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Chapter 2.4
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mixed effect models are used to calculate posterior probabilities of treatment response.
The methods result in a dynamic individualized update of the prediction of
response. The approaches were applied to data on the peginterferon treatment of
chronic hepatitis B and their predictive performance were compared.
The modelling approaches are very flexible in that they allow inclusion of more than
one biomarker. The biomarkers may be described by complex mixed modelling if
necessary, however one has to be aware not to overfit. For the indirect approach
splines were used to describe the decline of viral load and ALT of a hepatitis B patient.
Instead of linear mixed models, non-linear mixed models might be considered
or ordinal distributed biomarkers might be modelled. Fieuws et al. 15 studied multivariate
longitudinal profiles allowing a joint distribution of the random effects. They
further16 used non-linear mixed of longitudinal profiles designing a set of classification
rules. Komárek et al. 17 relaxed the normal assumption of the random effects
biomarkers studying a heteroscedastic multivariate normal mixture for the random
effects. The direct approach with the observed biomarkers enables as the term say
direct inclusion of any marker, ordinal or non-linear as well as inclusion of interaction
over time.
The indirect method and the direct method, which uses the parameters describing
the patterns of the biomarkers over time, have one small drawback being the computational
programming, which is elaborate and time consuming and new estimates
need to be established for a future subject before predictions can be calculated. In
contrast, standard statistical procedures are available for the direct method of the
observed markers and a prediction model can be expressed7 which directly can be
applied to a future subject. This model though, has limited memory of the patterns
of the biomarkers (depending on inclusion of the markers at previous visits), which
can be an advantage in the situation were the last observed biomarkers predicts
the outcome well, and a disadvantage if the prediction of the outcome is better
associated with the total pattern of the markers. In the situation of response of
peginterferon treatment the last observed load predicts just as well as the estimated
decline.
In our situation we studied a binary outcome. Brant and Morrell used the indirect
method in several clinical studies. 9,10,18 Especially they focused on longitudinal
measurements of the prostate specific antigen to predict prostate cancer. They
observe more than two outcome categories (ex. no cancer, low risk, high risk) and
constructs an elegant stopping rule depending on posterior probabilities over time.
Our clinical situation is simpler, but therefore also allows us to easily study different
stopping rules. In case of more than two outcome categories a generalized logit