Our goal is to estimate the probabilities of requiring one of a suite of candidate follow-up treatments following randomization to a given initial treatment for uterine fibroids. Specifically, we are interested in estimating:
$$Pr(I_2|I_1 =i,T=t)$$where $I_1$ is an initial intervention, which take specific values $i = 1, 2, \ldots , K$ for each of $K$ candidate intervention types, $I_2$ is the followup intervention that also may take any of the same values of $i$, and $T$ is followup time in months, which will generally be either 6 or 12 months.
Our current set of candidate interventions include:
Rather than model each conditional probability independently, we will instead model the outcomes for a treatment arm as a multinomial random variable. That is,
$$\{X_{I_2} \} ∼ \text{Multinomial}(N_{I_1}=i, \{\pi_i\})$$where $\{X_{I_2}\}$ is the vector of outcomes corresponding to each of the possible followup interventions listed above, $N_{I_1}=i$ is the number of women randomized to the initial intervention i, and $\{\pi_i\}$ is a vector of conditional transition probabilities corresponding to $Pr(I_2|I_1 = i, T = t)$, as specified above. The multinomial distribution is a multivariate generalization of the categorical distribution, which is what the above simplifies to when modeling the outcome for a single patient. The multivariate formulation allows us to model study-arm-specific outcomes, incorporating covariates that are specific to that arm or study.
The quantities of interest are the vectors of transition probabilities $\{\pi_i\}$ corresponding to each of the initial candidate interventions. A naive approach to modeling these is to assign a vague Dirichlet prior distribution to each set, and perform Bayesian inference using the multinomial likelihood, with which the Dirichlet is conjugate, to yield posterior estimates for each probability. However, there may be additional information with which to model these probabilities, which may include:
hence, a given transition probability $\pi_{ijk}$ – the probability of transitioning from initial intervention $i$ to followup intervention $j$ in study $k$ – may be modeled as:
$$\text{logit}(\pi_{ijk})= \theta_{ij} + X_k \beta_{ij} + \epsilon_k$$where $\theta_{ij}$ is a baseline transition probability (on the logit scale), $X_k$ a matrix of study(-arm)-specific covariates, $\beta_{ij}$ the corresponding coefficients, and $\epsilon_k$ a mean-zero random effect for study k. We will initially consider (1) follow-up time and (2) mean/median age as covariates.
An attractive benefit to using Bayesian inference to estimate this model is that it is easy to generate predictions from the model, via the posterior predictive distribution. For example, we could estimate the distribution of the expected proportion of women requiring a particular followup intervention; this estimate would factor in both the residual uncertainty in the transition probability estimates, as well as the sampling uncertainty of the intervention.
%matplotlib inline
import numpy as np
import pandas as pd
import pymc as pm
import seaborn as sns
import pdb
sns.set()
Import data from worksheets in Excel spreadsheet.
data_file = 'UF Subsequent Interventions Data_Master_updated.xlsx'
missing = ['NA', 'NR', 'ND', '?', 'null']
misc_data = pd.read_excel('data/' + data_file, sheetname='MISC (SP)', na_values=missing)
misc_data = misc_data[~misc_data['baseline_n'].isnull()].drop('notes', axis=1)
rows, cols = misc_data.shape
print('Occlusion rows={0}, columns={1}, missing={2}'.format(rows, cols,
misc_data.isnull().sum().sum()))
med_vs_iac_data = pd.read_excel('data/' + data_file, sheetname='Med vs IAC JW', na_values=missing)
med_vs_iac_data = med_vs_iac_data[~med_vs_iac_data['trial_arm'].isnull()].drop('notes', axis=1)
rows, cols = med_vs_iac_data.shape
print('Med vs IAC rows={0}, columns={1}, missing={2}'.format(rows, cols,
med_vs_iac_data.isnull().sum().sum()))
med_vs_med_data = pd.read_excel('data/' + data_file, sheetname='Med vs Med DVE', na_values=missing)
med_vs_med_data = med_vs_med_data[~med_vs_med_data['baseline_n'].isnull()].drop('notes', axis=1)
rows, cols = med_vs_med_data.shape
print('Med vs Med rows={0}, columns={1}, missing={2}'.format(rows, cols,
med_vs_med_data.isnull().sum().sum()))
uae_data = pd.read_excel('data/' + data_file, sheetname='UAE SK')
uae_data = uae_data[~uae_data['baseline_n'].isnull()].drop('notes', axis=1)
rows, cols = uae_data.shape
print('UAE rows={0}, columns={1}, missing={2}'.format(rows, cols,
uae_data.isnull().sum().sum()))
datasets = [misc_data, med_vs_iac_data, med_vs_med_data, uae_data]
Occlusion rows=31, columns=13, missing=6 Med vs IAC rows=49, columns=13, missing=46 Med vs Med rows=67, columns=13, missing=13 UAE rows=32, columns=13, missing=0
unique_inerventions = set(np.concatenate([d.intervention.values for d in datasets]))
Use the following lookup table to create "intervention category" field in each dataset.
# %load intervention_lookup.py
intervention_lookup = {'Ablation': 'ablation',
'Ablation+/- hysteroscopic myomectomy': 'ablation',
'Asoprisnil 10 mg': 'med_manage',
'Asoprisnil 25 mg': 'med_manage',
'Asoprisnil 5 mg': 'med_manage',
'CD20 (Ulipristal)': 'med_manage',
'CDB10 (Ulipristal)': 'med_manage',
'Hysterectomy': 'hysterectomy',
'LBCUV': 'uae',
'LP + GnRH agonist plus raloxifene': 'med_manage',
'LP + placebo': 'med_manage',
'LPA+ MPA / LPA+placebo': 'med_manage',
'LPA+ placebo / LPA+MPA': 'med_manage',
'LUNA plus LBCUV': 'ablation',
'Myomectomy': 'myomectomy',
'No treatment': 'control',
'No treatment (control)': 'control',
'Placebo': 'control',
'Raloxifene, 180mg/day': 'med_manage',
'SC implant of 3.6 goserelin + placebo (3 months) then tibolone 2.5 mg daily (3 months)': 'med_manage',
'SC implant of 3.6 goserelin + placebo (6 months)': 'med_manage',
'SC implant of 3.6 goserelin + tibolone 2.5 mg daily (6 months)': 'med_manage',
'Surgery': 'DROP',
'Tibolone': 'med_manage',
'UAE': 'uae',
'UAE only': 'uae',
'UAE plus goserelin acetate depot': 'uae',
'buserelin + goserelin': 'med_manage',
'buserelin, intranasal': 'med_manage',
'cabergoline': 'med_manage',
'diphereline': 'med_manage',
'gestrinone, 2.5mg': 'med_manage',
'gestrinone, 2.5mg oral + gestrinone, 5mg oral + gestrinone, 5mg vaginal': 'med_manage',
'gestrinone, 5mg': 'med_manage',
'gestrinone, 5mg vaginal': 'med_manage',
'goserelin, subcutaneous': 'med_manage',
'healthy controls': 'control',
'hormone replacement therapy, transdermal': 'DROP',
'hysterectomy or myomectomy': 'DROP',
'letrozole, 2.5mg': 'med_manage',
'leuprolide': 'med_manage',
'leuprolide acetate depot (11.25 mg q 3 months) + Placebo': 'med_manage',
'leuprolide acetate depot (11.25 mg q 3 months) + tibolone 2.5 mg/d orally': 'med_manage',
'leuprolide acetate depot (3.75 mg/28 d) + placebo (B)': 'med_manage',
'leuprolide plus (tibolone 2.5 mg daily) (A)': 'med_manage',
'leuprolide plus MPA': 'med_manage',
'leuprolide plus estrogen-progestin': 'med_manage',
'leuprolide plus placebo': 'med_manage',
'leuprolide plus progestin': 'med_manage',
'leuprolide plus raloxifene 60 mg daily': 'med_manage',
'leuprolide, 1.88mg': 'med_manage',
'leuprolide, 3.75mg': 'med_manage',
'mifepristone, 10mg': 'med_manage',
'mifepristone, 10mg + mifepristone, 5mg': 'med_manage',
'mifepristone, 2.5mg': 'med_manage',
'mifepristone, 5mg': 'med_manage',
'placebo': 'control',
'raloxifene 180 mg daily': 'med_manage',
'raloxifene 60 mg daily': 'med_manage',
'tamoxifen 20 mg daily': 'med_manage',
'tibolone': 'med_manage',
'tibolone, 2.5mg': 'med_manage',
'transdermal estrogen replacement therapy': 'med_manage',
'triptorelin, 100ug': 'med_manage',
'triptorelin, 100ug + triptorelin, 20ug + triptorelin, 5ug': 'med_manage',
'triptorelin, 20ug': 'med_manage',
'triptorelin, 3.6mg/mo': 'med_manage',
'triptorelin, 5ug': 'med_manage',
'ulipristal acetate followed by placebo': 'med_manage',
'ulipristal acetate followed by progestin': 'med_manage',
'ulipristal, 10mg': 'med_manage',
'ulipristal, 5mg': 'med_manage',
'HIFU': 'MRgFUS',
'HIFU with CEUS': 'MRgFUS',
'LUAO': 'uae',
'UAE plus PVA': 'uae',
'UAE plus TAG': 'uae',
'UAE with PVA': 'uae',
'UAE with PVA particles, large': 'uae',
'UAE with PVA particles, small': 'uae',
'UAE with SPA': 'uae',
'UAE with SPVA': 'uae',
'UAE with TAG': 'uae',
'UAE with TAG microspheres': 'uae',
'myomectomy': 'myomectomy',
'myomectomy with vasopressin': 'myomectomy',
'myomectomy, abdominal': 'myomectomy',
'myomectomy, laparoscopic': 'myomectomy',
'myomectomy, loop ligation with vasopressin': 'myomectomy',
'myomectomy, minilaparotomic': 'myomectomy'}
Assign intervention categories to each arm
datasets = [d.assign(intervention_cat=d.intervention.replace(intervention_lookup)) for d in datasets]
intervention_categories = set(intervention_lookup.values())
intervention_categories
{'DROP', 'MRgFUS', 'ablation', 'control', 'hysterectomy', 'med_manage', 'myomectomy', 'uae'}
Import demographic information
demographics = pd.read_excel('data/' + data_file, sheetname='ALL_DEMO_DATA', na_values=missing)
demographics.columns
Index(['study_id', 'Citation', 'FamCode', 'FamDesig', 'NCT', 'ArmsN', 'ArmCategory', 'Group_Desc', 'New Grouping', 'Demo_Category', 'Demo_specify', 'BL N', 'Denom_N', 'BL %', 'BL Mean', 'BL SD', 'BL_SE', 'BL_Median', 'BL Min', 'BL Max', 'BL 95% L', 'BL 95% H', 'BL_group_diff', 'Comments'], dtype='object')
Extract columns of interest
age_data = demographics.loc[demographics.Demo_Category=='Age', ['study_id', 'New Grouping', 'BL Mean', 'BL SD']]
Clean arm labels
age_data = age_data.assign(arm=age_data['New Grouping'].str.replace(':','')).drop('New Grouping', axis=1)
age_data.arm.unique()
array(['G2', 'G1', 'G1b', 'G1a', 'G3', 'CG', 'G1c', 'G1+G2', 'G1a+G1b+G1c'], dtype=object)
Concatenate all datasets
all_data = pd.concat(datasets)
Clean up study arm field
all_arm = all_data.trial_arm.str.replace(':','').str.replace(' ', '').str.replace('Group', 'G')
all_data = all_data.assign(arm=all_arm).drop('trial_arm', axis=1)
all_data.arm.unique()
array(['G1', 'G2', 'G3', 'CG', 'G1a', 'G1b', 'G1c', 'CG1', 'CG2', 'G1/CG', 'CG/G1', 'G1a+G1b', 'G1a+G1b+G1c', 'G1+G2'], dtype=object)
Clean up study ID field. Currently contains non-numeric entries. Will strip out the first study ID from the compund labels, as this is the parent study ID.
all_data.study_id.unique()
array([23, 347, 1400, 1529, 1806, 1889, 2375, 2967, 3382, 3690, 3785, 5186, 5474, 414, 1849, 3016, 3181, 3324, 3674, 4258, 4468, 4858, 4960, 5276, 5302, 6091, 6263, 6696, 7155, 7504, 7797, 7936, 95.0, 629.0, 757.0, 1290.0, 2318.0, 2555.0, 2635.0, 3312.0, 3978.0, 4787.0, 4961.0, 5721.0, 6393.0, 6903.0, 7139.0, 7309.0, 7530.0, 7589.0, 7763.0, '3803_3052', 1546, '3365_2026_1657_986', '3819_815_1986_2759_2971_\n3120_3175_3192_3678_3721', 4789, 2006], dtype=object)
str_mask = all_data.study_id.str.isnumeric()==False
all_data.loc[str_mask, 'study_id'] = all_data.study_id[str_mask].apply(lambda x: x[:x.find('_')])
all_data.study_id = all_data.study_id.astype(int)
all_data.study_id.unique()
array([ 23, 347, 1400, 1529, 1806, 1889, 2375, 2967, 3382, 3690, 3785, 5186, 5474, 414, 1849, 3016, 3181, 3324, 3674, 4258, 4468, 4858, 4960, 5276, 5302, 6091, 6263, 6696, 7155, 7504, 7797, 7936, 95, 629, 757, 1290, 2318, 2555, 2635, 3312, 3978, 4787, 4961, 5721, 6393, 6903, 7139, 7309, 7530, 7589, 7763, 3803, 1546, 3365, 3819, 4789, 2006])
Here is what the data look like after merging.
all_data.head()
study_id | intervention | baseline_n | followup_interval | followup_n | hysterectomy | myomectomy | uae | MRIgFUS | ablation | iud | no_treatment | intervention_cat | arm | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 23 | HIFU with CEUS | 17 | 12 | 17 | 0 | 0 | 0 | 1 | 0 | 0 | 16 | MRgFUS | G1 |
1 | 23 | HIFU | 16 | 12 | 16 | 0 | 0 | 0 | 3 | 0 | 0 | 13 | MRgFUS | G2 |
2 | 347 | UAE with SPVA | 30 | 12 | 27 | 1 | 0 | 0 | 0 | 0 | 0 | 26 | uae | G1 |
3 | 347 | UAE with TAG | 30 | 12 | 29 | 0 | 0 | 0 | 0 | 0 | 0 | 29 | uae | G2 |
4 | 1400 | UAE | 63 | 6 | 62 | 0 | 1 | 5 | 0 | 0 | 0 | 56 | uae | G1 |
all_data.groupby('intervention_cat')['study_id'].count()
intervention_cat DROP 8 MRgFUS 2 ablation 3 control 11 hysterectomy 7 med_manage 100 myomectomy 14 uae 34 Name: study_id, dtype: int64
Merge age data with outcomes
all_data_merged = pd.merge(all_data, age_data, on=['study_id', 'arm'])
For now, drop arms with no reported followup time (we may want to impute these):
all_data_merged = all_data_merged.dropna(subset=['followup_interval'])
Parse followup intervals that are ranges, creating fup_min
and fup_max
fields.
dataset = all_data_merged.assign(fup_min=0, fup_max=all_data.followup_interval.convert_objects(convert_numeric=True).max()+1)
range_index = dataset.followup_interval.str.contains('to').notnull()
range_vals = dataset[range_index].followup_interval.apply(lambda x: x.split(' '))
dataset.loc[range_index, ['fup_min']] = range_vals.apply(lambda x: float(x[0]))
dataset.loc[range_index, ['fup_max']] = range_vals.apply(lambda x: float(x[-1]))
dataset.loc[range_index, ['followup_interval']] = 30.33
dataset['followup_interval'] = dataset.followup_interval.astype(float)
/Users/fonnescj/anaconda3/lib/python3.5/site-packages/ipykernel/__main__.py:1: FutureWarning: convert_objects is deprecated. Use the data-type specific converters pd.to_datetime, pd.to_timedelta and pd.to_numeric. if __name__ == '__main__':
dataset.head()
study_id | intervention | baseline_n | followup_interval | followup_n | hysterectomy | myomectomy | uae | MRIgFUS | ablation | iud | no_treatment | intervention_cat | arm | BL Mean | BL SD | fup_max | fup_min | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 23 | HIFU with CEUS | 17 | 12 | 17 | 0 | 0 | 0 | 1 | 0 | 0 | 16 | MRgFUS | G1 | 43.1 | 5.3 | 61 | 0 |
1 | 23 | HIFU | 16 | 12 | 16 | 0 | 0 | 0 | 3 | 0 | 0 | 13 | MRgFUS | G2 | 42 | 5.4 | 61 | 0 |
2 | 347 | UAE with SPVA | 30 | 12 | 27 | 1 | 0 | 0 | 0 | 0 | 0 | 26 | uae | G1 | 43.9 | 5.0 | 61 | 0 |
3 | 347 | UAE with TAG | 30 | 12 | 29 | 0 | 0 | 0 | 0 | 0 | 0 | 29 | uae | G2 | 41.7 | 5.4 | 61 | 0 |
4 | 1400 | UAE | 63 | 6 | 62 | 0 | 1 | 5 | 0 | 0 | 0 | 56 | uae | G1 | 41 | 3.5 | 61 | 0 |
Fill missing values
dataset.loc[dataset.followup_n.isnull(), 'followup_n'] = dataset.loc[dataset.followup_n.isnull(), 'baseline_n']
dataset.loc[dataset.no_treatment.isnull(), 'no_treatment'] = dataset.followup_n - dataset[[ 'hysterectomy', 'myomectomy', 'uae',
'MRIgFUS', 'ablation', 'iud']].sum(1)[dataset.no_treatment.isnull()]
dataset.followup_interval.unique()
array([ 12. , 6. , 30.33, 24. , 2. , 1. , 3. , 5.5 , 9. , 18. , 0. , 7. , 60. ])
dataset['BL Mean'].unique()
array([43.1, 42, 43.9, 41.7, 41, 43.5, 40.3, 42.7, 45, 44, 38.26, 32.1, 34.3, 44.9, 42.5, 43.3, 38.4, 37.5, 45.9, 44.5, 33.97, 34, 41.3, 42.9, 42.1, 43.4, 37.7, 43, 40.2, 41.1, 49.1, 48.6, 36.3, 35.9, 37.2, 54.2, 51.2, 43.6, nan, 38.9, 37.1, 41.4, 36.9, 41.6, 39, 39.6, 39.67, 36.87, 30.94, 31, 39.5, 42.8, 56.2, 57.9, 50.2, 50.6, 34.4, 42.2, 49.2, 32.6, 48.4, 33.8, 38.1, 37, 32.3, 43.2, 44.6, 45.4, 46.4, 48.5, 48.3], dtype=object)
crossover_studies = 7155, 3324, 414, 95, 7139, 6903, 3721, 3181, 4858, 4960, 4258, 4789, 2006, 2318
outcome_cats = [ 'hysterectomy', 'myomectomy', 'uae',
'MRIgFUS', 'ablation', 'iud', 'no_treatment']
dataset.loc[dataset['BL Mean'].isnull(), 'BL Mean'] = 90
from numpy.ma import masked_values
def specify_model(intervention):
'''
Data preparation
'''
intervention_data = dataset[(dataset.intervention_cat==intervention)
& ~dataset[outcome_cats].isnull().sum(axis=1).astype(bool)]
followup_masked = masked_values(intervention_data.followup_interval.values, 30.33)
followup_min, followup_max = intervention_data[['fup_min', 'fup_max']].values.T
outcomes = intervention_data[[ 'hysterectomy', 'myomectomy', 'uae',
'MRIgFUS', 'ablation', 'iud', 'no_treatment']].values
if np.isnan(outcomes).any():
print('Missing values in outcomes for', intervention)
followup_n = intervention_data.followup_n.values
# Center age at 40
age_masked = masked_values(intervention_data['BL Mean'].values - 40, 50)
studies = intervention_data.study_id.unique()
study_index = np.array([np.argwhere(studies==i).squeeze() for i in intervention_data.study_id])
study_id = intervention_data.study_id.values
n_studies = len(set(study_id))
n_outcomes = 7
arms = len(outcomes)
'''
Model specification
'''
# Impute followup times uniformly over the observed range
if np.any(followup_masked.mask):
followup_time = pm.Uniform('followup_time', followup_min.min(), followup_max.max(),
observed=True,
value=followup_masked)
else:
followup_time = followup_masked.data.astype(float)
# Impute age using a T-distribution
if np.any(age_masked.mask):
nu = pm.Exponential('nu', 0.01, value=10)
age_centered = pm.T('age_centered', nu, observed=True, value=age_masked)
else:
age_centered = age_masked.data.astype(float)
# Mean probabilities (on logit scale)
μ = pm.Normal('μ', 0, 0.01, value=[-1.]*n_outcomes)
# Followup time covariates
β_fup = pm.Normal('β_fup', 0, 1e-6, value=[-0.5]*6 + [0])
# Age covariate
β_age = pm.Normal('β_age', 0, 1e-6, value=[-0.5]*6 + [0])
# Study random effect
σ = pm.Uniform('σ', 0, 100, value=1)
ϵ = pm.Normal('ϵ', 0, σ**-2, value=np.zeros(n_studies))
# Expected value (on logit scale)
θ_uae = [pm.Lambda('θ_uae_%i' % i, lambda μ=μ, β_fup=β_fup, β_age=β_age, ϵ=ϵ, t=followup_time, a=age_centered:
np.exp(μ + β_fup*t[i] + β_age*a[i] + ϵ[study_index[i]]))
for i in range(arms)]
# Inverse-logit transformation to convert to probabilities
π = [pm.Lambda('π_%i' % i, lambda t=t: t/t.sum()) for i,t in enumerate(θ_uae)]
# Multinomial data likelihood
y = [pm.Multinomial('y_%i' % i, outcomes[i].sum(), π[i],
value=outcomes[i], observed=True) for i in range(arms)]
p_6 = pm.Lambda('p_6', lambda μ=μ, β_fup=β_fup: np.exp(μ + β_fup*6)/np.exp(μ + β_fup*6).sum())
p_12 = pm.Lambda('p_12', lambda μ=μ, β_fup=β_fup: np.exp(μ + β_fup*12)/np.exp(μ + β_fup*12).sum())
p_6_50 = pm.Lambda('p_6_50', lambda μ=μ, β_fup=β_fup, β_age=β_age:
np.exp(μ + β_fup*6 + β_age*10)/np.exp(μ + β_fup*6 + β_age*10).sum())
return locals()
Instantiate models
n_iterations = 50000
n_burn = 40000
n_chains = 2
uae_model = pm.MCMC(specify_model('uae'))
for chain in range(n_chains):
print('\nchain',chain+1)
uae_model.sample(n_iterations, n_burn)
chain 1 [-----------------100%-----------------] 50000 of 50000 complete in 2139.6 sec chain 2 [---------------- 43% ] 21706 of 50000 complete in 9302.4 sec
plot_labels = dataset.columns[5:12]
uae_model.followup_time.trace()
array([[ 18.58231743, 28.32509498, 11.52847809, 58.35255279], [ 18.58231743, 28.32509498, 11.52847809, 58.35255279], [ 18.58231743, 28.32509498, 11.52847809, 58.35255279], ..., [ 6.41701153, 55.6964252 , 19.74318293, 44.20362134], [ 6.41701153, 55.6964252 , 19.74318293, 44.20362134], [ 6.41701153, 55.6964252 , 19.74318293, 44.20362134]])
pm.Matplot.summary_plot(uae_model.followup_time)
pm.Matplot.summary_plot(uae_model.μ, custom_labels=plot_labels)
Follow-up time effect size estimates. Positive values indicate higher probability of event with increased follow-up time.
pm.Matplot.summary_plot(uae_model.β_fup, custom_labels=plot_labels)
Age effect size estimates. Positive values suggest higher probability of event with each year above age 40.
pm.forestplot(trace_uae, vars=['β_age'], ylabels=plot_labels)
<matplotlib.gridspec.GridSpec at 0x12584a4e0>
Estimated probabilities of follow-up interventions for 6-month followup and age 40.
pm.forestplot(trace_uae, vars=['p_6'], ylabels=plot_labels)
<matplotlib.gridspec.GridSpec at 0x128ada4a8>
pm.summary(trace_uae, vars=['p_6'])
p_6: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------- 0.023 0.007 0.000 [0.012, 0.034] 0.033 0.007 0.000 [0.020, 0.048] 0.016 0.004 0.000 [0.009, 0.025] 0.000 0.002 0.000 [0.000, 0.001] 0.000 0.001 0.000 [0.000, 0.001] 0.000 0.004 0.000 [0.000, 0.001] 0.927 0.013 0.001 [0.907, 0.948] Posterior quantiles: 2.5 25 50 75 97.5 |--------------|==============|==============|--------------| 0.013 0.019 0.022 0.026 0.036 0.020 0.027 0.032 0.037 0.048 0.009 0.013 0.016 0.019 0.026 0.000 0.000 0.000 0.000 0.002 0.000 0.000 0.000 0.000 0.002 0.000 0.000 0.000 0.000 0.002 0.903 0.921 0.928 0.934 0.945
Estimated probabilities of follow-up interventions for 12-month followup and age 40.
pm.forestplot(trace_uae, vars=['p_12'], ylabels=plot_labels)
<matplotlib.gridspec.GridSpec at 0x11eb50a58>
pm.summary(trace_uae, vars=['p_12'])
p_12: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------- 0.029 0.008 0.000 [0.015, 0.042] 0.032 0.006 0.000 [0.020, 0.044] 0.019 0.005 0.000 [0.010, 0.028] 0.000 0.002 0.000 [0.000, 0.001] 0.000 0.001 0.000 [0.000, 0.001] 0.000 0.004 0.000 [0.000, 0.001] 0.920 0.013 0.001 [0.899, 0.940] Posterior quantiles: 2.5 25 50 75 97.5 |--------------|==============|==============|--------------| 0.016 0.024 0.028 0.033 0.044 0.021 0.027 0.031 0.036 0.045 0.011 0.016 0.019 0.022 0.029 0.000 0.000 0.000 0.000 0.002 0.000 0.000 0.000 0.000 0.002 0.000 0.000 0.000 0.000 0.001 0.897 0.914 0.921 0.927 0.938
Estimated probabilities of follow-up interventions for 12-month followup and age 50.
pm.forestplot(trace_uae, vars=['p_6_50'], ylabels=plot_labels)
<matplotlib.gridspec.GridSpec at 0x1286a26a0>
pm.summary(trace_uae, vars=['p_6_50'])
p_6_50: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------- 0.089 0.043 0.003 [0.007, 0.168] 0.001 0.002 0.000 [0.000, 0.002] 0.012 0.007 0.000 [0.001, 0.026] 0.001 0.003 0.000 [0.000, 0.005] 0.025 0.048 0.004 [0.000, 0.111] 0.173 0.255 0.024 [0.000, 0.788] 0.699 0.219 0.020 [0.170, 0.917] Posterior quantiles: 2.5 25 50 75 97.5 |--------------|==============|==============|--------------| 0.014 0.061 0.085 0.112 0.185 0.000 0.001 0.001 0.001 0.003 0.002 0.007 0.011 0.016 0.030 0.000 0.000 0.000 0.000 0.008 0.000 0.001 0.007 0.026 0.156 0.000 0.011 0.040 0.211 0.849 0.131 0.637 0.791 0.847 0.902
med_manage_model = specify_model(med_manage_model, 'med_manage')
Applied log-transform to nu and added transformed nu_log to model. Applied interval-transform to σ and added transformed σ_interval to model.
with med_manage_model:
trace_med_manage = pm.sample(2000)
/Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/gradient.py:545: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: ϵ handle_disconnected(elem) /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/gradient.py:571: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: <DisconnectedType> handle_disconnected(rval[i]) /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/gradient.py:545: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: ϵ handle_disconnected(elem) /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/gradient.py:571: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: <DisconnectedType> handle_disconnected(rval[i]) /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/gradient.py:545: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: σ_interval handle_disconnected(elem) /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/gradient.py:571: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: <DisconnectedType> handle_disconnected(rval[i]) /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/gradient.py:545: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: σ_interval handle_disconnected(elem) /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/gradient.py:571: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: <DisconnectedType> handle_disconnected(rval[i]) /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/gradient.py:545: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: β_age handle_disconnected(elem) /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/gradient.py:545: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: β_age handle_disconnected(elem) /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/gradient.py:571: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: <DisconnectedType> handle_disconnected(rval[i]) /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/gradient.py:545: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: β_fup handle_disconnected(elem) /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/gradient.py:545: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: μ handle_disconnected(elem) /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/gradient.py:545: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: age_centered_missing handle_disconnected(elem)
Assigned NUTS to followup_time_missing Assigned NUTS to nu_log Assigned NUTS to age_centered_missing Assigned NUTS to μ Assigned NUTS to β_fup Assigned NUTS to β_age Assigned NUTS to σ_interval Assigned NUTS to ϵ Assigned NUTS to followup_time_missing Assigned NUTS to nu_log Assigned NUTS to age_centered_missing Assigned NUTS to μ Assigned NUTS to β_fup Assigned NUTS to β_age Assigned NUTS to σ_interval Assigned NUTS to ϵ
--------------------------------------------------------------------------- IndexError Traceback (most recent call last) <ipython-input-46-5f5abf71fe8b> in <module>() 1 with med_manage_model: 2 ----> 3 trace_med_manage = pm.sample(2000) /Users/fonnescj/Repositories/pymc3/pymc3/sampling.py in sample(draws, step, start, trace, chain, njobs, tune, progressbar, model, random_seed) 122 model = modelcontext(model) 123 --> 124 step = assign_step_methods(model, step) 125 126 if njobs is None: /Users/fonnescj/Repositories/pymc3/pymc3/sampling.py in assign_step_methods(model, step, methods) 67 68 # Instantiate all selected step methods ---> 69 steps += [s(vars=selected_steps[s]) for s in selected_steps if selected_steps[s]] 70 71 if len(steps)==1: /Users/fonnescj/Repositories/pymc3/pymc3/sampling.py in <listcomp>(.0) 67 68 # Instantiate all selected step methods ---> 69 steps += [s(vars=selected_steps[s]) for s in selected_steps if selected_steps[s]] 70 71 if len(steps)==1: /Users/fonnescj/Repositories/pymc3/pymc3/step_methods/nuts.py in __init__(self, vars, scaling, step_scale, is_cov, state, Emax, target_accept, gamma, k, t0, model, profile, **kwargs) 67 68 if isinstance(scaling, dict): ---> 69 scaling = guess_scaling(Point(scaling, model=model), model=model, vars = vars) 70 71 /Users/fonnescj/Repositories/pymc3/pymc3/tuning/scaling.py in guess_scaling(point, vars, model) 107 model = modelcontext(model) 108 try: --> 109 h = find_hessian_diag(point, vars, model=model) 110 except NotImplementedError: 111 h = fixed_hessian(point, vars, model=model) /Users/fonnescj/Repositories/pymc3/pymc3/tuning/scaling.py in find_hessian_diag(point, vars, model) 101 """ 102 model = modelcontext(model) --> 103 H = model.fastfn(hessian_diag(model.logpt, vars)) 104 return H(Point(point, model=model)) 105 /Users/fonnescj/Repositories/pymc3/pymc3/memoize.py in memoizer(*args, **kwargs) 12 13 if key not in cache: ---> 14 cache[key] = obj(*args, **kwargs) 15 16 return cache[key] /Users/fonnescj/Repositories/pymc3/pymc3/theanof.py in hessian_diag(f, vars) 101 102 if vars: --> 103 return -t.concatenate([hessian_diag1(f, v) for v in vars], axis=0) 104 else: 105 return empty_gradient /Users/fonnescj/Repositories/pymc3/pymc3/theanof.py in <listcomp>(.0) 101 102 if vars: --> 103 return -t.concatenate([hessian_diag1(f, v) for v in vars], axis=0) 104 else: 105 return empty_gradient /Users/fonnescj/Repositories/pymc3/pymc3/theanof.py in hessian_diag1(f, v) 92 return gradient1(g[i], v)[i] 93 ---> 94 return theano.map(hess_ii, idx)[0] 95 96 /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/scan_module/scan_views.py in map(fn, sequences, non_sequences, truncate_gradient, go_backwards, mode, name) 67 go_backwards=go_backwards, 68 mode=mode, ---> 69 name=name) 70 71 /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/scan_module/scan.py in scan(fn, sequences, outputs_info, non_sequences, n_steps, truncate_gradient, go_backwards, mode, name, profile, allow_gc, strict) 473 # If not we need to use copies, that will be replaced at 474 # each frame by the corresponding slice --> 475 actual_slice = seq['input'][k - mintap] 476 _seq_val = tensor.as_tensor_variable(seq['input']) 477 _seq_val_slice = _seq_val[k - mintap] /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/tensor/var.py in __getitem__(self, args) 529 self, *theano.tensor.subtensor.Subtensor.collapse( 530 args, --> 531 lambda entry: isinstance(entry, Variable))) 532 533 def take(self, indices, axis=None, mode='raise'): /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/gof/op.py in __call__(self, *inputs, **kwargs) 649 thunk.outputs = [storage_map[v] for v in node.outputs] 650 --> 651 required = thunk() 652 assert not required # We provided all inputs 653 /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/gof/op.py in rval() 852 853 def rval(): --> 854 fill_storage() 855 for o in node.outputs: 856 compute_map[o][0] = True /Users/fonnescj/anaconda3/lib/python3.5/site-packages/theano/gof/cc.py in __call__(self) 1712 print(self.error_storage, file=sys.stderr) 1713 raise -> 1714 reraise(exc_type, exc_value, exc_trace) 1715 1716 /Users/fonnescj/anaconda3/lib/python3.5/site-packages/six.py in reraise(tp, value, tb) 684 if value.__traceback__ is not tb: 685 raise value.with_traceback(tb) --> 686 raise value 687 688 else: IndexError: index out of bounds
med_manage_model.vars
[followup_time_missing, nu_log, age_centered_missing, μ, β_fup, β_age, σ_interval, ϵ]
pm.forestplot(trace_med_manage, vars=['age_centered_missing'], ylabels=plot_labels)
--------------------------------------------------------------------------- IndexError Traceback (most recent call last) <ipython-input-44-ed6e9ecfa6a7> in <module>() ----> 1 pm.forestplot(trace_med_manage, vars=['age_centered_missing'], ylabels=plot_labels) /Users/fonnescj/Repositories/pymc3/pymc3/plots.py in forestplot(trace_obj, vars, alpha, quartiles, rhat, main, xtitle, xrange, ylabels, chain_spacing, vline, gs) 378 379 # Substitute HPD interval for quantile --> 380 quants[0] = var_hpd[0].T 381 quants[-1] = var_hpd[1].T 382 IndexError: index 0 is out of bounds for axis 0 with size 0
pm.summary(trace_med_manage, vars=['p_6', 'p_12'])
p_6: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------- 0.075 0.000 0.000 [0.075, 0.075] 0.075 0.000 0.000 [0.075, 0.075] 0.075 0.000 0.000 [0.075, 0.075] 0.075 0.000 0.000 [0.075, 0.075] 0.075 0.000 0.000 [0.075, 0.075] 0.075 0.000 0.000 [0.075, 0.075] 0.552 0.000 0.000 [0.552, 0.552] Posterior quantiles: 2.5 25 50 75 97.5 |--------------|==============|==============|--------------| 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.552 0.552 0.552 0.552 0.552 p_12: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------- 0.075 0.000 0.000 [0.075, 0.075] 0.075 0.000 0.000 [0.075, 0.075] 0.075 0.000 0.000 [0.075, 0.075] 0.075 0.000 0.000 [0.075, 0.075] 0.075 0.000 0.000 [0.075, 0.075] 0.075 0.000 0.000 [0.075, 0.075] 0.552 0.000 0.000 [0.552, 0.552] Posterior quantiles: 2.5 25 50 75 97.5 |--------------|==============|==============|--------------| 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.552 0.552 0.552 0.552 0.552
pm.forestplot(trace_med_manage, vars=['μ'], ylabels=plot_labels)
<matplotlib.gridspec.GridSpec at 0x116f27c18>
def get_data(intervention):
intervention_data = dataset[(dataset.intervention_cat==intervention)
& ~dataset[outcome_cats].isnull().sum(axis=1).astype(bool)]
followup_masked = masked_values(intervention_data.followup_interval.values, np.nan)
followup_min, followup_max = intervention_data[['fup_min', 'fup_max']].values.T
outcomes = intervention_data[[ 'hysterectomy', 'myomectomy', 'uae',
'MRIgFUS', 'ablation', 'iud', 'no_treatment']].values
if np.isnan(outcomes).any():
print('Missing values in outcomes for', intervention)
followup_n = intervention_data.followup_n.values
# Center age at 40
age_masked = masked_values(intervention_data['BL Mean'].values - 40, np.nan)
studies = intervention_data.study_id.unique()
study_index = np.array([np.argwhere(studies==i).squeeze() for i in intervention_data.study_id])
study_id = intervention_data.study_id.values
n_studies = len(set(study_id))
n_outcomes = 7
arms = len(outcomes)
intervention_data = dataset[(dataset.intervention_cat==intervention)
& ~dataset[outcome_cats].isnull().sum(axis=1).astype(bool)]
followup_masked = masked_values(intervention_data.followup_interval.values, 17.33)
followup_min, followup_max = intervention_data[['fup_min', 'fup_max']].values.T
outcomes = intervention_data[[ 'hysterectomy', 'myomectomy', 'uae',
'MRIgFUS', 'ablation', 'iud', 'no_treatment']].values
followup_n = intervention_data.followup_n.values
age_masked = masked_values(intervention_data['BL Mean'].values, 41.33)
studies = intervention_data.study_id.unique()
study_index = np.array([np.argwhere(studies==i).squeeze() for i in intervention_data.study_id])
study_id = intervention_data.study_id.values
n_studies = len(set(study_id))
n_outcomes = 7
arms = len(outcomes)
return locals()
foo = get_data('med_manage')
foo['age_masked'] - 40
masked_array(data = [2.5 4.5 3.6000000000000014 -- 1.6000000000000014 1.6000000000000014 1.1000000000000014 1.1000000000000014 -1 -1 -1 -0.3999999999999986 -0.3999999999999986 -0.3999999999999986 1.6000000000000014 1.6000000000000014 1.6000000000000014 1.6000000000000014 1.6000000000000014 1.6000000000000014 1.6000000000000014 1.6000000000000014 1.2999999999999972 1.2999999999999972 1.2999999999999972 1.2999999999999972 1.1000000000000014 1.1000000000000014 1.1000000000000014 1.1000000000000014 -0.3299999999999983 -3.1300000000000026 -9.059999999999999 -9 16.200000000000003 10.200000000000003 10.600000000000001 -5.600000000000001 1 4 2.200000000000003 2.200000000000003 2 2 -- 9.200000000000003 -7.399999999999999 -- 9.200000000000003 -7.399999999999999 -0.5 -1.8999999999999986 -3 -3 -- -- -- -- -- --], mask = [False False False True False False False False False False False False False False False False False False False False False False False False False False False False False False False False False False False False False False False False False False False False True False False True False False False False False False True True True True True True], fill_value = ?)