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CPS1995 Daniel B. et al.
d. An Application
Table 1 shows the interval counts for both the study drug and active
comparator where the intervals represent regions of efficacious response
based on some biomarker in a subgroup of a clinical trial population
considered as having a severe disease status.
Using (2) the goodness-of-fit test results for normal distribution are given
in Table 2. For the active comparator (standard drug) the approximate chi-
square statistic had a p-value equal to 0.9544. This means that the observed
proportions do not significantly differ from the null proportions of a normal
distribution. In the case of the study drug (test drug) the approximate chi-
square statistic yielded a p-value equal to 0.4256. This also shows that the
observed proportions do not significantly differ from the null proportions of a
normal distribution. Thus, the efficacy response for the study and active drugs
can be assumed to have come from the normal distribution.

4. Discussion and Conclusion
The preceding sections provide a generalized linear mixed model method
for estimation and testing of parameters in an extrapolation setting when
observed information comes in the form of interval data. A likelihood
procedure is obtained by assuming that the underlying distribution comes
from the family of exponential distributions. Application of the approach was
shown in an extrapolation construction for a normal latent measurement
variable and a homogeneous Poisson latent count of events. Then using large
sample approximation, an approach for goodness-of fit testing that can be
extended to accommodate an extrapolation setting was shown. Utility of the
construction was then shown in a setting where efficacy is evaluated in a
subgroup of a clinical trial population using a marker of efficacy.
In conclusion, the concept of estimand allows an extrapolation approach
that can cover a broad array of applications and settings, including the case
when censoring is allowed. Useful expressions of estimators and tests are
given for application purposes, though they require sufficiently large sample
to be efficient. These expressions have an intrinsic weighting mechanism for
the different sources of data. The approach presented can be extended to
allow utilization of prior information expressed in terms of a power or
commensurate power model [Gamalo-Siebers et. al., (2017)] under a
hierarchical Bayesian model setting. Irrespective of the approach taken, these
models can be useful tools for extrapolation allowing one to model the
uncertainty as between-estimand variance, evaluate different scenarios
through simulation and calculate sample sizes.

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