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Dynamic prediction of response using longitudinal profi les 91
Results of the longitudinal prediction with the direct approach
First the result of the logistic regression method is presented. In a previous study13,14 of the response to therapy a prognostic model of baseline factors were designed and
validated, and a alongside prognostic indexes (PI0) were calculated (as described
in Section 3). In this updating pooled logistic regression model the subject specific
PI’s are used as offsets. The final model to predict response using the data of all
patients, n=125 and the repeated measurements of the load and the ALT the first
32 weeks of therapy is
logit pi,j = logit Pr(Ri =1|visit week = ti,j, loadi,j,ln(alt)i,j, offset = PIi,0)
= α + βT ti,j + βloadloadi,j + βaltln(alti,j)+PIi,0
This model was obtained by comparing Akaike’s Information Criterium (AIC’s), the
log likelihood and the Area Under the receiver operating Curve (AUC); i.e. the cstatistic
of different models, Steyerberg, chapter 11 and 16. 11 The model did not
improve by adding B-splines (Steyerberg, chapter 12) 11 of load, of ALT or of time,
neither by adding interaction terms with baseline variables nor by extending with the
load or the ALT of the previous visit.
For individual prediction of the response for subject i, the model above was refitted
leaving out subject i. This gives a cross-validated prediction for each patient. To
illustrate the results of the fitted model the individual prediction of 3 typical subjects
are plotted in figure 3. Figure 3.a is a responder with an early drop of HBV DNA
around week 16 and a steady decline of ALT to normal-levels, the baseline prediction
of response was 62%. The dynamic prediction of response changes to around 90%
after week 16. Two non-responders are plotted in 3.b and 3.c. The subject in 3.b
had at baseline already a low prediction of response around 10%, the load declines
0.5 log the first 20 weeks and only from week 24 a decline is seen, the prediction
of response changes little over time and stays around 10%. In 3.c the subject with
genotype C experiences a sudden drop of HBV DNA at week 12 just to return to
baseline levels at the next visit. This pattern is not often seen (in this specific case
probably an error occurred at the laboratory, however this could not be confirmed)
but may illustrate what happens in the case where a dose-reduction is anticipated or
the subject does not adhere to treatment. However the direct prediction approach
with the observed markers do not seem to suffer from this; the prediction of response
gave an increase of response at week 12 and a decrease afterwards.
The individual predictions of response over time for all subjects are plotted in figure
4 separate for non-responders and responders.