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lines 27-246 of file: example/user/diabetes.py
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# {xrst_begin user_diabetes.py}
# {xrst_spell
#     bmi
#     def
#     elif
#     exp
#     mtspecific
#     rel
# }
# {xrst_comment_ch #}
#
# An Example Fitting Simulated Diabetes Data
# ##########################################
# This example fits iota and chi using only prevalence and mtspecific data.
# It is designed so that you are changed the setting documented below.
# See :ref:`user_example@Run One Example` for instruction on running this
# example.
#
# random_seed
# ***********
# This integer is used to seed the random number generator.
# If it is zero, the current number of seconds on the system clock is used.
# {xrst_code py}
random_seed = 0
# {xrst_code}
#
# age_list, time_list
# *******************
# These are the ages and times at which we simulate the data.
# They are also the ages and times where we model iota and chi.
# {xrst_code py}
age_list  = [ 0.0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 ]
time_list = [ 1980, 1990, 2000, 2010, 2020 ]
# {xrst_code}
#
# number_nodes
# ************
# This integer is the number of nodes.
# If it is one, there are no child nodes (hence no random effects).
# Otherwise, there are *number_nodes* - 1 child nodes.
# {xrst_code py}
number_nodes = 10
# {xrst_code}
#
# sim_std_random_effect
# *********************
# If there are child nodes, the random effect for each node is simulated
# using a Gaussian with this standard deviation.
# For each child node, the same random effect is used for both iota and chi.
# {xrst_code py}
sim_std_random_effect = 0.2
# {xrst_code}
#
# sim_mulcov
# **********
# This python dictionary contains the covariate multiplier values used
# to simulate the data.
# In this example, there is one covariate multiplier for each covariate,
# so we use the covariate names to identify the multipliers:
# {xrst_code py}
sim_mulcov = { 'sex':0.4, 'bmi':0.02, 'ms_2000':0.3  }
# {xrst_code}
#
# .. csv-table::
#  :header-rows: 1
#
#  Name,    Covariate Value,                Affects
#  sex,     (female=-0.5) (male=0.5),       chi
#  bmi,     body mass index,                iota
#  ms_2000, 1 (0) if year is (is not) 2000, prevalence
#
# sim_no_effect_rate
# ******************
# This is the value used to simulate the no effect rates; i.e.,
# the rates before the random effects and covariate effects are included.
# The dismod_at model for iota, chi and omega are constant with respect to
# age and time outside the grid limits for the corresponding rate.
# The last age is not included in the iota age grid because there
# is no prevalence data after it. Hence iota is constant for ages after
# the next to last age.
# The first age is not included in the chi age grid because prevalence
# is zero at that age (and mtspecific does not inform chi).
# Hence chi is constant for ages before the second age.
# {xrst_code py}
def sim_no_effect_rate(rate_name, age, time) :
   time     = min( time_list[-1], max(time_list[0], age) )
   age_exp  = - abs(age - 50.0) / 100.00
   time_exp = - abs(time - 2000.0) / 40.0
   if rate_name == 'iota' :
      age  = min( age_list[-2], max(age_list[0], age) )
      rate = 0.001 * ( 1.0 + math.exp(age_exp) + math.exp(time_exp) )
   elif rate_name == 'chi' :
      # chi is currently constant so age does not matter, but we set it here
      # incase you change that.
      age  = min( age_list[-1], max(age_list[1], age) )
      rate = 0.02
   elif rate_name == 'omega' :
      # For this example, omega must be constant for all age and time
      # (the value of omega does not affect prevalence or mtspecific).
      rate = 0.01
   else :
      rate = None
      assert False
   return rate
# {xrst_code}
#
# model_meas_cv
# *************
# The measurements are simulated without noise, but the model
# has this level of measurement nose (express as a coefficient of variation):
# {xrst_code py}
model_meas_cv = 0.1
# {xrst_code}
#
# minimum_prevalence_std
# **********************
# In this model, initial prevalence is zero. Hence a coefficient of variation
# model for the measurement noise does not work at age zero.
# We use a minimum prevalence standard deviation to avoid this problem:
# {xrst_code py}
minimum_prevalence_std = 1e-4
# {xrst_code}
#
# ode_step_size
# *************
# This is the option table :ref:`option_table@Age Average Grid@ode_step_size`
# value.
# {xrst_code py}
ode_step_size = 5.0
# {xrst_code}
#
# hold_out_max_fit
# ****************
# This is the hold out command :ref:`hold_out_command@max_fit` value.
# It is used to hold out prevalence and mtspecific data.
# {xrst_code py}
hold_out_max_fit = 250
# {xrst_code}
#
# fixed_effect_rel_error_bnd
# **************************
# This is a bound on the relative error in the fixed effects estimates.
# If the relative error is greater that this for a fixed effect,
# a message that identifies the fixed effect and the relative error is
# printed and this program will exit with a non-zero error flag.
# {xrst_code py}
fixed_effect_rel_error_bnd = 0.1
# {xrst_code}
#
# Priors
# ******
#
# parent_rate_value_prior
# =======================
# This prior is used for the value of iota and chi, for the parent node,
# at each of the grid points in the corresponding smoothings.
# Note that omega is constrained to the value used for it during simulation.
# Also note that eta does not affect the density but it does affect the
# :ref:`prior_table@eta@Scaling Fixed Effects` .
# {xrst_code py}
parent_rate_value_prior = {
   'density': 'gaussian',
   'mean':    0.01,
   'std':     1.0,
   'lower':   1e-6,
   'upper':   1.0,
   'eta':     1e-6,
}
# {xrst_code}
#
# child_rate_value_prior
# ======================
# This prior is used for the log of iota and chi for the child nodes.
# These are random effects and are constant w.r.t. age, time; i.e.,
# there is only one grid point (one variable)
# for each node and each rate (iota and chi) .
# {xrst_code py}
child_rate_value_prior = {
   'density': 'gaussian',
   'mean':    0.0,
   'std':     0.1,
}
# {xrst_code}
#
# difference_prior
# ================
# This is the prior used for the forward difference (w.r.t. age and time)
# of the value of iota and chi between grid points.
# {xrst_code py}
difference_prior = {
   'density': 'log_gaussian',
   'mean':    0.0,
   'std':     0.4,
   'eta':     1e-6,
}
# {xrst_code}
#
# mulcov_prior
# ============
# This is the value prior used for each of the covariate multipliers.
# These are fixed effects and are constant w.r.t age, time.
# The mean does not affect the density and
# is used as a starting point for the first optimization.
# (The first optimization is just w.r.t the fixed effects and is used to get
# a starting point for optimization w.r.t. both the fixed and random effects.)
# {xrst_code py}
mulcov_prior = {
   'density': 'uniform',
   'mean':    0.0,
}
# {xrst_code}
#
# Source Code
# ***********
# {xrst_literal
#     # BEGIN_SOURCE_CODE
#     # END_SOURCE_CODE
# }
#
# {xrst_end user_diabetes.py}