Design Operating Characteristics
evaluating_properties.Rmd
Design operating characteristics to evaluate the properties of a
particular design via simulation the function mams.sim
can
be used. It allows for flexible numbers of subjects per arm and stage in
the form of a J
× (K
+ 1) matrix
nMat
. In addition to the upper and lower boundaries
(u
and l
), a vector of true success
probabilities (pv
) is required (or alternatively a vector
of true effect sizes (deltav
) and a standard deviation
(sd
)). The parameter ptest
allows to specify
rejection of which hypotheses should be counted in the power
calculation. We evaluate the properties of the two-stage design
m2
under the global null hypothesis (i.e., a true effect
size of
or
for all treatments) with 100,000 simulation runs.
m2sim <- mams.sim(nsim = 1e5, nMat = t(m2$n * m2$rMat), u = m2$u, l = m2$l,
pv = rep(0.5, 3), ptest = 1:2)
m2sim
The probability of rejecting at least one hypothesis is 0.050, and
since we simulated under the global
,
this corresponds to a FWER of 5% as desired. The power
to reject the first hypothesis when it has the largest estimated effect
is 0.016, and the power to reject either
or
or both of them (as specified by ptest = 1:2
) is 0.034. The
expected number of patients required for the trial under the global
is 244.7 in contrast to the maximum required of 380. The function
mams.sim
is also useful to simulate and compare expected
sample sizes of different designs. We illustrate this for the designs
poc
, obf
and tri
(whose
boundaries are shown in Multi-stage
design) under the LFC of the alternative, i.e., one treatment’s
effect size equals.
Design | Minimum | Maximum | Expected (LFC) | Expected (H0) |
---|---|---|---|---|
Pocock | 132 | 396 | 232.2 | 385.6 |
O'Brien-Fleming | 112 | 336 | 259.1 | 322.0 |
Triangular | 136 | 408 | 217.8 | 222.1 |
whereas the effect sizes for all other treatments are equal to , using 100,000 simulation runs.
pocsim <- mams.sim(nsim = 1e5, nMat = t(poc$n * poc$rMat), u = poc$u, l = poc$l,
pv = c(0.65, rep(0.55, 2)), ptest = 1)
obfsim <- mams.sim(nsim = 1e5, nMat = t(obf$n * obf$rMat), u = obf$u, l = obf$l,
pv = c(0.65, rep(0.55, 2)), ptest = 1)
trisim <- mams.sim(nsim = 1e5, nMat = t(tri$n * tri$rMat), u = tri$u, l = tri$l,
pv = c(0.65, rep(0.55, 2)), ptest = 1)
Similarly, we can obtain the design properties under the global null
hypothesis by setting pv = rep(0.5, 3)
. Table summarizes
minimum, maximum, and expected sample sizes of the three designs. We see
that under both the LFC and the global
the triangular design is expected to require the lowest number of
patients. On the other hand, O’Brien-Fleming has the lowest minimum and
maximum but the highest expected sample size under the LFC of all three
designs. Under the global
both the Pocock and O’Brien-Fleming designs have expected sample sizes
that are very close to their respective maxima.