:orphan:

Sparse Individual Data
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One of the advantages of using population pharmacokinetics is that it allows the use of sparse data from each individual.

..
    :ref:`sparse_data_model` is an example of a two compartment model with first order absorption.

The drug is dosed at 100mg every 12 hours for 10 days. On the tenth day, three samples are taken from each of the 40 individuals. The first sample is taken between 0.5 and 2 hours after the last dose, the second sample between 4 and 8 hours after the last dose and the final sample between 10 and 11.9 hours after the last dose.

Despite the small amount of information on each individual, |popy| is able to produce estimates close to the those used to generate the data:

.. csv-table:: Parameter values estimated from sparse data
    :header: "Parameter", "Generation", "Start Value", "|popy| Estimate"
    
    KA            , 0.5           , 0.2          , 0.43
    CL            , 1.2           , 1.0          , 1.38
    V2            , 12            , 15           , 9.5
    Q             , 0.5           , 1.0          , 0.99
    V3            , 30            , 40           , 34.4
    PNOISE        , 0.3           , 0.5          , 0.28
    KA_isv        , 0.36          , 0.5          , 0.16
    CL_isv        , 0.2025        , 0.2          , 0.196
    V2_isv        , 0.16          , 0.2          , 0.11
    Q_isv         , 0.04          , 0.1          , 0.03
    V3_isv        , 0.25          , 0.2          , 0.14

Problems with Q. Doesn't move much away from starting value.
