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

### 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

1 2 3 4 5 6 7 8 9 | ```
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 |

`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 |

`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` |
a time point (in weeks) used, together with |

`minCnt2` |
a minumum number of infections after |

`week2` |
a time point (in weeks) used, together with |

`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- |

`upperVEnoneff` |
specifies criterion 2 for declaring non-efficacy: the upper bound of the two-sided (1- |

`highVE` |
specifies a criterion for declaring high-efficacy: the lower bound of the two-sided (1- |

`stage1VE` |
specifies a criterion for advancement of a treatment's evaluation into Stage 2: the lower bound of the two-sided (1- |

`lowerVEuncPower` |
a numeric vector with each component specifying a one-sided null hypothesis H0: VE(0– |

`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- |

`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 ( |

`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 |

`VEcutoffWeek` |
a time point (in weeks) defining the per-protocol VE estimand, i.e., VE( |

`saveDir` |
a character string specifying a path for |

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

### 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(`VEcutoffWeek`

–`stage1`

) 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 |

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

`stopInfectCnt` |
the pooled number of infections at |

`summObj` |
a |

`finalHRci` |
the final CI for the hazard ratio, available if |

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

`totInfecCnt` |
the total number of |

`totInfecSplit` |
a table with the numbers of |

`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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 | ```
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="./")
``` |