Introduction to cureAssess

library(cureAssess)
library(survival)
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union

Introduction

The cureAssess package provides tools for assessing whether a cure model may be appropriate for right-censored survival data. The package supports a two-stage workflow:

  1. initial screening using Kaplan-Meier curves and AIC comparison of cure and non-cure models,
  2. optional deeper testing using cure-appropriateness diagnostics.

In this vignette, we demonstrate the basic workflow using two datasets from the survival package.

‘nwtco’ dataset was used to demonstrate an example when a cure model is appropriate and ‘gbsg’ dataset is used to demonstrate an example when a cure model is not appropriate.

library(cureAssess)
library(survival)
library(dplyr)

Example 1: nwtco data set — an example where a cure model may be appropriate

We illustrate the use of cureAssess with the nwtco data set from the survival package.

head(survival::nwtco)
#>   seqno instit histol stage study rel edrel age in.subcohort
#> 1     1      2      2     1     3   0  6075  25        FALSE
#> 2     2      1      1     2     3   0  4121  50        FALSE
#> 3     3      2      2     1     3   0  6069   9        FALSE
#> 4     4      2      1     4     3   0  6200  28         TRUE
#> 5     5      2      2     2     3   0  1244  55        FALSE
#> 6     6      1      1     2     3   0  2932  32        FALSE

The nwtco data set contains 4028 observations on 9 variables:

seqno: subject identifier instit: histology from the local institution histol: histology from the central laboratory stage: disease stage study: study indicator rel: relapse indicator edrel: time to relapse age: age at diagnosis in.subcohort: indicator for inclusion in the subcohort used in the example paper

For this illustration, the data were grouped into two clinically meaningful risk categories based on the variable stage:

Low risk: stages 1 and 2, representing patients with relatively higher relapse-free survival High risk: stages 3 and 4, representing patients with relatively higher risk of relapse

This type of grouping should ideally be guided by subject-matter expertise and clinical knowledge of the disease.

In this example, age is assumed to be recorded in months, and edrel is assumed to be recorded in days. Therefore, the time variable is converted to years during data preparation.

The grouping step is performed as part of data preprocessing before applying the functions in cureAssess.

Step 1: Data preprocessing and risk-group creation

We first create the risk groups based on the disease stage.

nwtco_dat <- survival::nwtco %>%
  mutate(
    stage_group = case_when(
      stage %in% c(1, 2) ~ "Low risk",
      stage %in% c(3, 4) ~ "High risk",
      TRUE ~ NA_character_
    )
  ) %>%
  filter(!is.na(stage_group))

Step 2: Prepare the survival data

Next, we standardize the survival data into the format required by cureAssess. Here the relapse time (edrel) is assumed to be recorded in days, so it is converted to years.

nwtco_surv <- prepare.surv.data(
  data = nwtco_dat,
  time = "edrel",
  status = "rel",
  time_scale = "days_to_years"
)
head(nwtco_surv)
#>   seqno instit histol stage study rel edrel age in.subcohort stage_group
#> 1     1      2      2     1     3   0  6075  25        FALSE    Low risk
#> 2     2      1      1     2     3   0  4121  50        FALSE    Low risk
#> 3     3      2      2     1     3   0  6069   9        FALSE    Low risk
#> 4     4      2      1     4     3   0  6200  28         TRUE   High risk
#> 5     5      2      2     2     3   0  1244  55        FALSE    Low risk
#> 6     6      1      1     2     3   0  2932  32        FALSE    Low risk
#>           Y D
#> 1 16.632444 0
#> 2 11.282683 0
#> 3 16.616016 0
#> 4 16.974675 0
#> 5  3.405886 0
#> 6  8.027379 0

The prepared dataset contains the original columns plus: Y: survival time D: event indicator

Step 3: Fit candidate cure and non-cure models including KM curve

Next, we fit several candidate models and compare them using AIC.

fit_res <- model.fitting(nwtco_surv, plot_km = TRUE)
#> Ignoring unknown labels:
#> • fill : "Strata"
fit_res
#> 
#> Candidate model fitting results
#> --------------------------------
#> Best model by AIC: loglogistic_cure 
#> 
#>             model model_type      AIC                      parameter_estimates
#>  loglogistic_cure       cure 4339.369 theta=0.8489; shape=1.9818; scale=0.8285
#>        gamma_cure       cure 4380.428  theta=0.8507; shape=1.6097; rate=1.4284
#>      weibull_cure       cure 4407.184 theta=0.8504; shape=1.2304; scale=1.2211
#>  exponential_cure       cure 4444.078                  theta=0.8494; rate=0.85
#>       loglogistic   non-cure 4941.015              shape=0.504; scale=206.8519
#>           weibull   non-cure 4964.699               shape=0.4736; scale=323.56
#>             gamma   non-cure 4986.062                shape=0.4512; rate=0.0016
#>       exponential   non-cure 5464.789                                  =0.0227
#>  error
#>       
#>       
#>       
#>       
#>       
#>       
#>       
#>

The AIC table can be examined directly.

Display the Kaplan-Meier curve

If plot_km = TRUE, the Kaplan-Meier plot is stored in the fitted object.

print(fit_res$kmplot)
#> Ignoring unknown labels:
#> • fill : "Strata"
#> Ignoring unknown labels:
#> • fill : "Strata"
#> Ignoring unknown labels:
#> • fill : "Strata"
#> Ignoring unknown labels:
#> • colour : "Strata"

fit_res$aic_table
#>              model model_type      AIC                      parameter_estimates
#> 1 loglogistic_cure       cure 4339.369 theta=0.8489; shape=1.9818; scale=0.8285
#> 2       gamma_cure       cure 4380.428  theta=0.8507; shape=1.6097; rate=1.4284
#> 3     weibull_cure       cure 4407.184 theta=0.8504; shape=1.2304; scale=1.2211
#> 4 exponential_cure       cure 4444.078                  theta=0.8494; rate=0.85
#> 5      loglogistic   non-cure 4941.015              shape=0.504; scale=206.8519
#> 6          weibull   non-cure 4964.699               shape=0.4736; scale=323.56
#> 7            gamma   non-cure 4986.062                shape=0.4512; rate=0.0016
#> 8      exponential   non-cure 5464.789                                  =0.0227
#>   error
#> 1      
#> 2      
#> 3      
#> 4      
#> 5      
#> 6      
#> 7      
#> 8

The best-fitting model according to AIC is:

fit_res$best_model
#> [1] "loglogistic_cure"
fit_res$best_model_type
#> [1] "cure"

Step 4: Run cure-appropriateness tests

If desired, additional diagnostics can be computed.

test_res <- run.cure.tests(nwtco_surv, dist = "lnorm")

1. Maller-Zhou test

The Maller–Zhou test (Maller & Zhou, 1994; 1996) is a diagnostic method used to assess whether a cure fraction may exist in right-censored survival data.

test_res$mz
#> 
#> Maller-Zhou test statistic (1994)
#> ---------------------------------
#> Statistic: 0.04973145 
#> Alpha: 0.05 
#> Interpretation: Since the Maller-Zhou statistic (0.0497) is less than alpha = 0.05, there is evidence of sufficient follow-up, supporting cure model appropriateness.

2. qn statistic

The qn statistic, proposed by Maller and Zhou (1996), is a descriptive statistic used to evaluate whether a survival plateau may exist in right-censored survival data.

test_res$qn
#> 
#> qn statistic (Maller & Zhou 1996)
#> ---------------------------------
#> Statistic: 0.0007447865 
#> Interpretation: The qn statistic is 7e-04 (alpha_n-equivalent threshold for sufficient follow-up at the 0.05 level is 7e-04). Because qn exceeds this threshold, there is evidence of sufficient follow-up, consistent with a survival plateau and supporting cure model appropriateness. Larger values of qn provide stronger evidence.

3. Shen test

The Shen test is a statistical method used to assess whether a cure fraction may be present in right-censored survival data.

test_res$shen
#> 
#> Shen test (2000)
#> ----------------
#> Statistic: 0.3678338 
#> Alpha: 0.05 
#> Interpretation: Since the Shen test statistic (0.3678) is greater than or equal to alpha = 0.05, there is insufficient evidence of adequate follow-up to support cure model appropriateness.

4. Test for Immunes

test_res$immune
#> 
#> Maller-Zhou immune summary (1996)
#> ---------------------------------
#> p_hat: 0.1505957 
#> p_cens: 0.8582423 
#> Last observation: 16.99932 
#> Last observation censored: TRUE 
#> Interpretation: The last observed time is censored, suggesting a possible survival plateau. The estimated event probability by the end of follow-up is 0.1506, and the censoring proportion is 0.8582.

5. RECeUS method

The RECeUS method is a diagnostic approach used to assess whether a cure model is appropriate for survival data. It evaluates both the estimated cure fraction and the amount of remaining uncured subjects at the end of follow-up.

test_res$receus
#> 
#> RECeUS Cure Model Assessment
#> ----------------------------
#> Distribution: lnorm 
#> Tau: 16.9993 
#> 
#> Estimated cure fraction (pi_hat): 0.8495 
#> Remaining uncured ratio (r_hat): 3e-04 
#> 
#> Decision: Cure model appropriate 
#> 
#> Interpretation:
#> Both RECeUS conditions are satisfied: pi_hat > 0.025 and r_hat < 0.05. This suggests the presence of a cure fraction and sufficient follow-up for reliable cure model estimation.

Step 5: Run the full wrapper

The main wrapper function combines preparation, model fitting, and optional testing. Screening only.

res_screen <- cure.appropriateness(
  data = nwtco_dat,
  time = "edrel",
  status = "rel",
  time_scale = "days_to_years",
  dist = "lnorm",
  plot_km = FALSE,
  run_tests = "no"
)
res_screen
#> 
#> Cure model appropriateness analysis
#> -----------------------------------
#> Best model by AIC: loglogistic_cure 
#> Best model type: cure 
#> 
#> Initial decision:
#> The model with the smallest AIC is a cure model (loglogistic_cure). This provides initial support for cure model appropriateness. 
#> 
#> RECeUS distribution used: lnorm 
#> Testing status:
#> Tests were not run because `run_tests = "no"`. 
#> 
#> Final recommendation:
#> The model with the smallest AIC is a cure model (loglogistic_cure). This provides initial support for cure model appropriateness.

The screening results can be inspected through the screening component.

res_screen$screening$aic_table
#>              model model_type      AIC                      parameter_estimates
#> 1 loglogistic_cure       cure 4339.369 theta=0.8489; shape=1.9818; scale=0.8285
#> 2       gamma_cure       cure 4380.428  theta=0.8507; shape=1.6097; rate=1.4284
#> 3     weibull_cure       cure 4407.184 theta=0.8504; shape=1.2304; scale=1.2211
#> 4 exponential_cure       cure 4444.078                  theta=0.8494; rate=0.85
#> 5      loglogistic   non-cure 4941.015              shape=0.504; scale=206.8519
#> 6          weibull   non-cure 4964.699               shape=0.4736; scale=323.56
#> 7            gamma   non-cure 4986.062                shape=0.4512; rate=0.0016
#> 8      exponential   non-cure 5464.789                                  =0.0227
#>   error
#> 1      
#> 2      
#> 3      
#> 4      
#> 5      
#> 6      
#> 7      
#> 8
res_screen$screening$best_model
#> [1] "loglogistic_cure"
res_screen$screening$initial_decision
#> [1] "The model with the smallest AIC is a cure model (loglogistic_cure). This provides initial support for cure model appropriateness."

Automatic testing only if the best model is a cure model.

res_auto <- cure.appropriateness(
  data = nwtco_dat,
  time = "edrel",
  status = "rel",
  time_scale = "days_to_years",
  dist = "lnorm",
  plot_km = FALSE,
  run_tests = "auto"
)
res_auto
#> 
#> Cure model appropriateness analysis
#> -----------------------------------
#> Best model by AIC: loglogistic_cure 
#> Best model type: cure 
#> 
#> Initial decision:
#> The model with the smallest AIC is a cure model (loglogistic_cure). This provides initial support for cure model appropriateness. 
#> 
#> RECeUS distribution used: lnorm 
#> Testing status:
#> Tests were run automatically because the smallest-AIC model was a cure model. RECeUS used distribution: lnorm. 
#> 
#> Final recommendation:
#> The model with the smallest AIC is a cure model (loglogistic_cure). This provides initial support for cure model appropriateness. Additional cure-appropriateness diagnostics were run for further evaluation.

Force all tests to run, regardless of which model AIC selected.

res_full <- cure.appropriateness(
  data = nwtco_dat,
  time = "edrel",
  status = "rel",
  time_scale = "days_to_years",
  dist = "lnorm",
  plot_km = FALSE,
  run_tests = "yes"
)
res_full
#> 
#> Cure model appropriateness analysis
#> -----------------------------------
#> Best model by AIC: loglogistic_cure 
#> Best model type: cure 
#> 
#> Initial decision:
#> The model with the smallest AIC is a cure model (loglogistic_cure). This provides initial support for cure model appropriateness. 
#> 
#> RECeUS distribution used: lnorm 
#> Testing status:
#> Tests were run because `run_tests = "yes"`. RECeUS used distribution: lnorm. 
#> 
#> Final recommendation:
#> The model with the smallest AIC is a cure model (loglogistic_cure). This provides initial support for cure model appropriateness. Additional cure-appropriateness diagnostics were run for further evaluation.

Example 2: gbsg data set — an example where a cure model may not be appropriate.

head(survival::gbsg)
#>    pid age meno size grade nodes pgr er hormon rfstime status
#> 1  132  49    0   18     2     2   0  0      0    1838      0
#> 2 1575  55    1   20     3    16   0  0      0     403      1
#> 3 1140  56    1   40     3     3   0  0      0    1603      0
#> 4  769  45    0   25     3     1   0  4      0     177      0
#> 5  130  65    1   30     2     5   0 36      1    1855      0
#> 6 1642  48    0   52     2    11   0  0      0     842      1

The dataset contains 686 observations and the following variables:

pid: patient identifier age: age in years meno: menopausal status (0 = premenopausal, 1 = postmenopausal) size: tumor size (mm) grade: tumor grade nodes: number of positive lymph nodes pgr: progesterone receptor level (fmol/l) er: estrogen receptor level (fmol/l) hormon: hormonal therapy (0 = no, 1 = yes) rfstime: recurrence-free survival time (days to first recurrence, death, or last follow-up) status: event indicator (0 = alive without recurrence, 1 = recurrence or death)

Step 1: Data preprocessing and risk-group creation

We first create the groups based on the menopausal stage.

gbsg_grouped <- survival::gbsg %>%
  mutate(
    meno_group = case_when(
      meno == 0 ~ "Pre",
      meno == 1 ~ "Post"
    )
  )

table(gbsg_grouped$meno_group)
#> 
#> Post  Pre 
#>  396  290

Step 2: Prepare the survival data

Then we need to convert input data into the format required by cureAssess. Here, recurrence-free survival time is stored in days, so we convert it to years.

gbsg_dat <- prepare.surv.data(
  data = survival::gbsg,
  time = "rfstime",
  status = "status",
  time_scale = "days_to_years"
)
head(gbsg_dat)
#>    pid age meno size grade nodes pgr er hormon rfstime status         Y D
#> 1  132  49    0   18     2     2   0  0      0    1838      0 5.0321697 0
#> 2 1575  55    1   20     3    16   0  0      0     403      1 1.1033539 1
#> 3 1140  56    1   40     3     3   0  0      0    1603      0 4.3887748 0
#> 4  769  45    0   25     3     1   0  4      0     177      0 0.4845996 0
#> 5  130  65    1   30     2     5   0 36      1    1855      0 5.0787132 0
#> 6 1642  48    0   52     2    11   0  0      0     842      1 2.3052704 1

The prepared dataset contains the original columns plus: Y: survival time D: event indicator

Step 3: Fit candidate cure and non-cure models including KM curve

Next, we fit several candidate models and compare them using AIC.

fit_res <- model.fitting(gbsg_dat, plot_km = TRUE)
#> Ignoring unknown labels:
#> • fill : "Strata"
fit_res
#> 
#> Candidate model fitting results
#> --------------------------------
#> Best model by AIC: loglogistic_cure 
#> 
#>             model model_type      AIC                      parameter_estimates
#>  loglogistic_cure       cure 1719.696 theta=0.3238; shape=1.9556; scale=2.7033
#>        gamma_cure       cure 1723.476   theta=0.3805; shape=2.1055; rate=0.696
#>       loglogistic   non-cure 1731.346               shape=1.5325; scale=4.4994
#>      weibull_cure       cure 1733.922 theta=0.3839; shape=1.5654; scale=3.2983
#>             gamma   non-cure 1742.850                shape=1.4689; rate=0.2516
#>           weibull   non-cure 1750.005               shape=1.2715; scale=6.1871
#>       exponential   non-cure 1769.052                                  =0.1416
#>  exponential_cure       cure 1771.057                 theta=4e-04; rate=0.1416
#>  error
#>       
#>       
#>       
#>       
#>       
#>       
#>       
#>

The AIC table can be examined directly.

Display the Kaplan-Meier curve

If plot_km = TRUE, the Kaplan-Meier plot is stored in the fitted object.

print(fit_res$kmplot)
#> Ignoring unknown labels:
#> • fill : "Strata"
#> Ignoring unknown labels:
#> • fill : "Strata"
#> Ignoring unknown labels:
#> • fill : "Strata"
#> Ignoring unknown labels:
#> • colour : "Strata"

fit_res$aic_table
#>              model model_type      AIC                      parameter_estimates
#> 1 loglogistic_cure       cure 1719.696 theta=0.3238; shape=1.9556; scale=2.7033
#> 2       gamma_cure       cure 1723.476   theta=0.3805; shape=2.1055; rate=0.696
#> 3      loglogistic   non-cure 1731.346               shape=1.5325; scale=4.4994
#> 4     weibull_cure       cure 1733.922 theta=0.3839; shape=1.5654; scale=3.2983
#> 5            gamma   non-cure 1742.850                shape=1.4689; rate=0.2516
#> 6          weibull   non-cure 1750.005               shape=1.2715; scale=6.1871
#> 7      exponential   non-cure 1769.052                                  =0.1416
#> 8 exponential_cure       cure 1771.057                 theta=4e-04; rate=0.1416
#>   error
#> 1      
#> 2      
#> 3      
#> 4      
#> 5      
#> 6      
#> 7      
#> 8

The best-fitting model according to AIC is:

fit_res$best_model
#> [1] "loglogistic_cure"
fit_res$best_model_type
#> [1] "cure"

Step 4: Run cure-appropriateness tests

If desired, additional diagnostics can be computed.

test_res <- run.cure.tests(gbsg_dat, dist = "lnorm")

1. Maller-Zhou test

The Maller–Zhou test (Maller & Zhou, 1994; 1996) is a diagnostic method used to assess whether a cure fraction may exist in right-censored survival data.

test_res$mz
#> 
#> Maller-Zhou test statistic (1994)
#> ---------------------------------
#> Statistic: 0.0494606 
#> Alpha: 0.05 
#> Interpretation: Since the Maller-Zhou statistic (0.0495) is less than alpha = 0.05, there is evidence of sufficient follow-up, supporting cure model appropriateness.

2. qn statistic

The qn statistic, proposed by Maller and Zhou (1996), is a descriptive statistic used to evaluate whether a survival plateau may exist in right-censored survival data.

test_res$qn
#> 
#> qn statistic (Maller & Zhou 1996)
#> ---------------------------------
#> Statistic: 0.004373178 
#> Interpretation: The qn statistic is 0.0044 (alpha_n-equivalent threshold for sufficient follow-up at the 0.05 level is 0.0044). Because qn exceeds this threshold, there is evidence of sufficient follow-up, consistent with a survival plateau and supporting cure model appropriateness. Larger values of qn provide stronger evidence.

3. Shen test

The Shen test is a statistical method used to assess whether a cure fraction may be present in right-censored survival data.

test_res$shen
#> 
#> Shen test (2000)
#> ----------------
#> Statistic: 0.3676111 
#> Alpha: 0.05 
#> Interpretation: Since the Shen test statistic (0.3676) is greater than or equal to alpha = 0.05, there is insufficient evidence of adequate follow-up to support cure model appropriateness.

4. Test for Immunes

test_res$immune
#> 
#> Maller-Zhou immune summary (1996)
#> ---------------------------------
#> p_hat: 0.6572415 
#> p_cens: 0.5641399 
#> Last observation: 7.279945 
#> Last observation censored: TRUE 
#> Interpretation: The last observed time is censored, suggesting a possible survival plateau. The estimated event probability by the end of follow-up is 0.6572, and the censoring proportion is 0.5641.

5. RECeUS method

The RECeUS method is a diagnostic approach used to assess whether a cure model is appropriate for survival data. It evaluates both the estimated cure fraction and the amount of remaining uncured subjects at the end of follow-up.

test_res$receus
#> 
#> RECeUS Cure Model Assessment
#> ----------------------------
#> Distribution: lnorm 
#> Tau: 7.2799 
#> 
#> Estimated cure fraction (pi_hat): 0.2775 
#> Remaining uncured ratio (r_hat): 0.4083 
#> 
#> Decision: Follow-up insufficient for cure modeling 
#> 
#> Interpretation:
#> The remaining uncured ratio (r_hat = 0.4083 ) is greater than or equal to 0.05. This suggests that a large proportion of uncured subjects remain censored at the end of follow-up, indicating insufficient follow-up to reliably estimate a cure fraction.

Step 5: Run the full wrapper

The main wrapper function combines preparation, model fitting, and optional testing. Screening only.

res_screen <- cure.appropriateness(
  data = survival::gbsg,
  time = "rfstime",
  status = "status",
  time_scale = "days_to_years",
  dist = "lnorm",
  plot_km = FALSE,
  run_tests = "no"
)
res_screen
#> 
#> Cure model appropriateness analysis
#> -----------------------------------
#> Best model by AIC: loglogistic_cure 
#> Best model type: cure 
#> 
#> Initial decision:
#> The model with the smallest AIC is a cure model (loglogistic_cure). This provides initial support for cure model appropriateness. 
#> 
#> RECeUS distribution used: lnorm 
#> Testing status:
#> Tests were not run because `run_tests = "no"`. 
#> 
#> Final recommendation:
#> The model with the smallest AIC is a cure model (loglogistic_cure). This provides initial support for cure model appropriateness.

The screening results can be inspected through the screening component.

res_screen$screening$aic_table
#>              model model_type      AIC                      parameter_estimates
#> 1 loglogistic_cure       cure 1719.696 theta=0.3238; shape=1.9556; scale=2.7033
#> 2       gamma_cure       cure 1723.476   theta=0.3805; shape=2.1055; rate=0.696
#> 3      loglogistic   non-cure 1731.346               shape=1.5325; scale=4.4994
#> 4     weibull_cure       cure 1733.922 theta=0.3839; shape=1.5654; scale=3.2983
#> 5            gamma   non-cure 1742.850                shape=1.4689; rate=0.2516
#> 6          weibull   non-cure 1750.005               shape=1.2715; scale=6.1871
#> 7      exponential   non-cure 1769.052                                  =0.1416
#> 8 exponential_cure       cure 1771.057                 theta=4e-04; rate=0.1416
#>   error
#> 1      
#> 2      
#> 3      
#> 4      
#> 5      
#> 6      
#> 7      
#> 8
res_screen$screening$best_model
#> [1] "loglogistic_cure"
res_screen$screening$initial_decision
#> [1] "The model with the smallest AIC is a cure model (loglogistic_cure). This provides initial support for cure model appropriateness."

Automatic testing only if the best model is a cure model.

res_auto <- cure.appropriateness(
  data = survival::gbsg,
  time = "rfstime",
  status = "status",
  time_scale = "days_to_years",
  dist = "lnorm",
  plot_km = FALSE,
  run_tests = "auto"
)
res_auto
#> 
#> Cure model appropriateness analysis
#> -----------------------------------
#> Best model by AIC: loglogistic_cure 
#> Best model type: cure 
#> 
#> Initial decision:
#> The model with the smallest AIC is a cure model (loglogistic_cure). This provides initial support for cure model appropriateness. 
#> 
#> RECeUS distribution used: lnorm 
#> Testing status:
#> Tests were run automatically because the smallest-AIC model was a cure model. RECeUS used distribution: lnorm. 
#> 
#> Final recommendation:
#> The model with the smallest AIC is a cure model (loglogistic_cure). This provides initial support for cure model appropriateness. Additional cure-appropriateness diagnostics were run for further evaluation.

Force all tests to run

res_full <- cure.appropriateness(
  data = survival::gbsg,
  time = "rfstime",
  status = "status",
  time_scale = "days_to_years",
  dist = "lnorm",
  plot_km = FALSE,
  run_tests = "yes"
)
res_full
#> 
#> Cure model appropriateness analysis
#> -----------------------------------
#> Best model by AIC: loglogistic_cure 
#> Best model type: cure 
#> 
#> Initial decision:
#> The model with the smallest AIC is a cure model (loglogistic_cure). This provides initial support for cure model appropriateness. 
#> 
#> RECeUS distribution used: lnorm 
#> Testing status:
#> Tests were run because `run_tests = "yes"`. RECeUS used distribution: lnorm. 
#> 
#> Final recommendation:
#> The model with the smallest AIC is a cure model (loglogistic_cure). This provides initial support for cure model appropriateness. Additional cure-appropriateness diagnostics were run for further evaluation.