def get_varying_intercept_model_results():
# read in Cipriani data
df = get_model_input_df()
data_dict = {
'N': df.shape[0],
'Y_meas': df['lnSD'].values,
'X_meas': df['lnMean'].values,
'SD_Y': np.sqrt(df['var_lnSD'].values),
'SD_X': np.sqrt(df['var_lnMean'].values),
'K': len(df.scale.unique()),
'scale_group': df.scale_rank.values
}
varying_intercept_stan_model = compile_model(
os.path.join(stan_model_path, 'varying_intercept_regression.stan'),
model_name='varying_intercept_regression')
fit = varying_intercept_stan_model.sampling(data=data_dict,
iter=4000,
warmup=1000,
chains=3,
control={'adapt_delta': 0.99},
check_hmc_diagnostics=True,
seed=1)
pystan.check_hmc_diagnostics(fit)
data = az.from_pystan(
posterior=fit,
posterior_predictive=['Y_pred'],
observed_data=['X_meas', 'Y_meas'],
log_likelihood='log_lik',
)
return data
def get_shrinkage_plot(data):
df = get_model_input_df()
data_dict = {
'N': df.shape[0],
'Y_meas': df['lnSD'].values,
'X_meas': df['lnMean'].values,
'SD_Y': np.sqrt(df['var_lnSD'].values),
'SD_X': np.sqrt(df['var_lnMean'].values),
'K': len(df.scale.unique()),
'scale_group': df.scale_rank.values
}
fig, axes = plt.subplots(figsize=(10, 10))
x_meas = data_dict['X_meas']
y_meas = data_dict['Y_meas']
x_true_trace = np.reshape(
data.posterior.X.values,
(data.posterior.X.shape[0] * data.posterior.X.shape[1],
data.posterior.X.shape[2]))
y_true_trace = np.reshape(
data.posterior.Y.values,
(data.posterior.Y.shape[0] * data.posterior.Y.shape[1],
data.posterior.Y.shape[2]))
# get posterior means
x_true = x_true_trace.mean(axis=0)
y_true = y_true_trace.mean(axis=0)
axes.scatter(x_meas,
y_meas,
label='measured data of lnMean and lnSD',
alpha=0.7)
axes.scatter(x_true,
y_true,
label='estimated true values of lnMean and lnSD',
alpha=0.7)
for xm, ym, xt, yt in zip(x_meas, y_meas, x_true, y_true):
axes.arrow(xm,
ym,
xt - xm,
yt - ym,
color='gray',
linestyle='--',
length_includes_head=True,
alpha=0.4,
head_width=.015)
plt.tight_layout()
plt.xlabel('lnMean')
plt.ylabel('lnSD')
plt.title('Shrinkage effect of Bayesian varying intercept regression')
axes.legend(loc='upper left')
plt.savefig(os.path.join(parent_dir_name, f'output/shrinkage_plot.tiff'),
format='tiff',
dpi=500,
bbox_inches="tight")
return plt
def get_model_results_dict():
df = get_model_input_df()
model_res_dict = {}
# fixed effects meta analyses (lnVR and lnCVR)
for model in ['fema', 'rema'
]: # lnVR, # random effects meta analyses (lnVR and lnCVR)
stan_model = compile_model(os.path.join(stan_model_path,
f'{model}.stan'),
model_name=model)
for effect_statistic in ['lnVR', 'lnCVR']:
data_dict = get_data_dict(df, effect_statistic)
fit = stan_model.sampling(data=data_dict,
iter=4000,
warmup=1000,
chains=3,
control={'adapt_delta': 0.99},
check_hmc_diagnostics=True,
seed=1)
data = az.from_pystan(
posterior=fit,
posterior_predictive=['Y_pred'],
observed_data=['Y'],
log_likelihood='log_lik',
)
model_res_dict[f'{model}_{effect_statistic}'] = data
model = 'remr'
stan_model = compile_model(os.path.join(stan_model_path, f'{model}.stan'),
model_name=model)
effect_statistic = 'lnVR'
data_dict = get_data_dict(df, effect_statistic)
fit = stan_model.sampling(data=data_dict,
iter=4000,
warmup=1000,
chains=3,
control={'adapt_delta': 0.99},
check_hmc_diagnostics=True,
seed=1)
pystan.check_hmc_diagnostics(fit)
data = az.from_pystan(
posterior=fit,
posterior_predictive=['Y_pred'],
observed_data=['Y_meas', 'X_meas'],
log_likelihood='log_lik',
)
model_res_dict[f'{model}_{effect_statistic}'] = data
return model_res_dict
def get_lnMean_lnSD_plot():
df = get_model_input_df()
# check whether the standard deviation of the change variable is correlated with its mean (in active and placebo)
# and save the OLS summary as html file
scale_list = ['HAMD17', 'HAMD21', 'HAMD24', 'HAMDunspecified', 'MADRS']
for scale in scale_list:
for group in [0, 1]:
lm = sm.OLS(
df.query(f'scale == "{scale}" & is_active == {group}')
['lnSD'].values,
sm.add_constant(
df.query(f'scale == "{scale}" & is_active == {group}')
['lnMean'].values))
res = lm.fit()
with open(
os.path.join(parent_dir_name,
f'output/lm_res_{group}_{scale}.html'),
'w') as f:
f.write(res.summary2().as_html())
ax = df.query('is_active == 1').plot.scatter(
x='lnMean',
y='lnSD',
grid=True,
color='r',
figsize=(8, 6),
title='ln(mean of negative change) vs. ln(sd of change)')
_ = df.query('is_active == 0').plot.scatter(x='lnMean',
y='lnSD',
grid=True,
ax=ax) # NOQA
_ = ax.legend(('active', 'placebo')) # NOQA
for sid, df_ in df.groupby('study_id'):
df_a = df_.query('is_active == 1')
df_p = df_.query('is_active == 0')
plt.plot((df_a.lnMean.values[0], df_p.lnMean.values[0]),
(df_a.lnSD.values[0], df_p.lnSD.values[0]),
c='gray',
linestyle='-',
alpha=0.2)
plt.savefig(os.path.join(parent_dir_name, f'output/lnMean_lnSD_plot.tiff'),
format='tiff',
dpi=1200)
return plt
def get_bar_chart_studies_per_depression_scale():
df = get_model_input_df()
tmp = df.groupby('scale').agg({
'study_id': lambda x: len(x.unique())
}).reset_index()
fig, ax = plt.subplots()
_ = ax.bar(x=tmp.scale, height=tmp.study_id, color='grey')
_ = ax.set_title('studies per depression scale')
_ = plt.xticks(rotation=75)
_ = plt.ylabel('count')
plt.savefig(os.path.join(parent_dir_name,
f'output/bar_studies_per_depression_scale.tiff'),
format='tiff',
dpi=500,
bbox_inches="tight")
return plt
def get_prior_comparison():
df = get_model_input_df()
model_res_dict = {}
model = 'remr_prior'
stan_model = compile_model(os.path.join(stan_model_path, f'{model}.stan'),
model_name=model)
effect_statistic = 'lnVR'
data_dict = get_data_dict(df, effect_statistic)
prior_dict = {'reference': (0, 1), 'optimisitc': (np.log(2), 0.43)}
# from scipy import stats
# stats.norm.cdf(0, loc=np.log(2), scale=0.43)
# 0.05348421366569122
for prior, (mu_prior_loc, mu_prior_scale) in prior_dict.items():
data_dict_prior = data_dict.copy()
data_dict_prior['mu_prior_loc'] = mu_prior_loc
data_dict_prior['mu_prior_scale'] = mu_prior_scale
fit = stan_model.sampling(data=data_dict_prior,
iter=4000,
warmup=1000,
chains=3,
control={'adapt_delta': 0.99},
check_hmc_diagnostics=True,
seed=1)
pystan.check_hmc_diagnostics(fit)
data = az.from_pystan(
posterior=fit,
posterior_predictive=['Y_pred'],
observed_data=['Y_meas', 'X_meas'],
log_likelihood='log_lik',
)
model_res_dict[f'{model}_{effect_statistic}_{prior}'] = data
return model_res_dict
def plot_varying_intercept_regression_lines(data):
df = get_model_input_df()
# Extracting traces (and combine all chains)
alphas = np.reshape(
data.posterior.alpha.values,
(data.posterior.alpha.shape[0] * data.posterior.alpha.shape[1],
data.posterior.alpha.shape[2]))
beta = np.reshape(
data.posterior.beta.values,
(data.posterior.beta.shape[0] * data.posterior.beta.shape[1]))
# Plotting regression line
x_min, x_max = 1., 3.5
x = np.linspace(x_min, x_max, 100)
scale_list = sorted(df.scale.unique())
# get posterior means
alpha_means = alphas.mean(axis=0)
beta_mean = beta.mean()
# Plot a subset of sampled regression lines
np.random.shuffle(alphas)
np.random.shuffle(beta)
fig, axes = plt.subplots(nrows=4,
ncols=2,
figsize=(10, 10),
sharex=True,
sharey=True)
fig.suptitle('Fitted varying intercept regression')
d = df[[
'scale', 'scale_rank'
]].drop_duplicates().set_index('scale').to_dict('dict')['scale_rank']
for scale in scale_list:
scale_index = d[scale] - 1
# Plot mean regression line
y = alpha_means[scale_index] + beta_mean * x
row, col = int(scale_index / 2), scale_index % 2
_ = axes[row, col].plot(x, y, linestyle='--', alpha=0.5, color='black')
# Plot measured data
df_a = df.query(f'scale == "{scale}" & is_active == 1')
df_p = df.query(f'scale == "{scale}" & is_active == 0')
_ = axes[row, col].scatter(df_a.lnMean.values,
df_a.lnSD.values,
alpha=0.8)
_ = axes[row, col].scatter(df_p.lnMean.values,
df_p.lnSD.values,
alpha=0.8)
# Plot sample trace regression
for j in range(1000):
_ = axes[row, col].plot(x,
alphas[j, scale_index] + beta[j] * x,
color='lightsteelblue',
alpha=0.005) # NOQA
axes[row, col].set_ylabel('lnSD')
axes[row, col].set_title(f'{scale}')
axes[-1, 0].set_xlabel('lnMean')
axes[-1, 1].set_xlabel('lnMean')
plt.tight_layout()
plt.xlim(x_min, x_max)
plt.subplots_adjust(top=0.9, bottom=0.1)
plt.savefig(os.path.join(
parent_dir_name, f'output/varying_intercept_regression_lines.tiff'),
format='tiff',
dpi=500,
bbox_inches="tight")
return plt