Docetaxel with prednisone or prednisolone for the treatment of ...

TABLE 28 Regression coefficients from Weibull model
Treatment Intercept Scale
mean (SE) mean (SE)
D + P (3-weekly) 3.214 (0.0546) 0.6482 (0.0438)
D + P (weekly) 3.078 (0.0447) 0.597 (0.0368)
M + P 3.036 (0.0447) 0.6184 (0.0371)
model. Furthermore, the use of the Markov model
to estimate mean survival enabled discounting to
be incorporated. Details of the intercept and scale
parameters for the D + P (weekly) arm of TAX
327 were requested in addition to the standard
errors for these coefficients for each of the three
comparators in this trial. Details of the information
reported in the economic review are reported
alongside the additional information provided on
request from Sanofi-Aventis in Table 28.
For the purposes of the probabilistic analysis, it is
also important to reflect the covariance between
the intercept and scale parameters from the
Weibull regression. The covariance matrix for
each intervention was supplied on request by
Sanofi-Aventis. This matrix was used to derive
the Cholesky decomposition matrix, which was
then used to allow for correlation when
generating the random normal draws for the
intercept and scale parameters in the probabilistic
simulation. 72 The covariance matrix and
associated Cholesky decomposition matrix are
reported in Table 29.
Since hazards are instantaneous, these need to be
converted to a transition probability for a given
period (e.g. cycle) and require use of the
TABLE 29 Covariance matrix and Cholesky decomposition
© Queen’s Printer and Controller of HMSO 2007. All rights reserved.
integrated hazard function. For the Weibull
distribution the integrated hazard function is
H(t) =
Health Technology Assessment 2007; Vol. 11: No. 2
t
∫ 0 h(u)du = u
Using this equation, the hazard rate was estimated
for each of the monthly cycles of the model.
Following this procedure, the hazard rates were
then converted into transition probabilities using
standard techniques. The (mean) hazard and
associated transition probabilities used in the first
12 cycles of the model are shown in Table 30 for
illustrative purposes, demonstrating how the
probabilities differ by intervention and by number
of cycles.
Since patient-level data were not available for any
of the other comparators, it was necessary to
derive an estimate of the relative treatment effect
for these to be applied in the model. Using the
Bucher approach outlined in the clinical
effectiveness review, indirect HRs were estimated
in order to include other comparators in the
economic model. In order to reflect the potential
correlation between the different interventions,
docetaxel-based regimens were assessed via an
estimate of the indirect HR versus D + P (3weekly)
and mitoxantrone/prednisone strategies
were assessed via the indirect hazard ratio in
relation to M + P. The indirect hazard ratios for
these additional comparators are shown in
Tables 31 and 32. The uncertainty associated with
each HR was characterised by assigning a normal
distribution to ln(HR).
The HR was then applied to the absolute hazard
for either D + P (3-weekly) or M + P and then
Treatment Covariance matrix Cholesky decomposition
Intercept Scale Intercept Scale
D + P (3-weekly) Intercept 0.002981 Intercept 0.0546
Scale 0.000925 0.001918 Scale 0.016941 0.040391
Intercept Scale Intercept Scale
D + P (weekly) Intercept 0.001998 Intercept 0.0447
Scale 0.000413 0.001354 Scale 0.009239 0.035621
Intercept Scale Intercept Scale
M + P Intercept 0.001998 Intercept 0.0447
Scale 0.000356 0.001376 Scale 0.007964 0.036235
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