Modifying & Combining Distributions
Source:vignettes/modify-combine-survival-distributions.Rmd
modify-combine-survival-distributions.RmdOnce you’ve created survival distributions, herosurv provides various methods for combining modifying them.
Apply Hazard Ratio:
Hazard ratios can be applied to a survival distribution using the apply_hr function.
dist1 <- define_surv_param('weibull', shape = 1.2, scale = 5.3)
dist2 <- apply_hr(dist1, 0.85)
print(dist2)
#> A proportional hazards survival distribution:
#> * Hazard Ratio: 0.85
#> * Baseline Distribution: A Weibull (AFT) distribution (shape = 1.2, scale = 5.3).Apply Odds Ratio
Odds ratios can be applied to a survival distribution using the apply_or function.
dist1 <- define_surv_param('weibull', shape = 1.2, scale = 5.3)
dist2 <- apply_or(dist1, 0.45)
print(dist2)
#> A proportional odds survival distribution:
#> * Odds Ratio: 0.45
#> * Baseline Distribution: A Weibull (AFT) distribution (shape = 1.2, scale = 5.3).Apply Accleration Factor
Accleration factors, which proportionally scale event times, can be applied using the apply_af function.
dist1 <- define_surv_param('weibull', shape = 1.2, scale = 5.3)
dist2 <- apply_af(dist1, 0.75)
print(dist2)
#> An accelerated failure time survival distribution:
#> * Acceleration Factor: 0.75
#> * Baseline Distribution: A Weibull (AFT) distribution (shape = 1.2, scale = 5.3).Apply Time Shift
Hazards for a distribution can be shifted forward or backward by a fixed amount of time using the apply_shift function. Note that a positive value of shift will move hazards forward and a negative value will shift hazards backward (resulting in an initial period with no event risk).
dist1 <- define_surv_param('weibull', shape = 1.2, scale = 5.3)
dist2 <- apply_shift(dist1, 2.1)
print(dist2)
#> A shifted survival distribution:
#> * Shift: 2.1
#> * Baseline Distribution: A Weibull (AFT) distribution (shape = 1.2, scale = 5.3).Mix Distributions
Survival distributions can be mixed according to specified weights using the mix function.
dist1 <- define_surv_param('weibull', shape = 1.2, scale = 5.3)
dist2 <- define_surv_param('weibull', shape = 1.4, scale = 4.1)
dist3 <- mix(dist1, 0.8, dist2, 0.2) # Mix of 80% dist1 and 20% dist2
print(dist3)
#> A mixed survival distribution:
#> * Distribution 1 (80%): A Weibull (AFT) distribution (shape = 1.2, scale = 5.3).
#> * Distribution 2 (20%): A Weibull (AFT) distribution (shape = 1.4, scale = 4.1).Join Distributions
Survival distributions can be joined together at specified cutpoints using the join function.
dist1 <- define_surv_param('weibull', shape = 1.2, scale = 5.3)
dist2 <- define_surv_param('weibull', shape = 1.4, scale = 4.1)
dist3 <- join(dist1, 3, dist2) # Join dist2 and dist3 at time 3
print(dist3)
#> A joined survival distribution:
#> * Segment 1 (t = 0 - 3): A Weibull (AFT) distribution (shape = 1.2, scale = 5.3).
#> * Segment 2 (t = 3 - ∞): A Weibull (AFT) distribution (shape = 1.4, scale = 4.1).Add Hazards
Survival distributions can be combined as independent risks using the add_hazards function. This results in a survival distribution with survival function equal to the product of the survival functions of combined distributions.
dist1 <- define_surv_param('weibull', shape = 1.2, scale = 5.3)
dist2 <- define_surv_param('weibull', shape = 1.4, scale = 4.1)
dist3 <- add_hazards(dist1, dist2) # combined hazards of dist1 and dist2
print(dist3)
#> A survival distribution combining the hazards of:
#> * Distribution 1: A Weibull (AFT) distribution (shape = 1.2, scale = 5.3).
#> * Distribution 2: A Weibull (AFT) distribution (shape = 1.4, scale = 4.1).Set Covariates
Models fitted using survfit or flexsurvreg with predictors can be used to generate a survival distribution representing a subject or set of subjects using set_covariates.
library(flexsurv)
#> Loading required package: survival
library(tibble)
# Fit a model using bc dataset using good as predictor
print(as_tibble(bc))
#> # A tibble: 686 × 4
#> censrec rectime group recyrs
#> <int> <int> <fct> <dbl>
#> 1 0 1342 Good 3.68
#> 2 0 1578 Good 4.32
#> 3 0 1760 Good 4.82
#> 4 0 1152 Good 3.16
#> 5 0 967 Good 2.65
#> 6 0 629 Good 1.72
#> 7 0 461 Good 1.26
#> 8 1 991 Good 2.72
#> 9 0 758 Good 2.08
#> 10 0 1617 Good 4.43
#> # … with 676 more rows
fs1 <- flexsurvreg(Surv(recyrs, censrec)~group, data = bc, dist = 'weibull')
# Survival distribution representing patient w/ group = "Good"
good_model <- set_covariates(fs1, data.frame(group = 'Good'))
print(good_model)
#> Predicted survival from fitted model for specified cohort:
#> * Cohort:
#> group
#> <chr>
#> 1 Good
#> * Model:
#> Call:
#> flexsurvreg(formula = Surv(recyrs, censrec) ~ group, data = bc,
#> dist = "weibull")
#>
#> Estimates:
#> data mean est L95% U95% se exp(est) L95%
#> shape NA 1.3797 1.2548 1.5170 0.0668 NA NA
#> scale NA 11.4229 9.1818 14.2110 1.2728 NA NA
#> groupMedium 0.3338 -0.6136 -0.8623 -0.3649 0.1269 0.5414 0.4222
#> groupPoor 0.3324 -1.2122 -1.4583 -0.9661 0.1256 0.2975 0.2326
#> U95%
#> shape NA
#> scale NA
#> groupMedium 0.6943
#> groupPoor 0.3806
#>
#> N = 686, Events: 299, Censored: 387
#> Total time at risk: 2113.425
#> Log-likelihood = -811.9419, df = 4
#> AIC = 1631.884
#>
# Survival distribution with patient representing cohort w/
# equal mix of group = "Good" and group = "Poor"
good_and_poor_model <- set_covariates(fs1, data.frame(group = c('Good', 'Poor')))
print(good_and_poor_model)
#> Predicted survival from fitted model for specified cohort:
#> * Cohort:
#> group
#> <chr>
#> 1 Good
#> 2 Poor
#> * Model:
#> Call:
#> flexsurvreg(formula = Surv(recyrs, censrec) ~ group, data = bc,
#> dist = "weibull")
#>
#> Estimates:
#> data mean est L95% U95% se exp(est) L95%
#> shape NA 1.3797 1.2548 1.5170 0.0668 NA NA
#> scale NA 11.4229 9.1818 14.2110 1.2728 NA NA
#> groupMedium 0.3338 -0.6136 -0.8623 -0.3649 0.1269 0.5414 0.4222
#> groupPoor 0.3324 -1.2122 -1.4583 -0.9661 0.1256 0.2975 0.2326
#> U95%
#> shape NA
#> scale NA
#> groupMedium 0.6943
#> groupPoor 0.3806
#>
#> N = 686, Events: 299, Censored: 387
#> Total time at risk: 2113.425
#> Log-likelihood = -811.9419, df = 4
#> AIC = 1631.884
#>