sequse: Compute Group Sequential Use Function Boundaries

In raredd/desmon: Functions for design and monitoring of clinical trials

Compute Group Sequential Use Function Boundaries

Description

Computes the one-sided group sequential boundary for a specified use function at specified analysis times. Optionally, also computes an asymmetric lower boundary based on repeated confidence interval (RCI) monitoring for early stopping in favor of the null hypothesis.

Usage

sequse(
  inf,
  alpha = 0.025,
  use = 6,
  eta = 0,
  alphal = 0,
  usel = 6,
  oftr = alpha/50,
  oftrl = alphal/50
)

Arguments

inf	information times of analyses (length <= 30); must be positive, increasing and <= 1
alpha	one-sided significance level of the group sequential test
use	the type of use function: 1=O'Brien-Fleming, 2=Pocock, 3=linear, 4=one and a half, 5=quadratic, 6=truncated O'Brien-Fleming
eta	The mean parameter on the Brownian motion process scale. Only needed for the RCI lower boundary.
alphal	The one-sided significance level used in the RCI monitoring for stopping in favor of the null. The confidence level of the RCI is 1-2*alphal. If alphal <= 0, only the upper boundary is computed.
usel	The use function for determining critical values for the RCI lower boundary (same codes as use)
oftr	The significance level at which the truncated O-F boundary is truncated (upper boundary)
oftrl	The significance level at which the truncated O-F boundary is truncated (RCI lower boundary)

Details

Calculates the group sequential boundaries for repeated significance tests in group sequential analysis of clinical trials. The algorithm is based on the use function approach proposed by Lan and DeMets (1983, Biometrika) and investigated further by Kim and DeMets (1987, Biometrika). The information time corresponds to the proportion of statistical information, which is the essentially the same as the number of failures in a proportional hazards model for failure time endpoints.

For the truncated O-F boundary (use=6), first the regular O-F boundary is computed, but if the critical value is larger than the specified truncation value, the truncated value is used instead. The actual error spent is computed, and the early over-spending is made up as quickly as possible, after which the boundary is similar to the ordinary O-F boundary.

With asymmetric monitoring, the study is stopped early in favor of the null hypothesis if a ‘lower boundary’ is crossed. Here the lower boundary is based on a repeated confidence interval on the log hazard ratio (see Jennison and Turnbull, 1990). The RCI is constructed using the critical value from the one-sided boundary specified by usel and alphal. In the program, this is converted to a boundary on the logrank statistic. This requires information on the alternative and the total planned information for the study, which is specified through the parameter eta. The value of eta can be obtained from the functions seqopr and lr.inf. Introducing a lower boundary reduces the probability of crossing the upper boundary. After determining the lower boundary, the program computes the upper boundary taking into account the lower boundary. The upper boundary will thus be affected by the parameters specified for the lower boundary. It is quite easy to specify incompatible combinations for the upper and lower boundary, especially if alpha or alphal is very large or if eta is small.

Value

a matrix with length(inf) rows giving the critical values on the standard normal scale at the specified information times. If alphal<=0, there is a single column giving the critical values for the upper one-sided boundary. If alphal>0, then there is a second column giving the critical value for the lower boundary for early stopping in favor of the null. Note that these critical values are on the normalized test statistic scale, which are NOT the critical values used in constructing the RCI.

Note

Interface to the Fortran code for the program sequse, which was written by Kyungmann Kim and modified for truncated O-F boundaries and asymmetric lower boundaries by Bob Gray

References

Lan and DeMets (1983). Biometrika.

Kim and DeMets (1987). Biometrika.

Jennison and Turnbull (1990). Statistical Science 5:299-317.

See Also

seqopr; lr.inf; seqp

Examples

sequse((1:4) / 4)
sequse((1:4) / 4, use = 6)
sequse((1:4) / 4, use = 6, alphal = 0.025, eta = 2)

raredd/desmon documentation built on May 7, 2024, 3:46 p.m.