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Introduction to seerSurv: Cancer Recurrence Transition Probabilities

Sameer Mansoori, Shubhram Pandey, Rashi Rani, Barinder Singh, Murat Kurt

2026-03-21

Source: vignettes/seerSurv-intro.Rmd
seerSurv-intro.Rmd

Background

State-transition health economic models of early-stage cancers often include a local/regional recurrence (LR) state that sits between the disease-free state and distant recurrence (DR) or death. Populating such a model requires three monthly transition probabilities from LR:

Transition Symbol
Remain in LR \(P_{\text{LL}}\)
Progress to DR \(P_{\text{DL}}\)
Die while in LR \(P_{\text{death} \mid \text{LR}} = 1 - P_{\text{LL}} - P_{\text{DL}}\)

Trial-derived estimates are rarely available because clinical studies are typically powered for overall or disease-free survival, and LR follow-up is too short to observe the full recurrence cascade.

seerSurv fills this gap by deriving the three probabilities from aggregate (population-level) survival data extracted from the SEER-17 registry, covering ten cancer types.

Methodological overview

  1. Pseudo-IPD construction — Aggregate survival proportions at years 0–5 are converted to pseudo-individual patient data (prep_ipd()).

  2. Parametric modelling — Six distributions (exponential, Weibull, Gompertz, log-logistic, log-normal, gamma) are fitted to the pseudo-IPD using weighted maximum likelihood via flexsurv (fit_models()).

  3. Model averaging — The top-\(k\) distributions by AIC or BIC receive relative-likelihood weights; the final curve is a convex blend (compute_weights(), blend_survival()).

  4. Background mortality adjustment — Disease-specific survival is multiplied by age- and sex-specific background survival from the US-CDC life-table to obtain net (all-cause) survival (make_background_surv()).

  5. Sojourn time and \(P_{\text{LL}}\) — The mean LR sojourn time \(M\) (months) equals the area difference between the net LR and net DR curves. \(P_{\text{LL}}\) solves \(\sum_{t=0}^{N} P_{\text{LL}}^t = M\).

  6. Convolution for \(P_{\text{DL}}\) — The modelled LR survival is approximated as the sum of patients still in LR and those who have transitioned to DR. \(P_{\text{DL}}\) is estimated by least-squares (run_tumour_analysis()).

Quickstart: single tumour type 

library(seerSurv)
library(dplyr)

data(lifetable_seer)

# Five-year SEER-17 survival proportions — Melanoma
s_lr <- c(1, 0.9959, 0.9886, 0.9831, 0.9783, 0.9754)
s_dr <- c(1, 0.5491, 0.4396, 0.3945, 0.3630, 0.3410)

result <- run_tumour_analysis(
  tumour       = "Melanoma",
  surv_vec_LR  = s_lr,
  surv_vec_DR  = s_dr,
  N_L          = 64775L,
  N_D          = 3121L,
  prop_male_LR = 0.580,
  mean_age_LR  = 61,
  prop_male_DR = 0.692,
  mean_age_DR  = 62,
  lifetable    = lifetable_seer,
  scenario     = "lifetime",
  criterion    = "AIC"
)

knitr::kable(result, digits = 5,
             caption = "Monthly transition probabilities — Melanoma (lifetime, AIC)")
Monthly transition probabilities — Melanoma (lifetime, AIC)
P_LL P_DL_approach2 P_Death_L_approach2 RMST_L_years RMST_D_years M_years M_months
0.99336 0.00659 0.00005 21.1512 9.1799 11.9713 143.6556

Step-by-step walkthrough

Step 1: Prepare pseudo-IPD 

t    <- 0:5
ipd_L <- prep_ipd(t, s_lr)
ipd_D <- prep_ipd(t, s_dr)
ipd_L
#> # A tibble: 6 × 3
#>    time  weight event
#>   <int>   <dbl> <int>
#> 1     0 0.00410     1
#> 2     1 0.00730     1
#> 3     2 0.00550     1
#> 4     3 0.00480     1
#> 5     4 0.00290     1
#> 6     5 0.975       0

Step 2: Fit parametric models 

mods_L <- fit_models(ipd_L[-1, ])   # drop time = 0 row
mods_D <- fit_models(ipd_D[-1, ])

names(mods_L)
#> [1] "exp"      "weibull"  "gompertz" "llogis"   "lnorm"    "gamma"

Step 3: Compute AIC-based weights 

ic_L   <- extract_ic(mods_L, "AIC")
wts_L  <- compute_weights(ic_L, top_k = 3, criterion = "AIC")
wts_L
#> # A tibble: 3 × 4
#>   model    weight    ic criterion
#>   <chr>     <dbl> <dbl> <chr>    
#> 1 exp       0.576  2.27 AIC      
#> 2 lnorm     0.212  4.26 AIC      
#> 3 gompertz  0.212  4.26 AIC

Step 4: Blend survival curves 

grid     <- seq(0, 39, by = 1)   # 39-year lifetime horizon from age 61
S_blend_L <- blend_survival(mods_L, wts_L, grid)
#> New names:
#> • `surv` -> `surv...1`
#> • `surv` -> `surv...2`
#> • `surv` -> `surv...3`
head(S_blend_L)
#> # A tibble: 6 × 2
#>    time  surv
#>   <dbl> <dbl>
#> 1     0 1    
#> 2     1 0.996
#> 3     2 0.991
#> 4     3 0.987
#> 5     4 0.983
#> 6     5 0.979

Step 5: Adjust for background mortality 

lt <- lifetable_seer |>
  mutate(
    btrate_LR = Males * 0.580 + Females * 0.420,
    btrate_DR = Males * 0.692 + Females * 0.308
  )

B_LR <- make_background_surv(lt, mean_age = 61, rate_col = "btrate_LR",
                              time_grid_years = grid)
B_DR <- make_background_surv(lt, mean_age = 62, rate_col = "btrate_DR",
                              time_grid_years = grid)
head(B_LR)
#> # A tibble: 6 × 2
#>    time  surv
#>   <dbl> <dbl>
#> 1     0 1    
#> 2     1 0.990
#> 3     2 0.979
#> 4     3 0.967
#> 5     4 0.955
#> 6     5 0.942

Step 6: Visualise 

ic_D  <- extract_ic(mods_D, "AIC")
wts_D <- compute_weights(ic_D, top_k = 3, criterion = "AIC")
S_blend_D <- blend_survival(mods_D, wts_D, grid)
#> New names:
#> • `surv` -> `surv...1`
#> • `surv` -> `surv...2`
#> • `surv` -> `surv...3`

U_L <- left_join(S_blend_L, B_LR, by = "time") |>
  mutate(surv = surv.x * surv.y) |> select(time, surv)

U_D <- left_join(S_blend_D, B_DR, by = "time") |>
  mutate(surv = surv.x * surv.y) |> select(time, surv)

plot_survival_curves(S_blend_L, S_blend_D, U_L, U_D, tumour = "Melanoma")
Blended and net survival curves — Melanoma

Blended and net survival curves — Melanoma

Multi-tumour analysis using bundled data 

data(tumour_data_seer)

results_multi <- tumour_data_seer |>
  group_by(Tumor) |>
  summarise(
    out = list(
      run_tumour_analysis(
        tumour       = first(Tumor),
        surv_vec_LR  = c(S0[Recurrence == "LR"], S1[Recurrence == "LR"],
                         S2[Recurrence == "LR"], S3[Recurrence == "LR"],
                         S4[Recurrence == "LR"], S5[Recurrence == "LR"]),
        surv_vec_DR  = c(S0[Recurrence == "DR"], S1[Recurrence == "DR"],
                         S2[Recurrence == "DR"], S3[Recurrence == "DR"],
                         S4[Recurrence == "DR"], S5[Recurrence == "DR"]),
        N_L          = first(N_LR),
        N_D          = first(N_DR),
        prop_male_LR = prop_male[Recurrence == "LR"],
        mean_age_LR  = mean_age[Recurrence == "LR"],
        prop_male_DR = prop_male[Recurrence == "DR"],
        mean_age_DR  = mean_age[Recurrence == "DR"],
        lifetable    = lifetable_seer,
        scenario     = "lifetime",
        criterion    = "AIC"
      )
    ),
    .groups = "drop"
  ) |>
  tidyr::unnest(out)

knitr::kable(
  results_multi |> select(Tumor, P_LL, P_DL_approach2, P_Death_L_approach2,
                           M_months),
  digits  = 5,
  caption = "Monthly transition probabilities across 11 cancer types (lifetime, AIC)"
)
Monthly transition probabilities across 11 cancer types (lifetime, AIC)
Tumor P_LL P_DL_approach2 P_Death_L_approach2 M_months
Bladder 0.99101 0.00892 0.00007 108.79987
Breast 0.99519 0.00474 0.00006 185.87608
Colon & Rectum 0.99377 0.00619 0.00004 152.09926
Esophageal 0.98020 0.01974 0.00006 50.54718
Kidney 0.99419 0.00574 0.00008 160.60925
Liver 0.97702 0.02291 0.00007 43.48845
Lung 0.98460 0.01532 0.00008 64.85504
Melanoma 0.99336 0.00660 0.00005 143.60317
Ovarian 0.99288 0.00706 0.00005 136.40131
Pancreatic 0.96900 0.03094 0.00006 32.25437
Stomach 0.98993 0.01003 0.00004 98.20475

Sensitivity analysis: time horizons and model-selection criteria 

scenarios  <- c("lifetime", "20y", "5y")
criteria   <- c("AIC", "BIC")

sens_grid <- expand.grid(scenario = scenarios, criterion = criteria,
                         stringsAsFactors = FALSE)

sens_results <- lapply(seq_len(nrow(sens_grid)), function(i) {
  run_tumour_analysis(
    tumour       = "Melanoma",
    surv_vec_LR  = s_lr,
    surv_vec_DR  = s_dr,
    N_L          = 64775L,
    N_D          = 3121L,
    prop_male_LR = 0.580,
    mean_age_LR  = 61,
    prop_male_DR = 0.692,
    mean_age_DR  = 62,
    lifetable    = lifetable_seer,
    scenario     = sens_grid$scenario[i],
    criterion    = sens_grid$criterion[i]
  ) |>
    mutate(scenario  = sens_grid$scenario[i],
           criterion = sens_grid$criterion[i])
})

sens_df <- bind_rows(sens_results) |>
  select(scenario, criterion, P_LL, P_DL_approach2, P_Death_L_approach2)

knitr::kable(sens_df, digits = 5,
             caption = "Sensitivity analysis — Melanoma across scenarios and criteria")
Sensitivity analysis — Melanoma across scenarios and criteria
scenario criterion P_LL P_DL_approach2 P_Death_L_approach2
lifetime AIC 0.99336 0.00659 0.00005
20y AIC 0.99076 0.00917 0.00008
5y AIC 0.91780 0.08214 0.00006
lifetime BIC 0.99278 0.00716 0.00005
20y BIC 0.99004 0.00988 0.00008
5y BIC 0.92011 0.07983 0.00005

Interpreting the outputs

Column Interpretation
P_LL Per-month probability of remaining in LR state
P_DL_approach2 Per-month probability of progressing from LR to DR
P_Death_L_approach2 Per-month probability of dying while in LR
RMST_L_years Restricted mean survival time — LR population (net, years)
RMST_D_years Restricted mean survival time — DR population (net, years)
M_years / M_months Mean sojourn time in LR state

These probabilities can be plugged directly into a Markov cohort model or a partitioned survival model that includes an LR health state.

References

Mansoori S, Pandey S, Rani R, Singh B, Kurt M (2025). “Deriving Cancer Progression Rates After Local/Regional Recurrence Using Aggregate Survival Data: An R Package for Health Economic Evaluations.” Value in Health (submitted).

SEER Program. National Cancer Institute. https://seer.cancer.gov/.

Jackson C (2016). “flexsurv: A Platform for Parametric Survival Modelling in R.” Journal of Statistical Software, 70(8), 1–33. doi:[10.18637/jss.v070.i08](https://doi.org/10.18637/jss.v070.i08).