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This is a major release. It corrects the p-value of the exact unconditional tests, adds two-sided alternatives, the Berger-Boos procedure and a function for re-estimating the sample size from observed interim data, and moves the inner loops to compiled code. The user interface has changed in ways that are not backward compatible, which is why the major version number has been raised.
The exact unconditional tests accumulated the null probabilities
along an arbitrary ordering of the outcomes. Outcomes sharing the same
value of the ordering statistic were therefore split, and could receive
different p-values. With N1 = N2 = 7 the outcomes
(x1, x2) = (5, 1) and (6, 2) both have a
Fisher p-value of 2/39 and cannot be distinguished by the Boschloo test,
yet the old code assigned them 0.0216 and 0.0287 and rejected at the
first but not the second. Tied values are now grouped explicitly and
every member of a group receives the tail probability accumulated up to
the last member of that group. The rejection region no longer depends on
how the sorting routine breaks ties.
The Z-pooled branch indexed the matrix of binomial probabilities by the responder count rather than by the position of that count among the retained values. The two coincided in the configurations reached by the old code, so the results were correct, but the indexing broke as soon as the retained counts were not contiguous.
The Boschloo branch discarded outcomes whose Fisher p-value was not below the smallest Fisher p-value among outcomes with a non-positive risk difference. The truncation was sound but had no natural counterpart for a two-sided alternative, and it has been removed. The whole outcome grid is now scanned, which the move to compiled code makes affordable.
pmin(1, x) with a scalar first argument drops the
dim attribute of x. This affected the matrix
of p-values returned for a two-sided chi-squared test.
The allocation ratio was not preserved by the re-estimation when
r was not 1. The interim size of group 1 was
ceiling(omega N1) and the second-stage size was
ceiling(r N22), so the final size of group 1 was rounded up
three separate times and did not equal ceiling(r) times the
final size of group 2. With r = 2, N2 = 33 and
omega = 0.8 the interim allocation was 53 to 27 rather than
54 to 27, and a re-estimated control group of 40 gave 79 rather than 80
in group 1. Both the interim and the final size of group 1 are now
obtained from the size of group 2 by a single
ceiling(r ...), and the second stage follows as the
difference. The allocation ratio is therefore exact whenever
r is a whole number, and as close as whole numbers allow
otherwise. Results for r = 1 are unchanged.
BinaryBSSR() brings group 1 to
ceiling(r N2.final) for the same reason, which also
corrects an imbalance that is already present in the observed interim
data.
All five tests accept alternative = 'greater' (the
default, and the behaviour of version 1) or
alternative = 'two.sided'. For the conditional tests the
two-sided p-value follows the convention selected by
tsmethod, either 'minlike', which matches
stats::fisher.test, or 'central'. The
chi-squared and Z-pooled tests order outcomes by the absolute value of
the Z statistic when the alternative is two-sided.
The number of grid points used to search over the nuisance
parameter of the unconditional tests is now the argument
n.grid, which defaults to 100 and reproduces the grid of
version 1. A finer grid gives larger p-values and a more accurate
test.
The Berger-Boos procedure is available through the argument
bb.gamma. A positive value restricts the search over the
nuisance parameter to an exact Clopper-Pearson confidence interval
computed from the observed number of responders, and adds
bb.gamma to the resulting p-value. The default of 0
disables the procedure.
BinaryBSSR() re-estimates the sample size from the
blinded data of a trial that is under way. It takes the interim sample
size of each group and the pooled number of responders, and returns the
number of patients still to enrol in each group. This complements
BinaryPowerBSSR(), which evaluates a re-estimation rule at
the planning stage.
Every function returns a classed object with a
print() method, and BinaryRR(),
BinaryPower(), BinarySampleSize() and
BinaryPowerBSSR() also have a plot() method.
The classes are bbssr_rr, bbssr_power,
bbssr_samplesize, bbssr_powerbssr and
bbssr_bssr.
The plot() methods accept main,
sub, xlab, ylab,
base_size and colours, so the title, the axis
labels, the font size and the palette can be replaced without editing
the returned object. A label left at NULL keeps the text
built from the object and a label set to NA is dropped.
Where a legend is drawn, legend.title and
legend.labels rename it, and where a vertical scale is
continuous, ylim sets its range through
coord_cartesian(), which hides rather than removes the
points outside the range. The reference lines are no longer fixed:
plot.bbssr_powerbssr() and
plot.bbssr_samplesize() take ref.line, and
plot.bbssr_samplesize() also takes
ref.line.N2. The methods that draw a curve also take
show.points, which removes the marker at each evaluated
point and leaves the curve alone, so a fine grid stays legible. This
matters when Delta.T is 0, since the two power columns of
BinaryPowerBSSR() are then rejection probabilities under
the null hypothesis and the line belongs at the level of significance
rather than at the target power. The defaults reproduce the earlier
plots exactly.
BinaryPowerBSSR() reports the expected total sample
size in a new column E.N, and carries the interim sample
sizes as the attributes n1.interim and
n2.interim.
Arguments are validated, and invalid sample sizes, significance levels, allocation ratios and grid sizes now produce an informative error.
The maximization over the nuisance parameter and the summation of
the binomial mass over the rejection region are implemented in C++
through Rcpp.
BinaryPowerBSSR() evaluates
BinarySampleSize() once per distinct pair of recovered
response probabilities and BinaryRR() once per distinct
pair of final sample sizes, rather than once per interim
outcome.
The weighted argument of
BinaryPowerBSSR() has been removed, along with the weighted
design it selected. Calls that supply it will fail with an unused
argument error.
The asmd.p1 and asmd.p2 arguments of
BinaryPowerBSSR() have been removed. They entered the
calculation only through the weights of the weighted design, so with
that design gone they had no effect on the result. The planning
assumption is carried by Delta.A together with the initial
sample sizes N1 and N2. Calls that supply them
will fail with an unused argument error.
BinaryPower() returns a one-row-per-scenario data
frame of class bbssr_power rather than a bare numeric
vector. Code that used the returned value directly should now read the
Power column.
BinaryRR() returns a logical matrix carrying the
class bbssr_rr and the design settings as attributes. The
matrix itself is unchanged, so indexing and sum() behave as
before, but printing now goes through
print.bbssr_rr().
BinarySampleSize() and
BinaryPowerBSSR() gained columns in their output, and
BinarySampleSize() returns integer rather than double
sample sizes.
restricted now defaults to FALSE in
BinaryPowerBSSR() instead of having no default.
ggplot2 and Rcpp have moved into
Imports, so a compiler is required to install the package
from source.
The vignettes have been rewritten and a fourth has been added.
bbssr-introduction covers the whole package,
bbssr-statistical-methods derives the tests and the
re-estimation rules, bbssr-interim-reestimation follows a
single trial from planning to the interim decision, and
bbssr-validation compares the package against
stats, Exact and exact2x2 and
reports timings.
The test suite has been rewritten around reference implementations that follow the definitions of the tests directly, so the p-values are checked against a direct evaluation rather than against stored values.
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requested by CRAN.These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.