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

Usage

get_casecontrol_expectedCI_VE_or(
  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, 0.9), 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),
  controls_per_case = 2,
  calculate_relative_VE = T,
  alpha = 0.05,
  confounder_adjustment_Rsquared = 0,
  prob_missing_data = 0.1,
  total_cases = seq(50, 500, 10),
  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.
controls_per_case	the number of controls to be sampled per case in the study cohort. It should be a real number between 0 and Inf.
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_cases	a vector of the number of cases in our cohort for which calculations should be done.
nsims	total number of Monte Carlo simulations conducted.

Details

In this function efficacy is defined as VE = 1 - odds ratio, where 'odds ratio' is the ratio of odds of being vaccinated with a particular vaccine versus being unvaccinated among cases and the same odds in controls. 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 two conditional tables, one for cases, and another for controls. First an I x (M + 1) cross table of the probability of being unvaccinated or vaccinated with a vaccine, given that the subject is a case. The sum of the cells of this cases table is equal to 1. Second a 1 x (M + 1) vector of the probability of being unvaccinated or vaccinated with a vaccine, given that the subject is a controls. The sum of this controls vector is equal to 1. The first column in both of these corresponds to subjects who are unvaccinated 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 x (M + 1) cross table of cases data from a multinomial distribution with probabilities taken from our cases table. The total cases sampled in the cross table are are total_cases * (1 - prob_missing_data). We also sample a vector of 1 x (M + 1) controls data from a multinomial distribution with probabilities taken from our controls vector. The total controls sampled in the cross table are are controls_per_case * total_cases * (1 - prob_missing_data). We then estimate the absolute and relative VE of each vaccine using odds ration 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 odds 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_cases, 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.