Pointwise confidence interval for a Kaplan-Meier curve (Greenwood)

Greenwood's variance of the product-limit estimator, with n_j at risk and d_j events at t_j. The plain (linear) pointwise interval is S(t) +/- z sqrt(Var), truncated to [0, 1] because the linear scale can leave the unit interval near the tails. The curve is rebuilt from the risk table so the same fit object can be reused by the simultaneous band.

Usage

Kpmnci(fit, alpha)

Arguments

fit

Risk table: a list with time, n_risk and n_event, one entry per distinct event time in increasing time order.

alpha

Two-sided error rate.

Value

List with estimate (S at the last time), time, surv, se, sigma2, lower, upper, z, alpha, n_times, n_risk_start, n, method.

Details

Formula: Var[S(t)] = S(t)^2 sum_{t_j <= t} d_j / (n_j (n_j - d_j)).

References

Greenwood (1926), The natural duration of cancer, Reports on Public Health and Medical Subjects 33:1-26, HMSO.

Examples

fit <- list(time = c(2, 3, 5, 8), n_risk = c(10, 9, 7, 4), n_event = c(1, 1, 2, 1))
Kpmnci(fit, alpha = 0.05)[c("surv", "lower", "upper")]
#> $surv
#> [1] 0.9000000 0.8000000 0.5714286 0.4285714
#> 
#> $lower
#> [1] 0.71406149 0.55208199 0.25043603 0.08687608
#> 
#> $upper
#> [1] 1.0000000 1.0000000 0.8924211 0.7702668
#>