Group Sequential Monitoring of Simulated Efficacy Trials for the Event of Potential Harm, Non-Efficacy, and High Efficacy

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Description

monitorTrial applies a group sequential monitoring procedure to data-sets generated by simTrial, which may result in modification or termination of each simulated trial.

Usage

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monitorTrial(dataFile, stage1, stage2, harmMonitorRange, 
             alphaPerTest = NULL, minCnt, minPct, week1, 
             minCnt2, week2, nonEffInterval, lowerVEnoneff,
             upperVEnoneff, highVE, stage1VE, 
             lowerVEuncPower = NULL, alphaNoneff, alphaHigh, 
             alphaStage1, alphaUncPower = NULL,
             estimand = c("combined", "cox", "cuminc"), 
             post6moMonitor = FALSE, VEcutoffWeek, 
             saveDir = NULL, verbose = TRUE)

Arguments

dataFile

if saveDir = NULL, a list returned by simTrial; otherwise a name (character string) of an .RData file created by simTrial

stage1

the final week of stage 1 in a two-stage trial

stage2

the final week of stage 2 in a two-stage trial, i.e., the maximum follow-up time

harmMonitorRange

a 2-component numeric vector specifying the range for pooled numbers of infections (pooled over the placebo and vaccine arm accruing infections the fastest) for which potential-harm stopping boundaries will be computed

alphaPerTest

a per-test nominal/unadjusted alpha level for potential-harm monitoring. If NULL, a per-test alpha level is calculated that yields a cumulative alpha of 0.05 at the final potential-harm analysis.

minCnt

a minumum number of infections (pooled over the placebo and vaccine arm accruing infections the fastest) required for the initiation of non-efficacy monitoring [criterion 1]

minPct

a minimum proportion of infections after week1 (pooled over the placebo and vaccine arm accruing infections the fastest) required for the initiation of non-efficacy monitoring [criterion 2]

week1

a time point (in weeks) used, together with minPct, for defining criterion 2

minCnt2

a minumum number of infections after week2 (pooled over the placebo and vaccine arm accruing infections the fastest) required for the initiation of non-efficacy monitoring [criterion 3]

week2

a time point (in weeks) used, together with minCnt2, for defining criterion 3

nonEffInterval

a number of infections between two adjacent non-efficacy interim analyses

lowerVEnoneff

specifies criterion 1 for declaring non-efficacy: the lower bound of the two-sided (1-alphaNoneff) x 100% confidence interval(s) for the VE estimand(s) lie(s) below lowerVEnoneff (typically set equal to 0)

upperVEnoneff

specifies criterion 2 for declaring non-efficacy: the upper bound of the two-sided (1-alphaNoneff) x 100% confidence interval(s) for the VE estimand(s) lie(s) below upperVEnoneff (typically a number in the 0–0.5 range)

highVE

specifies a criterion for declaring high-efficacy: the lower bound of the two-sided (1-alphaHigh) x 100% confidence interval for the VE estimand lies above highVE (typically a number in the 0.5–1 range)

stage1VE

specifies a criterion for advancement of a treatment's evaluation into Stage 2: the lower bound of the two-sided (1-alphaStage1) x 100% confidence interval for the VE estimand lies above stage1VE (typically set equal to 0)

lowerVEuncPower

a numeric vector with each component specifying a one-sided null hypothesis H0: VE(0–stage1) lowerVEuncPower x 100%. Unconditional power (i.e., accounting for sequential monitoring) to reject each H0 is calculated, where the rejection region is defined by the lower bound of the two-sided (1-alphaUncPower) x 100% confidence interval for the VE estimand being above the respective component of lowerVEuncPower (typically values in the 0–0.5 range).

alphaNoneff

one minus the nominal confidence level of the two-sided confidence interval used for non-efficacy monitoring

alphaHigh

one minus the nominal confidence level of the two-sided confidence interval used for high efficacy monitoring

alphaStage1

one minus the nominal confidence level of the two-sided confidence interval used for determining whether a treatment's evaluation advances into Stage 2

alphaUncPower

one minus the nominal confidence level of the two-sided confidence interval used to test one-sided null hypotheses H0: VE(0-stage1) lowerVEuncPower x 100% against alternative hypotheses H1: VE(0–stage1) > lowerVEuncPower x 100%. The same nominal confidence level is applied for each component of lowerVEuncPower.

estimand

a character string specifying the choice of VE estimand(s) used in non- and high efficacy monitoring, advancement rule for Stage 2, and unconditional power calculations. Three options are implemented: (1) the ‘pure’ Cox approach ("cox"), where VE is defined as 1-hazard ratio (treatment/control) and estimated by the maximum partial likelihood estimator in the Cox model; (2) the ‘pure’ cumulative incidence-based approach ("cuminc"), where VE is defined as 1-cumulative incidence ratio (treatment/control) and estimated by the transformation of the Nelson-Aalen estimator for the cumulative hazard function; and (3) the combined approach ("combined"), where both aforementioned VE estimands are used for non-efficacy monitoring while the cumulative VE estimand is used for all other purposes. Only the first three characters are necessary.

post6moMonitor

a logical value indicating whether, additionally, post-6 months non-efficacy monitoring shoud be used as a more conservative non-efficacy monitoring approach. If TRUE and estimand = "combined", the cumulative VE estimand is considered only for non-efficacy monitoring.

VEcutoffWeek

a time point (in weeks) defining the per-protocol VE estimand, i.e., VE(VEcutoffWeekstage1). This VE estimand is also used in post-6 months non-efficacy monitoring. It is typically chosen as the date of the last immunization or the date of the visit following the last immunization.

saveDir

a character string specifying a path for dataFile. If supplied, the output is also saved as an .RData file in this directory; otherwise the output is returned as a list.

verbose

a logical value indicating whether information on the output directory, file name, and monitoring outcomes should be printed out (default is TRUE)

Details

All time variables use week as the unit of time. Month is defined as 52/12 weeks.

Potential harm monitoring starts at the harmMonitorRange[1]-th infection pooled over the placebo group and the vaccine regimen that accrues infections the fastest. The potential harm analyses continue at each additional infection until the first interim analysis for non-efficacy. The monitoring is implemented with exact one-sided binomial tests of H0: p ≤ p0 versus H1: p > p0, where p is the probability that an infected participant was assigned to the vaccine group, and p0 is a fixed constant that represents the null hypothesis that an infection is equally likely to be assigned vaccine or placebo. Each test is performed at the same prespecified nominal/unadjusted alpha-level (alphaPerTest), chosen based on simulations such that, for each vaccine regimen, the overall type I error rate by the harmMonitorRange[2]-th arm-pooled infection (i.e., the probability that the potential harm boundary is reached when the vaccine is actually safe, p = p0) equals 0.05.

Non-efficacy is defined as evidence that it is highly unlikely that the vaccine has a beneficial effect measured as VE(0–stage1) of upperVEnoneff x 100% or more. The non-efficacy analyses for each vaccine regimen will start at the first infection at or after the minCnt-th (pooled over the vaccine and placebo arm) when at least minPct x 100% of the accumulated infections are diagnosed after week1 and at least minCnt2 infections are diagnosed after week2. Stopping for non-efficacy will lead to a reported two-sided (1-alphaNoneff) x 100% CI for VE(0–stage1) with the lower confidence bound below lowerVEnoneff and the upper confidence bound below upperVEnoneff, where estimand determines the choice of the VE(0–stage1) estimand. This approach is similar to the inefficacy monitoring approach of Freidlin B, Korn EL, Gray R. (2010) A general inefficacy interim monitoring rule for randomized trials. Clinical Trials, 7:197-208. If estimand = "combined", stopping for non-efficacy will lead to reported (1-alphaNoneff) x 100% CIs for both VE parameters with lower confidence bounds below lowerVEnoneff and upper confidence bounds below upperVEnoneff. If post6moMonitor = TRUE, stopping for non-efficacy will lead to reported (1-alphaNoneff) x 100% CIs for both VE(0–stage1) and VE(VEcutoffWeekstage1) with lower confidence bounds below lowerVEnoneff and upper confidence bounds below upperVEnoneff.

High efficacy monitoring allows early detection of a highly protective vaccine if there is evidence that VE(0–stage2) > highVE x 100%, based on two planned interim analyses, the first at the time of the fifth planned non-efficacy analysis, and the second at the expected mid-point between the number of infections at the first interim analysis and the number of infections observed at the end of stage2. While monitoring for potential harm and non-efficacy restricts to stage1 infections, monitoring for high efficacy counts all infections during stage1 or stage2, given that early stopping for high efficacy would only be warranted under evidence for durability of the efficacy.

The following principles and rules are applied in the monitoring procedure:

  • Exclude all follow-up data from the analysis post-unblinding (and include all data pre-unblinding).

  • The monitoring is based on modified ITT analysis, i.e., all subjects documented to be free of the study endpoint at baseline are included and analyzed according to the treatment assigned by randomization, ignoring how many vaccinations they received (only pre-unblinding follow-up included).

  • If a vaccine hits the harm boundary, immediately discontinue vaccinations and accrual into this vaccine arm, and unblind this vaccine arm (continue post-unblinded follow-up until the end of Stage 1 for this vaccine arm).

  • If a vaccine hits the non-efficacy boundary, immediately discontinue vaccinations and accrual into this vaccine arm, keep blinded and continue follow-up until the end of Stage 1 for this vaccine arm.

  • If and when the last vaccine arm hits the non-efficacy (or harm) boundary, discontinue vaccinations and accrual into this vaccine arm, and unblind (the trial is over, completed in Stage 1).

  • Stage 1 for the whole trial is over on the earliest date of the two events: (1) all vaccine arms have hit the harm or non-efficacy boundary; and (2) the last enrolled subject in the trial reaches the final stage1 visit.

  • Continue blinded follow-up until the end of Stage 2 for each vaccine arm that reaches the end of stage1 with a positive efficacy (as defined by stage1VE) or high efficacy (as defined by highVE) result.

  • If at least one vaccine arm reaches the end of stage1 with a positive efficacy or high efficacy result, continue blinded follow-up in the placebo arm until the end of Stage 2.

  • Stage 2 for the whole trial is over on the earliest date of the two events: (1) all subjects in the placebo arm and each vaccine arm that registered efficacy or high efficacy in stage1 have failed or been censored; and (2) all subjects in the placebo arm and each vaccine arm that registered efficacy or high efficacy in stage1 have completed the final stage2 visit.

The above rules have the following implications:

  • If a vaccine hits the non-efficacy boundary but Stage 1 for the whole trial is not over, then one includes in the analysis all follow-up through the final stage1 visit for that vaccine regimen, including all individuals accrued up through the date of hitting the non-efficacy boundary (which will be the total number accrued to this vaccine arm).

  • If a vaccine hits the harm boundary, all follow-up information through the date of hitting the harm boundary is included for this vaccine; no follow-up data are included after this date.

  • If and when the last vaccine arm hits the non-efficacy (or harm) boundary, all follow-up information through the date of hitting the non-efficacy (or harm) boundary is included for this vaccine; no follow-up data are included after this date.

Value

If saveDir is specified, the output list (named out) is saved as an .RData file in saveDir (the path to saveDir is printed); otherwise it is returned. The output object is a list of length equal to the number of simulated trials, each of which is a list of length equal to the number of treatment arms, each of which is a list with (at least) the following components:

boundHit

a character string stating the monitoring outcome in this treatment arm, i.e., one of "Harm", "NonEffInterim", "NonEffFinal", "Eff", or "HighEff". The first four outcomes can occur in Stage 1, whereas the last outcome can combine data over Stage 1 and Stage 2.

stopTime

the time of hitting a stopping boundary since the first subject enrolled in the trial

stopInfectCnt

the pooled number of infections at stopTime

summObj

a data.frame containing summary information from each non-/high efficacy interim analysis

finalHRci

the final CI for the hazard ratio, available if estimand!="cuminc" and there is at least 1 infection in each arm

firstNonEffCnt

the number of infections that triggered non-efficacy monitoring (if available)

totInfecCnt

the total number of stage1 (stage2 if boundHit = "HighEff") infections

totInfecSplit

a table with the numbers of stage1 (stage2 if boundHit = "HighEff") infections in the treatment and control arm

lastExitTime

the time between the first subject's enrollment and the last subject's exiting from the trial

See Also

simTrial, censTrial, and rankTrial

Examples

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simData <- simTrial(N=c(1000, rep(700, 2)), aveVE=seq(0, 0.4, by=0.2), 
                    VEmodel="half", vePeriods=c(1, 27, 79), enrollPeriod=78, 
                    enrollPartial=13, enrollPartialRelRate=0.5, dropoutRate=0.05, 
                    infecRate=0.04, fuTime=156, 
                    visitSchedule=c(0, (13/3)*(1:4), seq(13*6/3, 156, by=13*2/3)),
                    missVaccProb=c(0,0.05,0.1,0.15), VEcutoffWeek=26, nTrials=5, 
                    stage1=78, randomSeed=300)
                    
monitorData <- monitorTrial(dataFile=simData, stage1=78, stage2=156, 
                            harmMonitorRange=c(10,100), alphaPerTest=0.0106, 
                            minCnt=50, minPct=0.33, week1=26, minCnt2=2, week2=52, 
                            nonEffInterval=20, lowerVEnoneff=0, upperVEnoneff=0.4, 
                            highVE=0.7, stage1VE=0, lowerVEuncPower=0, alphaNoneff=0.05,
                            alphaHigh=0.05, alphaStage1=0.05, alphaUncPower=0.05,
                            estimand="cuminc", VEcutoffWeek=26)

### alternatively, to save the .RData output file (no '<-' needed):
###
### simTrial(N=c(1400, rep(1000, 2)), aveVE=seq(0, 0.4, by=0.2), VEmodel="half", 
###          vePeriods=c(1, 27, 79), enrollPeriod=78, enrollPartial=13, 
###          enrollPartialRelRate=0.5, dropoutRate=0.05, infecRate=0.04, fuTime=156, 
###          visitSchedule=c(0, (13/3)*(1:4), seq(13*6/3, 156, by=13*2/3)), 
###          missVaccProb=c(0,0.05,0.1,0.15), VEcutoffWeek=26, nTrials=30, 
###          stage1=78, saveDir="./", randomSeed=300)
###
### monitorTrial(dataFile=
###          "simTrial_nPlac=1400_nVacc=1000_1000_aveVE=0.2_0.4_infRate=0.04.RData", 
###          stage1=78, stage2=156, harmMonitorRange=c(10,100), alphaPerTest=0.0106, 
###          minCnt=50, minPct=0.33, week1=26, minCnt2=2, week2=52, nonEffInterval=20, 
###          lowerVEnoneff=0, upperVEnoneff=0.4, highVE=0.7, stage1VE=0, 
###          lowerVEuncPower=0, alphaNoneff=0.05, alphaHigh=0.05, alphaStage1=0.05, 
###          alphaUncPower=0.05, estimand="cuminc", VEcutoffWeek=26, saveDir="./")