The only change from the ordinary estimator is the risk set: a subject enters at
entry rather than at time zero, so it is at risk only over (entry, time].
Usage
Ltkm(entry, time, event, alpha = 0.05)
morie_survival_left_truncated_km(entry, time, event, alpha = 0.05)Value
list with the survival estimate, its standard error, the confidence interval and the risk-set sizes.
References
Klein, J. P. and Moeschberger, M. L. (2003). Survival Analysis, 2nd ed., Springer, Section 3.4.
Examples
ST <- c(5, 6, 6, 2.5, 4, 4, 3, 3, 1, 2, 2, 3, 7, 8, 9, 10)
SE <- c(1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1)
en <- c(0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2)
Ltkm(en, ST, SE)
#> $time
#> [1] 1.0 2.0 2.5 3.0 4.0 5.0 6.0 7.0 9.0 10.0
#>
#> $surv
#> [1] 0.8750000 0.7954545 0.7342657 0.5506993 0.4895105 0.4195804 0.3496503
#> [8] 0.2622378 0.1311189 0.0000000
#>
#> $se
#> [1] 0.1169268 0.1305807 0.1341082 0.1361643 0.1340803 0.1319075 0.1271150
#> [8] 0.1217363 0.1109099 0.0000000
#>
#> $n_risk
#> [1] 8 11 13 12 9 7 6 4 2 1
#>
#> $n_event
#> [1] 1 1 1 3 1 1 1 1 1 1
#>
#> $lower
#> [1] 0.64582770 0.53952104 0.47141853 0.28382213 0.22671796 0.16104647
#> [7] 0.10050950 0.02363903 0.00000000 0.00000000
#>
#> $upper
#> [1] 1.0000000 1.0000000 0.9971129 0.8175765 0.7523030 0.6781144 0.5987912
#> [8] 0.5008365 0.3484983 0.0000000
#>
#> $ignoring_truncation
#> [1] 0.9375000 0.8750000 0.8076923 0.6057692 0.5384615 0.4615385 0.3846154
#> [8] 0.2884615 0.1442308 0.0000000
#>
#> $max_difference
#> [1] 0.07954545
#>
#> $empty_risk_sets
#> numeric(0)
#>
#> $n
#> [1] 16
#>
#> $n_events
#> [1] 12
#>
#> $method
#> [1] "Kaplan-Meier with the risk set restricted to entry < t <= time"
#>