DOVE (version 1.10)

dove2: Durability of Vaccine Efficacy

Description

Estimates the potentially waning long-term efficacy of vaccines in randomized, placebo-controlled clinical trials with staggered enrollment of participants and sequential crossover of placebo recipients. The log hazard ratio for the vaccine effect is assumed to be a piecewise linear function of time since vaccination, whereas the baseline hazard function is nonparametric.

Usage

dove2(
  formula,
  data,
  plots = TRUE,
  changePts = NULL,
  constantVE = FALSE,
  timePts = NULL
)

Value

An S3 object of class DOVE containing a list with elements

call

The unevaluated call.

changePts

The changePts of the analysis.

covariates

A matrix containing the estimated (log) hazard ratio of each covariate, together with the estimated standard error, the 95% confidence interval, and the two-sided p-value for testing no covariate effect. NA if no covariate is included in the model.

vaccine

A list containing one or three elements, depending on the value of constantVE. If constantVE = TRUE, the only element is named 'VE' and is a vector containing the estimate of constant VE, its standard error estimate, and the 95% confidence interval. If constantVE = FALSE, three matrices are returned. The first matrix named 'VE_a' contains the daily VE estimates in reducing the attack rate, together with the 95% confidence intervals. The second matrix named 'VE_h' contains the daily VE estimates in reducing the hazard rate, together with the 95% confidence intervals. The third matrix named 'VE_period' contains the estimates of VE in reducing the attack rate over successive time periods according to timePts, together with the 95% confidence intervals.

Arguments

formula

A formula object, with the response on the left-hand side of a '~' operator, and the covariates and vaccine() function on the right-hand side. The response must be a survival analysis object as returned by the 'Surv' function of the survival package. See Details for further information. The vaccine() function must be used to specify the entry time and vaccination information. See ?vaccine and Details for further information.

data

A data.frame object. The data.frame in which to interpret the variable names in formula. Must contain the entry time, the event time, the event status, the vaccination status, the vaccination time, and the covariates. See Details.

plots

A logical object. If TRUE (default), plots of the estimated VE in reducing the attack rate, the estimated VE in reducing the hazard rate, and their 95% confidence intervals will be automatically generated. If FALSE, plots will not be generated.

changePts

A numerical vector object or NULL. The potential change points (in days) of the piece-wise log-linear hazard ratio for the vaccine effect. See Details for further information. If NULL, one change point will automatically be selected among {28, 35, 42, 49, 56} (Weeks 4, 5, 6, 7, 8) by the Akaike information criterion (AIC).

constantVE

A logical object. If FALSE (default), VE is allowed to vary after the last change point. If TRUE, VE is assumed to be constant after the last change point.

timePts

A numerical vector object or NULL. The endpoints (in days) of the time periods for which the VE in reducing the attack rate are to be estimated. If NULL, a default sequence \(t_1, 2t_1, 3t_1, \dots\) will be used, where \(t_1\) is the first change point. The sequence ends at the maximum of the event times from all participants. This input is ignored when constantVE = TRUE.

Details

In dove2(), the log hazard ratio for the vaccine effect is a piecewise linear function of time since vaccination. Its sister function, dove(), allows the hazard ratio to be a nonparametric function of time for which confidence intervals are not provided. The approach implemented in dove2() provides more precise and more stable estimates of vaccine efficacy on the hazard rate and includes proper confidence intervals.

The information required for an analysis is

Entry Time:

Calendar time when the participant enters the trial.

Event Time:

Calendar time when the participant experiences the clinical event of interest (e.g., symptomatic COVID-19) or the follow-up ends, whichever occurs first.

Event Status:

Binary indicator taking value 1 if the clinical event of interest occurs before the end of follow-up and 0 otherwise.

Vaccination Status:

Binary indicator taking value 1 if vaccination occurs before the end of follow-up and 0 otherwise.

Vaccination Time:

Calendar time when vaccination takes place, with NA, Inf, or an arbitrary non-negative value if the participant is not vaccinated.

Covariates:

Baseline covariates (e.g., priority group, age, ethnicity).

Note that all the time variables are measured from the start of the clinical trial and are specified in units of days. For each individual, the entry_time, event_time, and vaccination_time must satisfy entry_time \(\le\) event_time and entry_time \(\le\) vaccination_time. If entry_time > event_time or entry_time > vaccination_time, the case will be removed from the analysis and a message will be generated.

The general structure of the formula input is

  Surv(event_time, event_status) ~ covariates + 
    vaccine(entry_time, vaccination_status, vaccination_time)
  

The response variable must be a survival analysis object as returned by the 'Surv()' function of package survival, where event_time is the observation time (formal argument 'time') and event_status is the status indicator input (formal argument 'event'). Specifically,

Surv(time = event_time, event = event_status)

The covariates can be either numerical or categorical. If categorical covariates are provided, all other categories are compared to the first category. A model without covariates is also allowed.

References

Lin, D-Y, Gu, Y., Zeng, D., Janes, H. E., and Gilbert, P. B. (2021). Evaluating vaccine efficacy against SARS-CoV-2 infection. Clinical Infectious Diseases, ciab630, https://doi.org/10.1093/cid/ciab630.

Examples

# \dontshow{
  RcppArmadillo::armadillo_throttle_cores(2)
# }
data(doveData)

set.seed(1234)
smp <- sample(1L:nrow(x = doveData), size = 2500L)

# NOTE: This sample size is chosen for example only -- larger data sets
# should be used.
# See the vignette for a full analysis of the doveData dataset

# Fit the model with default settings
dove2(formula = Surv(event.time, event.status) ~ priority + sex + 
                vaccine(entry.time, vaccine.status, vaccine.time), 
      data = doveData[smp,])

# Specify Week 4 as the change point
# Assume a potentially waning VE after 4 weeks
# Estimate VE_a over 0-4, 4-16, 16-28, 28-40 weeks
dove2(formula = Surv(event.time, event.status) ~ priority + sex + 
                vaccine(entry.time, vaccine.status, vaccine.time), 
      data = doveData[smp,],
      changePts = 4*7,
      timePts = c(4, 16, 28, 40)*7)
      
# Specify multiple change points at Weeks 4 and 8
# Assume a constant VE after 8 weeks
dove2(formula = Surv(event.time, event.status) ~ priority + sex + 
                vaccine(entry.time, vaccine.status, vaccine.time), 
      data = doveData[smp,],
      changePts = c(4, 8)*7,
      constantVE = TRUE)