lrstat-package: Power and Sample Size Calculation for Non-Proportional...

In lrstat: Power and Sample Size Calculation for Non-Proportional Hazards and Beyond

Power and Sample Size Calculation for Non-Proportional Hazards and Beyond

Description

Performs power and sample size calculation for non-proportional hazards model using the Fleming-Harrington family of weighted log-rank tests.

Details

For proportional hazards, the power is determined by the total number of events and the constant hazard ratio along with information rates and spending functions. For non-proportional hazards, the hazard ratio varies over time and the calendar time plays a key role in determining the mean and variance of the log-rank test score statistic. It requires an iterative algorithm to find the calendar time at which the targeted number of events will be reached for each interim analysis. The lrstat package uses the analytic method in Lu (2021) to find the mean and variance of the weighted log-rank test score statistic at each interim analysis. In addition, the package approximates the variance and covariance matrix of the sequentially calculated log-rank test statistics under the alternative hypothesis with that under the null hypothesis to take advantage of the independent increments structure in Tsiatis (1982) applicable for the Fleming-Harrington family of weighted log-rank tests.

The most useful functions in the package are lrstat, lrpower, lrsamplesize, and lrsim, which calculate the mean and variance of log-rank test score statistic at a sequence of given calendar times, the power of the log-rank test, the sample size in terms of accrual duration and follow-up duration, and the log-rank test simulation, respectively. The accrual function calculates the number of patients accrued at given calendar times. The caltime function finds the calendar times to reach the targeted number of events. The exitprob function calculates the stagewise exit probabilities for specified boundaries with a varying mean parameter over time based on an adaptation of the recursive integration algorithm described in Chapter 19 of Jennison and Turnbull (2000).

The development of the lrstat package is heavily influenced by the rpact package. We find their function arguments to be self-explanatory. We have used the same names whenever appropriate so that users familiar with the rpact package can learn the lrstat package quickly. However, there are notable differences:

• lrstat uses direct approximation, while rpact uses the Schoenfeld method for log-rank test power and sample size calculation.

• lrstat uses accrualDuration to explicitly set the end of accrual period, while rpact incorporates the end of accrual period in accrualTime.

• lrstat considers the trial a failure at the last stage if the log-rank test cannot reject the null hypothesis up to this stage and cannot stop for futility at an earlier stage.

• the lrsim function uses the variance of the log-rank test score statistic as the information.

In addition to the log-rank test power and sample size calculations, the lrstat package can also be used for the following tasks:

• design generic group sequential trials.

• design generic group sequential equivalence trials.

• design adaptive group sequential trials for changes in sample size, error spending function, number and spacing or future looks.

• calculate the terminating and repeated confidence intervals for standard and adaptive group sequential trials.

• calculate the conditional power for non-proportional hazards with or without design changes.

• perform multiplicity adjustment based on graphical approaches using weighted Bonferroni tests, Bonferroni mixture of weighted Simes test, and Bonferroni mixture of Dunnett test as well as group sequential trials with multiple hypotheses.

• perform multiplicity adjustment using stepwise gatekeeping procedures for two sequences of hypotheses and the standard or modified mixture gatekeeping procedures in the general case.

• design parallel-group trials with the primary endpoint analyzed using mixed-model for repeated measures (MMRM).

• design crossover trials to estimate direct treatment effects while accounting for carryover effects.

• design one-way repeated measures ANOVA trials.

• design two-way ANOVA trials.

• design Simon's 2-stage trials.

• design modified toxicity probability-2 (mTPI-2) trials.

• design Bayesian optimal interval (BOIN) trials.

• design group sequential trials for negative binomial endpoints with censoring.

• design trials using Wilcoxon, Fisher's exact, and McNemar's test.

• calculate Clopper-Pearson confidence interval for single proportions.

• calculate Brookmeyer-Crowley confidence interval for quantiles of censored survival data.

• calculate Miettinen & Nurminen confidence interval for stratified risk difference, risk ratio, odds ratio, rate difference, and rate ratio.

• perform power and sample size calculation for logistic regression.

• perform power and sample size calculation for Cohen's kappa.

• calculate Hedges' g effect size.

• generate random numbers from truncated piecewise exponential distribution.

• perform power and sample size calculations for negative binomial data.

Author(s)

Kaifeng Lu, [e-mail]

References

Anastasios A. Tsiatis. Repeated significance testing for a general class of statistics used in censored survival analysis. J Am Stat Assoc. 1982;77:855-861.

Christopher Jennison, Bruce W. Turnbull. Group Sequential Methods with Applications to Clinical Trials. Chapman & Hall/CRC: Boca Raton, 2000, ISBN:0849303168

Kaifeng Lu. Sample size calculation for logrank test and prediction of number of events over time. Pharm Stat. 2021;20:229-244.

See Also

rpact, gsDesign

Examples

lrpower(kMax = 2, informationRates = c(0.8, 1),
        criticalValues = c(2.250, 2.025), accrualIntensity = 20,
        piecewiseSurvivalTime = c(0, 6),
        lambda1 = c(0.0533, 0.0309), lambda2 = c(0.0533, 0.0533),
        gamma1 = 0.00427, gamma2 = 0.00427,
        accrualDuration = 22, followupTime = 18)

lrstat documentation built on Oct. 18, 2024, 9:06 a.m.