In [ ]:
%matplotlib inline
from pymc3 import Gamma, Poisson, Normal, Model, sample, forestplot, NUTS, Metropolis, find_MAP, starting
import theano.tensor as tt
from theano import function as fn
from theano import printing
import numpy as np
import scipy as sp


Here is the original model, implemented in BUGS:

model
{
# Set up data
for(i in 1:Nsubj) {
for(j in 1:T) {
# risk set = 1 if obs.t >= t
Y[i,j] <- step(obs.t[i] - t[j] + eps)
# counting process jump = 1 if obs.t in [ t[j], t[j+1] )
#                      i.e. if t[j] <= obs.t < t[j+1]
dN[i, j] <- Y[i, j] * step(t[j + 1] - obs.t[i] - eps) * FAIL[i]
}
}

# Model
for(j in 1:T) {
for(i in 1:Nsubj) {
dN[i, j]   ~ dpois(Idt[i, j])              # Likelihood
Idt[i, j] <- Y[i, j] * exp(beta[1]*pscenter[i] + beta[2]*
hhcenter[i] + beta[3]*ncomact[i] + beta[4]*rleader[i] + beta[5]*dleader[i] + beta[6]*inter1[i] + beta[7]*inter2[i]) * dL0[j]    # Intensity
}
dL0[j] ~ dgamma(mu[j], c)
mu[j] <- dL0.star[j] * c    # prior mean hazard
}

c ~ dgamma(0.0001, 0.00001)
r ~ dgamma(0.001, 0.0001)

for (j in 1 : T) {  dL0.star[j] <- r * (t[j + 1] - t[j])  }
# next line indicates number of covariates and is for the corresponding betas
for(i in 1:7) {beta[i] ~ dnorm(0.0,0.00001)}

}
In [ ]:
dta = dict(T=73, Nsubj=430, eps=0.0,  t=[1, 21, 85, 128, 129, 148, 178, 204,
206, 210, 211, 212, 225, 238, 241,
248, 259, 273, 275, 281, 286, 289,
301, 302, 303, 304, 313, 317, 323,
344, 345, 349, 350, 351, 355, 356,
359, 364, 385, 386, 389, 390, 391,
392, 394, 395, 396, 397, 398, 399,
400, 406, 415, 416, 426, 427, 434,
435, 437, 441, 447, 448, 449, 450,
451, 453, 455, 456, 458, 459, 460,
461, 462, 463],
obs_t = [460, 313, 435, 350, 435, 350, 350, 460, 460, 448, 225, 225, 396, 435, 396, 396, 453, 396, 456, 397, 397, 396, 395, 275, 449, 395, 395, 462, 302, 302, 458, 461, 396, 241, 389, 458, 304, 304, 395, 395, 364, 460, 415, 463, 396, 459, 441, 435, 396, 458, 437, 396, 356, 356, 396, 455, 396, 462, 399, 400, 350, 350, 395, 395, 441, 355, 85, 458, 128, 396, 386, 386, 386, 462, 458, 390, 390, 396, 396, 396, 427, 458, 395, 275, 275, 395, 359, 395, 395, 441, 395, 463, 178, 275, 463, 396, 396, 259, 396, 396, 458, 441, 396, 463, 396, 463, 435, 396, 437, 396, 398, 463, 460, 462, 460, 460, 210, 396, 435, 458, 385, 323, 323, 359, 396, 396, 460, 238, 441, 450, 392, 458, 396, 458, 396, 396, 462, 435, 396, 394, 396, 435, 458, 1, 395, 395, 451, 462, 458, 462, 396, 286, 396, 349, 449, 462, 455, 21, 463, 461, 461, 456, 435, 396, 460, 462, 462, 435, 435, 460, 386, 396, 458, 386, 461, 441, 435, 435, 463, 456, 396, 275, 460, 406, 460, 406, 317, 406, 461, 396, 359, 458, 463, 435, 462, 458, 396, 396, 273, 396, 435, 281, 275, 396, 447, 225, 447, 396, 435, 416, 396, 248, 396, 435, 435, 396, 461, 385, 396, 458, 458, 396, 461, 396, 448, 396, 396, 460, 455, 456, 463, 462, 458, 463, 396, 462, 395, 456, 396, 463, 396, 435, 459, 396, 396, 396, 395, 435, 455, 395, 461, 344, 396, 395, 396, 317, 396, 395, 426, 461, 396, 289, 441, 395, 396, 458, 396, 396, 435, 396, 395, 396, 441, 345, 396, 359, 435, 435, 396, 396, 395, 458, 461, 458, 212, 301, 458, 456, 395, 396, 395, 435, 396, 396, 303, 458, 460, 400, 396, 462, 359, 458, 396, 206, 441, 396, 458, 396, 462, 396, 396, 275, 396, 395, 435, 435, 462, 225, 458, 462, 396, 396, 289, 396, 303, 455, 400, 400, 359, 461, 396, 462, 460, 463, 463, 463, 204, 435, 435, 396, 396, 396, 463, 458, 396, 455, 435, 396, 396, 463, 396, 461, 463, 460, 441, 460, 435, 435, 460, 455, 460, 395, 460, 460, 460, 435, 449, 463, 462, 129, 391, 396, 391, 391, 434, 356, 462, 396, 349, 225, 396, 435, 461, 391, 391, 351, 211, 461, 212, 434, 148, 356, 458, 456, 455, 435, 463, 463, 462, 435, 463, 437, 460, 396, 406, 451, 460, 435, 396, 460, 455, 396, 398, 456, 458, 396, 456, 449, 396, 128, 396, 462, 463, 396, 396, 396, 435, 460, 396, 458],
FAIL= [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
pscenter= [
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inter1= [ -.01434325, -.01460965, 0, 0, 0, -.01113493, 0, 0, 0, -.0553269, -.03238896, 0, 0, -.07062459, -.07464545, -.07032613, 0, 0, -.01408955, 0, -.00219072, 0, 0, 0, 0, 0, .07300876, .01394272, 0, 0, 0, 0, 0, 0, .05120398, 0, -.00550709, -.02062663, -.03077685, -.01688493, 0, .01149963, 0, .01149963, .01149963, 0, 0, 0, 0, 0, 0, 0, 0, 0, .01149963, .0034338, .0376236, .00733331, 0, .03832785, .03832785, -.02622275, -.02622275, -.02622275, -.01492678, 0, 0, -.02897806, -.02847666, 0, 0, -.04224754, -.04743705, -.0510477, -.031893, 0, 0, 0, -.01503116, .003101, -.00083466, .02395027, -.07952866, 0, 0, -.06586029, 0, -.0613939, -.081205, -.07540084, -.08488011, -.08488011, 0, -.07492433, -.08907269, -.09451609, 0, -.08980743, 0, -.0771635, 0, 0, -.0771635, -.08204606, 0, -.05263504, 0, -.05109092, -.04696729, 0, -.04696729, 0, -.05303248, -.05348096, 0, 0, .00584956, -.00792241, -.01719816, 0, -.01576016, 0, -.04014061, 0, 0, 0, 0, 0, .0471441, 0, .04233112, 0, .04233112, 0, 0, .0493324, .04512087, .03205975, .02913185, 0, .05324252, 0, 0, 0, 0, .05054695, 0, .14026688, .01734403, .06078221, 0, 0, 0, -.03138622, 0, .01637333, 0, 0, 0, 0, .01897239, .01591935, 0, -.0619156, 0, -.06851645, 0, -.03889525, -.05023452, -.05013452, 0, 0, -.01362136, 0, 0, -.02634164, 0, 0, 0, 0, -.00890537, -.00611669, 0, 0, 0, -.01513384, 0, -.03551984, 0, -.01978032, 0, .06706496, .10551275, 0, .03092981, .06556855, 0, 0, 0, .09362991, 0, 0, 0, 0, 0, 0, .02610553, .03546937, 0, 0, .034415, 0, 0, 0, .07546701, 0, 0, 0, 0, -.02919447, -.01016712, 0, 0, 0, 0, -.04845615, -.05010044, 0, 0, 0, 0, 0, 0, -.07666632, 0, 0, -.07226554, -.08216553, -.0777643, 0, 0, -.04727952, 0, -.06870384, -.05999847, 0, 0, 0, .02772475, .02883079, .03642944, 0, .04148949, 0, 0, 0, .04268012, .03225577, 0, -.05140995, -.05399637, 0, 0, .02432223, 0, .0490674, .0490674, .0490674, 0, 0, 0, 0, 0, 0, 0, 0, .10476315, 0, 0, 0, 0, 0, .07008056, 0, 0, .01667466, 0, .05253941, .04293926, 0, .02692172, 0, 0, .08742411, .04533176, 0, .01831875, 0, .09834951, .09952456, 0, .02945534, .038731, 0, .04435538, 0, -.02357505, 0, 0, -.02357505, .09324722, 0, 0, 0, -.03490683, 0, -.05054474, 0, -.0474724, -.04905931, 0, .02879751, 0, 0, 0, 0, 0, 0, 0, .04439012, 0, .02989959, .02989959, .05468828, .04463226, 0, 0, 0, 0, 0, .01231324, -.01399783, .04595331, .00145386, 0, .06459354, -.0007196, 0, -.07614055, -.08435525, 0, -.10299519, 0, 0, 0, -.00210284, -.00797183, 0, 0, 0, 0, -.03545086, 0, 0, 0, 0, -.061286, -.07666647, 0, -.05902354, -.07652324, -.07645561, 0, 0, 0, -.03292062, 0, 0, 0, 0, -.075417, 0, -.07922532, 0, -.08583414, -.07450142, -.08066016, 0, 0, -.06249051, 0, 0, 0, 0, -.0618688, 0, -.06524737, -.04419825, -.04489509, 0, 0, 0, -.04520512, -.04187583, 0, 0, -.03753508, 0, 0, 0, 0, 0, 0, 0, 0, .06862645, 0, 0, -.00120631, .01947345, 0, 0, .03561932, 0, .03158225, .03608047, 0, 0, 0, -.02899643],

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In [ ]:
def load_data_cox(dta):
array = lambda x : np.array(dta[x], dtype=float)
t = array('t')
obs_t = array('obs_t')
pscenter = array('pscenter')
hhcenter = array('hhcenter')
ncomact = array('ncomact')
inter1 = array('inter1')
inter2 = array('inter2')
fail = array('FAIL')
return (t, obs_t, pscenter, hhcenter, ncomact,

In [ ]:
(t, obs_t, pscenter, hhcenter, ncomact, rleader,

In [ ]:
X = np.array([pscenter, hhcenter, ncomact, rleader, dleader, inter1, inter2])

In [ ]:
X.shape

In [ ]:
with Model() as model:

T = len(t) - 1
nsubj = len(obs_t)

# risk set equals one if obs_t >= t
Y = np.array([[int(obs >= time) for time in t] for obs in obs_t])
# counting process. jump = 1 if obs_t \in [t[j], t[j+1])
dN = np.array([[Y[i,j]*int(t[j+1] >= obs_t[i])*fail[i] for j in range(T)] for i in
range(nsubj)])

c = Gamma('c', .0001, .00001)
r = Gamma('r', .001, .0001)

dL0_star = r*np.diff(t)

mu = dL0_star * c # prior mean hazard

dL0 = Gamma('dL0', mu, c, shape=T)

beta = Normal('beta', np.zeros(7),
np.ones(7)*.00001, shape=7)

linear_model = tt.exp(tt.dot(X.T, beta))
idt = Y[:, :-1] * tt.outer(linear_model, dL0)

dn_like = Poisson('dn_like', idt, observed=dN)

In [ ]:
with model:
start = find_MAP()
step = NUTS(scaling=start)
trace = sample(2000, step)

In [ ]:
forestplot(trace, vars=['beta'])