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lines 5-123 of file: xrst/table/integrand_table.xrst
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{xrst_begin integrand_table}

The Integrand Table
###################

Discussion
**********
The ``integrand`` table is used to identify data integrands.
It has the following columns:

integrand_id
************
This column has type ``integer``
and is the primary key for this table.
Its initial value is zero, and it increments by one for each row.

minimum_meas_cv
***************
This column has type ``real`` and is non-negative
and less than or equal one.
It specifies the minimum coefficient of variation for measurement values
with this integrand.
To be specific; for the data table
:ref:`data_table@integrand_id` is the same,
:ref:`data_table@meas_value` is the measurement value, and
:ref:`data_table@meas_std` is the measurement standard,
the minimum cv measurement standard deviation is

   *Delta* = ``max`` ( *meas_std* , *minimum_meas_cv* * | *meas_value* | )

see :ref:`Delta<data_like@Notation@Minimum CV Standard Deviation, Delta_i>`
in the data likelihood section.

integrand_name
**************
This column has type ``text`` .
The following is a list of the possible values for *integrand_name* .
This column is unique; i.e., each name can only appear once in this table.
All of the *integrand_id* values that appear in the
:ref:`data<data_table@integrand_id>` and
:ref:`avgint<avgint_table@integrand_id>` tables
need to appear in the integrand table.

ODE
===
If the column ODE below is yes, and a data point has a
:ref:`rate covariate<mulcov_table@mulcov_type@rate_value>`
that is not equal to its
:ref:`covariate_table@reference` value, the
:ref:`avg_integrand@Differential Equation`
needs to be solved for each cohort
that intersects or surrounds the age-time span for this data point.
(The space between cohorts is determined by the
:ref:`option_table@Age Average Grid@ode_step_size` .)

This computation is preformed each time the :ref:`model_variables-name` change.

Names
=====

.. list-table::
   :widths: auto

   * - Integrand Name
     - Description
     - ODE
   * - :ref:`avg_integrand@Integrand, I_i(a,t)@Sincidence`
     - incidence rate relative to susceptible population
     - no
   * - :ref:`avg_integrand@Integrand, I_i(a,t)@remission`
     - remission rate
     - no
   * - :ref:`avg_integrand@Integrand, I_i(a,t)@mtexcess`
     - excess mortality rate
     - no
   * - :ref:`avg_integrand@Integrand, I_i(a,t)@mtother`
     - other cause mortality rate
     - no
   * - :ref:`avg_integrand@Integrand, I_i(a,t)@mtwith`
     - with condition mortality rate
     - no
   * - :ref:`avg_integrand@Integrand, I_i(a,t)@relrisk`
     - relative risk
     - no
   * - :ref:`avg_integrand@Integrand, I_i(a,t)@susceptible`
     - susceptible fraction of the population
     - yes
   * - :ref:`avg_integrand@Integrand, I_i(a,t)@withC`
     - with condition fraction of the population
     - yes
   * - :ref:`avg_integrand@Integrand, I_i(a,t)@prevalence`
     - prevalence of the condition
     - yes
   * - :ref:`avg_integrand@Integrand, I_i(a,t)@Tincidence`
     - incidence rate relative to total population
     - yes
   * - :ref:`avg_integrand@Integrand, I_i(a,t)@mtspecific`
     - cause specific mortality rate
     - yes
   * - :ref:`avg_integrand@Integrand, I_i(a,t)@mtall`
     - all cause mortality rate
     - yes
   * - :ref:`avg_integrand@Integrand, I_i(a,t)@mtstandard`
     - standardized mortality ratio
     - yes
   * - ``mulcov_`` *mulcov_id*
     - the group covariate multiplier specified by
       :ref:`mulcov_table@mulcov_id`
     - no

{xrst_toc_hidden
   example/table/integrand_table.py
}
Example
*******
The file :ref:`integrand_table.py-name`
contains an example ``integrand`` table.

{xrst_end integrand_table}