PEM vs. PAM split point sensitivity

Last updated: 2018-05-22

• ✔ R Markdown file: up-to-date

  Great! Since the R Markdown file has been committed to the Git repository, you know the exact version of the code that produced these results.

• ✔ Environment: empty

  Great job! The global environment was empty. Objects defined in the global environment can affect the analysis in your R Markdown file in unknown ways. For reproduciblity it’s best to always run the code in an empty environment.

• ✔ Seed: set.seed(20180517)

  The command set.seed(20180517) was run prior to running the code in the R Markdown file. Setting a seed ensures that any results that rely on randomness, e.g. subsampling or permutations, are reproducible.

• ✔ Session information: recorded

  Great job! Recording the operating system, R version, and package versions is critical for reproducibility.

• ✔ Repository version: 14e326b

  Great! You are using Git for version control. Tracking code development and connecting the code version to the results is critical for reproducibility. The version displayed above was the version of the Git repository at the time these results were generated.
  
  Note that you need to be careful to ensure that all relevant files for the analysis have been committed to Git prior to generating the results (you can use wflow_publish or wflow_git_commit). workflowr only checks the R Markdown file, but you know if there are other scripts or data files that it depends on. Below is the status of the Git repository when the results were generated:

  
  Ignored files:
      Ignored:    analysis/ll_selection_cache/
      Ignored:    analysis/pem_vs_pam_cache/
  
  Untracked files:
      Untracked:  output/sim-lag-lead-registry/
      Untracked:  output/sim-pem-vs-pam-registry/
      Untracked:  sandbox/
  
  Unstaged changes:
      Modified:   analysis/_site.yml
      Modified:   analysis/about.Rmd
  
  

  Note that any generated files, e.g. HTML, png, CSS, etc., are not included in this status report because it is ok for generated content to have uncommitted changes.

library(ggplot2)
theme_set(theme_bw())
library(batchtools)

Loading required package: data.table

Breaking change introduced in batchtools v0.9.6: The format of the returned data.table of the functions `reduceResultsDataTable()`, getJobTable()`, `getJobPars()`, and `getJobResources()` has changed. List columns are not unnested automatically anymore. To manually unnest tables, batchtools provides the helper function `unwrap()` now, e.g. `unwrap(getJobPars())`. The previously introduced helper function `flatten()` will be deprecated due to a name clash with `purrr::flatten()`.

Function for data simulation (using pammtools::sim_pexp):

## simulation function
sim_wrapper <- function(data, job, n = 250, time_grid = seq(0, 10, by = 0.05)) {

  # create data set with covariates
  df <- tibble::tibble(x1 = runif(n, -3, 3), x2 = runif(n, 0, 6))
  # baseline hazard
  f0 <- function(t) {dgamma(t, 8, 2) * 6}
  # define function that generates nz exposures z(t_{z,1}), ..., z(t_{z,Q})

  sim_pexp(formula = ~ -3.5 + f0(t), data = df, cut = time_grid)

}

Function to estimate hazard from simulated data, either by a PEM or PAM

## estimation function
pam_wrapper <- function(data, job, instance,
  cut      = NA,
  bs       = "ps",
  mod_type = c("pem", "pam") ,
  max_time = 10) {

  if(is.na(cut)) {
    cut <- NULL
  } else {
    if(cut == "rough") {
      cut <- seq(0, max_time, by = 0.5)
    } else {
      if(cut == "fine") {
        cut <- seq(0, max_time, by = 0.2)
      }
    }
  }

  ped <- as_ped(data = instance, formula = Surv(time, status) ~ ., cut = cut, id="id")

  form <- "ped_status ~ s(tend) + s(x1) + s(x2)"
  if(mod_type == "pem") {
    form     <- ped_status ~ interval
    time_var <- "interval"
  } else {
    form     <- ped_status ~ s(tend, bs = bs,k = k)
    time_var <- "tend"
  }

  mod <- gam(formula = form, data = ped, family = poisson(), offset = offset, method = "REML")
  # summary(mod)

  make_newdata(ped, tend=unique(tend)) %>%
    add_hazard(mod, type="link", se_mult = qnorm(0.975), time_var = time_var) %>%
    mutate(truth = -3.5 + dgamma(tend, 8, 2) * 6)

}

Setup simulation using batchtools:

if(!checkmate::test_directory_exists("output/sim-pem-vs-pam-registry")) {
  reg <- makeExperimentRegistry("output/sim-pem-vs-pam-registry",
    packages = c("mgcv", "dplyr", "tidyr", "pammtools"),
    seed     = 20052018)
  reg$cluster.functions = makeClusterFunctionsMulticore(ncpus = 2)
  addProblem(name   = "pem-vs-pam", fun = sim_wrapper)
  addAlgorithm(name = "pem-vs-pam", fun = pam_wrapper)

  algo_df <- tidyr::crossing(
    cut = c(NA, "fine", "rough"),
    mod_type = c("pem", "pam"))

  addExperiments(algo.design  = list("pem-vs-pam" = algo_df), repls = 20)
  submitJobs()
  waitForJobs()
}

Warning: replacing previous import 'dplyr::vars' by 'ggplot2::vars' when
loading 'pammtools'

[1] FALSE

Evaluate Simulation:

reg     <- loadRegistry("output/sim-pem-vs-pam-registry", writeable = TRUE)

Reading registry in read-write mode

Loading required package: mgcv

Loading required package: nlme

This is mgcv 1.8-23. For overview type 'help("mgcv-package")'.

Loading required package: dplyr

Attaching package: 'dplyr'

The following object is masked from 'package:nlme':

    collapse

The following objects are masked from 'package:data.table':

    between, first, last

The following object is masked from 'package:ggplot2':

    vars

The following objects are masked from 'package:stats':

    filter, lag

The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union

Loading required package: tidyr

Loading required package: pammtools

Warning: replacing previous import 'dplyr::vars' by 'ggplot2::vars' when
loading 'pammtools'

Attaching package: 'pammtools'

The following object is masked from 'package:stats':

    filter

No configuration file found

ids_pam <- findExperiments(prob.name="pem-vs-pam", algo.name="pem-vs-pam")
pars    <- unwrap(getJobPars()) %>% as_tibble()
res     <- reduceResultsDataTable(ids=findDone(ids_pam)) %>%
  as_tibble() %>%
  tidyr::unnest() %>%
  left_join(pars) %>%
  mutate(cut = case_when(is.na(cut) ~ "default", TRUE ~ cut))

Warning in bind_rows_(x, .id): Unequal factor levels: coercing to character

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Warning in bind_rows_(x, .id): binding character and factor vector,
coercing into character vector

Joining, by = "job.id"

res %>%
  mutate(
    sq_error = (truth - hazard)^2,
    covered = (truth >= ci_lower) & (truth <= ci_upper)) %>%
  group_by(job.id, mod_type, cut) %>%
  summarize(
    RMSE = sqrt(mean(sq_error)),
    coverage = mean(covered)) %>%
  group_by(mod_type, cut) %>%
  summarize(
    RMSE     = mean(RMSE),
    coverage = mean(coverage))

# A tibble: 3 x 4
# Groups:   mod_type [?]
  mod_type cut      RMSE coverage
  <chr>    <chr>   <dbl>    <dbl>
1 pem      default  1.38    0.870
2 pem      fine     6.84    0.966
3 pem      rough    3.02    0.920

ggplot(res, aes(x=tend, y = hazard)) +
  geom_step(aes(group = job.id), alpha = 0.3) +
  geom_line(aes(y = truth, col = "truth"), lwd = 2) +
  facet_grid(cut ~ mod_type) +
  coord_cartesian(ylim=c(-5, 0)) +
  geom_smooth(aes(col="average estimate"), method="gam", formula = y ~ s(x),
    se=FALSE) +
  scale_color_brewer("Method", palette = "Dark2") +
  xlab("time")

sessionInfo()

R version 3.4.4 (2018-03-15)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 16.04.4 LTS

Matrix products: default
BLAS: /usr/lib/openblas-base/libblas.so.3
LAPACK: /usr/lib/libopenblasp-r0.2.18.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=de_DE.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=de_DE.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=de_DE.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] bindrcpp_0.2.2       pammtools_0.0.9.9003 tidyr_0.8.0         
[4] dplyr_0.7.4          mgcv_1.8-23          nlme_3.1-137        
[7] batchtools_0.9.8     data.table_1.10.4-3  ggplot2_2.2.1.9000  

loaded via a namespace (and not attached):
 [1] progress_1.1.2     tidyselect_0.2.4   reshape2_1.4.3    
 [4] purrr_0.2.4        splines_3.4.4      lattice_0.20-35   
 [7] expm_0.999-2       colorspace_1.3-2   htmltools_0.3.6   
[10] yaml_2.1.18        utf8_1.1.3         survival_2.42-3   
[13] rlang_0.2.0.9001   R.oo_1.21.0        pillar_1.2.1      
[16] glue_1.2.0         withr_2.1.2        R.utils_2.6.0     
[19] rappdirs_0.3.1     RColorBrewer_1.1-2 plyr_1.8.4        
[22] bindr_0.1.1        stringr_1.3.0      munsell_0.4.3     
[25] gtable_0.2.0       workflowr_1.0.1    R.methodsS3_1.7.1 
[28] mvtnorm_1.0-7      evaluate_0.10.1    labeling_0.3      
[31] knitr_1.20         Rcpp_0.12.16       scales_0.5.0.9000 
[34] backports_1.1.2    checkmate_1.8.5    debugme_1.1.0     
[37] brew_1.0-6         digest_0.6.15      stringi_1.1.7     
[40] msm_1.6.6          grid_3.4.4         rprojroot_1.3-2   
[43] cli_1.0.0          tools_3.4.4        magrittr_1.5      
[46] base64url_1.3      lazyeval_0.2.1     tibble_1.4.2      
[49] Formula_1.2-3      crayon_1.3.4       whisker_0.3-2     
[52] pkgconfig_2.0.1    Matrix_1.2-13      prettyunits_1.0.2 
[55] assertthat_0.2.0   rmarkdown_1.9      R6_2.2.2          
[58] git2r_0.21.0       compiler_3.4.4    

This reproducible R Markdown analysis was created with workflowr 1.0.1