| Title: | Vaccine Efficacy Estimation Package |
|---|---|
| Description: | Set of functions that implement the PoDBAY method, described in the publication 'A method to estimate probability of disease and vaccine efficacy from clinical trial immunogenicity data' by Julie Dudasova, Regina Laube, Chandni Valiathan, Matthew C. Wiener, Ferdous Gheyas, Pavel Fiser, Justina Ivanauskaite, Frank Liu and Jeffrey R. Sachs (NPJ Vaccines, 2021), <doi:10.1038/s41541-021-00377-6>. |
| Authors: | Pavel Fiser (MSD) [aut], Tomas Bartonek (MSD) [aut], Julie Dudasova (MSD) [aut, cre], Regina Laube (MSD) [aut] |
| Maintainer: | Julie Dudasova (MSD) <[email protected]> |
| License: | GPL-3 |
| Version: | 1.4.3 |
| Built: | 2024-11-06 04:12:03 UTC |
| Source: | https://github.com/cran/PoDBAY |
Function assigns subject-level probability of disease based on PoD curve and subject level titer.
x |
numeric vector - vector of estimated PoD values |
The input into the function is either calculated using PoD function or if the PoD curve is unknown the same arbitrary PoD can be assigned to the whole population.
Subject level probability of disease for the population
Function creates non-diseased immunogenicity subset, and vaccinated and control immunogenicity subsets based on chosen method. The immunogenicity subsets are provided in the form of population class objects (see the Population-class function for more details).
BlindSampling(diseased, nondiseased, method = list(name = "Full", value = NA))BlindSampling(diseased, nondiseased, method = list(name = "Full", value = NA))
diseased |
|
nondiseased |
|
method |
named list: "name" possible inputs "Full", "Ratio", "Fixed"; "value" = numeric value |
For details about the method parameter see ImmunogenicitySubset function.
ImmunogenicityVaccinated: vaccinated subjects in the immunogenicity subset, Population-class object (N, mean, stdDev, titers)
ImmunogenicityControl: control subjects in the immunogenicity subset, Population-class object (N, mean, stdDev, titers)
ImmunogenicityNondiseased: non-diseased subjects in the immunogenicity subset, Population-class object (N, mean, stdDev, titers)
# Data preparation data(diseased) data(nondiseased) ## Example 1 # Creating immunogenicity subset, method = "Full" ImmunogenicitySubsetFull <- BlindSampling(diseased, nondiseased, method = list(name = "Full", value = NA)) ## Example 2 # Creating of immunogenicity subset, method = "Ratio" ImmunogenicitySubsetRatio <- BlindSampling(diseased, nondiseased, method = list(name = "Ratio", value = 4)) ## Example 3 # Creating of immunogenicity subset, method = "Fixed" ImmunogenicitySubsetFixed <- BlindSampling(diseased, nondiseased, method = list(name = "Fixed", value = 100))# Data preparation data(diseased) data(nondiseased) ## Example 1 # Creating immunogenicity subset, method = "Full" ImmunogenicitySubsetFull <- BlindSampling(diseased, nondiseased, method = list(name = "Full", value = NA)) ## Example 2 # Creating of immunogenicity subset, method = "Ratio" ImmunogenicitySubsetRatio <- BlindSampling(diseased, nondiseased, method = list(name = "Ratio", value = 4)) ## Example 3 # Creating of immunogenicity subset, method = "Fixed" ImmunogenicitySubsetFixed <- BlindSampling(diseased, nondiseased, method = list(name = "Fixed", value = 100))
Function assigns disease status (DS) to vaccinated and control groups and based on that calculates the case-count efficacy. Vaccinated and control groups are provided in the form of population class objects (see the Population-class function for more details).
Input populations need to contain information about Probability of disease (PoD) for each subject - calculated using population$assignPoD(PoD(x)). See PoD function for further details.
ClinicalTrial(vaccinated, control, CI = 0.95)ClinicalTrial(vaccinated, control, CI = 0.95)
vaccinated |
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control |
|
CI |
numeric: value from (0, 1) interval, confidence level of interest |
vaccinated: vaccinated subjects with assigned DS, Population-class object
control: control subjects with assigned DS, Population-class object
efficacy: case-count efficacy
confidenceInterval: case-count efficacy confidence interval calculated with waldCI() function
# Loading vaccinated, control population data with PoD information data(vaccinated) data(control) # Estimating the disease status and case-count efficacy with 95\% confidence interval CT <- ClinicalTrial(vaccinated, control, CI = 0.95) CT$efficacy CT$confidenceInterval CT$vaccinated# Loading vaccinated, control population data with PoD information data(vaccinated) data(control) # Estimating the disease status and case-count efficacy with 95\% confidence interval CT <- ClinicalTrial(vaccinated, control, CI = 0.95) CT$efficacy CT$confidenceInterval CT$vaccinated
Function works the same way as ClinicalTrial function but it also calculates 80% and 90% confidence intervals.
ClinicalTrialCoverage(vaccinated, control, CI = 0.95)ClinicalTrialCoverage(vaccinated, control, CI = 0.95)
vaccinated |
|
control |
|
CI |
numeric: value from (0, 1) interval, confidence level of interest |
vaccinated: vaccinated subjects with assigned DS, Population-class object
control: control subjects with assigned DS, Population-class object
efficacy: case-count efficacy
confidenceInterval: confidence interval calculated with waldCI function
confidenceInterval90: 90% confidence interval calculated with waldCI function
confidenceInterval80: 80% confidence interval calculated with waldCI function
A dataset containing the N, mean, stdDev, titers of control subjects. The dataset is provided in the form of population class object (see the Population-class function for more details).
controlcontrol
Population class object:
number of subjects
mean of titers
standard deviation of titers
subject level titers
Function calculates the log likelihood value which is used after the initial guesses of the parameters are set in the PoDMLE function.
cppMLE(params, nondiseasedTiters, diseasedTiters, adjustTiters = FALSE, adjustFrom = log2(10), adjustTo = log2(5))cppMLE(params, nondiseasedTiters, diseasedTiters, adjustTiters = FALSE, adjustFrom = log2(10), adjustTo = log2(5))
params |
named numeric vector: PoD curve parameters ("et50", "slope", "pmax") |
nondiseasedTiters |
numeric vector: non-diseased subjects titers |
diseasedTiters |
numeric vector: diseased subjects titers |
adjustTiters |
boolean: set to TRUE if titer values should be adjusted, for details see |
adjustFrom |
numeric: value specifying the detection limit, all values below the detection limit will be adjusted to adjustTo value |
adjustTo |
numeric: value to which titers below the detection limit will be adjusted |
cppMLE function is used inside of PoDMLE function and estimates the PoD curve paramers.
Based on the provided titers for diseased and non-diseased groups the PoD curve parameters which maximize the log likelihood are chosen as optimal.
Difference between MLE and cppMLE is only that cppMLE use cppPoD function instead of PoD. This step significantly improves the computation speed and provides the same results.
log likelihood, numeric value
# Data preparation data(diseased) data(nondiseased) data(PoDParams) # MLE calculation cppMLE(PoDParams, nondiseased$titers, diseased$titers)# Data preparation data(diseased) data(nondiseased) data(PoDParams) # MLE calculation cppMLE(PoDParams, nondiseased$titers, diseased$titers)
Function calculates probability of disease (PoD) for given titers according to a PoD curve.
cppPoD(titer, pmax, et50, slope, adjustTiters = FALSE, adjustFrom = 0, adjustTo = 0)cppPoD(titer, pmax, et50, slope, adjustTiters = FALSE, adjustFrom = 0, adjustTo = 0)
titer |
numeric vector: vector of subject level titers |
pmax |
numeric: maximum PoD |
et50 |
numeric: titer value corresponding to pmax/2 value, PoD(et50) = pmax/2 |
slope |
numeric: slope of the PoD curve |
adjustTiters |
boolean: set to TRUE if titer values should be adjusted, for details see |
adjustFrom |
numeric: value specifying the detection limit, all values below the detection limit will be adjusted to adjustTo value |
adjustTo |
numeric: value to which titers below the detection limit will be adjusted |
See PoD function for more details. These two functions are equivalent. Usage of cppPoD significantly improves the computation speed over the PoD function.
vector of PoDs
A dataset containing the N, mean, stdDev, titers of diseased subjects. The dataset is provided in the form of population class object (see the Population-class function for more details).
diseaseddiseased
Population class object:
number of subjects
mean of titers
standard deviation of titers
subject level titers
Function summarizes PoDBAY efficacy statistics (mean, median, confidence intervals) based on the set of estimated efficacies and chosen condfidence level. (Set of efficacies is a vector obtained by number of replications specified by repeatCount. These replications are performed for calculation of a confidence interval. For more details, see the supplementary material of the article).
EfficacyCI(efficacySet, ci = 0.95)EfficacyCI(efficacySet, ci = 0.95)
efficacySet |
numeric vector: estimated PoDBAY efficacies from |
ci |
numeric: required confidence level |
Confidence intervals are calculated using quantiles of estimated efficacies.
named list: mean, median, CILow, CIHigh
## Data preparation data(efficacySet) ## Example 1 EfficacyCI(efficacySet, ci = 0.95)## Data preparation data(efficacySet) ## Example 1 EfficacyCI(efficacySet, ci = 0.95)
Function summarizes PoDBAY efficacy statistics (mean, median, confidence intervals) at 80%, 90% and user-defined confidence levels, based on the set of estimated efficacies. (Set of efficacies is a vector obtained by number of replications specified by repeatCount. These replications are performed for calculation of a confidence interval. For more details, see the supplementary material of the article).
EfficacyCICoverage(efficacySet, ci = 0.95)EfficacyCICoverage(efficacySet, ci = 0.95)
efficacySet |
numeric vector: estimated PoDBAY efficacies from |
ci |
numeric: value from (0, 1) interval, confidence level of interest |
Confidence intervals are calculated using quantiles of estimated efficacies.
named list: mean, median, CILow, CIHigh
## Data preparation data(efficacySet) ## Example 1 EfficacyCICoverage(efficacySet, ci = 0.95)## Data preparation data(efficacySet) ## Example 1 EfficacyCICoverage(efficacySet, ci = 0.95)
Function calculates the PoDBAY efficacy based on the PoD curve parameters and titer distribution parameters (mean, sd) for vaccinated and control groups.
efficacyComputation(PoDParameters, means = NA, standardDeviations = NA, adjustTiters = FALSE, adjustFrom = NA, adjustTo = NA)efficacyComputation(PoDParameters, means = NA, standardDeviations = NA, adjustTiters = FALSE, adjustFrom = NA, adjustTo = NA)
PoDParameters |
named data frame ("pmax", "slope", "et50"): PoD curve parameters |
means |
named list ("vaccinated", "control"): mean values of vaccinated and control subjects titers |
standardDeviations |
named list ("vaccinated", "control"): standard deviations of vaccinated and control subjects titers |
adjustTiters |
boolean: set to TRUE if titer values should be adjusted, for details see |
adjustFrom |
numeric: value specifying the detection limit, all values below the detection limit will be adjusted to adjustTo value |
adjustTo |
numeric: value to which titers below the detection limit will be adjusted |
.
E[PoD] for each group is calculated as integral from -Inf to Inf of (titer density function) * (PoD Curve); for further details see Example2 andExpectedPoD function.
efficacy: numeric value
## Data preparation data(vaccinated) data(control) data(PoDParams) ## Example 1 means <- list(vaccinated = vaccinated$mean, control = control$mean) standardDeviations <- list(vaccinated = vaccinated$stdDev, control = control$stdDev) efficacyComputation(PoDParams, means, standardDeviations)## Data preparation data(vaccinated) data(control) data(PoDParams) ## Example 1 means <- list(vaccinated = vaccinated$mean, control = control$mean) standardDeviations <- list(vaccinated = vaccinated$stdDev, control = control$stdDev) efficacyComputation(PoDParams, means, standardDeviations)
A dataset containing estimated set of PoDBAY efficacies. (Set of efficacies is a vector obtained by number of replications specified by repeatCount. These replications are performed for calculation of a confidence interval. For more details, see the supplementary material of the article).
efficacySetefficacySet
vector
PoDBAY efficacies
Function calculates squared difference between input (reference value, or for example true in the simulation setup) efficacy and efficacy calculated based on input parameters of PoD curve and input titer distributions of vaccinated and control groups.
efficacySquaredError(params, TrueEfficacy, titerFun, adjustTiters = FALSE, adjustFrom = 0, adjustTo = 0)efficacySquaredError(params, TrueEfficacy, titerFun, adjustTiters = FALSE, adjustFrom = 0, adjustTo = 0)
params |
numeric vector: vector of et50 and slope; efficacy calculation is independent of Pmax and thus Pmax is excluded |
TrueEfficacy |
numeric value: input efficacy value |
titerFun |
list: list of probability density functions for vaccinated and control groups |
adjustTiters |
boolean: set to TRUE if titer values should be adjusted, for details see |
adjustFrom |
numeric: value specifying the detection limit, all values below the detection limit will be adjusted to adjustTo value |
adjustTo |
numeric: value to which titers below the detection limit will be adjusted |
Function is used inside the PoDEfficacySquaredError function for calculation of the PoD parameters.
Squared difference between calculated and reference efficacy
## Example 1 data(vaccinated) data(control) data(PoDParams) # Choosing et50 and slope as the inputs params <- list("et50" = 4, "slope" = 6) # Using probability density function from the populations titerFun <- list( function(x) {dnorm(x, mean = vaccinated$mean, sd = vaccinated$stdDev)}, function(x) {dnorm(x, mean = control$mean, sd = control$stdDev)} ) # Assigning true efficacy TrueEfficacy <- 0.53 # Sqaured difference between true and calcuated efficacy efficacySquaredError(params, TrueEfficacy, titerFun)## Example 1 data(vaccinated) data(control) data(PoDParams) # Choosing et50 and slope as the inputs params <- list("et50" = 4, "slope" = 6) # Using probability density function from the populations titerFun <- list( function(x) {dnorm(x, mean = vaccinated$mean, sd = vaccinated$stdDev)}, function(x) {dnorm(x, mean = control$mean, sd = control$stdDev)} ) # Assigning true efficacy TrueEfficacy <- 0.53 # Sqaured difference between true and calcuated efficacy efficacySquaredError(params, TrueEfficacy, titerFun)
A dataset containing estimated set of PoD curve parameters. (Set of PoD curve parameters is a vector obtained by number of replications specified by repeatCount. These replications are performed for calculation of a confidence interval. For more details, see the supplementary material of the article).
estimatedParametersestimatedParameters
data frame
pmax: maximum PoD
et50: titer value corresponding to the pmax/2
slope: slope of the PoD curve
Function calculates the integral of multiplication of two functions: PoD curve and titer probability density function.
ExpectedPoD(f.pod, f.titer)ExpectedPoD(f.pod, f.titer)
f.pod |
function(x): PoD curve, estimated sigmoid function relating titers to a probability of disease |
f.titer |
function(x): titer probability density function, distribution of titer values in a group. |
Function calculates integral from -Inf to +Inf of titer probability density function multiplied by the PoD curve.
It is used mainly in the PoDBAY efficacy calculation efficacyComputation.
Value of the integral of the multiplication of the two functions
# Example 1 data(vaccinated) data(control) data(PoDParams) # Defining the PoD curve funPoD <- function(x) PoD(x, pmax = PoDParams$pmax, et50 = PoDParams$et50, slope = PoDParams$slope) # Defining the titer distribution for vaccinated and control groups funVaccinated <- function(x) dnorm(x, mean = vaccinated$mean, sd = vaccinated$stdDev) funControl <- function(x) dnorm(x, mean = control$mean, sd = control$stdDev) # Calculating the expected probability of disease aucVaccinated <- ExpectedPoD(funPoD, funVaccinated) aucControl <- ExpectedPoD(funPoD, funControl) # PoDBAY efficacy estimation efficacy <- 1 - aucVaccinated/aucControl# Example 1 data(vaccinated) data(control) data(PoDParams) # Defining the PoD curve funPoD <- function(x) PoD(x, pmax = PoDParams$pmax, et50 = PoDParams$et50, slope = PoDParams$slope) # Defining the titer distribution for vaccinated and control groups funVaccinated <- function(x) dnorm(x, mean = vaccinated$mean, sd = vaccinated$stdDev) funControl <- function(x) dnorm(x, mean = control$mean, sd = control$stdDev) # Calculating the expected probability of disease aucVaccinated <- ExpectedPoD(funPoD, funVaccinated) aucControl <- ExpectedPoD(funPoD, funControl) # PoDBAY efficacy estimation efficacy <- 1 - aucVaccinated/aucControl
Function extracts diseased subjects from vaccinated and control groups if the data have assigned disease status (for example using ClinicalTrial function). The vaccinated and control data are provided in the form of population class objects (see the Population-class function for more details).
ExtractDiseased(vaccinated, control)ExtractDiseased(vaccinated, control)
vaccinated |
|
control |
|
diseased subjects, Population-class object: a subset of control and vaccinated subjects with disease status = TRUE.
## Example 1 # Data preparation data(vaccinated) data(control) # Estimating the disease status and case-count efficacy with CI ClinicalTrial(vaccinated, control, CI = 0.95) # Extracting the disease cases ExtractDiseased(vaccinated, control)## Example 1 # Data preparation data(vaccinated) data(control) # Estimating the disease status and case-count efficacy with CI ClinicalTrial(vaccinated, control, CI = 0.95) # Extracting the disease cases ExtractDiseased(vaccinated, control)
Function extracts non-diseased subjects from vaccinated and control groups if the data have assigned disease status (for example using ClinicalTrial function). The vaccinated and control data are provided in the form of population class objects (see the Population-class function for more details).
ExtractNondiseased(vaccinated, control)ExtractNondiseased(vaccinated, control)
vaccinated |
|
control |
|
non-diseased subjects, Population-class object: a subset of control and vaccinated subjects with disease status = FALSE.
## Example 1 # Data preparation data(vaccinated) data(control) # Estimating the disease status and case-count efficacy with CI ClinicalTrial(vaccinated, control, CI = 0.95) # Extracting the non-diseased subjects ExtractNondiseased(vaccinated, control)## Example 1 # Data preparation data(vaccinated) data(control) # Estimating the disease status and case-count efficacy with CI ClinicalTrial(vaccinated, control, CI = 0.95) # Extracting the non-diseased subjects ExtractNondiseased(vaccinated, control)
Function calculates the root mean squared error (RMSE) between provided PoD values and calculated PoD values. The latter are calculated using for provided titers and provided PoD curve parameters.
By using the input titers PoDParamPointEstimation function and median of the estimated set of PoD curve parameters (output of PoDParamEstimation function), the point estimate of PoD curve can be obtained (for details see PoDParamPointEstimation function).
fitPoD(params, TitersInput, CurveTitersMedian)fitPoD(params, TitersInput, CurveTitersMedian)
params |
named data frame ("pmax", "slope", "et50"): provided PoD curve parameters |
TitersInput |
numeric vector: provided titers |
CurveTitersMedian |
numeric vector: provided PoD values |
negative RMSE
## Data preparation data(estimatedParameters) data(PoDParams) ## Example 1 # grid of titers TitersInput <- seq(from = 0, to = 20, by = 0.01) # for each estimated PoD curve calculate functional values functionValues <- matrix(NA, nrow = nrow(estimatedParameters$resultsPriorReset), ncol = length(TitersInput)) for (i in 1:nrow(estimatedParameters$resultsPriorReset)) { functionValues[i,] <- PoD(TitersInput, pmax = estimatedParameters$resultsPriorReset[i,1], et50 = estimatedParameters$resultsPriorReset[i,3], slope = estimatedParameters$resultsPriorReset[i,2], adjustTiters = FALSE) } # functional values corresponding to the median of the estimated PoD curve parameters CurveTitersMedian <- apply(functionValues, 2, median) # squared error of CurveTitersMedian and functional values of "params" curve fitPoD(PoDParams, TitersInput, CurveTitersMedian)## Data preparation data(estimatedParameters) data(PoDParams) ## Example 1 # grid of titers TitersInput <- seq(from = 0, to = 20, by = 0.01) # for each estimated PoD curve calculate functional values functionValues <- matrix(NA, nrow = nrow(estimatedParameters$resultsPriorReset), ncol = length(TitersInput)) for (i in 1:nrow(estimatedParameters$resultsPriorReset)) { functionValues[i,] <- PoD(TitersInput, pmax = estimatedParameters$resultsPriorReset[i,1], et50 = estimatedParameters$resultsPriorReset[i,3], slope = estimatedParameters$resultsPriorReset[i,2], adjustTiters = FALSE) } # functional values corresponding to the median of the estimated PoD curve parameters CurveTitersMedian <- apply(functionValues, 2, median) # squared error of CurveTitersMedian and functional values of "params" curve fitPoD(PoDParams, TitersInput, CurveTitersMedian)
Function upsamples (by random sampling with replacement) titers from the immunogenicity subset to the required size.
If the size of the immunogenicity subset matches the required size, nothing happens and the original titers from the immunogenicity subset are returned.
GenerateNondiseased(blindNondiseasedTiters, nondiseasedCount)GenerateNondiseased(blindNondiseasedTiters, nondiseasedCount)
blindNondiseasedTiters |
numeric vector: vector of non-diseased subjects titer values |
nondiseasedCount |
numeric: total number of non-diseased subjects, required size of the non-diseased population |
The inputs should come from immunogenicity subset. "nondiseasedCount" represents number of all non-diseased patients in the clinical trial.
Immunogenicity subset populations are obtained from function BlindSampling. Immunogenicity subset represents a sample from the non-diseased population.
In this function, sampling with replacement to the required "nondiseasedCount" of the immunogenecitry subset is performed. The function is used inside PoDParamEstimation function.
nondiseasedTiters: numeric vector of all non-diseased subjects titers
## Data preparation data(nondiseased) ## Example 1 # Creating imunogenicity subset, method = "Full" NondiseasedImmunogenicitySubset <- ImmunogenicitySubset(diseased, nondiseased, method = list(name = "Full", value = "NA")) # Number of all non-diseased subjects in the clinical trial nondiseasedGenerationCount <- nondiseased$N # Upsampling of non-diseased titers GenerateNondiseased(NondiseasedImmunogenicitySubset$titers, nondiseasedGenerationCount)## Data preparation data(nondiseased) ## Example 1 # Creating imunogenicity subset, method = "Full" NondiseasedImmunogenicitySubset <- ImmunogenicitySubset(diseased, nondiseased, method = list(name = "Full", value = "NA")) # Number of all non-diseased subjects in the clinical trial nondiseasedGenerationCount <- nondiseased$N # Upsampling of non-diseased titers GenerateNondiseased(NondiseasedImmunogenicitySubset$titers, nondiseasedGenerationCount)
Function generates the population class object using provided summary statistics.
generatePopulation(N, mean, stdDev, unknownDistribution = FALSE, UDFunction = NULL)generatePopulation(N, mean, stdDev, unknownDistribution = FALSE, UDFunction = NULL)
N |
numeric: number of subjects in the population |
mean |
numeric: mean of titers |
stdDev |
numeric: standard deviation of titers |
unknownDistribution |
logical: TRUE if there is an unknown factor affacting the shape of titer distribution |
UDFunction |
function: function defining the unknown factor affecting the shape of titer distribution |
generated population class object with all its characteristics defined in the input parameters
# Example 1: empty population population0 <- generatePopulation() # Example 2 population1 <- generatePopulation(N = 100, mean = 5, stdDev = 2)# Example 1: empty population population0 <- generatePopulation() # Example 2 population1 <- generatePopulation(N = 100, mean = 5, stdDev = 2)
Function calculates the number of diseased subjects (disease status = TRUE) in the Population-class object.
Input into the function, "diseaseStatus", is taken from the Population-class object attribute. Information about disease status is written into the Population-class object by the ClinicalTrial() function.
numeric: number of the diseased subjects in the Population-class object
Function returns titers of diseased subjects (disease status = TRUE) in the Population-class object.
Input into the function, "diseaseStatus", is taken from the Population-class object attribute. Information about disease status is written into the Population-class object by the ClinicalTrial() function.
numeric vector: titers of diseased subjects in the Population-class object
Function calculates the number of non-diseased subjects (disease status = FALSE) in the Population-class object.
Input into the function, "diseaseStatus", is taken from the Population-class object attribute. Information about disease status is written into the Population-class object by the ClinicalTrial() function.
numeric: number of the non-diseased subjects in the Population-class object
Function returns titers of non-diseased subjects (disease status = FALSE) in the Population-class object.
Input into the function, "diseaseStatus", is taken from the Population-class object attribute. Information about disease status is written into the Population-class object by the ClinicalTrial() function.
numeric vector: titers of non-diseased subjects in the Population-class object
Returns subject level titers. If titers are not yet generated, the function generates them based on Population-class object attributes: N, mean, stdDev.
Inputs into the function (N, mean, stdDev) are taken from the Population-class object attributes.
Subject level titers
Function generates unknown part of the titers which is eventually added to the original titers in popX and to the original titer distribution in popFun.
n |
numeric: number of subjects in the population |
Input into the function: UDFunction is taken from the Population-class object. UDFunction is used for generating the unknown part of the titer distribution.
unknown part of the titers
Function creates the immunogenicity subset based on the chosen method.
ImmunogenicitySubset(diseased, nondiseased, method = list(name = "Full", value = NA))ImmunogenicitySubset(diseased, nondiseased, method = list(name = "Full", value = NA))
diseased |
|
nondiseased |
|
method |
named list: a selected method for creating the immunogenicity subset method$name
method$value
|
The total immunogenicity subset consists of the diseased immunogenicity subset and non-diseased immunogenicity subset. For all three methods implemented, we assume that the diseased immunogenicity subset contains all disease cases in the trial. Based on the chosen method, the the size of the non-diseaded immunogenicity subset can be derived as follows:
Size = number of subjects in the non-diseased immunogenicity subset
Titers = values of titers from which we want to sample in order to simulate the non-diseased immunogenicity subset
#Diseased = total number of diseased in the clinical trial
#Nondiseased = total number of non-diseased in the clinical trial
method$name = "Full"
Size = #Nondiseased
Titers = Nondiseased Titers
method$name = "Ratio"
Size = method$value * #Diseased
Titers = Nondiseased Titers
method$name = "Fixed"
Size = method$value
Titers = Nondiseased Titers + Diseased Titers
Immunogenicity subset with subject level information about vaccination status and disease status, provided in the form of Population-class object
## Example 1 # Data preparation data(diseased) data(nondiseased) ImmunogenicitySubset(diseased, nondiseased, method = list(name = "Ratio", value = 4))## Example 1 # Data preparation data(diseased) data(nondiseased) ImmunogenicitySubset(diseased, nondiseased, method = list(name = "Ratio", value = 4))
Error meassage: the input value for "name" is incorrent
incorrectInput(name)incorrectInput(name)
name |
name of the input value |
error message: "the input value for "name" is incorrect"
Error meassage: the input value for "name" is incorrect.
incorrectPopulationInput(name)incorrectPopulationInput(name)
name |
name of the input value |
error message: "The input value for "name" is incorrect. Input needs to be a population class object."
Function jitters the mean of the population.
Jittering is adding noise to the mean. The jittered mean is sampled from the distribution with the population mean and population standard deviation divided by the number of subjects in the population. The input population is provided in the form of population class objects (see the Population-class function for more details).
JitterMean(blindPopulation)JitterMean(blindPopulation)
blindPopulation |
|
Jittered mean, numeric value
## Data preparation data(vaccinated) ## Example 1 vaccinated$mean JitterMean(vaccinated)## Data preparation data(vaccinated) ## Example 1 vaccinated$mean JitterMean(vaccinated)
Function calculates the log likelihood value which is used after the initial guesses of the parameters are set in the PoDMLE function.
MLE(params, nondiseasedTiters, diseasedTiters, adjustTiters = FALSE, adjustFrom = log2(10), adjustTo = log2(5))MLE(params, nondiseasedTiters, diseasedTiters, adjustTiters = FALSE, adjustFrom = log2(10), adjustTo = log2(5))
params |
named numeric vector: PoD curve parameters (et50, slope, pmax) |
nondiseasedTiters |
numeric vector: non-diseased subjects titers |
diseasedTiters |
numeric vector: diseased subjects titers |
adjustTiters |
boolean: set to TRUE if titer values should be adjusted, for details see |
adjustFrom |
numeric: value specifying the detection limit, all values below the detection limit will be adjusted to adjustTo value |
adjustTo |
numeric: value to which titers below the detection limit will be adjusted |
MLE function is used inside of PoDMLE function and esimates the PoD curve parameters.
Based on the provided titers for diseased and non-diseased subjects the PoD curve parameters which maximize the log likelihood are chosen as optimal estimates of parameters.
log likelihood, numeric value
# Data preparation data(diseased) data(nondiseased) data(PoDParams) # MLE calculation MLE(PoDParams, nondiseased$titers, diseased$titers)# Data preparation data(diseased) data(nondiseased) data(PoDParams) # MLE calculation MLE(PoDParams, nondiseased$titers, diseased$titers)
A dataset containing the N, mean, stdDev, titers of non-diseased subjects. The dataset is provided in the form of population class object (see the Population-class function for more details).
nondiseasednondiseased
Population class object:
number of subjects
mean of titers
standard deviation of titers
subject level titers
Converts numeric format to boolean format.
numToBool(x)numToBool(x)
x |
numeric value (0, 1) |
If the function is supposed to be used on a vector, the form sapply("vector", numToBool) needs to be applied.
boolean value (T, F)
dStatus <- c(0,0,1,1,0,1) sapply(dStatus, numToBool)dStatus <- c(0,0,1,1,0,1) sapply(dStatus, numToBool)
Function finds the pmax parameter of the PoD curve using control subjects summary statistics (mean, sd), observed incidence rate and previsouly estimated et50 and slope by PoDEfficacySquaredError function.
PmaxEstimation(IncidenceRate, params, control, adjustTiters = FALSE, adjustFrom = NA, adjustTo = NA)PmaxEstimation(IncidenceRate, params, control, adjustTiters = FALSE, adjustFrom = NA, adjustTo = NA)
IncidenceRate |
numeric: observed incidence rate in overall (control) subjects |
params |
numeric vector: et50 and slope |
control |
|
adjustTiters |
boolean: set to TRUE if titer values should be adjusted, for details see |
adjustFrom |
numeric: value specifying the detection limit, all values below the detection limit will be adjusted to adjustTo value |
adjustTo |
numeric: value to which titers below the detection limit will be adjusted |
PoD curve parameter pmax
## Example 1 data(vaccinated) data(control) # Assigning true efficacy TrueEfficacy <- 0.53 # PoD curve parameters (et50, slope) estimation params <- PoDEfficacySquaredError(TrueEfficacy, vaccinated, control) # Assigning incidence rate (observed incidence rate) IncidenceRate <- 0.2 # pmax estimation pmax <- PmaxEstimation(IncidenceRate, params, control) # combining PoD curve parameters PoDParams <- unlist(c(params, pmax))## Example 1 data(vaccinated) data(control) # Assigning true efficacy TrueEfficacy <- 0.53 # PoD curve parameters (et50, slope) estimation params <- PoDEfficacySquaredError(TrueEfficacy, vaccinated, control) # Assigning incidence rate (observed incidence rate) IncidenceRate <- 0.2 # pmax estimation pmax <- PmaxEstimation(IncidenceRate, params, control) # combining PoD curve parameters PoDParams <- unlist(c(params, pmax))
Function calculates probability of disease (PoD) corresponding to given titers according to a sigmoid PoD curve.
PoD(titer, pmax, et50, slope, adjustTiters = FALSE, adjustFrom = 0, adjustTo = 0)PoD(titer, pmax, et50, slope, adjustTiters = FALSE, adjustFrom = 0, adjustTo = 0)
titer |
numeric vector: subject level titers |
pmax |
numeric: maximum PoD |
et50 |
numeric: titer values corresponding to pmax/2 value, PoD(et50) = pmax/2 |
slope |
numeric: slope of the PoD curve |
adjustTiters |
boolean: set to TRUE if titer values should be adjusted, for details see |
adjustFrom |
numeric: value specifying the detection limit, all values below the detection limit will be adjusted to adjustTo value |
adjustTo |
numeric: value to which titers below the detection limit will be adjusted |
PoD is calculated as:
and
.
vector of PoDs
data(vaccinated) data(PoDParams) PoD(vaccinated$titers, pmax = PoDParams$pmax, et50 = PoDParams$et50, slope = PoDParams$slope)data(vaccinated) data(PoDParams) PoD(vaccinated$titers, pmax = PoDParams$pmax, et50 = PoDParams$et50, slope = PoDParams$slope)
PoDBAY package accompanies the article 'A method to estimate probability of disease and vaccine efficacy from clinical trial immunogenicity data'. It helps to setup the workflow for vaccine efficacy estimation and clinical trial simulation using the PoDBAY method.
It has two main applications:
Estimation of vaccine efficacy using subject level immunogenicity data
Simulation of clinical trial
Pavel Fiser, Tomas Bartonek, Julie Dudasova
Function calculates the PoDBAY efficacy based on the set of PoD curve parameters calculated in PoDParamEstimation function, vaccinated and control immunogenicity subset means and standard deviations.
PoDBAYEfficacy(estimatedParameters, blindVaccinated, blindControl, adjustTiters = FALSE, adjustFrom = log2(10), adjustTo = log2(5))PoDBAYEfficacy(estimatedParameters, blindVaccinated, blindControl, adjustTiters = FALSE, adjustFrom = log2(10), adjustTo = log2(5))
estimatedParameters |
named data frame ("pmax", "slope", "et50"): set of estimated PoD curve parameters |
blindVaccinated |
|
blindControl |
|
adjustTiters |
boolean: set to TRUE if titer values should be adjusted, for details see |
adjustFrom |
numeric: value specifying the detection limit, all values below the detection limit will be adjusted to adjustTo value |
adjustTo |
numeric: value to which titers below the detection limit will be adjusted |
Application of efficacyComputation function to the all PoD curves (each characterized by three PoD parameters) estimated by PoDParamEstimation function.
Inputs into the efficacyComputation are:
PoDParameters: i'th estimated PoD parameters from PoDParamEstimation. i = 1, ..., N, where N = number of estimations in which MLE converges. See PoDMLE for details.
means: jittered means of immunogenicity subset. See JitterMeans for details.
standardDeviations: standard deviations of the vaccinated and control subjects from the immunogenicity subset.
efficacySet, set of PoDBAY effficacies corresponding to estimated set of PoD curve parameters
## Data preparation data(diseased) data(nondiseased) data(estimatedParameters) ## Example 1 # Creating imunogenicity subset, method = "Ratio", value = 4 ImmunogenicitySubset <- BlindSampling(diseased, nondiseased, method = list(name = "Ratio", value = 4)) # Estimating PoD curve parameters nondiseasedGenerationCount <- nondiseased$N estimatedParameters <- PoDParamEstimation(diseased$titers, ImmunogenicitySubset$ImmunogenicityNondiseased$titers, nondiseasedGenerationCount, repeatCount = 10) # Estimating PoDBAY efficacy PoDBAYEfficacy(estimatedParameters$results, ImmunogenicitySubset$ImmunogenicityVaccinated, ImmunogenicitySubset$ImmunogenicityControl)## Data preparation data(diseased) data(nondiseased) data(estimatedParameters) ## Example 1 # Creating imunogenicity subset, method = "Ratio", value = 4 ImmunogenicitySubset <- BlindSampling(diseased, nondiseased, method = list(name = "Ratio", value = 4)) # Estimating PoD curve parameters nondiseasedGenerationCount <- nondiseased$N estimatedParameters <- PoDParamEstimation(diseased$titers, ImmunogenicitySubset$ImmunogenicityNondiseased$titers, nondiseasedGenerationCount, repeatCount = 10) # Estimating PoDBAY efficacy PoDBAYEfficacy(estimatedParameters$results, ImmunogenicitySubset$ImmunogenicityVaccinated, ImmunogenicitySubset$ImmunogenicityControl)
Supplementary function for PoDCurvePlot function. Function calculates the confidence ribbon around the PoD curve.
PoDCI(data, ci = 0.95)PoDCI(data, ci = 0.95)
data |
numeric vector for which we the confidence intervals should be calculated |
ci |
numeric: required confidence level |
lower bound of CI median value upper bound of CI
## Data preparation data <- 0:100 ## Example 1 PoDCI(data, ci = 0.95)## Data preparation data <- 0:100 ## Example 1 PoDCI(data, ci = 0.95)
Supplementary function for plotting the PoD curve with the confidence ribbon (of a required level). Input values are related to PoDBAY package structure.
See vignette("EfficacyEstimation", package = "PoDBAY") for an example of application of this function.
PoDCurvePlot(titers, estimatedParameters, ci = 0.95)PoDCurvePlot(titers, estimatedParameters, ci = 0.95)
titers |
numeric vector: grid of titers at which the confidence ribbon should be calculated |
estimatedParameters |
estimatedParameters named data frame (pmax, slope, et50): set of estimated PoD curve parameters, output of |
ci |
numeric, required confidence level |
PoD curve plot
## Data preparation library(ggplot2) data(PoDParams) data(estimatedParameters) ## Example 1 # titers for which we want calculate the confidence intervals titers <- seq(from = 0, to = 15, by = 0.01) # squared error of CurveTitersMedian and functional values of "params" curve PoDCurvePlot(titers, estimatedParameters, ci = 0.95)## Data preparation library(ggplot2) data(PoDParams) data(estimatedParameters) ## Example 1 # titers for which we want calculate the confidence intervals titers <- seq(from = 0, to = 15, by = 0.01) # squared error of CurveTitersMedian and functional values of "params" curve PoDCurvePlot(titers, estimatedParameters, ci = 0.95)
Function finds PoD curve parameters (et50, slope) using population summary statistics (mean, sd) and input (reference value, or for example true in the simulation setup) efficacy.
Efficacy is independent of pmax parameter thus pmax is estimated separately using PmaxEstimation function.
PoDEfficacySquaredError(TrueEfficacy, vaccinated, control, initialSlope = 6, adjustTiters = FALSE, adjustFrom = NA, adjustTo = NA)PoDEfficacySquaredError(TrueEfficacy, vaccinated, control, initialSlope = 6, adjustTiters = FALSE, adjustFrom = NA, adjustTo = NA)
TrueEfficacy |
numeric: input reference efficacy |
vaccinated |
|
control |
|
initialSlope |
numeric: initial slope parameter for the optimization function |
adjustTiters |
boolean: set to TRUE if titer values should be adjusted, for details see |
adjustFrom |
numeric: value specifying the detection limit, all values below the detection limit will be adjusted to adjustTo value |
adjustTo |
numeric: value to which titers below the detection limit will be adjusted |
Function returns et50 and slope PoD curve parameters obtained using efficacySquaredError
i.e. the opimal (output) parameters et50 and slope correspond to the minimal squared difference between input reference efficacy and calculated efficacy.
Pmax parameter is not obtained as efficacy is independent on pmax.
The optim function is used for optimization with method = "L-BFGS-B", 1000 maximum itiretations, (0.1,Inf) boundaries for et50 and (-slopeBoundary, slopeBoundary) boundaries for slope.
NOTE: The reason for slope boundary settings is because from certain value of slope parameter the shape of the PoD curve and the corresponding PoD values for given titers are almost identical. This parameter is supposed to limit the resulting slope value and help MLE to converge to optimal parameters. The value of "slopeBoundaries" is calculated from data according to Dunning, 2015 (https://doi.org/10.1186/s12874-015-0096-9).
PoD curve parameters (et50, slope)
## Example 1 data(vaccinated) data(control) # Assigning reference efficacy TrueEfficacy <- 0.53 # PoD curve parameter estimation PoDEfficacySquaredError(TrueEfficacy, vaccinated, control)## Example 1 data(vaccinated) data(control) # Assigning reference efficacy TrueEfficacy <- 0.53 # PoD curve parameter estimation PoDEfficacySquaredError(TrueEfficacy, vaccinated, control)
Function estimates the optimal PoD curve parameters (pmax, et50, slope) using diseased and non-diseased titers. Initial guess of the slope parameter needs to be provided as an input to the optimization, as well as the lowTiterPercent parameter, which is needed for initial guess of the pmax parameter calculation.
PoDMLE(nondiseasedTiters, diseasedTiters, adjustTiters = FALSE, adjustFrom = log2(10), adjustTo = log2(5), initialSlope = 6, lowTiterPercent = 0.2)PoDMLE(nondiseasedTiters, diseasedTiters, adjustTiters = FALSE, adjustFrom = log2(10), adjustTo = log2(5), initialSlope = 6, lowTiterPercent = 0.2)
nondiseasedTiters |
numeric vector: non-diseased subjects titers |
diseasedTiters |
numeric vector: diseased subjects titers |
adjustTiters |
boolean: set to TRUE if titer values should be adjusted, for details see |
adjustFrom |
numeric: value specifying the detection limit, all values below the detection limit will be adjusted to adjustTo value |
adjustTo |
numeric: value to which titers below the detection limit will be adjusted |
initialSlope |
numeric: initial guess of the slope parameter for the optimization function |
lowTiterPercent |
numeric: value in the interval (0,1) - it represents a fraction of bottom titer values of the whole clinical trial used for calculation of inital guess of the pmax parameter. |
Initial guess of pmax = (number of diseased in the bottom titers + 0.5) / (number of non-diseased and diseased in the bottom titers + 0.5), Initial et50 = intersection point of distributions of non-diseased and diseased groups. If L-BFGS-B optimization fails to converge, a new et50 initial guess is set to median value of all titers.
PoDMLE function estimates the PoD curve parameters by maximizing the likelihood value (see MLE function for details) based on the provided titers for diseased and non-diseased groups.
The optim function is used for optimization with method = "L-BFGS-B", 500 maximum iterations, (0.1,Inf) boundaries for et50, (1e-6,1) boundaries for pmax and (-slopeBoundary, slopeBoundary) boundaries for slope.
NOTE: The reason for slope boundary settings is because from certain value of slope parameter the shape of the PoD curve and the corresponding PoD values for given titers are almost identical. This parameter is expected to limit the resulting slope value and help MLE to converge to optimal parameters. The value of "slopeBoundaries" is calculated as described by Dunning, 2015 (https://doi.org/10.1186/s12874-015-0096-9).
list("et50", "slope", "pmax"), named list of PoD paraters: if MLE converges.
Null: if MLE does not converge.
## EXAMPLE 1: # Data preparation data(diseased) data(nondiseased) # PoD curve parameter estimation PoDMLE(nondiseased$titers, diseased$titers) ## EXAMPLE 2: ## initialSlope and lowTiterPercent variables are adjusted. PoDMLE(nondiseased$titers, diseased$titers, initialSlope = 5, lowTiterPercent = 0.3)## EXAMPLE 1: # Data preparation data(diseased) data(nondiseased) # PoD curve parameter estimation PoDMLE(nondiseased$titers, diseased$titers) ## EXAMPLE 2: ## initialSlope and lowTiterPercent variables are adjusted. PoDMLE(nondiseased$titers, diseased$titers, initialSlope = 5, lowTiterPercent = 0.3)
Function estimates the PoD curve parameters (pmax, slope, et50) using PoDMLE function. Number of PoD curves estimated equals to the repeatCount input parameter.
The estimation is performed using provided diseased and non-diseased subject level data.
PoDParamEstimation(diseasedTiters, nondiseasedTiters, nondiseasedGenerationCount, repeatCount = 500, adjustTiters = FALSE, adjustFrom = log2(10), adjustTo = log2(5))PoDParamEstimation(diseasedTiters, nondiseasedTiters, nondiseasedGenerationCount, repeatCount = 500, adjustTiters = FALSE, adjustFrom = log2(10), adjustTo = log2(5))
diseasedTiters |
numeric vector: all diseased titers, subject level data |
nondiseasedTiters |
numeric vector: non-diseased titers from immunogenicity subset, subject level data |
nondiseasedGenerationCount |
numeric: total number of non-diseased subjects in the clinical trial |
repeatCount |
numeric: how many times is the dataset bootstrapped and the PoD curve parameter estimation performed |
adjustTiters |
boolean: set to TRUE if titer values should be adjusted, for details see |
adjustFrom |
numeric: value specifying the detection limit, all values below the detection limit will be adjusted to adjustTo value |
adjustTo |
numeric: value to which titers below the detection limit will be adjusted |
diseasedTiters: subject level titers of all diseased in the clinical trial
nondiseasedTiters: subject level titers of non-diseased subjects in the immunogenicity subset
There are two possible scenarios
Full: Full information about non-diseased titers is available, i.e subject level data for all non-diseased subjects from the clinical trial (nondiseasedGenerationCount = number of all non-diseased subjects in the clinical trial).
Ratio or Fixed: Information about non-diseased titers is available only for the immunogenicity subset. In order to compensate for these missing titers we upsampling of this subset to the total number of non-diseased (nondiseasedGenerationCount) in the trial is needed.
nondiseasedGenerationCount: number of all non-diseased subjects in the clinical trial
NOTE: Number of estimated parameters can be lower than repeatCount as MLE does not necessary converge in all estimations; failcount (number of iterations in which MLE failed to converge) is also returned; for details see MLE function.
Function steps
Upsample non-diseased if needed (needed for methods Ratio and Fixed) - from immunogenicity subset size (N = NondiseasedImmunogenicitySubset$N) to the whole trial size (N = nondiseasedGenerationCount). For details see GenerateNondiseased function.
Estimate PoD curve: resultsPriorReset
Reset disease status: the purpose is to estimate the confidence intervals of the PoD curve and its parameters
Part of the reset disease status procedure is the non-parametric bootstrap: titers of diseased and non-diseased subjects are pooled, and associated PoDs are calculated using their titer values and estimated PoD curve. Based on the subject level probabilities (PoDs), the disease status is reestimated.
Re-estimate PoD curve: new diseased and non-diseased titers are used to reestimate the PoD curve
results: PoD curve parameters after resetting the disease status, named data.frame of estimated PoD curve parameters (pmax, slope, et50); see details for more information
resultsPriorReset: PoD curve parameters prior to resetting the status, named data.frame of estimated PoD curve parameters (pmax, slope, et50); see details for more information
failcount: number of iterations in which MLE failed to converge; see details for more information
## Data preparation data(diseased) data(nondiseased) ## Example 1 # Creating imunogenicity subset, method = "Full" NondiseasedImmunogenicitySubset <- ImmunogenicitySubset(diseased, nondiseased, method = list(name = "Full", value = "NA")) # Number of all non-diseased subjects in the clinical trial nondiseasedGenerationCount <- nondiseased$N PoDParamEstimation(diseased$titers, NondiseasedImmunogenicitySubset$titers, nondiseasedGenerationCount, repeatCount = 10) ## Example 2 # Creating imunogenicity subset, method = "Ratio", value = 4 NondiseasedImmunogenicitySubset <- ImmunogenicitySubset(diseased, nondiseased, method = list(name = "Ratio", value = 4)) # Number of all non-diseased subjects in the clinical trial nondiseasedGenerationCount <- nondiseased$N PoDParamEstimation(diseased$titers, NondiseasedImmunogenicitySubset$titers, nondiseasedGenerationCount, repeatCount = 10)## Data preparation data(diseased) data(nondiseased) ## Example 1 # Creating imunogenicity subset, method = "Full" NondiseasedImmunogenicitySubset <- ImmunogenicitySubset(diseased, nondiseased, method = list(name = "Full", value = "NA")) # Number of all non-diseased subjects in the clinical trial nondiseasedGenerationCount <- nondiseased$N PoDParamEstimation(diseased$titers, NondiseasedImmunogenicitySubset$titers, nondiseasedGenerationCount, repeatCount = 10) ## Example 2 # Creating imunogenicity subset, method = "Ratio", value = 4 NondiseasedImmunogenicitySubset <- ImmunogenicitySubset(diseased, nondiseased, method = list(name = "Ratio", value = 4)) # Number of all non-diseased subjects in the clinical trial nondiseasedGenerationCount <- nondiseased$N PoDParamEstimation(diseased$titers, NondiseasedImmunogenicitySubset$titers, nondiseasedGenerationCount, repeatCount = 10)
Function returns PoD curve parameters corresponding to the point estimate of PoD curve.
PoDParamPointEstimation(resultsPriorReset, titers = seq(from = 0, to = 20, by = 0.01), optim_titers = FALSE)PoDParamPointEstimation(resultsPriorReset, titers = seq(from = 0, to = 20, by = 0.01), optim_titers = FALSE)
resultsPriorReset |
named data frame ("pmax", "slope", "et50"): set of estimated PoD curve parameters before resetting the disease status; for further details see |
titers |
numeric vector: a grid of titers for PoD curve point estimate calculation |
optim_titers |
logical: TRUE for a predefined sequence of titers |
For each of estimated PoD curves in resultsPriorReset, the function values (probabilities of disease, PoD) for provided grid of titers are calculated.
Median of function values (PoDs) at each provided titer is calculated.
Subsequently, the PoD curve model is fitted to the median datapoins using fitPoD function, in order to get PoD curve parameters close to this median curve.
paramsPointEstimate: named data frame of PoD curve parameters corresponding to the PoD curve point estimate
## Data preparation data(estimatedParameters) ## Example 1 # titers for which we want to optimize the functional values titers <- seq(from = 0, to = 20, by = 0.01) # Point estimate of PoD curve PoDParamPointEstimation(estimatedParameters$resultsPriorReset, titers)## Data preparation data(estimatedParameters) ## Example 1 # titers for which we want to optimize the functional values titers <- seq(from = 0, to = 20, by = 0.01) # Point estimate of PoD curve PoDParamPointEstimation(estimatedParameters$resultsPriorReset, titers)
A dataset containing PoD curve parameters
PoDParamsPoDParams
data frame
pmax: maximum PoD
et50: titer value corresponding to the pmax/2
slope: slope of the PoD curve
Function calculates confidence intervals of the PoD curve parameters (pmax, et50, slope) at user-defined confidence level.
PoDParamsCI(estimatedParameters, ci = 0.95)PoDParamsCI(estimatedParameters, ci = 0.95)
estimatedParameters |
output of |
ci |
numeric: value from (0, 1) interval, confidence level of interest |
CI of all PoD curve parameters
Function calculates confidence intervals (80%, 90% and user-defined) of the PoD curve parameters (pmax, et50, slope).
PoDParamsCICoverage(estimatedParameters, ci = 0.95)PoDParamsCICoverage(estimatedParameters, ci = 0.95)
estimatedParameters |
output of |
ci |
numeric: value from (0, 1) interval, confidence level of interest |
CI of all PoD curve parameters
Function describing the titer distribution of the population: mean, standard deviation and an additional unknown factor affecting the shape of the distribution (e.g. mixture of two normals or other shapes defined by user).
Inputs into the function (mean, stdDev, Unknowndistribution) and getUnknown method are taken from the Population-class object.
Titer distribution function
Population reference class which provides summary and subject level information about the population
Nnumeric: number of subjects in the population
meannumeric: mean value of titers
stdDevnumeric: standard deviation of titers
unknownDistributionlogical: TRUE if titer distribution is not normally /log-normally distributed; titer disrtibution function needs to be defined by user
UDFunctionfunction: user-defined titer distribution
titersnumeric: subject level titers, generated with getTiters method
PoDsnumeric: subject level probability of disease (PoD), generated with assginPoD method
diseaseStatuslogical: subject level disease status (TRUE if diseased), generated with ClinicilaTrial function
Function adds noise to population titers accounting for an unknown factor affecting the titer distibution.
Inputs into the function: N, unknownDistribution and getUnknown() method are taken from the Population-class object.
subject level titers
A dataset containing the N, mean, stdDev, titers of vaccinated subjects. The dataset is provided in the form of population class object (see the Population-class function for more details).
vaccinatedvaccinated
Population class object:
number of subjects
mean of titers
standard deviation of titers
subject level titers
Function calculates and returns case-count efficacy confidence intervals estimated using Wald's method.
Input data need to contain information about disease status on individual level.
waldCI(vaccinated, control, confLevel = 0.95)waldCI(vaccinated, control, confLevel = 0.95)
vaccinated |
|
control |
|
confLevel |
numeric: value from (0, 1) interval, confidence level of interest |
Confidence interval of the relative risk is calculated using the Wald method. (Wald, A. Tests of statistical hypotheses concerning several parameters when the number of observations is large. Transactions of the American Mathematical Society 54, 426-482 (1943)).
Named list of lower and upper confidence interval bound
# Loading vaccinated and control populations data with PoD information data(vaccinated) data(control) # Estimating the disease status and case-count efficacy with 95\% confidence interval set.seed(1) CT <- ClinicalTrial(vaccinated, control, CI = 0.95) waldCI(vaccinated, control)# Loading vaccinated and control populations data with PoD information data(vaccinated) data(control) # Estimating the disease status and case-count efficacy with 95\% confidence interval set.seed(1) CT <- ClinicalTrial(vaccinated, control, CI = 0.95) waldCI(vaccinated, control)