PEM vs. PAM split point sensitivity

Last updated: 2018-05-22

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

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)

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

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))

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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    

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