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❈❛❧✐❜r❛t✐♦♥ ♣❧♦ts ❢♦r r✐s❦ ♣r❡❞✐❝t✐♦♥ ♠♦❞❡❧s ✐♥ t❤❡ ♣r❡s❡♥❝❡ ♦❢ ❝♦♠♣❡t✐♥❣ r✐s❦s ❚❤♦♠❛s ❆ ●❡r❞s✱ ❚❤♦♠❛s ❍ ❙❝❤❡✐❦❡✱ P❡r ❑ ❆♥❞❡rs❡♥ ❛♥❞ ▼✐❝❤❛❡❧ ❲ ❑❛tt❛♥ ❏✉♥❡ ✷✻✱ ✷✵✶✹ ✶ ✴ ✷✽

▼♦t✐✈❛t✐♦♥✿ ♣❛t✐❡♥t ❝♦✉♥s❡❧✐♥❣ ❯s✐♥❣ ❛ st❛t✐st✐❝❛❧ ♠♦❞❡❧✱ ❛ ❞❛t❛❜❛s❡ ❝❛♥ ❜❡ q✉❡r✐❡❞ t♦ ♦❜t❛✐♥ ❛ t❛✐❧♦r❡❞ ♣r❡❞✐❝t✐♦♥ ❢♦r t❤❡ ♣r❡s❡♥t ♣❛t✐❡♥t✳ ❆ ♣r❡❞✐❝t❡❞ r✐s❦ ♦❢ ✶✼✪ ✐s ❝❛❧❧❡❞ r❡❧✐❛❜❧❡✱ ✐❢ ✐t ❝❛♥ ❜❡ ❡①♣❡❝t❡❞ t❤❛t t❤❡ ❡✈❡♥t ✇✐❧❧ ♦❝❝✉r t♦ ❛❜♦✉t ✶✼ ♦✉t ♦❢ ✶✵✵ ♣❛t✐❡♥ts ✇❤♦ ❛❧❧ r❡❝❡✐✈❡❞ ❛ ♣r❡❞✐❝t❡❞ r✐s❦ ♦❢ ✶✼✪✳ ❆ st❛t✐st✐❝❛❧ ♠♦❞❡❧ t❤❛t ♣r❡❞✐❝ts t❤❡ ❛❜s♦❧✉t❡ r✐s❦ ♦❢ ❛♥ ❡✈❡♥t s❤♦✉❧❞ ❜❡ ❝❛❧✐❜r❛t❡❞ ✐♥ t❤❡ s❡♥s❡ t❤❛t ✐t ♣r♦✈✐❞❡s r❡❧✐❛❜❧❡ ♣r❡❞✐❝t✐♦♥s ❢♦r ❛❧❧ s✉❜❥❡❝ts✳ ❆ ❝❛❧✐❜r❛t✐♦♥ ♣❧♦t ❞✐s♣❧❛②s ❤♦✇ ✇❡❧❧ ♦❜s❡r✈❡❞ ❛♥❞ ♣r❡❞✐❝t❡❞ ❡✈❡♥t st❛t✉s ❝♦♥♥❡❝t ♦♥ t❤❡ ❛❜s♦❧✉t❡ ♣r♦❜❛❜✐❧✐t② s❝❛❧❡✳ ✷ ✴ ✷✽

❈❛❧✐❜r❛t✐♦♥ ♣❧♦t Cause−specific Cox regression Fine−Gray regression 100 % Observed event status 75 % 50 % 25 % 0 % 0 % 25 % 50 % 75 % 100 % Predicted event probability ✸ ✴ ✷✽

Pr❡❞✐❝t✐♥❣ ❛❜s♦❧✉t❡ r✐s❦s ✐♥ t✐♠❡✲t♦✲❡✈❡♥t ❛♥❛❧②s✐s ❋✐rst ♣✐❝❦ ❛ t✐♠❡ ♦r✐❣✐♥ ❛t ✇❤✐❝❤ ✐t ✐s ♦❢ ✐♥t❡r❡st t♦ ♣r❡❞✐❝t t❤❡ ❢✉t✉r❡ st❛t✉s ♦❢ ❛ ♣❛t✐❡♥t✳ ❯♥t✐❧ t✐♠❡ t ❛❢t❡r t❤❡ t✐♠❡ ♦r✐❣✐♥ t❤r❡❡ t❤✐♥❣s ❝❛♥ ❤❛♣♣❡♥✿ ✶✳ t❤❡ ❡✈❡♥t ❤❛s ♦❝❝✉rr❡❞ ✷✳ ❛ ❝♦♠♣❡t✐♥❣ ❡✈❡♥t ❤❛s ♦❝❝✉rr❡❞ ✸✳ t❤❡ ♣❛t✐❡♥t ✐s ❛❧✐✈❡ ❛♥❞ ❡✈❡♥t✲❢r❡❡✳ ❚❤❡ ♣❛t✐❡♥t ♥❡❡❞s t♦ ❦♥♦✇ t❤❡ ❛❜s♦❧✉t❡ r✐s❦s ♦❢ ❛❧❧ ❡✈❡♥ts ✭❞❡❛t❤✱ ❞✐s❡❛s❡✱ r❡❝✉rr❡♥❝❡✱ ❡t❝✳✮✳ ✹ ✴ ✷✽

❏♦❤♥ ❑❧❡✐♥✬s ❞❛t❛ ❢r♦♠ ❜♦♥❡ ♠❛rr♦✇ tr❛♥s♣❧❛♥t ♣❛t✐❡♥ts ❆ ❞❛t❛ ❢r❛♠❡ ✇✐t❤ ✶✼✶✺ ♦❜s❡r✈❛t✐♦♥s ✶ Transplant ❚❤❡ r❡♠❛✐♥✐♥❣ n = ✽✹✼ ♣❛t✐❡♥ts ✇❡r❡ ✐♥ r❡♠✐ss✐♦♥ ❜② t❤❡ ❡♥❞ ♦❢ t❤❡ ❢♦❧❧♦✇✲✉♣ ♣❡r✐♦❞✳ n= 311 n= 557 ❲❡ ❛r❡ ✐♥t❡r❡st❡❞ ✐♥ ♣r❡❞✐❝t✐♥❣ t❤❡ ❝✉♠✉❧❛t✐✈❡ ✐♥❝✐❞❡♥❝❡s ♦❢ r❡❧❛♣s❡ ❛♥❞ ❞❡❛t❤✳ Relapse Death ✶ ❙③②❞❧♦✱ ●♦❧❞♠❛♥✱ ❑❧❡✐♥ ❡t ❛❧✳ ❏♦✉r♥❛❧ ♦❢ ❈❧✐♥✐❝❛❧ ❖♥❝♦❧♦❣②✱ ✶✾✾✼✳ ✺ ✴ ✷✽

❖❜s❡r✈❡❞ ♦✉t❝♦♠❡ Kaplan−Meier estimate Aalen−Johansen estimate of censoring probability 100 % 100 % Event Relapse Cumulative incidence Cumulative incidence Death without relapse 75 % 75 % 50 % 50 % 25 % 25 % 0 % 0 % 0 12 36 60 84 0 12 36 60 84 Months since transplantation Months since transplantation ❲✐t❤♦✉t ❝♦✈❛r✐❛t❡s t❤❡ ♠❛r❣✐♥❛❧ ❆❛❧❡♥✲❏♦❤❛♥s❡♥ ❡st✐♠❛t❡ ✐s t❤❡ ❜❡st ♣r❡❞✐❝t✐♦♥ ♠♦❞❡❧✳ ✻ ✴ ✷✽

❋♦r♠✉❧❛ ■ ▲❡t ❳ ❜❡ ❛ ✈❡❝t♦r ♦❢ ❝♦✈❛r✐❛t❡s✿ F ✶ ( t | X ) = ❈✉♠✉❧❛t✐✈❡ ✐♥❝✐❞❡♥❝❡ ♦❢ ❡✈❡♥t ✶ � t � s � � ❡①♣ − { λ ✶ ( u | X ) + λ ✷ ( u | X ) } ❞ u λ ✶ ( s | X ) ❞ s . ✵ ✵ � �� � � �� � ❊✈❡♥t t②♣❡ ✶ ❛t s ◆♦ ❡✈❡♥t ♦❢ ❛♥② ❝❛✉s❡ ✉♥t✐❧ s ❘❡q✉✐r❡s ❛ r❡❣r❡ss✐♦♥ ♠♦❞❡❧ ❢♦r t❤❡ ❤❛③❛r❞ ♦❢ t❤❡ ❝♦♠♣❡t✐♥❣ r✐s❦s ♦r ❛ r❡❣r❡ss✐♦♥ ♠♦❞❡❧ ❢♦r t❤❡ ❡✈❡♥t✲❢r❡❡ s✉r✈✐✈❛❧ ♣r♦❜❛❜✐❧✐t②✳ ✼ ✴ ✷✽

❋♦r♠✉❧❛ ■■ ❚r❛♥s❢♦r♠❛t✐♦♥ ♠♦❞❡❧ h ( F ✶ ( t | X )) = β ✵✶ ( t ) + β ✶ X ✶ + · · · + β K X K ◮ ❤✭♣✮ ❂ ❧♦❣✭✲❧♦❣✭♣✮✮ ✭❋✐♥❡✲●r❛② ♠♦❞❡❧✮ ◮ ❤✭♣✮ ❂ ❧♦❣✭♣✴✭✶✲♣✮✮ ✭▲♦❣✐st✐❝ ♠♦❞❡❧✮ ◮ ❤✭♣✮ ❂ ❧♦❣✭♣✮ ✭▲♦❣✲❜✐♥♦♠✐❛❧ ♠♦❞❡❧✮ ❘❡q✉✐r❡s ❛ r❡❣r❡ss✐♦♥ ♠♦❞❡❧ ❢♦r t❤❡ ❝✉♠✉❧❛t✐✈❡ ♣r♦❜❛❜✐❧✐t② ♦❢ ❜❡✐♥❣ ✉♥❝❡♥s♦r❡❞✿ ●✭t⑤❳✮ ❂ P✭❚❃t⑤❳✮ ✐♥ ✇❤❛t ❢♦❧❧♦✇s✿ ●✭t⑤❳✮❂● ✵ ✭t✮✳ ✽ ✴ ✷✽

Pr♦♣♦s❛❧✿ ❲❡ ❛r❡ ✐♥t❡r❡st❡❞ ✐♥ r❡❣r❡ss✐♦♥ ♠♦❞❡❧s ❢♦r t❤❡ ❛❜s♦❧✉t❡ r✐s❦ ♦❢ r❡❧❛♣s❡ ✐♥ ✇❤✐❝❤ t❤❡ r❡❣r❡ss✐♦♥ ❝♦❡✣❝✐❡♥ts ❤❛✈❡ t❤❡ ❢♦❧❧♦✇✐♥❣ ✐♥t❡r♣r❡t❛t✐♦♥✿ ❚❤❡ ✺✲②❡❛r r✐s❦ ♦❢ r❡❧❛♣s❡ ❝❤❛♥❣❡s ✇✐t❤ ❛ ❢❛❝t♦r ❡①♣ ✶ ❢♦r ❛ ♦♥❡ ✉♥✐t ❝❤❛♥❣❡ ♦❢ ✶ ❛♥❞ ❣✐✈❡♥ ✈❛❧✉❡s ❢♦r t❤❡ ♦t❤❡r ♣r❡❞✐❝t♦r ✈❛r✐❛❜❧❡s ✳ ✷ ■♥t❡r♣r❡t❛t✐♦♥ ❝r✐s✐s ✐♥ ❝♦♠♣❡t✐♥❣ r✐s❦s Pr♦❜❧❡♠s✿ ◮ ❚❤❡ ❤❛③❛r❞ r❛t✐♦s ♦❜t❛✐♥❡❞ ❜② ❝❛✉s❡✲s♣❡❝✐✜❝ ❈♦① r❡❣r❡ss✐♦♥ ♠♦❞❡❧s ❛r❡ ♥♦t ❞✐r❡❝t❧② r❡❧❛t❡❞ t♦ t❤❡ ♣r❡❞✐❝t✐♦♥ ♦❢ t❤❡ ❝✉♠✉❧❛t✐✈❡ ✐♥❝✐❞❡♥❝❡✳ ◮ ❚❤❡ ❛❜s♦❧✉t❡ ✈❛❧✉❡s ♦❢ t❤❡ r❡❣r❡ss✐♦♥ ❝♦❡✣❝✐❡♥ts ✐♥ t❤❡ ❋✐♥❡✲●r❛② ♠♦❞❡❧ ❤❛✈❡ ♥♦ ❞✐r❡❝t ✐♥t❡r♣r❡t❛t✐♦♥✳ ✾ ✴ ✷✽

■♥t❡r♣r❡t❛t✐♦♥ ❝r✐s✐s ✐♥ ❝♦♠♣❡t✐♥❣ r✐s❦s Pr♦❜❧❡♠s✿ ◮ ❚❤❡ ❤❛③❛r❞ r❛t✐♦s ♦❜t❛✐♥❡❞ ❜② ❝❛✉s❡✲s♣❡❝✐✜❝ ❈♦① r❡❣r❡ss✐♦♥ ♠♦❞❡❧s ❛r❡ ♥♦t ❞✐r❡❝t❧② r❡❧❛t❡❞ t♦ t❤❡ ♣r❡❞✐❝t✐♦♥ ♦❢ t❤❡ ❝✉♠✉❧❛t✐✈❡ ✐♥❝✐❞❡♥❝❡✳ ◮ ❚❤❡ ❛❜s♦❧✉t❡ ✈❛❧✉❡s ♦❢ t❤❡ r❡❣r❡ss✐♦♥ ❝♦❡✣❝✐❡♥ts ✐♥ t❤❡ ❋✐♥❡✲●r❛② ♠♦❞❡❧ ❤❛✈❡ ♥♦ ❞✐r❡❝t ✐♥t❡r♣r❡t❛t✐♦♥✳ Pr♦♣♦s❛❧✿ ❲❡ ❛r❡ ✐♥t❡r❡st❡❞ ✐♥ r❡❣r❡ss✐♦♥ ♠♦❞❡❧s ❢♦r t❤❡ ❛❜s♦❧✉t❡ r✐s❦ ♦❢ r❡❧❛♣s❡ ✐♥ ✇❤✐❝❤ t❤❡ r❡❣r❡ss✐♦♥ ❝♦❡✣❝✐❡♥ts ❤❛✈❡ t❤❡ ❢♦❧❧♦✇✐♥❣ ✐♥t❡r♣r❡t❛t✐♦♥✿ ❚❤❡ ✺✲②❡❛r r✐s❦ ♦❢ r❡❧❛♣s❡ ❝❤❛♥❣❡s ✇✐t❤ ❛ ❢❛❝t♦r ❡①♣ ( β ✶ ) ❢♦r ❛ ♦♥❡ ✉♥✐t ❝❤❛♥❣❡ ♦❢ X ✶ ❛♥❞ ❣✐✈❡♥ ✈❛❧✉❡s ❢♦r t❤❡ ♦t❤❡r ♣r❡❞✐❝t♦r ✈❛r✐❛❜❧❡s ( X ✷ , ..., X K ) ✳ ✾ ✴ ✷✽

❆❜s♦❧✉t❡ r✐s❦ r❡❣r❡ss✐♦♥ ❚❤❡ r❡❣r❡ss✐♦♥ ♣❛r❛♠❡t❡rs ✐♥ t❤❡ ❧♦❣✲❜✐♥♦♠✐❛❧ ♠♦❞❡❧ ❤❛✈❡ t❤❡ ❞❡s✐r❡❞ ✐♥t❡r♣r❡t❛t✐♦♥✿ F ✶ ( t | X ) = exp ( β ✵✶ ( t )) ❡①♣ ( β ✶ X ✶ + · · · + β K X K ) ❆ ♦♥❡ ✉♥✐t ❝❤❛♥❣❡ ♦❢ t❤❡ ❦t❤ ❝♦✈❛r✐❛t❡✿ F ✶ ( t | X ✶ , . . . , X k = x k , . . . , X K ) F ✶ ( t | X ✶ , . . . , X k = ( x k + ✶ ) , . . . , X K ) = ❡①♣ { β k ( x k − x k + ✶ ) } = ❡①♣ ( β k ) . ✶✵ ✴ ✷✽