:orphan: 



..
	Hazard/survival functions
	Check out Holford and Peace's paper on Alzheimer's
	Look at the example that uses the Richards function - should be possible to code it up in PoPy.
	Also has an example of an exponential model.
	Discuss symptomatic effects and progression-altering effects.

.. _disease_progression_models:
    
Disease Progression Models
==========================
Disease progression models [CookBies2016]_ describe the change in disease status over time. Most diseases will progress if left untreated and a disease progression model aims to capture this progress and model the effects of any treatment. Biomarkers are often used as proxies to measure disease status eg tumour size to measure cancer or fasting plasma glucose to measure Type II diabetes.

There are a number of possible disease progression models (see https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4294073/pdf/bcp0079-0018.pdf). A few simple models will be considered here.


Linear Disease Progression Model
--------------------------------
.. include:: disease_progression/linear_model.txt


Compartmental Disease Progression Model
---------------------------------------
.. include:: disease_progression/compartmental_model.txt
        

Exponential Disease Progression Model
-------------------------------------
.. include:: disease_progression/exponential_model.txt

        
EMAX Disease Progression Model
------------------------------
.. include:: disease_progression/emax_model.txt


Disease Progression Model with Placebo
--------------------------------------
.. include:: disease_progression/placebo_model.txt


Tumour Growth Model
-------------------
.. include:: disease_progression/tumour_growth_model.txt


..
    Leaving this out for the time being until I decide how to deal with IOV for a single individual.
    (It is perfectly sensible to consider this case.)
    
    Disease Progression Model with Interoccasional Variability
    -----------------------------------------------------------
    .. include:: disease_progression/interoccasion_variability_model.txt
