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

Source: R/lrstat-package.R
lrstat-package.Rd

A comprehensive clinical trial design and analysis package with a focus on non-proportional hazards and weighted log-rank methods, plus broad support for group sequential design, adaptive design, multiplicity, dose-finding, and endpoint-specific power and sample size calculations.

Details

For proportional hazards, power is determined by the total number of events and the constant hazard ratio together with information rates and spending functions. For non-proportional hazards, the hazard ratio varies over time and calendar time determines the mean and variance of the weighted log-rank score statistic. The package uses the analytic approach in Lu (2021) and approximates the variance-covariance matrix of sequential statistics under the alternative by that under the null to leverage the independent increments structure in Tsiatis (1982) for the Fleming-Harrington family.

The package capabilities can be grouped as follows:

  • Time-to-event design under proportional and non-proportional hazards: weighted log-rank statistics and design operating characteristics (for example lrstat, lrpower, lrsamplesize, lrsim, lrschoenfeld), including equivalence settings, event prediction, accrual modeling, and calendar time determination (for example accrual, caltime, nevent, pevent, patrisk, natrisk, getDurationFromNevents, getNeventsFromHazardRatio).

  • Group sequential and adaptive designs: standard, adaptive, multi-arm multi-stage (MAMS), and seamless frameworks, including boundaries, conditional power, confidence intervals, and exit probabilities (for example getDesign, adaptDesign, getBound, getCP, getCI, getRCI, getADCI, getADRCI, exitprob, and their _mams and _seamless variants).

  • Fixed and sequential sample size/power across endpoint types: binary, continuous, ordinal/multinomial, paired, crossover/carryover, MMRM, repeated measures ANOVA, two-way ANOVA, Wilcoxon, Fisher's exact, McNemar, one-sample exact, agreement, logistic regression, and negative binomial endpoints (for example getDesign*, power*Exact, samplesize*Exact, kmpower, rmpower, nbpower, and associated *samplesize and *equiv functions).

  • Multiplicity and graphical procedures: weighted Bonferroni and graph-based updates, Bonferroni mixtures of weighted Simes and Dunnett, and gatekeeping procedures for multiple hypotheses (for example fadjpbon, fadjpsim, fadjpdun, fseqbon, fstp2seq, fstdmix, fmodmix, fwgtmat, updateGraph).

  • Early-phase and dose-finding tools: Simon's two-stage, Bayesian Simon designs, mTPI-2, and BOIN utilities (for example simon2stage, simonBayesAnalysis, simonBayesSim, mTPI2Table, BOINTable).

  • Estimation, confidence intervals, and supporting utilities: Clopper-Pearson, exact risk ratio/risk difference, Brookmeyer-Crowley survival quantiles, Miettinen-Nurminen and REML intervals/statistics for stratified measures, Hedges' g, piecewise-exponential distribution tools, multivariate normal integration, and model diagnostics (for example ClopperPearsonCI, riskRatioExactCI, riskDiffExactCI, survQuantile, mnRiskDiffCI, remlRiskDiff, hedgesg, dtpwexp, ptpwexp, qtpwexp, rtpwexp, pbvnorm, pmvnormr, qmvnormr, phregr, liferegr, residuals_phregr, survfit_phregr, zph_phregr).

  • Interactive use: a bundled Shiny interface for exploratory design workflows (runShinyApp_lrstat).

The development of lrstat was strongly influenced by rpact, with argument naming aligned where possible for ease of adoption. Key differences include direct approximation (rather than Schoenfeld-based approximation) for weighted log-rank design calculations, explicit use of accrualDuration to define the accrual end, and treatment of final stage trial outcome when early futility stopping does not occur.

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

Author

Kaifeng Lu, kaifenglu@gmail.com

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)
#>                                                                      
#> Group-sequential design with 2 stages for log-rank test              
#> Overall power: 0.7786, overall significance level (1-sided): 0.025   
#> Maximum # events: 296.6, expected # events: 271.1                    
#> Maximum # dropouts: 28.1, expected # dropouts: 25.4                  
#> Maximum # subjects: 440, expected # subjects: 440                    
#> Maximum information: 73.36, expected information: 67.23              
#> Total study duration: 40, expected study duration: 35.7              
#> Accrual duration: 22, follow-up duration: 18, fixed follow-up: FALSE 
#> Allocation ratio: 1                                                  
#> Alpha spending: Lan-DeMets O'Brien-Fleming, beta spending: None      
#>                                                                      
#>                        Stage 1 Stage 2
#> Information rate       0.800   1.000  
#> Efficacy boundary (Z)  2.250   2.025  
#> Cumulative rejection   0.4286  0.7786 
#> Cumulative alpha spent 0.0122  0.0250 
#> Number of events       237.2   296.6  
#> Number of dropouts     21.8    28.1   
#> Number of subjects     440.0   440.0  
#> Analysis time          29.9    40.0   
#> Efficacy boundary (HR) 0.745   0.789  
#> Efficacy boundary (p)  0.0122  0.0214 
#> Information            59.06   73.36  
#> HR                     0.764   0.722