interim.tsd.in: Interim analysis of first stage data of 2-stage 2x2 crossover...

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

Following the design scheme according to power.tsd.in the function performs the interim analysis of the first stage data.

Usage

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interim.tsd.in(alpha, weight, max.comb.test = TRUE, targetpower = 0.8,
                  GMR1, n1, CV1, df1 = NULL, SEM1 = NULL, theta1, theta2, 
                  GMR, usePE = FALSE, min.n2 = 4, max.n = Inf, 
                  fCpower = targetpower, fCrit = "CI", fClower, fCupper, fCNmax, 
                  ssr.conditional = c("error_power", "error", "no"), 
                  pmethod = c("exact", "nct", "shifted"))

Arguments

alpha

If one element is given, the overall one-sided significance level (not the adjusted level for stage 1). If two elements are given, the adjusted one-sided alpha levels for stage 1 and stage 2, respectively.
If missing, defaults to 0.05.

weight

Pre-defined weight(s) of stage 1. Note that using the notation from Maurer et al weight corresponds to information fraction, other literature may refer to sqrt(weight) as being the weight. weight must either contain one element (in case of max.comb.test = FALSE) or two elements (in case of max.comb.test = TRUE).
If missing, defaults to 0.5 for max.comb.test = FALSE and to c(0.5, 0.25) for max.comb.test = TRUE.

max.comb.test

Logical; if TRUE (default) the maximum combination test will be used, otherwise the standard combination test.

targetpower

Desired (overall) target power to declare BE at the end of the trial.

GMR1

Observed ratio of geometric means (T/R) of stage 1 data.

n1

Sample size of stage 1.

CV1

Observed coefficient of variation of the intra-subject variability of stage 1 (use e.g., 0.3 for 30%).

df1

Optional; Error degrees of freedom of stage 1 that can be specified in addition to n1.

SEM1

Optional; Standard error of the difference of means of stage 1 that can be specified in addition to CV1. Must be on additive scale (i.e. usually log-scale).

theta1

Lower bioequivalence limit. Defaults to 0.8.

theta2

Upper bioequivalence limit. Defaults to 1.25.

GMR

Assumed ratio of geometric means (T/R) to be used in power calculation for stage 1 and sample size re-estimation for stage 2.

usePE

If TRUE the sample size re-estimation is done with the observed point estimate (PE) of the treatment difference in stage 1.
Defaults to FALSE.
Note: The futility inspection via the power of stage 1 is always done with the planning value GMR.

min.n2

Minimum sample size of stage 2. Defaults to 4.
If the sample size re-estimation step gives a sample size for stage 2 less than min.n2, then min.n2 will be used for stage 2.

max.n

Maximum overall sample size stage 1 + stage 2.
This is not a futility criterion regarding the maximum sample size! If max.n is set to a finite value and the sample size re-estimation gives a sample size for stage 2 (n2) such that n1 + n2 > max.n, then the sample size for stage 2 will be set to n2 = max.n - n1.
Defaults to Inf, i.e., no constraint on the re-estimated sample size.

fCpower

Threshold for power monitoring step to decide on futility for cases where BE has not been achieved after stage 1: If BE has not been achieved after stage 1 and the power for stage 1 is greater than or equal to fCpower, then the study will be considered a failure.

See ‘Details’ for more information on the choice of fCpower.

fCrit

Futility criterion to use: "No" (no futility criterion regarding observed point estimate, confidence interval and maximum sample size), "PE" (observed point estimate of the geometric mean ratio from stage 1), "CI" (90% confidence interval of the geometric mean ratio from stage 1), "Nmax" (overall maximum sample size); or a combination thereof (concatenate abbreviations). Defaults to "CI".

fClower

Lower futility limit for the PE or CI of stage 1.
If the PE or CI is completely outside of fClower ... fCupper the study is to be stopped due to futility (not BE).
May be missing. If "PE" or "CI" is specified within fCrit, the default will be set to 0.8 for fCrit = "PE" or 0.95 for fCrit = "CI". If neither "PE" nor "CI" is specified within fCrit, there will be no futility constraint regarding point estimate or confidence interval from stage 1 (regardless of any specification of fClower and/or fCupper).

fCupper

Upper futility limit for the PE or CI of stage 1.
Analogous to fClower: Will be set to 1/fClower if missing.

fCNmax

Futility criterion regarding maximum sample size. If the determined sample size for stage 2 (n2) is such that n1 + n2 > fCNmax, the study will not continue to stage 2 and stopped due to futility (not BE).
If "Nmax" is specified within fCrit and argument fCNmax is missing, the value will be set to fCNmax = 4*n1. If "Nmax" is not specified within fCrit, then there will be no futility constraint regarding maximum sample size (regardless of any specification of fCNmax).

ssr.conditional

Method for sample size re-estimation step: "no" does not use conditional error rates nor the conditional estimated target power for the second stage, "error" uses conditional error rates for the second stage, and "error_power" uses both conditional error rates and the conditonal estimated target power for the second stage.
Defaults to "error_power".

See also ‘Details’.

pmethod

Power calculation method, also to be used in the sample size estimation for stage 2.
Implemented are "nct" (approximate calculations via non-central t-distribution, "exact" (exact calculations via Owen’s Q), and "shifted" (approximate calculation via shifted central t-distribution like in the paper of Potvin et al.)
In contast to power.tsd.in the default value here is "exact".

Details

The observed values of stage 1 (e.g. GMR1, n1, CV1) may be obtained based on the first stage data via the usual ANOVA approach.

The optional arguments df1 and SEM1 require a somewhat advanced knowledge (provided in the raw output from for example the software SAS, or may be obtained via emmeans::emmeans). However, it has the advantage that if there were missing data the exact degrees of freedom and standard error of the difference can be used, the former possibly being non-integer valued (e.g. if the Kenward-Roger method was used).

If ssr.conditional = "error_power", the design scheme generally calculates the conditional estimated target power of the second stage and uses this value as desired target power in the sample size re-estimation process. If fCpower > targetpower, then the conditional power may actually be negative. This does not seem sensible. Therefore, for such cases the desired target power for the sample size re-calculation will be set to targetpower.

Value

Returns an object of class "evaltsd" with all the input arguments and results as components. As part of the input arguments a component cval is also presented, containing the critical values for stage 1 and 2 according to the input based on alpha, weight and max.comb.test.
The class "evaltsd" has an S3 print method.

The results are in the components:

p11

Observed p-value for first hypothesis.

p12

Observed p-value for second hypothesis.

z1

Test statistic value for first null hypothesis.

z2

Test statistic value for second null hypothesis.

RCI

(Exact) repeated confidence interval for stage 1.

futility

Three dimensional vector with either 0 or 1. The first component represents futility due to Power of first stage > fCpower, the second futility due to CI (or PE) outside of fClower ... fCupper, the third futility due to n1 + n2 > fCNmax.
Note that the futility rules can be applied in a non-binding manner.

CI90

90% Confidence interval for observed ratio of geometric means from stage 1. If fCrit != "CI" results will be NULL.

Power Stage 1

Calculated power of stage 1.

stop_s1

Logical, indicating whether to stop after stage 1 (due to BE or due to futility).

stop_fut

Logical, indicating whether study is recommended to be stopped after stage 1 due to futility.

stop_BE

Logical, indicating whether BE could be concluded after stage 1 or not (regardless of any futility criterion).

n2

Required (total) sample size for stage 2 (will be zero if BE has been shown after stage 1).

alpha_ssr

Only applicable if BE has not been shown after stage 1. Contains alpha values for the two hypotheses required for sample size re-calculation. If ssr.conditional = "no" the result is equal to alpha, otherwise it contains the conditional error rates for the standard combination test (in case of max.comb.test = FALSE) or maximum combination test (in case of max.comb.test = TRUE).

GMR_ssr

Only applicable if BE has not been shown after stage 1. Contains the geometric mean ratio used for sample size re-calculation (accounts for adaptive planning step).

targetpower_ssr

Only applicable if BE has not been shown after stage 1. Contains the target power used for the sample size re-calculation (see also 'Details').

Author(s)

B. Lang

References

Patterson SD, Jones B. Bioequivalence and Statistics in Clinical Pharmacology.
Boca Raton: CRC Press; 2nd edition 2017.

Maurer W, Jones B, Chen Y. Controlling the type 1 error rate in two-stage sequential designs when testing for average bioequivalence.
Stat Med. 2018;1–21. doi: 10.1002/sim.7614

Wassmer G, Brannath W. Group Sequential and Confirmatory Adaptive Designs in Clinical Trials.
Springer 2016. doi: 10.1007/978-3-319-32562-0

See Also

power.tsd.in, final.tsd.in

Examples

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# Example from Maurer et al
interim.tsd.in(GMR1 = exp(0.0424), CV1 = 0.3682, n1 = 20, max.n = 4000)

Power2Stage documentation built on April 3, 2018, 9:04 a.m.