Value of estimated risk = 1 cannot be achieved with tidy_survfit()?

[uriahf]

Hi, thank you for this wonderful package!

I wonder why I can't get the value of 1 from the estimated risk once I fill a custom time point bigger than the maximum observed time-to-event?

library(ggsurvfit)
#> Loading required package: ggplot2

survfit2(Surv(time, status) ~ 1, data = df_lung)  |> 
  tidy_survfit(times = c(33, max(df_lung$time), 34), 
               type = "risk")
#> # A tibble: 3 x 14
#>    time n.risk n.event n.censor cum.event cum.censor estimate std.error conf.low
#>   <dbl>  <dbl>   <dbl>    <dbl>     <dbl>      <dbl>    <dbl>     <dbl>    <dbl>
#> 1  33        2     165       61       165         61    0.950     0.454    0.877
#> 2  33.6      1       0        2       165         63    0.950     0.454    0.877
#> 3  34        0       0        0       165         63   **NA**        NA       NA    
#> # i 5 more variables: conf.high <dbl>, estimate_type <chr>,
#> #   estimate_type_label <chr>, monotonicity_type <chr>, conf.level <dbl>

[ddsjoberg]

While the KM curve theoretically will go to 1 (on the risk scale) as time goes to infinity, we don't always observe this. Consider an example where the observed rate of the outcome are low.

library(ggsurvfit)
#> Loading required package: ggplot2

survfit2(
  Surv(time, status) ~ 1, 
  df_lung |> 
    dplyr::mutate( # lower the event rate
      status = ifelse(dplyr::row_number() > 5, 1, status)
    )
) |> 
  ggsurvfit(type = "risk") +
  scale_y_continuous(limits = c(0, 1))

^{Created on 2024-03-29 with reprex v2.1.0}

In this case, we would not want to assume the risk at time 34 is 100%, simply because 34 is larger than any of the observed followup times.

Hope that helps illustrate the logic. Also, we're really just plotting results from the {survival} package, so you can also find answers in their functions' documentation as well (where we are lacking 😱 ).

[uriahf]

Thanks! That's reasonable.

A related question:
If I calculate the CIF for each subgroup, the last estimate is defined by the latest observed time-to-event for each specific group. For example on the df_lung data-set the latest observed outcome happened at time 33.6 (male), why I can't get an estimate for that time point to females as well?

library(ggsurvfit)
#> Warning: package 'ggsurvfit' was built under R version 4.3.3
#> Loading required package: ggplot2

survfit2(Surv(time, status) ~ sex, data = df_lung)  |> 
  tidy_survfit(times = c(33, max(df_lung$time), 34), 
               type = "risk")
#> # A tibble: 6 × 16
#>    time n.risk n.event n.censor cum.event cum.censor estimate std.error conf.low
#>   <dbl>  <dbl>   <dbl>    <dbl>     <dbl>      <dbl>    <dbl>     <dbl>    <dbl>
#> 1  33        0      53       37        53         37   NA        NA       NA    
#> 2  33.6      0       0        0        53         37   NA        NA       NA    
#> 3  34        0       0        0        53         37   NA        NA       NA    
#> 4  33        2     112       24       112         24    0.964     0.605    0.883
#> 5  33.6      1       0        2       112         26    0.964     0.605    0.883
#> 6  34        0       0        0       112         26   NA        NA       NA    
#> # ℹ 7 more variables: conf.high <dbl>, strata <fct>, estimate_type <chr>,
#> #   estimate_type_label <chr>, monotonicity_type <chr>, strata_label <chr>,
#> #   conf.level <dbl>

library(ggsurvfit)
#> Warning: package 'ggsurvfit' was built under R version 4.3.3
#> Loading required package: ggplot2

survfit2(
  Surv(time, status) ~ sex, 
  df_lung |> 
    dplyr::mutate( # lower the event rate
      status = ifelse(dplyr::row_number() > 5, 1, status)
    )
) |> 
  ggsurvfit(type = "risk") +
  scale_y_continuous(limits = c(0, 1))

[ddsjoberg]

These calculations are done entirely separate by group, so when there is not enough data in one group to calculate an estimate it's independent of any other groups' estimates and followup.