drift: Drift and Probabilities for Group Sequential Boundaries In ldbounds: Lan-DeMets Method for Group Sequential Boundaries

Description

'drift' calculates drift (effect), confidence interval for drift, or power and other probabilities given drift for specified group sequential boundaries for interim analyses of accumulating data in clinical trials.

Usage

 ```1 2``` ```drift(za = -zb, zb, t, t2 = t, pow = NULL, drft = NULL, conf = NULL, zval = zb[length(zb)]) ```

Arguments

 `za` the vector of lower boundaries. Symmetric to `zb` by default. `zb` the vector of upper boundaries. `t` the vector of analysis times, which must be increasing and in (0,1]. `t2` the second time scale, usually in terms of amount of accumulating information. By default, same as `t`. `pow` the desired power when drift is not specified. `drft` the true drift (i.e. treatment effect when t=1). `conf` the confidence level when a confidence interval for drift is wanted. `zval` the final observed Z statistic (i.e. when trial is stopped). Used for confidence interval.

Details

This is based on a Fortran program, 'ld98', by Reboussin, DeMets, Kim, and Lan. It has some advantages, like making use of probability distributions in R. Only one of `pow`, `drft`, and `conf` is to be specified and `zval` is only used in the last case.

Value

'drift' returns an object of 'class' '"drift"'.

An object of class '"drift"' is a list containing the following components:

 `type` Type of computation performed: 1 is drift given power, 2 is exit probabilities given drift, and 3 is confidence interval for drift given final Z statistic. `time` the original time scale. `time2` the second (information) time scale. `lower.bounds` the vector of lower boundaries given. `upper.bounds` the vector of upper boundaries given. `power` the power. If power is given, it is returned here. If drift is given, the resulting power is calculated. `drift` the drift. If drift is given, it is returned here. If power is given, the drift resulting in given power is calculated. `lower.probs` the vector of exit probabilities across the lower boundary. Returned if power or drift is given. `upper.probs` the same for upper boundary. `exit.probs` the probability at each analysis of crossing the boundary. The sum of `lower.probs` and `upper.probs`. `cum.exit` the cumulative probability of crossing. `conf.level` the desired confidence level, if given. `final.zvalue` the final Z statistic, if given. `conf.interval` the confidence interval for drift, if `conf` and `zval` are given.

Author(s)

Charlie Casper [email protected] and Oscar A. Perez

References

Reboussin, D. M., DeMets, D. L., Kim, K. M., and Lan, K. K. G. (2000) Computations for group sequential boundaries using the Lan-DeMets spending function method. Controlled Clinical Trials, 21:190-207.

Fortran program 'ld98' by the same authors as above.

DeMets, D. L. and Lan, K. K. G. (1995) Recent Advances in Clinical Trial Design and Analysis, Thall, P. F. (ed.). Boston: Kluwer Academic Publishers.

Lan, K. K. G. and DeMets, D. L. (1983) Discrete sequential boundaries for clinical trials. Biometrika, 70:659-63.

Generic functions `summary.drift` and `plot.drift`.
`bounds` for computation of boundaries using alpha spending function method.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ``` ## From Reboussin, et al. (2000) t <- c(0.13,0.4,0.69,0.9,0.98,1) upper <- c(5.3666,3.7102,2.9728,2.5365,2.2154,1.9668) drift.pr <- drift(zb=upper,t=t,drft=3.242) summary(drift.pr) t <- c(0.2292,0.3333,0.4375,0.5833,0.7083,0.8333) upper <- c(2.53,2.61,2.57,2.47,2.43,2.38) drift.ci <- drift(zb=upper,t=t,conf=0.95,zval=2.82) summary(drift.ci) plot(drift.ci) ## Using output from 'bounds' t <- seq(0.2,1,length=5) obf.bd <- bounds(t,iuse=c(1,1),alpha=c(0.025,0.025)) drift.dr <- drift(obf.bd\$lower.bounds,obf.bd\$upper.bounds,t,pow=0.9) summary(drift.dr) ```