Usage

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)
#> Call: status ~ logHI
#> 
#> Parameter estimates
#>       theta      beta_0  beta_logHI 
#> -0.03497876 -5.42535734  2.14877741 
#> 
#> 95% confidence intervals
#>                 2.5 %      97.5 %
#> theta      -0.1350572  0.06509969
#> beta_0     -6.4417802 -4.40893449
#> beta_logHI  1.8146909  2.48286390
#> 
#> Log likelihood: -2469.765

# Two-titre fit to included simulated data
fit2 <- sclr(status ~ logHI + logNI, two_titre_data)
summary(fit2)
#> Call: status ~ logHI + logNI
#> 
#> Parameter estimates
#>      theta     beta_0 beta_logHI beta_logNI 
#> -0.1231823 -5.6536038  2.2098460  1.0409995 
#> 
#> 95% confidence intervals
#>                 2.5 %       97.5 %
#> theta      -0.2395860 -0.006778714
#> beta_0     -6.6252070 -4.682000646
#> beta_logHI  1.8981507  2.521541192
#> beta_logNI  0.8738325  1.208166538
#> 
#> Log likelihood: -1858.46

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")])
#> # A tibble: 6 x 4
#>   logHI  prot_l prot_point prot_u
#>   <dbl>   <dbl>      <dbl>  <dbl>
#> 1  0    0.00159    0.00438 0.0120
#> 2  0.08 0.00194    0.00520 0.0139
#> 3  0.16 0.00236    0.00617 0.0160
#> 4  0.24 0.00288    0.00732 0.0185
#> 5  0.32 0.00351    0.00868 0.0213
#> 6  0.4  0.00427    0.0103  0.0246

# 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")])
#> # A tibble: 6 x 5
#>   logHI logNI  prot_l prot_point prot_u
#>   <dbl> <dbl>   <dbl>      <dbl>  <dbl>
#> 1  0        1 0.00432    0.00983 0.0222
#> 2  0.08     1 0.00527    0.0117  0.0258
#> 3  0.16     1 0.00643    0.0139  0.0299
#> 4  0.24     1 0.00785    0.0166  0.0347
#> 5  0.32     1 0.00957    0.0197  0.0402
#> 6  0.4      1 0.0117     0.0235  0.0466

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)
#> # A tibble: 3 x 3
#>   logHI prot_prob est        
#>   <dbl>     <dbl> <chr>      
#> 1  2.39       0.5 low bound  
#> 2  2.52       0.5 point      
#> 3  2.64       0.5 upper bound

prot_lvls2 <- data.frame(logNI = log(c(0.1, 10, 40)))
protHI2 <- get_protection_level(fit2, "logHI", prot_lvls2)
print(protHI2)
#>       logNI     logHI prot_prob         est
#> 1 -2.302585 3.4024635       0.5   low bound
#> 2  2.302585 1.3380153       0.5   low bound
#> 3  3.688879 0.6568784       0.5   low bound
#> 4 -2.302585 3.6430566       0.5       point
#> 5  2.302585 1.4736837       0.5       point
#> 6  3.688879 0.8206373       0.5       point
#> 7 -2.302585 3.8723188       0.5 upper bound
#> 8  2.302585 1.5883861       0.5 upper bound
#> 9  3.688879 0.9605298       0.5 upper bound