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example_simu_onesided.R
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# Example 3: one-sided selection models
## Simulate data
library(tidyverse)
library(brms)
library(rstan)
library(MCMCvis)
library(publipha)
library(RoBMA)
rstan_options(auto_write = TRUE)
set.seed(2021)
N_exp <- 60 # number of studies
theta_exp <- 0.3 # the true effect
tau_e_exp <- 0.15 # the standard deviation of the true effects for studies
SE_exp <- 0.2 # the standard deviation of the sampling distribution
# the probablity to publish the study based the p-value
w_publish <- c(0.2, 0.5, 1) # (0.10, 1] (0.05, 0.10] [0, 0.05]
alpha_e <- rnorm(N_exp, 0, tau_e_exp) # studies
df_simu_one <- tibble(
SE = extraDistr::rtnorm(N_exp, 0.1, SE_exp, a = 0)) %>%
mutate(g = rnorm(n(), theta_exp+alpha_e, SE), #
experiment = paste0("E",1:n()),
pvalue = round((1-pnorm(g, 0, SE))*2, 3), # still two-sided p-value
# pvalue = round(1-pnorm(g, 0, SE), 3), # one-sdied p-value (should not use this)
# p-value intervals
K = case_when(pvalue <= .05 ~ 3,
(pvalue > .05 & pvalue <= .1) ~ 2,
pvalue > .1 ~ 1),
published = extraDistr::rbern(n(), w_publish[K]))
df3 <- filter(df_simu_one, published==1)
df_simu_one %>%
group_by(K) %>%
summarize(mean(published), n())
df3 %>%
summarize(mean(g))
##################### Fit with brms #####################
### Fit the brm model (without publication bias)
# Note: brms still fit two-sided models
bf3 <- bf(g | se(SE) ~ 1 + (1|experiment))
brmfit_one <- brm(bf3, data = df3,
chains = 6, cores = 6, seed = 12,
control = list(adapt_delta = .9))
##################### Equivalent codes Set 1 ##################################
# 1.28 and 1.65
# Below functions essentially use one-sided p-value of 0.10 and 0.05 to set
# intervals for selection models.
## with custom Stan codes.
data_ls_one1 <- make_standata(bf3, data=df3)
data_ls_one1$alpha <- c(0.10, 0.05)
data_ls_one1$N_alpha <- length(data_ls_one1$alpha) # number of intervals
data_ls_one1$side <- 1
ex4_bias_one1 <- stan(file = 'stan_models/ma_bias_twosided.stan', # 'stan_bias.stan',
data = data_ls_one1,
iter = 4000, warmup = 2000,
chains = 6, cores = 6, seed = 12,
control = list(adapt_delta = .9))
MCMCsummary(ex4_bias_one1, params=c("b_Intercept", "omega", "cutoff_output"))
# pairs(ex4_bias_one, pars=c("omega", "b_Intercept"))
## With library(publipha)
psmafit1 <- psma(yi = df3$g, vi = df3$SE^2, alpha = c(0, 0.05, 0.1, 1),
iter = 4000, warmup = 2000,
chains = 6, cores = 6, seed = 12,
control = list(adapt_delta = .9))
MCMCsummary(psmafit1, params=c("theta0", "eta"))
## with modified Stan codes from library(publipha)
psmafit_ls1 <- list(
N = data_ls_one1$N,
k = 2,
alpha = c(0.1, 0.05),
yi = data_ls_one1$Y,
vi = data_ls_one1$se^2,
eta0 = c(1,1,1),
tau_prior = 1
)
# the following results should be the same as psmafit
psmafit1_stan <- stan(file = 'stan_models/psma_stan.stan', # 'stan_bias.stan',
data = psmafit_ls1,
iter = 4000, warmup = 2000,
chains = 6, cores = 6, seed = 12,
control = list(adapt_delta = .9))
MCMCsummary(psmafit1_stan, params=c("theta0", "eta", "cutoff_output"))
psmafit1_stan_gamma <- stan(file = 'stan_models/psma_stan_gamma_prior.stan', # 'stan_bias.stan',
data = psmafit_ls1,
iter = 4000, warmup = 2000,
chains = 6, cores = 6, seed = 12,
control = list(adapt_delta = .9))
MCMCsummary(psmafit1_stan_gamma, params=c("theta0", "eta", "cutoff_output"))
# Note: it seems that using gamma or dirichlet make differences.
## With library(RoMBA)
robma_1 <- RoBMA(d = df3$g, se = df3$SE,
priors_omega = list(prior(distribution = "one.sided",
parameters = list(alpha = c(1, 1, 1),
steps = c(.05, .10)),
prior_odds = 1)),
priors_mu_null = NULL,
priors_tau_null = NULL,
priors_omega_null = NULL)
robma_1$models
##################### Equivalent codes Set 2 ##################################
# 1.65 and 1.96
# Below functions essentially use one-sided p-value of 0.05 and 0.025 to set
# intervals for selection models. This is equivalent to two-sided tests but only
# the positive effects are easier to be published.
## Fit the model with the publication bias (with one-sided)
data_ls_one2 <- make_standata(bf3, data=df3)
data_ls_one2$alpha <- c(0.05, .025)
data_ls_one2$N_alpha <- length(data_ls_one2$alpha) # number of intervals
data_ls_one2$side <- 1
ex4_bias_one2 <- stan(file = 'stan_models/ma_bias_twosided.stan', # 'stan_bias.stan',
data = data_ls_one2,
chains = 6, cores = 6, seed = 12,
iter = 4000, warmup = 2000,
control = list(adapt_delta = .9))
MCMCsummary(ex4_bias_one2, params=c("b_Intercept", "omega", "cutoff_output"))
# pairs(ex4_bias_one, pars=c("omega", "b_Intercept"))
## with library(publipha)
psmafit2 <- psma(yi = df3$g, vi = df3$SE^2, alpha = c(0, 0.025, 0.05, 1),
chains = 6, cores = 6, seed = 12,
iter = 4000, warmup = 2000,
control = list(adapt_delta = .9))
MCMCsummary(psmafit2, params=c("theta0", "eta"))
## with Stan code modified from library(publipha)
psmafit_ls2 <- list(
N = data_ls_one2$N,
k = 2,
alpha = c(0.05, 0.025),
yi = data_ls_one2$Y,
vi = data_ls_one2$se^2,
eta0 = c(1,1,1),
tau_prior = 1
)
# the following results should be the same as psmafit
psmafit2_stan <- stan(file = 'stan_models/psma_stan.stan', # 'stan_bias.stan',
data = psmafit_ls2,
iter = 4000, warmup = 2000,
chains = 6, cores = 6, seed = 12,
control = list(adapt_delta = .9))
MCMCsummary(psmafit2_stan, params=c("theta0", "eta", "cutoff_output"))
psmafit2_stan_gamma <- stan(file = 'stan_models/psma_stan_gamma_prior.stan', # 'stan_bias.stan',
data = psmafit_ls2,
iter = 4000, warmup = 2000,
chains = 6, cores = 6, seed = 12,
control = list(adapt_delta = .9))
MCMCsummary(psmafit2_stan_gamma, params=c("theta0", "eta", "cutoff_output"))
# Note: it seems that using gamma or dirichlet make differences.
## With library(RoMBA)
robma_2 <- RoBMA(d = df3$g, se = df3$SE,
priors_omega = list(prior(distribution = "one.sided",
parameters = list(alpha = c(1, 1, 1),
steps = c(.025, .05)),
prior_odds = 1)),
priors_mu_null = NULL,
priors_tau_null = NULL,
priors_omega_null = NULL)
robma_2$models