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total_probability_of_positive_result <- function(
pij, survey_sensitivity, survey_specificity) {
n_f <- nrow(pij)
n_pu <- ncol(pij)
out <- matrix(NA, nrow = n_f, ncol = n_pu)
for (i in seq_len(n_pu)) {
out[, i] <-
(survey_sensitivity * pij[, i]) +
((1.0 - survey_specificity) * (1.0 - pij[, i]))
}
out[] <- pmin(out[], 1.0 - 1e-10)
out[] <- pmax(out[], 1e-10)
out
}
total_probability_of_negative_result <- function(
pij, survey_sensitivity, survey_specificity) {
n_f <- nrow(pij)
n_pu <- ncol(pij)
out <- matrix(NA, nrow = n_f, ncol = n_pu)
for (i in seq_len(n_pu)) {
out[, i] <-
((1 - survey_sensitivity) * pij[, i]) +
(survey_specificity * (1.0 - pij[, i]))
}
out[] <- pmin(out[], 1.0 - 1e-10)
out[] <- pmax(out[], 1e-10)
out
}
total_probability_of_positive_model_result <- function(
pij_subset, model_sensitivity, model_specificity) {
n_f <- nrow(pij_subset)
n_pu <- ncol(pij_subset)
out <- matrix(NA, nrow = n_f, ncol = n_pu)
for (j in seq_len(n_pu)) {
for (i in seq_len(n_f)) {
out[i, j] <-
(model_sensitivity[i] * pij_subset[i, j]) +
((1.0 - model_specificity[i]) * (1.0 - pij_subset[i, j]))
}}
out[] <- pmin(out[], 1.0 - 1e-10)
out[] <- pmax(out[], 1e-10)
out
}
total_probability_of_negative_model_result <- function(
pij_subset, model_sensitivity, model_specificity) {
n_f <- nrow(pij_subset)
n_pu <- ncol(pij_subset)
out <- matrix(NA, nrow = n_f, ncol = n_pu)
for (j in seq_len(n_pu)) {
for (i in seq_len(n_f)) {
out[i, j] <-
((1 - model_sensitivity[i]) * pij_subset[i, j]) +
((model_specificity[i]) * (1.0 - pij_subset[i, j]))
}}
out[] <- pmin(out[], 1.0 - 1e-10)
out[] <- pmax(out[], 1e-10)
out
}
probability_of_outcome <- function(
oij, total_probability_of_survey_positive_log,
total_probability_of_survey_negative_log, idx) {
sum(
(oij[idx] *
total_probability_of_survey_positive_log[idx]) +
((1 - oij[idx]) *
total_probability_of_survey_negative_log[idx]))
}
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