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A Multitask Multiple Kernel Learning Algorithm for Survival Analysis with Application to Cancer Biology Onur Dereli, Ceyda O guz, Mehmet Gnen Ko University, Istanbul, Turkey odereli14@ku.edu.tr coguz@ku.edu.tr mehmetgonen@ku.edu.tr

  1. A Multitask Multiple Kernel Learning Algorithm for Survival Analysis with Application to Cancer Biology Onur Dereli, Ceyda O˘ guz, Mehmet Gönen Koç University, ˙ Istanbul, Turkey odereli14@ku.edu.tr coguz@ku.edu.tr mehmetgonen@ku.edu.tr June 12, 2019 / Long Beach Dereli, O., O˘ guz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 1 / 9

  2. multiple kernel learning Vital follow-up Genes Patients Genes Patients death status Days to last Days to Patients Patients Patients 456 Patients analysis Survival analysis Patients Patients Survival Patients Patients Multitask Patients Patients Dead Patients Patients . NA 1891 Dead 2208 NA Alive . . . . . . Genes . . NA 3200 Dead NA Genes Patients Genes Patients Genes Patients Patients Proposed Approach Vital Days to Days to last X 1 , 1 K 1 , 1 status death follow-up η 1 Alive NA 678 f 1 · · · · · · · · · Dead 364 NA . . . Gene set 1 η P . . . . . . X 1 ,P K 1 ,P G1 Alive NA 2555 K 1 ,η Dead 520 NA X 1 G17 G42 Y 1 G28 G6 · · · G3 G19 · · · · · · · · · · · · · · · · · · G42 G19 · · · Y T G8 G47 X T K T,η X T, 1 K T, 1 G12 G25 η 1 Gene set P f T · · · · · · · · · η P X T,P K T,P Dereli, O., O˘ guz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 2 / 9

  3. multiple kernel learning Vital follow-up Genes Patients Genes Patients death status Days to last Days to Patients Patients Patients 456 Patients analysis Survival analysis Patients Patients Survival Patients Patients Multitask Patients Patients Dead Patients Patients . NA 1891 Dead 2208 NA Alive . . . . . . Genes . . NA 3200 Dead NA Genes Patients Genes Patients Genes Patients Patients Proposed Approach Vital Days to Days to last X 1 , 1 K 1 , 1 status death follow-up η 1 Alive NA 678 f 1 · · · · · · · · · Dead 364 NA . . . Gene set 1 η P . . . . . . X 1 ,P K 1 ,P G1 Alive NA 2555 X 1 K 1 ,η Dead 520 NA G17 G42 Y 1 G28 G6 · · · G3 G19 · · · · · · · · · · · · · · · · · · G42 G19 · · · Y T G8 G47 K T,η X T X T, 1 K T, 1 G12 G25 η 1 Gene set P f T · · · · · · · · · η P X T,P K T,P Dereli, O., O˘ guz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 2 / 9

  4. multiple kernel learning Vital follow-up Genes Patients Genes Patients death status Days to last Days to Patients Patients Patients 456 Patients analysis Survival analysis Patients Patients Survival Patients Patients Multitask Patients Patients Dead Patients Patients . NA 1891 Dead 2208 NA Alive . . . . . . Genes . . NA 3200 Dead NA Genes Patients Genes Patients Genes Patients Patients Proposed Approach Vital Days to Days to last X 1 , 1 K 1 , 1 status death follow-up η 1 Alive NA 678 f 1 · · · · · · · · · Dead 364 NA . . . Gene set 1 η P . . . . . . X 1 ,P K 1 ,P G1 Alive NA 2555 X 1 K 1 ,η Dead 520 NA G17 G42 Y 1 G28 G6 · · · G3 G19 · · · · · · · · · · · · · · · · · · G42 G19 · · · Y T G8 G47 K T,η X T X T, 1 K T, 1 G12 G25 η 1 Gene set P f T · · · · · · · · · η P X T,P K T,P Dereli, O., O˘ guz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 2 / 9

  5. multiple kernel learning Vital follow-up Genes Patients Genes Patients death status Days to last Days to Patients Patients Patients 456 Patients analysis Survival analysis Patients Patients Survival Patients Patients Multitask Patients Patients Dead Patients Patients . NA 1891 Dead 2208 NA Alive . . . . . . Genes . . NA 3200 Dead NA Genes Patients Genes Patients Genes Patients Patients Proposed Approach Vital Days to Days to last X 1 , 1 K 1 , 1 status death follow-up η 1 Alive NA 678 f 1 · · · · · · · · · Dead 364 NA . . . Gene set 1 η P . . . . . . X 1 ,P K 1 ,P G1 Alive NA 2555 K 1 ,η Dead 520 NA X 1 G17 G42 Y 1 G28 G6 · · · G3 G19 · · · · · · · · · · · · · · · · · · G42 G19 · · · Y T G8 G47 X T K T,η X T, 1 K T, 1 G12 G25 η 1 Gene set P f T · · · · · · · · · η P X T,P K T,P Dereli, O., O˘ guz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 2 / 9

  6. Multitask Survival MKL Formulation N t T � � 1 � � ( ξ + minimize 2 w ⊤ ti + ( 1 − δ ti ) ξ − t w t + C ti ) t = 1 i = 1 with respect to w t ∈ R D t , ξ + t ∈ R N t , ξ − t ∈ R N t , b t ∈ R subject to ǫ + ξ + ti ≥ y ti − w ⊤ t x ti − b t ∀ ( t , i ) ǫ + ξ − ti ≥ w ⊤ t x ti + b t − y ti ∀ ( t , i ) ξ + ti ≥ 0 ∀ ( t , i ) ξ − ti ≥ 0 ∀ ( t , i ) Dereli, O., O˘ guz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 3 / 9

  7. Multitask Survival MKL Formulation N t N t T T � � � � minimize − y ti ( α + ( α + ti − α − ti ) + ǫ ti + α − ti ) t = 1 i = 1 t = 1 i = 1 T N t N t P + 1 � � � � ( α + ti )( α + tj ) η m k m ( x ti , x tj ) ti − α − tj − α − 2 t = 1 i = 1 j = 1 m = 1 with respect to α + t ∈ R N t , α − t ∈ R N t , η ∈ R P N t � ( α + subject to ti ) = 0 ∀ t ti − α − i = 1 C ≥ α + ti ≥ 0 ∀ ( t , i ) C ( 1 − δ ti ) ≥ α − ti ≥ 0 ∀ ( t , i ) P � η m = 1 m = 1 η m ≥ 0 ∀ m Dereli, O., O˘ guz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 3 / 9

  8. Multitask Survival MKL Formulation � T N t N t η ( s ) α ( s ) ti α ( s ) � � � tj k m ( x ti , x tj ) m t = 1 i = 1 j = 1 η ( s + 1 ) = ∀ m m � T P N t N t η ( s ) α ( s ) ti α ( s ) � � � � tj k o ( x ti , x tj ) o t = 1 o = 1 i = 1 j = 1 Dereli, O., O˘ guz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 3 / 9

  9. Data Sets BLCA BRCA CESC COAD ESCA GBM HNSC KIRC KIRP LAML LGG LIHC LUAD LUSC OV PAAD READ SARC STAD UCEC ● (402) (1067) (291) (433) (160) (152) (498) (526) (285) (130) (506) (365) (500) (493) (372) (176) (156) (256) (348) (539) • 20 cancer data sets from TCGA database Gene expression profiles and survival characteristics • Hallmark Gene Set [1] & PID Pathway [2] Collections Dereli, O., O˘ guz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 4 / 9

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