_map_patient_data(
y = df$y, trial = df$trial, time = df$time,
a_alpha = 1 / 3, a_beta = 1 / 3,
b_alpha = 5, b_beta = 5,
refresh = 0, seed = seed
)
map_large## Prob(Event): Mean 0.132 (HPDI 0.117, 0.147)
## MAP Prob(Event): Mean 0.132 (HPDI 0.099, 0.163)map_large$fit## Inference for Stan model: map_prior_patient_data.
## 4 chains, each with iter=2000; warmup=1000; thin=1;
## post-warmup draws per chain=1000, total post-warmup draws=4000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5%
## a 0.13 0.00 0.01 0.12 0.13 0.13 0.14 0.15
## b 0.55 0.00 0.14 0.28 0.45 0.55 0.64 0.81
## pi_h[1] 0.13 0.00 0.01 0.11 0.13 0.13 0.14 0.16
## pi_h[2] 0.13 0.00 0.01 0.10 0.12 0.13 0.13 0.15
## pi_h[3] 0.13 0.00 0.01 0.10 0.12 0.13 0.13 0.15
## pi_h[4] 0.14 0.00 0.01 0.11 0.13 0.14 0.14 0.16
## pi_h[5] 0.13 0.00 0.01 0.10 0.12 0.12 0.13 0.15
## pi_h[6] 0.14 0.00 0.01 0.11 0.13 0.14 0.15 0.17
## pi_h[7] 0.14 0.00 0.01 0.11 0.13 0.14 0.15 0.16
## pi_h[8] 0.12 0.00 0.01 0.10 0.12 0.12 0.13 0.15
## pi_h[9] 0.13 0.00 0.01 0.11 0.12 0.13 0.14 0.15
## pi_h[10] 0.14 0.00 0.01 0.11 0.13 0.14 0.15 0.17
## pi_star 0.13 0.00 0.02 0.10 0.12 0.13 0.14 0.17
## pi_star_alpha 72.25 0.32 18.34 36.69 59.84 71.99 84.64 109.30
## pi_star_beta 475.40 1.97 117.98 241.88 393.29 476.76 556.90 703.40
## avg 0.13 0.00 0.01 0.12 0.13 0.13 0.14 0.15
## ess 547.66 2.26 135.77 278.93 453.45 549.21 641.56 811.34
## lp__ -592.31 0.07 2.86 -599.19 -593.98 -591.87 -590.25 -587.99
## n_eff Rhat
## a 1486 1
## b 3601 1
## pi_h[1] 3422 1
## pi_h[2] 3225 1
## pi_h[3] 3977 1
## pi_h[4] 3515 1
## pi_h[5] 3762 1
## pi_h[6] 2903 1
## pi_h[7] 3927 1
## pi_h[8] 3640 1
## pi_h[9] 3121 1
## pi_h[10] 3031 1
## pi_star 3005 1
## pi_star_alpha 3334 1
## pi_star_beta 3604 1
## avg 1486 1
## ess 3601 1
## lp__ 1587 1
##
## Samples were drawn using NUTS(diag_e) at Wed Nov 15 12:39:32 2023.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).mix_large <- fit_mixture(map_large)
mix_large## EM for Beta Mixture Model
## Log-Likelihood = 10647.76
##
## Univariate beta mixture
## Mixture Components:
## comp1
## w 1.00000
## a 52.44163
## b 344.85923The prior on the active arm (arm 2) is constant throughoit:
w2 <- as.array(c(1))
pi2_alpha <- as.array(c(0.3))
pi2_beta <- as.array(c(0.3))df <- read.csv("small_current.csv")w1 <- mix_small["w",]
pi1_alpha <- mix_small["a",]
pi1_beta <- mix_small["b",]fit <- stan_bssd(y = df$y, time = df$time, prob_arm1 = prob_arm1,
w1 = w1, pi1_alpha = pi1_alpha, pi1_beta = pi1_beta,
w2 = w2, pi2_alpha = pi2_alpha, pi2_beta = pi2_beta)##
## SAMPLING FOR MODEL 'bssd' NOW (CHAIN 1).
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## Chain 4:fit## Prob(Event) in arm 1: 0.175
## Prob(Event) in arm 2: 0.203
## Prob(Event rate in arm 2 > arm 1): 0.59625fit$fit## Inference for Stan model: bssd.
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##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] -1.75 0.02 0.51 -2.94 -2.04 -1.68 -1.38 -0.90 1090 1
## mu[2] -1.57 0.02 0.53 -2.72 -1.79 -1.49 -1.24 -0.84 1061 1
## pi1 0.17 0.00 0.07 0.05 0.12 0.17 0.22 0.33 1233 1
## pi2 0.20 0.00 0.07 0.06 0.15 0.20 0.25 0.35 1726 1
## lp__ -50.35 0.04 1.13 -53.39 -50.78 -50.00 -49.56 -49.25 886 1
##
## Samples were drawn using NUTS(diag_e) at Wed Nov 15 12:39:33 2023.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).fit <- stan_bssd(y = df$y, time = df$time, tmt = df$tmt,
w1 = w1, pi1_alpha = pi1_alpha, pi1_beta = pi1_beta,
w2 = w2, pi2_alpha = pi2_alpha, pi2_beta = pi2_beta)##
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## Chain 4:fit## Prob(Event) in arm 1: 0.178
## Prob(Event) in arm 2: 0.205
## Prob(Event rate in arm 2 > arm 1): 0.6545fit$fit## Inference for Stan model: bssd_unblinded.
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## post-warmup draws per chain=1000, total post-warmup draws=4000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] -1.67 0.01 0.31 -2.34 -1.87 -1.65 -1.45 -1.11 2944 1
## mu[2] -1.50 0.01 0.29 -2.10 -1.70 -1.49 -1.30 -0.98 3152 1
## pi1 0.18 0.00 0.05 0.09 0.14 0.17 0.21 0.28 3273 1
## pi2 0.21 0.00 0.05 0.12 0.17 0.20 0.24 0.31 3297 1
## lp__ -50.23 0.02 0.98 -52.88 -50.64 -49.94 -49.52 -49.23 1703 1
##
## Samples were drawn using NUTS(diag_e) at Wed Nov 15 12:39:34 2023.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).w1 <- mix_large["w",]
pi1_alpha <- mix_large["a",]
pi1_beta <- mix_large["b",]fit <- stan_bssd(y = df$y, time = df$time, prob_arm1 = prob_arm1,
w1 = w1, pi1_alpha = pi1_alpha, pi1_beta = pi1_beta,
w2 = w2, pi2_alpha = pi2_alpha, pi2_beta = pi2_beta)##
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## Chain 4:fit## Prob(Event) in arm 1: 0.132
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## Prob(Event rate in arm 2 > arm 1): 0.923fit$fit## Inference for Stan model: bssd.
## 4 chains, each with iter=2000; warmup=1000; thin=1;
## post-warmup draws per chain=1000, total post-warmup draws=4000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] -1.96 0.00 0.14 -2.24 -2.05 -1.96 -1.87 -1.70 2691 1
## mu[2] -1.40 0.01 0.33 -2.14 -1.60 -1.38 -1.17 -0.81 2646 1
## pi1 0.13 0.00 0.02 0.10 0.12 0.13 0.14 0.17 2974 1
## pi2 0.23 0.00 0.06 0.11 0.18 0.22 0.27 0.36 3067 1
## lp__ -49.01 0.02 1.01 -51.67 -49.41 -48.69 -48.29 -48.00 1744 1
##
## Samples were drawn using NUTS(diag_e) at Wed Nov 15 12:39:35 2023.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).fit <- stan_bssd(y = df$y, time = df$time, tmt = df$tmt,
w1 = w1, pi1_alpha = pi1_alpha, pi1_beta = pi1_beta,
w2 = w2, pi2_alpha = pi2_alpha, pi2_beta = pi2_beta)##
## SAMPLING FOR MODEL 'bssd_unblinded' NOW (CHAIN 1).
## Chain 1:
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## SAMPLING FOR MODEL 'bssd_unblinded' NOW (CHAIN 4).
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## Chain 4:fit## Prob(Event) in arm 1: 0.136
## Prob(Event) in arm 2: 0.204
## Prob(Event rate in arm 2 > arm 1): 0.90175fit$fit## Inference for Stan model: bssd_unblinded.
## 4 chains, each with iter=2000; warmup=1000; thin=1;
## post-warmup draws per chain=1000, total post-warmup draws=4000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] -1.93 0.00 0.13 -2.19 -2.02 -1.93 -1.84 -1.67 3664 1
## mu[2] -1.51 0.01 0.30 -2.13 -1.69 -1.50 -1.30 -0.96 2802 1
## pi1 0.14 0.00 0.02 0.11 0.12 0.14 0.15 0.17 3771 1
## pi2 0.20 0.00 0.05 0.11 0.17 0.20 0.24 0.32 2880 1
## lp__ -49.33 0.02 1.02 -52.09 -49.74 -49.01 -48.61 -48.32 1930 1
##
## Samples were drawn using NUTS(diag_e) at Wed Nov 15 12:39:35 2023.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).df <- read.csv("large_current.csv")w1 <- mix_small["w",]
pi1_alpha <- mix_small["a",]
pi1_beta <- mix_small["b",]fit <- stan_bssd(y = df$y, time = df$time, prob_arm1 = prob_arm1,
w1 = w1, pi1_alpha = pi1_alpha, pi1_beta = pi1_beta,
w2 = w2, pi2_alpha = pi2_alpha, pi2_beta = pi2_beta)##
## SAMPLING FOR MODEL 'bssd' NOW (CHAIN 1).
## Chain 1: Rejecting initial value:
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## SAMPLING FOR MODEL 'bssd' NOW (CHAIN 2).
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## SAMPLING FOR MODEL 'bssd' NOW (CHAIN 4).
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## Chain 4:fit## Prob(Event) in arm 1: 0.157
## Prob(Event) in arm 2: 0.239
## Prob(Event rate in arm 2 > arm 1): 0.77275fit$fit## Inference for Stan model: bssd.
## 4 chains, each with iter=2000; warmup=1000; thin=1;
## post-warmup draws per chain=1000, total post-warmup draws=4000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] -1.84 0.02 0.41 -2.49 -2.15 -1.92 -1.56 -0.95 522 1.01
## mu[2] -1.32 0.01 0.23 -1.77 -1.49 -1.28 -1.14 -0.92 558 1.01
## pi1 0.16 0.00 0.06 0.08 0.11 0.14 0.19 0.32 495 1.01
## pi2 0.24 0.00 0.05 0.16 0.20 0.24 0.27 0.33 581 1.01
## lp__ -558.58 0.03 0.92 -561.00 -558.91 -558.34 -557.95 -557.64 1268 1.00
##
## Samples were drawn using NUTS(diag_e) at Wed Nov 15 12:39:55 2023.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).fit <- stan_bssd(y = df$y, time = df$time, tmt = df$tmt,
w1 = w1, pi1_alpha = pi1_alpha, pi1_beta = pi1_beta,
w2 = w2, pi2_alpha = pi2_alpha, pi2_beta = pi2_beta)##
## SAMPLING FOR MODEL 'bssd_unblinded' NOW (CHAIN 1).
## Chain 1: Rejecting initial value:
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## SAMPLING FOR MODEL 'bssd_unblinded' NOW (CHAIN 2).
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## SAMPLING FOR MODEL 'bssd_unblinded' NOW (CHAIN 4).
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## Chain 4:fit## Prob(Event) in arm 1: 0.148
## Prob(Event) in arm 2: 0.229
## Prob(Event rate in arm 2 > arm 1): 1fit$fit## Inference for Stan model: bssd_unblinded.
## 4 chains, each with iter=2000; warmup=1000; thin=1;
## post-warmup draws per chain=1000, total post-warmup draws=4000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] -1.83 0.00 0.07 -1.99 -1.88 -1.83 -1.79 -1.69 3643 1
## mu[2] -1.35 0.00 0.05 -1.44 -1.38 -1.35 -1.31 -1.25 3502 1
## pi1 0.15 0.00 0.01 0.13 0.14 0.15 0.15 0.17 3661 1
## pi2 0.23 0.00 0.01 0.21 0.22 0.23 0.24 0.25 3476 1
## lp__ -545.34 0.02 0.94 -547.85 -545.70 -545.04 -544.68 -544.45 1951 1
##
## Samples were drawn using NUTS(diag_e) at Wed Nov 15 12:39:58 2023.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).w1 <- mix_large["w",]
pi1_alpha <- mix_large["a",]
pi1_beta <- mix_large["b",]fit <- stan_bssd(y = df$y, time = df$time, prob_arm1 = prob_arm1,
w1 = w1, pi1_alpha = pi1_alpha, pi1_beta = pi1_beta,
w2 = w2, pi2_alpha = pi2_alpha, pi2_beta = pi2_beta)##
## SAMPLING FOR MODEL 'bssd' NOW (CHAIN 1).
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## SAMPLING FOR MODEL 'bssd' NOW (CHAIN 2).
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## SAMPLING FOR MODEL 'bssd' NOW (CHAIN 3).
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## SAMPLING FOR MODEL 'bssd' NOW (CHAIN 4).
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## Chain 4:fit## Prob(Event) in arm 1: 0.127
## Prob(Event) in arm 2: 0.255
## Prob(Event rate in arm 2 > arm 1): 1fit$fit## Inference for Stan model: bssd.
## 4 chains, each with iter=2000; warmup=1000; thin=1;
## post-warmup draws per chain=1000, total post-warmup draws=4000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] -2.00 0.00 0.13 -2.26 -2.09 -2.00 -1.91 -1.74 1469 1
## mu[2] -1.23 0.00 0.11 -1.43 -1.30 -1.23 -1.16 -1.02 1447 1
## pi1 0.13 0.00 0.02 0.10 0.12 0.13 0.14 0.16 1443 1
## pi2 0.25 0.00 0.02 0.21 0.24 0.25 0.27 0.30 1459 1
## lp__ -557.14 0.03 0.97 -559.77 -557.49 -556.87 -556.45 -556.20 1457 1
##
## Samples were drawn using NUTS(diag_e) at Wed Nov 15 12:40:11 2023.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).fit <- stan_bssd(y = df$y, time = df$time, tmt = df$tmt,
w1 = w1, pi1_alpha = pi1_alpha, pi1_beta = pi1_beta,
w2 = w2, pi2_alpha = pi2_alpha, pi2_beta = pi2_beta)##
## SAMPLING FOR MODEL 'bssd_unblinded' NOW (CHAIN 1).
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## SAMPLING FOR MODEL 'bssd_unblinded' NOW (CHAIN 4).
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## Chain 4:fit## Prob(Event) in arm 1: 0.143
## Prob(Event) in arm 2: 0.229
## Prob(Event rate in arm 2 > arm 1): 1fit$fit## Inference for Stan model: bssd_unblinded.
## 4 chains, each with iter=2000; warmup=1000; thin=1;
## post-warmup draws per chain=1000, total post-warmup draws=4000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] -1.87 0.00 0.07 -2.01 -1.92 -1.87 -1.82 -1.74 3590 1
## mu[2] -1.35 0.00 0.05 -1.45 -1.38 -1.35 -1.31 -1.25 3022 1
## pi1 0.14 0.00 0.01 0.13 0.14 0.14 0.15 0.16 3666 1
## pi2 0.23 0.00 0.01 0.21 0.22 0.23 0.24 0.25 3023 1
## lp__ -544.37 0.02 0.98 -547.05 -544.72 -544.09 -543.69 -543.43 1651 1
##
## Samples were drawn using NUTS(diag_e) at Wed Nov 15 12:40:14 2023.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).