# logbin

`logbin` provides methods for performing relative risk regression by fitting log-link GLMs and GAMs to binomial data. As well as providing a consistent interface to use the usual Fisher scoring algorithm (via `glm` or `glm2`) and an adaptive barrier approach (via `constrOptim`), it implements EM-type algorithms that have more stable convergence properties than other methods.

An example of periodic non-convergence using `glm` (run with `trace = TRUE` to see deviance at each iteration):

``````require(glm2, quietly = TRUE)
data(heart)

start.p <- sum(heart\$Deaths) / sum(heart\$Patients)
t.glm <- system.time(
fit.glm <- logbin(cbind(Deaths, Patients-Deaths) ~ factor(AgeGroup) + factor(Severity) +
factor(Delay) + factor(Region), data = heart,
start = c(log(start.p), -rep(1e-4, 8)), method = "glm", maxit = 10000)
)
``````

The combinatorial EM method (Marschner and Gillett, 2012) provides stable convergence:

``````t.cem <- system.time(fit.cem <- update(fit.glm, method = "cem"))
``````

...but it can take a while. Using an overparameterised EM approach removes the need to run 34 = 81 separate EM algorithms:

``````t.em <- system.time(fit.em <- update(fit.glm, method = "em"))
``````

...while generic EM acceleration algorithms (from the `turboEM` package) can speed this up further still:

``````t.cem.acc <- system.time(fit.cem.acc <- update(fit.cem, accelerate = "squarem"))
t.em.acc <- system.time(fit.em.acc <- update(fit.em, accelerate = "squarem"))
``````

Comparison of results:

``````#>         converged    logLik iterations   time
#> glm         FALSE -186.7366      10000   2.28
#> cem          TRUE -179.9016     445161 101.01
#> em           TRUE -179.9016       7403   1.80
#> cem.acc      TRUE -179.9016       7974   8.58
#> em.acc       TRUE -179.9016         92   0.11
``````

An adaptive barrier algorithm can also be applied using `method = "ab"`, with user-specified options via `control.method`: see `help(logbin)` for more details.

Semi-parametric regression using B-splines (Donoghoe and Marschner, 2015) can be incorporated by using the `logbin.smooth` function. See `example(logbin.smooth)` for a simple example.

## Installation

Get the released version from CRAN:

``````install.packages("logbin")
``````

Or the development version from github:

``````# install.packages("devtools")
devtools::install_github("mdonoghoe/logbin")
``````

## References

• Donoghoe, M. W. and I. C. Marschner (2015). Flexible regression models for rate differences, risk differences and relative risks. International Journal of Biostatistics 11(1): 91-108.
• Marschner, I. C. and A. C. Gillett (2012). Relative risk regression: reliable and flexible methods for log-binomial models. Biostatistics 13(1): 179-192.

mdonoghoe/logbin documentation built on May 22, 2017, 2:16 a.m.