Survival data for 310 patients who underwent repair of atrioventricular septal defects (congenital heart disease) at the Cleveland Clinic between 1977 and 1993. Exhibits two identifiable hazard phases: an early post-operative risk and a constant late phase.
Format
A data frame with 310 rows and 11 variables:
- study
Patient identifier
- status
NYHA functional class (1–4)
- inc_surg
Surgical grade of AV valve incompetence
- opmos
Date of operation (months since January 1967)
- age
Age at repair (months)
- mal
Malalignment indicator (0/1)
- com_iv
Interventricular communication indicator (0/1)
- orifice
Associated cardiac anomaly indicator (0/1)
- dead
Death indicator (1 = dead, 0 = censored)
- int_dead
Follow-up interval to death or last contact (months)
- op_age
Interaction term: opmos x age
Source
Blackstone, Naftel, and Turner (1986) doi:10.1080/01621459.1986.10478314 . Cleveland Clinic Foundation.
Examples
data(avc)
avc <- na.omit(avc)
# Kaplan-Meier survival
km <- survival::survfit(survival::Surv(int_dead, dead) ~ 1, data = avc)
plot(km, xlab = "Months after AVC repair", ylab = "Survival",
main = "AVC: Kaplan-Meier survival estimate")
# \donttest{
# Two-phase hazard fit (early CDF + constant -- what AVC supports)
fit <- hazard(
survival::Surv(int_dead, dead) ~ 1, data = avc,
dist = "multiphase",
phases = list(
early = hzr_phase("cdf", t_half = 0.5, nu = 1, m = 1),
constant = hzr_phase("constant")
),
fit = TRUE, control = list(n_starts = 5, maxit = 1000)
)
#> Warning: Hessian is not positive-definite at the optimum; standard errors may be unreliable
#> Warning: Non-positive variance estimates; the optimum may not be a proper maximum
#> Warning: Hessian is not positive-definite at the optimum; standard errors may be unreliable
#> Warning: Non-positive variance estimates; the optimum may not be a proper maximum
#> Warning: Hessian is not positive-definite at the optimum; standard errors may be unreliable
#> Warning: Non-positive variance estimates; the optimum may not be a proper maximum
#> Warning: Hessian is not positive-definite at the optimum; standard errors may be unreliable
#> Warning: Non-positive variance estimates; the optimum may not be a proper maximum
#> Warning: Hessian is not positive-definite at the optimum; standard errors may be unreliable
#> Warning: Non-positive variance estimates; the optimum may not be a proper maximum
summary(fit)
#> Multiphase hazard model (2 phases)
#> observations: 305
#> predictors: 0
#> dist: multiphase
#> phase 1: early - cdf (early risk)
#> phase 2: constant - constant (flat rate)
#> engine: native-r-m2
#> converged: TRUE
#> log-lik: -211.468
#> evaluations: fn=4, gr=1
#>
#> Coefficients (internal scale):
#>
#> Phase: early (cdf)
#> estimate std_error z_stat p_value
#> log_mu -1.4575139 0.1412477 -10.318850 5.791249e-25
#> log_t_half -1.7947622 0.3641513 -4.928617 8.281363e-07
#> nu 1.4541539 0.5504106 2.641944 8.243171e-03
#> m 0.9266039 0.7085506 1.307746 1.909596e-01
#>
#> Phase: constant (constant)
#> estimate std_error z_stat p_value
#> log_mu -7.523126 0.4714346 -15.95794 2.508668e-57
# }