-
Notifications
You must be signed in to change notification settings - Fork 10
/
schiz_forest.py
219 lines (160 loc) · 7.05 KB
/
schiz_forest.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
""" Fit data with several rate models and generate forest plot"""
import sys
sys.path += ['..', 'book']
import pylab as pl
import pymc as mc
import dismod3
import book_graphics
reload(book_graphics)
results = {}
n_pred = 10000
iter = 20000
burn = 10000
thin = 10
# set font
book_graphics.set_font()
### @export 'data'
# TODO: migrate data into a csv, load with pandas
dm = dismod3.load_disease_model(15630)
dm.calc_effective_sample_size(dm.data)
some_data = ([d for d in dm.data
if d['data_type'] == 'prevalence data'
and d['sex'] == 'male'
and 15 <= d['age_start'] < 20
and d['age_end'] == 99
and d['effective_sample_size'] > 1])
countries = pl.unique([s['region'] for s in some_data])
min_year = min([s['year_start'] for s in some_data])
max_year = max([s['year_end'] for s in some_data])
cy = ['%s-%d'%(s['region'], s['year_start']) for s in some_data]
n = pl.array([s['effective_sample_size'] for s in some_data])
r = pl.array([dm.value_per_1(s) for s in some_data])
s = pl.sqrt(r * (1-r) / n)
### @export 'binomial-model'
pi = mc.Uniform('pi', lower=0, upper=1, value=.5)
@mc.potential
def obs(pi=pi):
return mc.binomial_like(r*n, n, pi)
@mc.deterministic
def pred(pi=pi):
return mc.rbinomial(n_pred, pi) / float(n_pred)
### @export 'binomial-fit'
mc.MCMC([pi, obs, pred]).sample(iter, burn, thin, verbose=False, progress_bar=False)
### @export 'binomial-store'
# mc.Matplot.plot(pi)
# pl.savefig('book/graphics/ci-prev_meta_analysis-binomial_diagnostic.png')
results['Binomial'] = dict(pi=pi.stats(), pred=pred.stats())
### @export 'beta-binomial-model'
alpha = mc.Uninformative('alpha', value=4.)
beta = mc.Uninformative('beta', value=1000.)
pi_mean = mc.Lambda('pi_mean', lambda alpha=alpha, beta=beta: alpha/(alpha+beta))
pi = mc.Beta('pi', alpha, beta, value=r)
@mc.potential
def obs(pi=pi):
return mc.binomial_like(r*n, n, pi)
@mc.deterministic
def pred(alpha=alpha, beta=beta):
return mc.rbinomial(n_pred, mc.rbeta(alpha, beta)) / float(n_pred)
### @export 'beta-binomial-fit'
mcmc = mc.MCMC([alpha, beta, pi_mean, pi, obs, pred])
mcmc.use_step_method(mc.AdaptiveMetropolis, [alpha, beta])
mcmc.use_step_method(mc.AdaptiveMetropolis, pi)
mcmc.sample(iter*10, burn*10, thin*10, verbose=False, progress_bar=False)
### @export 'beta-binomial-store'
#mc.Matplot.plot(alpha)
#mc.Matplot.plot(beta)
# mc.Matplot.plot(pi)
# pl.savefig('book/graphics/ci-prev_meta_analysis-beta_binomial_diagnostic.png')
results['Beta binomial'] = dict(pi=pi_mean.stats(), pred=pred.stats())
### @export 'poisson-model'
pi = mc.Uniform('pi', lower=0, upper=1, value=.5)
@mc.potential
def obs(pi=pi):
return mc.poisson_like(r*n, pi*n)
@mc.deterministic
def pred(pi=pi):
return mc.rpoisson(pi*n_pred) / float(n_pred)
### @export 'poisson-fit-and-store'
mc.MCMC([pi, obs, pred]).sample(iter, burn, thin, verbose=False, progress_bar=False)
results['Poisson'] = dict(pi=pi.stats(), pred=pred.stats())
### @export 'negative-binomial-model'
pi = mc.Uniform('pi', lower=0, upper=1, value=.5)
delta = mc.Uninformative('delta', value=100.)
@mc.potential
def obs(pi=pi, delta=delta):
return mc.negative_binomial_like(r*n, pi*n, delta)
@mc.deterministic
def pred(pi=pi, delta=delta):
return mc.rnegative_binomial(pi*n_pred, delta) / float(n_pred)
### @export 'negative-binomial-fit-and-store'
mc.MCMC([pi, delta, obs, pred]).sample(iter, burn, thin, verbose=False, progress_bar=False)
results['Negative binomial'] = dict(pi=pi.stats(), pred=pred.stats())
### @export 'normal-model'
pi = mc.Uniform('pi', lower=0, upper=1, value=.5)
sigma = mc.Uniform('sigma', lower=0, upper=10, value=.01)
@mc.potential
def obs(pi=pi, sigma=sigma):
return mc.normal_like(r, pi, 1./(s**2 + sigma**2))
@mc.deterministic
def pred(pi=pi, sigma=sigma):
s_pred = pl.sqrt(pi*(1-pi)/n_pred)
return mc.rnormal(pi, 1./(s_pred + sigma))
### @export 'normal-fit-and-store'
mc.MCMC([pi, sigma, obs, pred]).sample(iter, burn, thin, verbose=False, progress_bar=False)
results['Normal'] = dict(pi=pi.stats(), pred=pred.stats())
### @export 'log-normal-model'
pi = mc.Uniform('pi', lower=0, upper=1, value=.5)
sigma = mc.Uniform('sigma', lower=0, upper=10, value=.01)
@mc.potential
def obs(pi=pi, sigma=sigma):
return mc.normal_like(pl.log(r), pl.log(pi), 1./((s/r)**2 + sigma**2))
pred_s = pl.sqrt(r * (1-r) / n_pred)
@mc.deterministic
def pred(pi=pi, sigma=sigma):
s_pred = pl.sqrt(pi*(1-pi)/n_pred)
return pl.exp(mc.rnormal(pl.log(pi), 1./((s_pred/pi)**2 + sigma**2)))
### @export 'log-normal-fit-and-store'
mc.MCMC([pi, sigma, obs, pred]).sample(iter, burn, thin, verbose=False, progress_bar=False)
results['Lognormal'] = dict(pi=pi.stats(), pred=pred.stats())
### @export 'offset-log-normal-model'
pi = mc.Uniform('pi', lower=0, upper=1, value=.5)
zeta = mc.Uniform('zeta', lower=0, upper=.005, value=.001)
sigma = mc.Uniform('sigma', lower=0, upper=10, value=.01)
@mc.potential
def obs(pi=pi, zeta=zeta, sigma=sigma):
return mc.normal_like(pl.log(r+zeta), pl.log(pi+zeta), 1./((s/(r+zeta))**2 + sigma**2))
@mc.deterministic
def pred(pi=pi, zeta=zeta, sigma=sigma):
s_pred = pl.sqrt(pi*(1-pi)/n_pred)
return pl.exp(mc.rnormal(pl.log(pi+zeta),
1./((s_pred/(pi+zeta))**2 + sigma**2))) \
- zeta
### @export 'offset-log-normal-fit-and-store'
mc.MCMC([pi, zeta, sigma, obs, pred]).sample(iter, burn, thin, verbose=False, progress_bar=False)
results['Offset lognormal'] = dict(pi=pi.stats(), pred=pred.stats())
### @export 'save'
pi_median = []
pi_spread = []
for i, k in enumerate(results):
pi_median.append(results[k]['pi']['quantiles'][50])
pi_spread.append(results[k]['pi']['95% HPD interval'][1]-results[k]['pi']['95% HPD interval'][0])
min_est = min(pi_median).round(4)
max_est = max(pi_median).round(4)
min_spread = min(pi_spread).round(4)
max_spread = max(pi_spread).round(4)
book_graphics.save_json('schiz_forest.json', vars())
### data only plot, for computational infrastructure appendix
book_graphics.forest_plot(r, n, data_labels=cy,
xmax=.0115,
subplot_params=dict(bottom=.1, right=.99, top=.95, left=.15),
figparams=book_graphics.quarter_page_params,
fname='book/graphics/ci-prev_meta_analysis-schiz_data.png')
### master graphic of data and models, for rate model section of stats chapter
book_graphics.forest_plot(r, n, data_labels=cy,
xmax=.0115,
model_keys=['Binomial', 'Poisson', 'Beta binomial', 'Negative binomial', 'Normal', 'Lognormal', 'Offset lognormal'],
results=results,
#subplot_params=dict(bottom=.1, right=.99, top=.95, left=.15),
fig_params=dict(figsize=(11, 8.5), dpi=120),
fname='book/graphics/schiz_forest.pdf')
pl.show()