def setup(dm, key, data_list, rate_stoch):
""" Generate the PyMC variables for a log-normal model of
a function of age
Parameters
----------
dm : dismod3.DiseaseModel
the object containing all the data, priors, and additional
information (like input and output age-mesh)
key : str
the name of the key for everything about this model (priors,
initial values, estimations)
data_list : list of data dicts
the observed data to use in the beta-binomial liklihood function
rate_stoch : pymc.Stochastic
a PyMC stochastic (or deterministic) object, with
len(rate_stoch.value) == len(dm.get_estimation_age_mesh()).
Results
-------
vars : dict
Return a dictionary of all the relevant PyMC objects for the
log-normal model. vars['rate_stoch'] is of particular
relevance, for details see the beta_binomial_model
"""
vars = {}
est_mesh = dm.get_estimate_age_mesh()
vars['rate_stoch'] = rate_stoch
# set up priors and observed data
prior_str = dm.get_priors(key)
generate_prior_potentials(vars, prior_str, est_mesh)
vars['observed_rates'] = []
for d in data_list:
age_indices = indices_for_range(est_mesh, d['age_start'], d['age_end'])
age_weights = d.get('age_weights', np.ones(len(age_indices)) / len(age_indices))
lb, ub = dm.bounds_per_1(d)
se = (np.log(ub) - np.log(lb)) / (2. * 1.96)
if np.isnan(se) or se <= 0.:
se = 1.
print 'data %d: log(value) = %f, se = %f' % (d['id'], np.log(dm.value_per_1(d)), se)
@mc.observed
@mc.stochastic(name='obs_%d' % d['id'])
def obs(f=vars['rate_stoch'],
age_indices=age_indices,
age_weights=age_weights,
value=np.log(dm.value_per_1(d)),
tau=se**-2, data=d):
f_i = rate_for_range(f, age_indices, age_weights)
return mc.normal_like(value, np.log(f_i), tau)
vars['observed_rates'].append(obs)
return vars
def values_from(dm, d, min_val=1.e-5, max_se=.1):
""" Extract the normalized values from a piece of data
Parameters
----------
dm : disease model
d : data dict
min_val : float, optional
the value to use instead of zero, since logit cannot model true zero
max_se : float, optional
the standard error to use for data with missing or zero standard error
"""
est_mesh = dm.get_estimate_age_mesh()
# get the index vector and weight vector for the age range
age_indices = indices_for_range(est_mesh, d['age_start'], d['age_end'])
age_weights = d.get('age_weights', np.ones(len(age_indices)))
# ensure all rate data is valid
d_val = dm.value_per_1(d)
if d_val < 0 or d_val > 1:
debug('WARNING: data %d not in range (0,1)' % d['id'])
raise ValueError
elif d_val == 0.:
d_val = min_val / 10. # TODO: determine if this is an acceptible way to deal with zero
elif d_val == 1.:
d_val = 1. - min_val / 10.
logit_val = mc.logit(d_val)
d_se = dm.se_per_1(d)
if d_se == MISSING:
d_se = max_se #TODO: determine if this is an acceptible way to deal with missing
elif d_se == 0.:
d_se = max_se
logit_se = (1/d_val + 1/(1-d_val)) * d_se
return age_indices, age_weights, logit_val, logit_se
def values_from(dm, d):
""" Extract the normalized values from a piece of data
Parameters
----------
dm : disease model
d : data dict
"""
est_mesh = dm.get_estimate_age_mesh()
# get the index vector and weight vector for the age range
age_indices = indices_for_range(est_mesh, d['age_start'], d['age_end'])
age_weights = d.get('age_weights', np.ones(len(age_indices))/len(age_indices))
# ensure all rate data is valid
Y_i = dm.value_per_1(d)
# TODO: allow Y_i > 1, extract effective sample size appropriately in this case
if Y_i < 0:
debug('WARNING: data %d < 0' % d['id'])
raise ValueError
N_i = max(1., d['effective_sample_size'])
return age_indices, age_weights, Y_i, N_i
def setup(dm, key="%s", data_list=None):
""" Generate the PyMC variables for a generic disease model
Parameters
----------
dm : dismod3.DiseaseModel
the object containing all the data, priors, and additional
information (like input and output age-mesh)
key : str, optional
a string for modifying the names of the stochs in this model,
must contain a single %s that will be substituted
data_list : list of data dicts
the observed data to use in the rate stoch likelihood functions
Results
-------
vars : dict of PyMC stochs
returns a dictionary of all the relevant PyMC objects for the
generic disease model.
"""
vars = {}
# setup all-cause mortality
param_type = "all-cause_mortality"
data = [d for d in data_list if d["data_type"] == "all-cause mortality data"]
m_all_cause = dm.mortality(key % param_type, data)
# make covariate vectors and estimation vectors to know dimensions of these objects
covariate_dict = dm.get_covariates()
derived_covariate = dm.get_derived_covariate_values()
X_region, X_study = rate_model.regional_covariates(key, covariate_dict, derived_covariate)
est_mesh = dm.get_estimate_age_mesh()
# update age_weights on non-incidence/prevalence data to reflect
# prior prevalence distribution, if available
prior_prev = dm.get_mcmc("emp_prior_mean", key % "prevalence")
if len(prior_prev) > 0:
for d in data:
if d["data_type"].startswith("incidence") or d["data_type"].startswith("prevalence"):
continue
age_indices = indices_for_range(est_mesh, d["age_start"], d["age_end"])
d["age_weights"] = prior_prev[age_indices]
d["age_weights"] /= sum(
d["age_weights"]
) # age weights must sum to 1 (optimization of inner loop removed check on this)
# create negative binomial models for incidence, remission, and
# excess-mortality (which are all treated as "free" parameters)
for param_type in ["incidence", "remission", "excess-mortality"]:
data = [d for d in data_list if d["data_type"] == "%s data" % param_type]
lower_bound_data = [] # TODO: include lower bound data when appropriate (this has not come up yet)
prior_dict = dm.get_empirical_prior(
param_type
) # use empirical priors for the type/region/year/sex if available
if prior_dict == {}: # otherwise use weakly informative priors
prior_dict.update(
alpha=np.zeros(len(X_region)),
beta=np.zeros(len(X_study)),
gamma=-5 * np.ones(len(est_mesh)),
sigma_alpha=[1.0],
sigma_beta=[1.0],
sigma_gamma=[10.0],
# delta is filled in from the global prior dict in neg_binom setup
)
vars[key % param_type] = rate_model.setup(
dm, key % param_type, data, emp_prior=prior_dict, lower_bound_data=lower_bound_data
)
# create nicer names for the rate stochastic from each neg-binom rate model
i = vars[key % "incidence"]["rate_stoch"]
r = vars[key % "remission"]["rate_stoch"]
f = vars[key % "excess-mortality"]["rate_stoch"]
# initial fraction of population with the condition
logit_C_0 = mc.Normal(
"logit_%s" % (key % "C_0"), -5.0, 10.0 ** -2, value=-5.0
) # represet C_0 in logit space to allow unconstrained posterior maximization
@mc.deterministic(name=key % "C_0")
def C_0(logit_C_0=logit_C_0):
return mc.invlogit(logit_C_0)
# initial fraction population with and without condition
@mc.deterministic(name=key % "S_0")
def SC_0(C_0=C_0):
return np.array([1.0 - C_0, C_0]).ravel()
vars[key % "bins"] = {"initial": [SC_0, C_0, logit_C_0]}
# iterative solution to difference equations to obtain bin sizes for all ages
import scipy.linalg
@mc.deterministic(name=key % "bins")
def SCpm(SC_0=SC_0, i=i, r=r, f=f, m_all_cause=m_all_cause, age_mesh=dm.get_param_age_mesh()):
SC = np.zeros([2, len(age_mesh)])
p = np.zeros(len(age_mesh))
m = np.zeros(len(age_mesh))
SC[:, 0] = SC_0
p[0] = SC_0[1] / (SC_0[0] + SC_0[1])
m[0] = trim(
m_all_cause[age_mesh[0]] - f[age_mesh[0]] * p[0], 0.1 * m_all_cause[age_mesh[0]], 1 - NEARLY_ZERO
) # trim m[0] to avoid numerical instability
for ii, a in enumerate(age_mesh[:-1]):
A = np.array([[-i[a] - m[ii], r[a]], [i[a], -r[a] - m[ii] - f[a]]]) * (age_mesh[ii + 1] - age_mesh[ii])
SC[:, ii + 1] = np.dot(scipy.linalg.expm(A), SC[:, ii])
p[ii + 1] = trim(SC[1, ii + 1] / (SC[0, ii + 1] + SC[1, ii + 1]), NEARLY_ZERO, 1 - NEARLY_ZERO)
m[ii + 1] = trim(
m_all_cause[age_mesh[ii + 1]] - f[age_mesh[ii + 1]] * p[ii + 1],
0.1 * m_all_cause[age_mesh[ii + 1]],
1 - NEARLY_ZERO,
)
SCpm = np.zeros([4, len(age_mesh)])
SCpm[0:2, :] = SC
SCpm[2, :] = p
SCpm[3, :] = m
return SCpm
vars[key % "bins"]["age > 0"] = [SCpm]
# prevalence = # with condition / (# with condition + # without)
@mc.deterministic(name=key % "p")
def p(SCpm=SCpm, param_mesh=dm.get_param_age_mesh(), est_mesh=dm.get_estimate_age_mesh()):
return dismod3.utils.interpolate(param_mesh, SCpm[2, :], est_mesh)
data = [d for d in data_list if d["data_type"] == "prevalence data"]
prior_dict = dm.get_empirical_prior("prevalence")
if prior_dict == {}:
prior_dict.update(
alpha=np.zeros(len(X_region)),
beta=np.zeros(len(X_study)),
gamma=-5 * np.ones(len(est_mesh)),
sigma_alpha=[1.0],
sigma_beta=[1.0],
sigma_gamma=[10.0],
# delta is filled in from the global prior dict in neg_binom setup
)
vars[key % "prevalence"] = rate_model.setup(dm, key % "prevalence", data, p, emp_prior=prior_dict)
p = vars[key % "prevalence"][
"rate_stoch"
] # replace perfectly consistent p with version including level-bound priors
# make a blank prior dict, to avoid weirdness
blank_prior_dict = dict(
alpha=np.zeros(len(X_region)),
beta=np.zeros(len(X_study)),
gamma=-5 * np.ones(len(est_mesh)),
sigma_alpha=[1.0],
sigma_beta=[1.0],
sigma_gamma=[10.0],
delta=100.0,
sigma_delta=1.0,
)
# cause-specific-mortality is a lower bound on p*f
@mc.deterministic(name=key % "pf")
def pf(p=p, f=f):
return (p + NEARLY_ZERO) * f
data = [d for d in data_list if d["data_type"] == "prevalence x excess-mortality data"]
lower_bound_data = [d for d in data_list if d["data_type"] == "cause-specific mortality data"]
vars[key % "prevalence_x_excess-mortality"] = rate_model.setup(
dm, key % "pf", rate_stoch=pf, data_list=data, lower_bound_data=lower_bound_data, emp_prior=blank_prior_dict
)
# m = m_all_cause - f * p
@mc.deterministic(name=key % "m")
def m(SCpm=SCpm, param_mesh=dm.get_param_age_mesh(), est_mesh=dm.get_estimate_age_mesh()):
return dismod3.utils.interpolate(param_mesh, SCpm[3, :], est_mesh)
vars[key % "m"] = m
# m_with = m + f
@mc.deterministic(name=key % "m_with")
def m_with(m=m, f=f):
return m + f
data = [d for d in data_list if d["data_type"] == "mortality data"]
# TODO: test this
# prior_dict = dm.get_empirical_prior('excess-mortality') # TODO: make separate prior for with-condition mortality
vars[key % "mortality"] = rate_model.setup(dm, key % "m_with", data, m_with, emp_prior=blank_prior_dict)
# mortality rate ratio = mortality with condition / mortality without
@mc.deterministic(name=key % "RR")
def RR(m=m, m_with=m_with):
return m_with / (m + 0.0001)
data = [d for d in data_list if d["data_type"] == "relative-risk data"]
vars[key % "relative-risk"] = log_normal_model.setup(dm, key % "relative-risk", data, RR)
# standardized mortality rate ratio = mortality with condition / all-cause mortality
@mc.deterministic(name=key % "SMR")
def SMR(m_with=m_with, m_all_cause=m_all_cause):
return m_with / (m_all_cause + 0.0001)
data = [d for d in data_list if d["data_type"] == "smr data"]
vars[key % "smr"] = log_normal_model.setup(dm, key % "smr", data, SMR)
# duration = E[time in bin C]
@mc.deterministic(name=key % "X")
def X(r=r, m=m, f=f):
hazard = r + m + f
pr_not_exit = np.exp(-hazard)
X = np.empty(len(hazard))
X[-1] = 1 / hazard[-1]
for i in reversed(range(len(X) - 1)):
X[i] = pr_not_exit[i] * (X[i + 1] + 1) + 1 / hazard[i] * (1 - pr_not_exit[i]) - pr_not_exit[i]
return X
data = [d for d in data_list if d["data_type"] == "duration data"]
vars[key % "duration"] = normal_model.setup(dm, key % "duration", data, X)
# YLD[a] = disability weight * i[a] * X[a] * regional_population[a]
@mc.deterministic(name=key % "i*X")
def iX(i=i, X=X, p=p, pop=rate_model.regional_population(key)):
birth_yld = np.zeros_like(p)
birth_yld[0] = p[0] * pop[0]
return i * X * (1 - p) * pop + birth_yld
vars[key % "incidence_x_duration"] = {"rate_stoch": iX}
return vars
def setup(dm, key, data_list, rate_stoch=None, emp_prior={}):
""" Generate the PyMC variables for a beta binomial model of
a single rate function
Parameters
----------
dm : dismod3.DiseaseModel
the object containing all the data, priors, and additional
information (like input and output age-mesh)
key : str
the name of the key for everything about this model (priors,
initial values, estimations)
data_list : list of data dicts
the observed data to use in the beta-binomial liklihood function
rate_stoch : pymc.Stochastic, optional
a PyMC stochastic (or deterministic) object, with
len(rate_stoch.value) == len(dm.get_estimation_age_mesh()).
This is used to link beta-binomial stochs into a larger model,
for example.
emp_prior : dict, optional
the empirical prior dictionary, retrieved from the disease model
if appropriate by::
>>> t, r, y, s = type_region_year_sex_from_key(key)
>>> emp_prior = dm.get_empirical_prior(t)
Results
-------
vars : dict
Return a dictionary of all the relevant PyMC objects for the
beta binomial model. vars['rate_stoch'] is of particular
relevance; this is what is used to link the beta-binomial model
into more complicated models, like the generic disease model.
Details
-------
The beta binomial model parameters are the following:
* the mean age-specific rate function
* dispersion of this mean
* the p_i value for each data observation that has a standard
error (data observations that do not have standard errors
recorded are fit as observations of the beta r.v., while
observations with standard errors recorded have a latent
variable for the beta, and an observed binomial r.v.).
"""
vars = {}
est_mesh = dm.get_estimate_age_mesh()
if np.any(np.diff(est_mesh) != 1):
raise ValueError, "ERROR: Gaps in estimation age mesh must all equal 1"
# set up age-specific rate function, if it does not yet exist
if not rate_stoch:
param_mesh = dm.get_param_age_mesh()
if emp_prior.has_key("mu"):
initial_value = emp_prior["mu"]
else:
initial_value = dm.get_initial_value(key)
# find the logit of the initial values, which is a little bit
# of work because initial values are sampled from the est_mesh,
# but the logit_initial_values are needed on the param_mesh
logit_initial_value = mc.logit(interpolate(est_mesh, initial_value, param_mesh))
logit_rate = mc.Normal(
"logit(%s)" % key, mu=-5.0 * np.ones(len(param_mesh)), tau=1.0e-2, value=logit_initial_value
)
# logit_rate = [mc.Normal('logit(%s)_%d' % (key, a), mu=-5., tau=1.e-2) for a in param_mesh]
vars["logit_rate"] = logit_rate
@mc.deterministic(name=key)
def rate_stoch(logit_rate=logit_rate):
return interpolate(param_mesh, mc.invlogit(logit_rate), est_mesh)
if emp_prior.has_key("mu"):
@mc.potential(name="empirical_prior_%s" % key)
def emp_prior_potential(f=rate_stoch, mu=emp_prior["mu"], tau=1.0 / np.array(emp_prior["se"]) ** 2):
return mc.normal_like(f, mu, tau)
vars["empirical_prior"] = emp_prior_potential
vars["rate_stoch"] = rate_stoch
# create stochastic variable for over-dispersion "random effect"
mu_od = emp_prior.get("dispersion", 0.001)
dispersion = mc.Gamma("dispersion_%s" % key, alpha=10.0, beta=10.0 / mu_od)
vars["dispersion"] = dispersion
@mc.deterministic(name="alpha_%s" % key)
def alpha(rate=rate_stoch, dispersion=dispersion):
return rate / dispersion ** 2
@mc.deterministic(name="beta_%s" % key)
def beta(rate=rate_stoch, dispersion=dispersion):
return (1.0 - rate) / dispersion ** 2
vars["alpha"] = alpha
vars["beta"] = beta
# create potentials for priors
vars["priors"] = generate_prior_potentials(dm.get_priors(key), est_mesh, rate_stoch, dispersion)
# create latent and observed stochastics for data
vars["data"] = data_list
vars["ab"] = []
vars["latent_p"] = []
vars["observations"] = []
for d in data_list:
# set up observed stochs for all relevant data
id = d["id"]
if d["value"] == MISSING:
print "WARNING: data %d missing value" % id
continue
# ensure all rate data is valid
d_val = dm.value_per_1(d)
d_se = dm.se_per_1(d)
if d_val < 0 or d_val > 1:
print "WARNING: data %d not in range [0,1]" % id
continue
if d["age_start"] < est_mesh[0] or d["age_end"] > est_mesh[-1]:
raise ValueError, "Data %d is outside of estimation range---([%d, %d] is not inside [%d, %d])" % (
d["id"],
d["age_start"],
d["age_end"],
est_mesh[0],
est_mesh[-1],
)
age_indices = indices_for_range(est_mesh, d["age_start"], d["age_end"])
age_weights = d["age_weights"]
@mc.deterministic(name="a_%d^%s" % (id, key))
def a_i(alpha=alpha, age_indices=age_indices, age_weights=age_weights):
return rate_for_range(alpha, age_indices, age_weights)
@mc.deterministic(name="b_%d^%s" % (id, key))
def b_i(beta=beta, age_indices=age_indices, age_weights=age_weights):
return rate_for_range(beta, age_indices, age_weights)
vars["ab"] += [a_i, b_i]
if d_se > 0:
# if the data has a standard error, model it as a realization
# of a beta binomial r.v.
latent_p_i = mc.Beta(
"latent_p_%d^%s" % (id, key), alpha=a_i, beta=b_i, value=trim(d_val, NEARLY_ZERO, 1 - NEARLY_ZERO)
)
vars["latent_p"].append(latent_p_i)
denominator = d_val * (1 - d_val) / d_se ** 2.0
numerator = d_val * denominator
obs_binomial = mc.Binomial(
"data_%d^%s" % (id, key), value=numerator, n=denominator, p=latent_p_i, observed=True
)
vars["observations"].append(obs_binomial)
else:
# if the data is a point estimate with no uncertainty
# recorded, model it as a realization of a beta r.v.
obs_p_i = mc.Beta(
"latent_p_%d" % id, value=trim(d_val, NEARLY_ZERO, 1 - NEARLY_ZERO), alpha=a_i, beta=b_i, observed=True
)
vars["observations"].append(obs_p_i)
return vars
def setup(dm, key='%s', data_list=None):
""" Generate the PyMC variables for a generic disease model
Parameters
----------
dm : dismod3.DiseaseModel
the object containing all the data, priors, and additional
information (like input and output age-mesh)
key : str, optional
a string for modifying the names of the stochs in this model,
must contain a single %s that will be substituted
data_list : list of data dicts
the observed data to use in the rate stoch likelihood functions
Results
-------
vars : dict of PyMC stochs
returns a dictionary of all the relevant PyMC objects for the
generic disease model.
"""
vars = {}
param_type = 'all-cause_mortality'
data = [d for d in data_list if d['data_type'] == 'all-cause mortality data']
m_all_cause = dm.mortality(key % param_type, data)
covariate_dict = dm.get_covariates()
X_region, X_study = rate_model.regional_covariates(key, covariate_dict)
est_mesh = dm.get_estimate_age_mesh()
# update age_weights on non-incidence/prevalence data to reflect
# prior prevalence distribution, if available
prior_prev = dm.get_mcmc('emp_prior_mean', key % 'prevalence')
if len(prior_prev) > 0:
for d in data:
if d['data_type'].startswith('incidence') or d['data_type'].startswith('prevalence'):
continue
age_indices = indices_for_range(est_mesh, d['age_start'], d['age_end'])
d['age_weights'] = prior_prev[age_indices]
d['age_weights'] /= sum(d['age_weights']) # age weights must sum to 1 (optimization of inner loop removed check on this)
for param_type in ['incidence', 'remission', 'excess-mortality']:
data = [d for d in data_list if d['data_type'] == '%s data' % param_type]
lower_bound_data = []
# TODO: include lower bound data when appropriate
prior_dict = dm.get_empirical_prior(param_type)
if prior_dict == {}:
prior_dict.update(alpha=np.zeros(len(X_region)),
beta=np.zeros(len(X_study)),
gamma=-5*np.ones(len(est_mesh)),
sigma_alpha=[1.],
sigma_beta=[1.],
sigma_gamma=[10.],
# delta is filled in from the global prior dict in neg_binom setup
)
vars[key % param_type] = rate_model.setup(dm, key % param_type, data,
emp_prior=prior_dict, lower_bound_data=lower_bound_data)
i = vars[key % 'incidence']['rate_stoch']
r = vars[key % 'remission']['rate_stoch']
f = vars[key % 'excess-mortality']['rate_stoch']
# Initial population with condition
logit_C_0 = mc.Normal('logit_%s' % (key % 'C_0'), -5., 10.**-2, value=-5.)
@mc.deterministic(name=key % 'C_0')
def C_0(logit_C_0=logit_C_0):
return mc.invlogit(logit_C_0)
# Initial population without condition
@mc.deterministic(name=key % 'S_0')
def SC_0(C_0=C_0):
return np.array([1. - C_0, C_0]).ravel()
vars[key % 'bins'] = {'initial': [SC_0, C_0, logit_C_0]}
# iterative solution to difference equations to obtain bin sizes for all ages
import scipy.linalg
@mc.deterministic(name=key % 'bins')
def SCpm(SC_0=SC_0, i=i, r=r, f=f, m_all_cause=m_all_cause, age_mesh=dm.get_param_age_mesh()):
SC = np.zeros([2, len(age_mesh)])
p = np.zeros(len(age_mesh))
m = np.zeros(len(age_mesh))
SC[:,0] = SC_0
p[0] = SC_0[1] / (SC_0[0] + SC_0[1])
m[0] = trim(m_all_cause[age_mesh[0]] - f[age_mesh[0]] * p[0], .1*m_all_cause[age_mesh[0]], 1-NEARLY_ZERO)
for ii, a in enumerate(age_mesh[:-1]):
A = np.array([[-i[a]-m[ii], r[a] ],
[ i[a] , -r[a]-m[ii]-f[a]]]) * (age_mesh[ii+1] - age_mesh[ii])
SC[:,ii+1] = np.dot(scipy.linalg.expm(A), SC[:,ii])
p[ii+1] = trim(SC[1,ii+1] / (SC[0,ii+1] + SC[1,ii+1]), NEARLY_ZERO, 1-NEARLY_ZERO)
m[ii+1] = trim(m_all_cause[age_mesh[ii+1]] - f[age_mesh[ii+1]] * p[ii+1], .1*m_all_cause[age_mesh[ii+1]], 1-NEARLY_ZERO)
SCpm = np.zeros([4, len(age_mesh)])
SCpm[0:2,:] = SC
SCpm[2,:] = p
SCpm[3,:] = m
return SCpm
vars[key % 'bins']['age > 0'] = [SCpm]
# prevalence = # with condition / (# with condition + # without)
@mc.deterministic(name=key % 'p')
def p(SCpm=SCpm, param_mesh=dm.get_param_age_mesh(), est_mesh=dm.get_estimate_age_mesh()):
return dismod3.utils.interpolate(param_mesh, SCpm[2,:], est_mesh)
data = [d for d in data_list if d['data_type'] == 'prevalence data']
prior_dict = dm.get_empirical_prior('prevalence')
if prior_dict == {}:
prior_dict.update(alpha=np.zeros(len(X_region)),
beta=np.zeros(len(X_study)),
gamma=-5*np.ones(len(est_mesh)),
sigma_alpha=[1.],
sigma_beta=[1.],
sigma_gamma=[10.],
# delta is filled in from the global prior dict in neg_binom setup
)
vars[key % 'prevalence'] = rate_model.setup(dm, key % 'prevalence', data, p, emp_prior=prior_dict)
p = vars[key % 'prevalence']['rate_stoch'] # replace perfectly consistent p with version including level-bound priors
# make a blank prior dict, to avoid weirdness
blank_prior_dict = dict(alpha=np.zeros(len(X_region)),
beta=np.zeros(len(X_study)),
gamma=-5*np.ones(len(est_mesh)),
sigma_alpha=[1.],
sigma_beta=[1.],
sigma_gamma=[10.],
delta=100.,
sigma_delta=1.
)
# cause-specific-mortality is a lower bound on p*f
@mc.deterministic(name=key % 'pf')
def pf(p=p, f=f):
return (p+NEARLY_ZERO)*f
# TODO: add a 'with-condition population mortality rate date' type
# data = [d for d in data_list if d['data_type'] == 'with-condition population mortality rate data']
data = []
lower_bound_data = [d for d in data_list if d['data_type'] == 'cause-specific mortality data']
vars[key % 'prevalence_x_excess-mortality'] = rate_model.setup(dm, key % 'pf', rate_stoch=pf, data_list=data, lower_bound_data=lower_bound_data, emp_prior=blank_prior_dict)
# m = m_all_cause - f * p
@mc.deterministic(name=key % 'm')
def m(SCpm=SCpm, param_mesh=dm.get_param_age_mesh(), est_mesh=dm.get_estimate_age_mesh()):
return dismod3.utils.interpolate(param_mesh, SCpm[3,:], est_mesh)
vars[key % 'm'] = m
# m_with = m + f
@mc.deterministic(name=key % 'm_with')
def m_with(m=m, f=f):
return m + f
data = [d for d in data_list if d['data_type'] == 'mortality data']
# TODO: test this
#prior_dict = dm.get_empirical_prior('excess-mortality') # TODO: make separate prior for with-condition mortality
vars[key % 'mortality'] = rate_model.setup(dm, key % 'm_with', data, m_with, emp_prior=blank_prior_dict)
# mortality rate ratio = mortality with condition / mortality without
@mc.deterministic(name=key % 'RR')
def RR(m=m, m_with=m_with):
return m_with / (m + .0001)
data = [d for d in data_list if d['data_type'] == 'relative-risk data']
vars[key % 'relative-risk'] = log_normal_model.setup(dm, key % 'relative-risk', data, RR)
# standardized mortality rate ratio = mortality with condition / all-cause mortality
@mc.deterministic(name=key % 'SMR')
def SMR(m_with=m_with, m_all_cause=m_all_cause):
return m_with / (m_all_cause + .0001)
data = [d for d in data_list if d['data_type'] == 'smr data']
vars[key % 'smr'] = log_normal_model.setup(dm, key % 'smr', data, SMR)
# duration = E[time in bin C]
@mc.deterministic(name=key % 'X')
def X(r=r, m=m, f=f):
hazard = r + m + f
pr_not_exit = np.exp(-hazard)
X = np.empty(len(hazard))
X[-1] = 1 / hazard[-1]
for i in reversed(range(len(X)-1)):
X[i] = pr_not_exit[i] * (X[i+1] + 1) + 1 / hazard[i] * (1 - pr_not_exit[i]) - pr_not_exit[i]
return X
data = [d for d in data_list if d['data_type'] == 'duration data']
vars[key % 'duration'] = normal_model.setup(dm, key % 'duration', data, X)
# YLD[a] = disability weight * i[a] * X[a] * regional_population[a]
@mc.deterministic(name=key % 'i*X')
def iX(i=i, X=X, p=p, pop=rate_model.regional_population(key)):
return i * X * (1-p) * pop
vars[key % 'incidence_x_duration'] = {'rate_stoch': iX}
return vars
def setup(dm, key, data_list, rate_stoch):
""" Generate the PyMC variables for a normal model of
a function of age
Parameters
----------
dm : dismod3.DiseaseModel
the object containing all the data, priors, and additional
information (like input and output age-mesh)
key : str
the name of the key for everything about this model (priors,
initial values, estimations)
data_list : list of data dicts
the observed data to use in the beta-binomial liklihood function
rate_stoch : pymc.Stochastic
a PyMC stochastic (or deterministic) object, with
len(rate_stoch.value) == len(dm.get_estimation_age_mesh()).
Results
-------
vars : dict
Return a dictionary of all the relevant PyMC objects for the
normal model. vars['rate_stoch'] is of particular
relevance, for details see the beta_binomial_model
"""
vars = {}
est_mesh = dm.get_estimate_age_mesh()
if np.any(np.diff(est_mesh) != 1):
raise ValueError, 'ERROR: Gaps in estimation age mesh must all equal 1'
vars['rate_stoch'] = rate_stoch
# set up priors and observed data
prior_str = dm.get_priors(key)
generate_prior_potentials(vars, prior_str, est_mesh)
vars['observed_rates'] = []
for d in data_list:
# set up observed stochs for all relevant data
id = d['id']
if d['value'] == MISSING:
print 'WARNING: data %d missing value' % id
continue
# ensure all rate data is valid
d_val = dm.value_per_1(d)
d_se = dm.se_per_1(d)
if d['age_start'] < est_mesh[0] or d['age_end'] > est_mesh[-1]:
raise ValueError, 'Data %d is outside of estimation range---([%d, %d] is not inside [%d, %d])' \
% (d['id'], d['age_start'], d['age_end'], est_mesh[0], est_mesh[-1])
age_indices = indices_for_range(est_mesh, d['age_start'], d['age_end'])
age_weights = d.get('age_weights', np.ones(len(age_indices)) / len(age_indices))
# data must have standard error to use normal model
if d_se == 0:
raise ValueError, 'Data %d has invalid standard error' % d['id']
@mc.observed
@mc.stochastic(name='obs_%d' % id)
def obs(f=rate_stoch,
age_indices=age_indices,
age_weights=age_weights,
value=d_val,
tau=1./(d_se)**2):
f_i = rate_for_range(f, age_indices, age_weights)
return mc.normal_like(value, f_i, tau)
vars['observed_rates'].append(obs)
return vars