# Script comparisons with 32-bit Epicure

    Sys.setenv("OMP_THREAD_LIMIT" = 1) # Reducing core use, to avoid accidental use of too many cores
    library(Colossus)
    library(data.table)
    library(parallel)

## Introduction to Colossus

Colossus was developed in the context of radiation epidemiologists wanting to use new methods and more data. At the time of development, 32-bit Epicure was a popular software for running radiation epidemiological analysis. This vignette was written with that in mind to help any transitioning users see how the two are similar and different, in addition to providing guidance for converting between the two. The script provided will discuss both Colossus-specific differences as well as general R capabilities that differ from Epicure.

### Example Epicure Analysis

The following peanuts script was used as part of validation efforts for Colossus. The script runs three regressions. A linear excess relative risk model, a log-linear hazard ratio model for dose overall, and a log-linear hazard ratio model for categorical bins of dose. Similar regressions were performed with radiation cohort data to assess the relationship between the risk of different mortality events and cumulative radiation exposure to organs.

The script starts by loading the dataset. In this example, we assume there is a file called “EX_DOSE.csv” in the local directory.

    RECORDS 4100000 @
    WSOPT VARMAX 30 @
    USETXT EX_DOSE.csv @
    INPUT @

Next, the script sets the interval start column and interval end column, and designates which columns have multiple levels.

    ENTRY age_entry @
    EXIT age_exit @
    EVENT nonCLL @

    levels SES_CAT YOB_CAT sexm dose_cat @

Past this point, the script specifies which columns belong to each subterm and term number. In this case, the model has a product-linear element in the first term. The script additionally sets the convergence options. The maximum iterations are set to 100 and the convergence criteria are set to 1e-9. The regression is also set to print deviance and parameter estimates for each iteration and to print the final parameter estimates and covariance after the regression concludes.

    LOGLINEAR 0 SES_CAT YOB_CAT sexm @
    PLINEAR 0 cumulative_dose @

    FITOPT P V ITER 100 CONV -9 @

Finally, the regression is run and results are printed to the console.

    FIT @

Past this point, the same general process is followed for the two hazard ratio regressions. The model definition is reset, the subterm/term description is set, and the regression is run.

    NOMODEL @

    LOGLINEAR 0 SES_CAT YOB_CAT sexm cumulative_dose @

    FIT @

    NOMODEL @

    LOGLINEAR 0 SES_CAT YOB_CAT sexm dose_cat @

    FIT @

### Colossus Script

For the most part, the same steps are performed in Colossus. The script starts by reading the input file. The only difference is that R does not require memory to be set aside before reading the file.

    df_Dose <- fread("EX_DOSE.csv")

Colossus defines the model as a formula. The left-hand side of the formula defines the type of model, the time observed, and the event columns. The right-hand side defines the risk factors in each term and subterm. The model is a Cox regression, the intervals are defined by the age_entry/age_exit columns, and the event status is stored in the nonCLL column. This is denoted by ‘Cox(age_entry, age_exit, nonCLL)’. The loglinear and product-linear subterms are added to the formula by specifying the subterm type, included columns, and term number, i.e. ‘subterm(column 1, column 2, …, term number)’. Factored columns are added by using ‘factor(column)’, the default level is assumed to be the first level.

    model_ERR <- Cox(age_entry, age_exit, nonCLL) ~ plinear(cumulative_dose, 0) +
      loglinear(factor(SES_CAT), factor(YOB_CAT), sexm)

Next, the script defines the control information. The “control” variable serves a similar purpose as the “FITOPT” option in Epicure. This control list specifies that two cores should be used to perform calculations in parallel, up to 100 iterations should be used, and the iterations should stop if the step size is below 1e-9 or the first derivatives are all below 1e-9. The verbose options specifies that any errors or warnings should be printed to the console.

    control <- list(
      "Ncores" = 1, "maxiter" = 100, "verbose" = 2,
      "epsilon" = 1e-9, "der_epsilon" = 1e-9
    )

Finally, the regression is run and a list of the results is returned to a variable “e”. Regressions in Colossus return a list of results, a summary can be printed.

    e <- CoxRun(model_ERR, df_dose, control = control)
    print(e)

A similar process is run for the two hazard ratio regressions.

    # HR
    model_HR <- Cox(age_entry, age_exit, nonCLL) ~ loglinear(cumulative_dose, factor(SES_CAT), factor(YOB_CAT), sexm)
    e <- CoxRun(model_HR, df_dose, control = control)
    print(e)

    # Categorical
    model_categ <- Cox(age_entry, age_exit, nonCLL) ~ loglinear(factor(dose_cat), factor(SES_CAT), factor(YOB_CAT), sexm)
    e <- CoxRun(model_categ, df_dose, control = control)
    print(e)