Zusammenfassung
Die Survival-Analyse modelliert Überlebenszeiten (Hosmer Jr, Lemeshow, & May, 2008; Klein & Moeschberger, 2003). Diese geben allgemein an, wieviel Zeit bis zum Eintreten eines bestimmten Ereignisses verstrichen ist und sollen hier deshalb gleichbedeutend mit Ereigniszeiten sein. Es kann sich dabei etwa um die Zeitdauer handeln, die ein Patient nach einer Behandlung weiter am Leben ist, um die verstrichene Zeit, bis ein bestimmtes Bauteil im Gebrauch einen Defekt aufweist, oder um die Dauer, die ein Kleinkind benötigt, um ein vordefiniertes Entwicklungsziel zu erreichen – z. B. einen Mindestwortschatz besitzt. Bei der Analyse von Überlebenszeiten kann sowohl die Form ihres grundsätzlichen Verlaufs von Interesse sein, als auch inwiefern ihr Verlauf systematisch von Einflussgrößen abhängt.
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Notes
- 1.
\(f(t) =\lim _{\Delta _{t}\rightarrow 0^{+}} \frac{P(t\leq T<t+\Delta _{t})} {\Delta _{t}}\) in Abhängigkeit von der Zeit t und der Intervallbreite \(\Delta _{t}\).
- 2.
#Personen | Ereignis ≥ t ist die Größe des risk set bzw. die Anzahl der Beobachtungsobjekte at risk zum Zeitpunkt t.
- 3.
Für Intervall-zensierte Daten vgl. ?Surv. Vergleiche Abschn. 9.2.2 für zeitabhängige Prädiktoren und Fälle, in denen mehrere Ereignisse pro Beobachtungsobjekt möglich sind.
- 4.
Bei nicht wiederkehrenden Ereignissen ist die Einteilung der Gesamtbeobachtungszeit in einzelne, bündig aneinander anschließende Intervalle beliebig: Die einzelne Beobachtung im (〈Zeitpunkt〉, 〈Status〉)-Format (10, TRUE) ist sowohl äquivalent zu den zwei Beobachtungen in Zählprozess-Darstellung (0, 4, FALSE), (4, 10, TRUE) als auch zu den drei Beobachtungen (0, 2, FALSE), (2, 6, FALSE), (6, 10, TRUE).
- 5.
Für eine exakte Alternative vgl. logrank_test() aus dem Paket coin (Hothorn, Hornik, van de Wiel & Zeileis, 2008).
- 6.
Aus diesem Grund ist der Aussagebereich eines angepassten Cox PH-Modells auch auf die in der Stichprobe tatsächlich vorliegenden Überlebenszeiten begrenzt, eine Extrapolation über die maximal beobachtete Überlebenszeit hinaus also unzulässig.
- 7.
Lässt man die Annahme proportionaler hazards fallen, kommen auch weitere Verteilungen für T in Betracht, über die ?survreg Auskunft gibt.
- 8.
Für die \(\hat{\beta }_{j}\) ergibt sich 0. 51 (X), − 0. 41 (IVB) und 0. 63 (IVC) – also Schätzungen, die hier denen des Cox PH-Modells sehr ähnlich sind (s. S. 362).
- 9.
Abschnitt 9.4.2 demonstriert die analoge Verwendung von newdata in survfit().
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Wollschläger, D. (2017). Survival-Analyse. In: Grundlagen der Datenanalyse mit R. Statistik und ihre Anwendungen. Springer Spektrum, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53670-4_9
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