Cox regression IV. Competing risks.
Cox regression IV. Competing risks.
Cox regression IV. Competing risks.
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u n i v e r s i t y o f c o p e n h a g e nd e p a r t m e n t o f b i o s t a t i s t i c sAlternativ beregning af KMFor hvert dødstidspunkt t i er sandsynligheden for død af type 1:P 1 (T ≤ t i ) = P 1 (T ≤ 1) + P 1 (1 < T ≤ 2) + . . . + P 1 (t i−1 < T ≤ t i )= P 1 (T ≤ 1) · 1 +P 1 (T ≤ 2|T > 1) · S(1) + . . . + P 1 (T ≤ t i |T > t i−1 ) · S(t i−1 ).Hvis vi beregner S ved at censurere de døde fås10 9 8 7 6 5 4 3 2 11 0 1 0 0 1 0 0 1 00 1 2 3 4 5 6 7 8 9 1010 +10 · 1 + 18 · 91+105 · 9 71+10 82 · 9 7 410 8 50 + 0.1 + 0.1125 + 0.1575 + 0.315= 0 0.1 0.2125 0.37 0.685dvs. præcis 1 minus KM-estimatoren.✲32 / 47