This project extends the work on jointly modelling mixed and truncated longitudinal data and survival data by Dr. Tingting Yu, Dr. Lang Wu and Dr. Peter B. Gilbert 1 to a couple of alternative survival models, Weibull Regression Model and Loglogistic Accelarated Failure Time Model. The project is motivated by higher efficiency of the parametric survival models compared to nonparametric ones when the distributional assumptions hold.

The original study by Yu et al 1 is motivated by the VAX004 trial. The special type of response variables NAb is visualized as in Figure 1 below. Figure 1 is from [1].

This work extends the original work by replacing the nonparametric survival model, Cox proportional hazards model, by two parametric alternatives, Weibull Regression Model and Loglogistic Accelarated Failure Time Model, which are more efficient when the distributional assumptions hold.

The folder src contains the modified R package HHJMs.p based on HHJMs developed by Yu, R code for applying the joint models on real data in dat and also in the R packages. The folder doc includes the .tex files of the report. References of the report are included in ref.

The orignal package HHJMs was developed by Yu, Tingting. Here the models used in the package are extended to accepting alternative survival models, i.e., distributional assumptions.

Users can either clone the repo or solely downlown the package, and install the package locally. For Mac users,

`install.packages("~/HHJMs-p.tar.gz", repos = NULL, type = "source")

library(HHJMs.p)`

If you are interesed in the original package, it can be easily downloaded from the Github repo HHJMs. Some helpful code is:

`library(devtools)

install_github('oliviayu/HHJMs')`

The package is further modified in multiple ways to be more user-friendly; the modifications are listed below.

• Fix the issue that some dependencies are not successully loaded when installing the HHJMs package.

• Fix the issue that users need to source the R files locally when using some functions in the package.

• Fix the numeric issue when summarizing the fitted model.

• Add ellipses into some functions to call arguments in the functions they call.

• Example code is modified by combining repeated code.

I'd like to thank Dr. Lang Wu for his generous help and precious advice.

[1] Yu T, Wu L, Gilbert PB. A joint model for mixed and truncated longitudinal data and survival data, with application to HIV vaccine studies. Biostatistics. 2018 Jul 1;19(3):374-90.

[2] Lee Y, Nelder JA, Pawitan Y. Generalized linear models with random effects: unified analysis via H-likelihood. CRC Press; 2018 Jul 11.