get_cohort_mindet_VE_crr: Minimum detectable variant and vaccine-specific efficacy...

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

Description

The function get_cohort_mindet_VE_crr calculates the minimum detectable variant and vaccine-specific efficacy (VE) for a given sample size, power, and type-I error rate. The efficacy is defined as VE = 1 - cumulative-risk ratio, and the function returns both absolute and relative minimum detectable VE. The NULL hypothesis is that VE = 0 and the alternate hypothesis in that VE is not equal to 0.

Usage

get_cohort_mindet_VE_crr(
  anticipated_VE_for_each_brand_and_variant = matrix(data = c(0.8, 0.5, 0.3, 0.3, 0.5,
    0.8, 0.9, 0.5, 1), nrow = 3, ncol = 3, byrow = F, 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,
  power = 0.8,
  alpha = 0.05,
  confounder_adjustment_Rsquared = 0,
  prob_missing_data = 0.1,
  total_subjects = seq(1000, 10000, 25)
)

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).
power	the power to detect the VE. It is equal to 1 - Type-II error. It is a numeric that must take a value between 0 and 1.
alpha	Type-I error probability. 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.

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.

In general, while calculating minimum detectable VE it is not necessary to ask for anticipated_VE_for_each_brand_and_variant. The reason we need it in the multiple variant and multiple vaccine scenario is explained next.

After we obtain the cumulative risk table our next step is to calculate the minimum detectable VE for each absolute and relative VE combination. For absolute VE we extract a I x 2 sub-table of cumulative-risk from the larger (I + 1) x (M + 1) cross table of cumulative-risks. The two columns are for the vaccine of interest and placebo. The effective sample size for this sub-table and the absolute VE is then total_subjects * sub_table_probability_sum * (1 - prob_missing_data) * (1 - confounder_adjustment_Rsquared). Here sub_table_probability_sum is the sum of the cells of the sub_table. This sum corresponds to the percentage of the total_subjects that can be used for a specific absolute VE calculation. The effective overall coverage in this sub-table is the rescaled probability of being vaccinated in the I x 2 sub-table. The effective overall attack rate in unvaccinated in this sub-table is the cumulative-risk of being a case of strain of interest among the unvaccinated subjects in the I x 2 sub-table. We then simply pass these adjusted parameters to the function epi.sscohortc of the R package epiR to obtain the minimum detectable absolute VE. For relative VE the process is similar to absolute VE, except that instead of placebo we select a I x 2 sub-table where the columns are the two vaccines of interest.

Value

A data frame consisting of the input parameters, absolute and relative VE combinations, and the minimum detectable VE 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.