Usage
In sclr: Scaled Logistic Regression

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(sclr)

Model

See vignette("sclr-math") for model specification, log-likelihood, scores and second derivatives.

Model fitting

Model fitting is done with a function called sclr. It is used in the same way as other fitting functions like lm.

# One-titre fit to included simulated data
fit1 <- sclr(status ~ logHI, one_titre_data)
summary(fit1)

# Two-titre fit to included simulated data
fit2 <- sclr(status ~ logHI + logNI, two_titre_data)
summary(fit2)

Expected protection

The predict method will return the point estimate and a confidence interval of $\beta_0 + \beta_1X_1 + ... + \beta_kX_k$ where $k$ is the number of covariates. It will also apply the inverse logit transformation to these estimates and interval bounds to get the point estimate and the interval for the probability of protection on the original scale.

# One-titre fit
preddata1 <- data.frame(logHI = seq(0, 8, length.out = 101))
pred1 <- predict(fit1, preddata1)
head(pred1[, c("logHI", "prot_l", "prot_point", "prot_u")])

# Two-titre fit
preddata2 <- data.frame(logHI = seq(0, 8, length.out = 101), logNI = 1)
pred2 <- predict(fit2, preddata2)
head(pred2[, c("logHI", "logNI", "prot_l", "prot_point", "prot_u")])

Protective titres

To get the estimated titre (and the confidence interval) that corresponds to a particular protection level (eg. 50%), use the get_protection_level function. Its interface is similar to that of predict.

protHI1 <- get_protection_level(fit1, "logHI", lvl = 0.5)
print(protHI1)

prot_lvls2 <- data.frame(logNI = log(c(0.1, 10, 40)))
protHI2 <- get_protection_level(fit2, "logHI", prot_lvls2)
print(protHI2)