vlad (version 0.1.0)

optimal_k: Compute optimal k

Description

Compute optimal k.

Usage

optimal_k(QA, parsonnetscores, coeff)

Arguments

QA

double. Defines the performance of a surgeon with the odds ratio ratio of death Q.

parsonnetscores

NumericVector. Vector of Parsonnet Scores.

coeff

NumericVector. Estimated coefficients \(\alpha\) and \(\beta\) from the binary logistic regression model. For more information see details.

Value

Returns a single value which is the approximate optimal k for a set of given Parsonnet scores.

Details

Formula deterioration: $$ k{det} = \frac{Q{A} - 1 - log(Q{A})}{log(Q{A})}\bar{p} , Q{A} > 1 $$ Formula improvement: $$ k{imp} = \frac{1 - Q{A} + log(Q{A})}{log(Q{A})}\bar{p} , Q{A} < 1 $$

Examples

# NOT RUN {
library("vlad"); library("spcadjust")
data("cardiacsurgery")
cardiacsurgery <- dplyr::mutate(cardiacsurgery, phase=factor(ifelse(date < 2*365, "I", "II")))
S2I <- subset(cardiacsurgery, c(surgeon==2 & phase=="I"), c("Parsonnet", "status"))
coeff <- coef(glm(status ~ Parsonnet, data=S2I, family="binomial"))
kopt <- optimal_k(QA=2, parsonnetscores=S2I$Parsonnet, coeff=coeff)
kopt ## (Deterioration)
# manually find optimal k for detecting improvement
QA <- 2
pbar <- mean(sapply(S2I[, 1], gettherisk, coef=coeff))
kopt <- pbar * ( QA - 1 - log(QA) ) / log(QA)
all.equal(kopt, optimal_k(QA=2, parsonnetscores=S2I$Parsonnet, coeff=coeff) )
kopt <- optimal_k(QA=1/2, parsonnetscores=S2I$Parsonnet, coeff=coeff)
kopt ##(Improvement)
## k_opt = 0.02555328
### k = kopt
QA <- 1/2
# manually find optimal k for detecting improvement
pbar <- mean(sapply(S2I[, 1], gettherisk, coef=coeff))
kopt <- pbar * ( 1 - QA + log(QA) ) / log(QA)
all.equal(kopt, optimal_k(QA=1/2, parsonnetscores=S2I$Parsonnet, coeff=coeff) )
# }