get_cohort_expectedCI_VE_crr: Expected lower and expected upper limit of the confidence...

In anirudhtomer/vess: Vaccine Efficacy Sample Size Calculations in a Multiple Vaccine and Multiple Pathogen Variant Scenario

Description

The function get_cohort_expectedCI_VE_crr simulates confindence intervals for variant and vaccine-specific efficacy (VE) for a given sample size. The efficacy is defined as VE = 1 - cumulative-risk ratio, and the function returns expected lower and expected upper confidence interval limit for both absolute and relative VE.

Usage

get_cohort_expectedCI_VE_crr(
  anticipated_VE_for_each_brand_and_variant = matrix(data = c(0.1, 0.2, 0.3, 0.4, 0.5,
    0.6, 0.7, 0.8, 1), nrow = 3, ncol = 3, byrow = T, dimnames = list(paste0("brand",
    1:3), paste0("variant", 1:3))),
  brand_proportions_in_vaccinated = c(brand1 = 0.3, brand2 = 0.5, brand3 = 0.2),
  overall_vaccine_coverage = 0.3,
  proportion_variants_in_unvaccinated_cases = c(variant1 = 0.6, variant2 = 0.3,
    variant3 = 0.1),
  overall_attack_rate_in_unvaccinated = 0.1,
  calculate_relative_VE = T,
  alpha = 0.05,
  confounder_adjustment_Rsquared = 0,
  prob_missing_data = 0.1,
  total_subjects = seq(1000, 10000, 25),
  nsims = 500
)

Arguments

anticipated_VE_for_each_brand_and_variant	a matrix of vaccine efficacy of each vaccine (row) against each variant (column). Each value must be a real number between 0 and 1.
brand_proportions_in_vaccinated	a vector denoting the proportion in which vaccines are given in the vaccinated subjects of the study cohort. Each value of this vector must be a real number between 0 and 1 and the sum of the values of this vector must be equal to 1.
overall_vaccine_coverage	the proportion of the study cohort that will be vaccinated. It should be a real number between 0 and 1.
proportion_variants_in_unvaccinated_cases	a vector of the proportions in which each variant is expected to be present in the unvaccinated and infected subjects in the study cohort. Each value of this vector must be a real number between 0 and 1 and the sum of the values of this vector must be equal to 1.
overall_attack_rate_in_unvaccinated	the proportion of the study cohort that is expected to infected over the study period. It should be a real number between 0 and 1.
calculate_relative_VE	a logical indicating if calculations should also be done for relative vaccine efficacy (default TRUE).
alpha	controls the width [100*alpha/2, 100*(1 - alpha/2)]% of the confidence interval. It is a numeric that must take a value between 0 and 1.
confounder_adjustment_Rsquared	we use this parameter to adjust the calculations for potential confounders using the methodology proposed by Hsieh and Lavori (2000). It represents the amount of variance (R^2) explained in a regression model where vaccination status is the outcome and confounders of interest are predictors. It is a numeric that must take a value between 0 (no adjustment for confounders) and 1.
prob_missing_data	to adjust the calculations for non-informative and random subject loss to follow-up/dropout. it should take a numeric value between 0 and 1.
total_subjects	a vector of study cohort size for which calculations should be done.
nsims	total number of Monte Carlo simulations conducted.

Details

In this function efficacy is defined as VE = 1 - cumulative-risk ratio, where 'cumulative-risk ratio' is the ratio of cumulative-risk of being a case of a particular variant/variant among the groups being compared. When the groups being compared are a particular vaccine versus placebo then we call the VE as the absolute VE of the vaccine. For M vaccines there are M absolute VE, one each for the M vaccines. When the groups being compared are a particular vaccine versus another vaccine then we call the VE as the relative VE of the vaccines, for a particular variant. For M vaccines and I variants there are I x 2 x utils::combn(M, 2) permutations of relative VE of two vaccines against the same variant.

We first transform the user inputs for I variants and M vaccines into a (I + 1) x (M + 1) cross table of cumulative-risks of being a case or a control over the study period. The overall sum of all cumulative-risks, i.e., all cells, of this table is 1. The first row of our cumulative-risk table contain cumulative-risk of being a control. The first column corresponds to subjects who are unvaccinated. Thus, the cell {1,1} contains the probability (cumulative-risk) that over the study period a subject will be a control and unvaccinated. The remaining Ì rows correspond to subjects who are cases of a particular variant/variant of the pathogen, and the remaining M columns correspond to subjects who are vaccinated with a particular vaccine.

The next step is to simulate the data. To speed up our computations we sample an (I + 1) x (M + 1) cross table of data from a multinomial distribution with probabilities taken from our cumulative-risk table. The total subjects sampled in the cross table are are total_subjects * (1 - prob_missing_data). We then estimate the absolute and relative VE of each vaccine using the cumulative-risks based on the sampled data. The confidence intervals with widths [100*alpha/2, 100*(1 - alpha/2)]% are obtained using normal approximation to the distribution of log of cumulative-risk ratio (Morris and Gardner, 1988). To adjust for confounders, the standard-error used in the confidence interval is rescaled to SE/(1 - confounder_adjustment_Rsquared) (Hsieh and Lavori, 2000) We repeat this procedure nsims times, and in each such simulation we obtain nsims confidence intervals.

To conduct simulations faster all the calculations are done without using for loops. Instead we use a three-dimensional R arrays, with one-dimension for nsims, another for the sample size vector total_subjects, and another for a vector containing the flattened cross table of simulated data on cases and controls.

Value

A data frame consisting of the input parameters, absolute and relative VE combinations, and the expected lower and expected upper width of the confidence intervals for each absolute and relative VE combination.

References

1. Hsieh, F. Y., & Lavori, P. W. (2000). Sample-size calculations for the Cox proportional hazards regression model with nonbinary covariates. Controlled clinical trials, 21(6), 552-560.

2. Morris, J. A., & Gardner, M. J. (1988). Statistics in medicine: Calculating confidence intervals for relative risks (odds ratios) and standardised ratios and rates. British medical journal (Clinical research ed.), 296(6632), 1313.

Examples

As an example we recommend running the function without passing any parameter to it.
The default scenario is for three vaccines and three pathogen variants.

anirudhtomer/vess documentation built on Feb. 24, 2022, 3 p.m.