:orphan: 

.. _simultaneous_vs_separate_fit:

Separate Vs Simultaneous Fitting
###################################

When we want to model both the time course of the drug in the plasma and the effect it has on a biomarker, there are two options open to us.

We can write one simultaneous model where the concentration of a drug in one compartment directly affects the biomarker in another.

Alternatively, we can write one model for the PK part and then a separate model for the PD part, using estimates from the first part to fix parameters in the PD model.

Both strategies have advantages and disadvantages in different situations.

In most cases, a separate fit is used because it takes less computational time and the results are similar (http://www.ncbi.nlm.nih.gov/pubmed/15000421).

However, when the PK data is sparse (few measurements per individual) and the PD data is rich (more measurements per individual), the extra information provided by the PD data may lead to a more accurate model if a simultaneous fit is used. In a real modelling situation we would not know the generating values, in contrast to the following examples, which means we do not know which method is more accurate. If there are are more PD observations than PK observations it is worth considering a simultaneous fit. 

Here are some examples of PKPD model where models are fitted simultaneously, then both PK and PD models are fit separately.

For each model, we then take away some of the PK data to see how this affects the simultaneous and separate fits. 

Simple PKPD Model
==================

Simultaneous fit with same number of observations
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.. include:: simul_vs_sep_pd/simple_equal_simul_fit.txt

PK fit with same number of observations
------------------------------------------------------    
.. include:: simul_vs_sep_pd/simple_equal_pk_fit.txt
            
PD fit with same number of observations
------------------------------------------------------   
.. include:: simul_vs_sep_pd/simple_equal_pd_fit.txt

Simultaneous fit with sparse PK data and rich PD data
------------------------------------------------------
.. include:: simul_vs_sep_pd/simple_unequal_simul_fit.txt

PK fit with sparse PK data 
------------------------------------------------------
.. include:: simul_vs_sep_pd/simple_unequal_pk_fit.txt

PD fit with sparse PK data and rich PD data
------------------------------------------------------   
.. include:: simul_vs_sep_pd/simple_unequal_pd_fit.txt


Emax PKPD Model
==================

Emax Simultaneous fit with same number of observations
------------------------------------------------------
.. include:: simul_vs_sep_pd/emax_equal_simul_fit.txt

Emax PK fit with same number of observations
------------------------------------------------------    
.. include:: simul_vs_sep_pd/emax_equal_pk_fit.txt
            
Emax PD fit with same number of observations
------------------------------------------------------   
.. include:: simul_vs_sep_pd/emax_equal_pd_fit.txt

Emax Simultaneous fit with sparse PK data and rich PD data
------------------------------------------------------------
.. include:: simul_vs_sep_pd/emax_unequal_simul_fit.txt

Emax PK fit with sparse PK data 
------------------------------------------------------
.. include:: simul_vs_sep_pd/emax_unequal_pk_fit.txt

PD fit with sparse PK data and rich PD data
------------------------------------------------------   
.. include:: simul_vs_sep_pd/emax_unequal_pd_fit.txt


Absorption PKPD Model
========================
.. include:: simul_vs_sep_pd/abs_equal_simul_fit.txt

Absorption PK fit with same number of observations
------------------------------------------------------------    
.. include:: simul_vs_sep_pd/abs_equal_pk_fit.txt
    
Absorption PD fit with same number of observations
------------------------------------------------------------   
.. include:: simul_vs_sep_pd/abs_equal_pd_fit.txt

Absorption Simultaneous fit with sparse PK data and rich PD data
------------------------------------------------------------------
.. include:: simul_vs_sep_pd/abs_unequal_simul_fit.txt

Absorption PK fit with sparse PK data 
------------------------------------------------------------
.. include:: simul_vs_sep_pd/abs_unequal_pd_fit.txt
    
Absorption PD fit with sparse PK data and rich PD data
------------------------------------------------------------  
.. include:: simul_vs_sep_pd/abs_unequal_pd_fit.txt

