Survival Prediction Based on Compound Covariate under Cox Proportional Hazard Models

Transcription

1 Ieraoal Bomerc Coferece 22/8/3, Kobe JAPAN Survval Predco Based o Compoud Covarae uder Co Proporoal Hazard Models PLoS ONE 7. do:.37/oural.poe hp://d.plos.org/.37/oural.poe Takesh Emura Graduae Isue of Sascs, Naoal Ceral Uversy, Tawa Jo work wh Y-Hau Che ad Dr. Hsua-Yu Che Isue of Sascal Scece, Academa Sca, Tawa

2 h Survval Daa wh Mcroarrays p gees h,..., pae : Survval me Cesorg dcaor Lug cacer daa from Beer e al., 22

3 Esg mehods for hgh-dmesoal survval daa Lasso Co-regresso wh L pealy Gu & L 25 Boformacs, Segal 26 Bosascs Rdge regresso Co-regresso wh L 2 pealy Verve & va Howelge994 Sa. Med., Zhao e al. 2 PLoS ONE Gee seleco va uvarae Co-regresso Jesse e al. 22 Naure Med., Che e al. 27 NEJM, ame bu a few Ohers PC, supervsed PC, paral lease square, ec. Amog above mehods, rdge regresso has he bes performace erms of survval predco Bovelsad e al., 27; va Weerge e al., 29; Bovelsad ad Borga, 2

4 Two obecves of our sudy:. Revve compoud covarae predco mehod *Prevously used mcroarrays daases Tukey 993 Corolled Clcal Tral, Beer e al. 22 Naure Med. Che e al. 27 NEJM, Radamacher e al 22 J. of Theorecal Bo. Masu 26 BMC Boformacs *Bu, o heorecal aalyss ad comparave sudes have o ye repored 2. Propose o refe he compoud covarae predco va shrkage echque

5 Se up Survval daa : {,, ;,..., } : eher me o deah or f deah f cesorg,..., p, possbly cesorg p Eample: Lug cacer daa Che e al., 27 =25, p=672, Cesored proporo = 7% Daa aalyss laer

6 Compoud covarae predco Sep: For each gee,..., p, f a uvarae Co model Pr d, / d h ep Sep2: A se of p regresso coeffces βˆ ˆ,..., ˆ, where ˆ p Remark: Ths s possble eve whe p > Sep 3: Compoud covarae predco βˆ argma c Good progoss ; βˆ ep For a fuure pae wh gees,...,, l p ep l c Poor progoss

7 Compoud covarae mehod: A smple mehod o resolve he hgh dmesoaly Is heorecal usfcao has o bee dscussed he leraure

8 Assumpo: The Co model holds wh h h ep β h ep p β β,, a he rue parameer p,, p Remark: Uder he mulvarae Co model assumpo, he uvarae Co model does o hold,.e, h log S log E[ep{ H ep. ep β } ]

9 Uvarae Co model for each gee s a msspecfed model a workg model Ref: Sruhers & Kalbflesch 986 Msspecfed proporoal hazard models, Bomerka 73 pp Uvarae paral lkelhood equao ep /, Pr h d d,..., p I I U ep ep o Soluo : ˆ o Soluo * P U u

10 ˆ P * rue value he Assumpo Remark I: If all gees,..., p are depede * * sg sg, Remark II: Le β The, * β * * *,, p s bewee ad β,, ad.. Above resuls deduced from : Sruhers & Kalbflesch 986 Bomerka ; Breagolle & Huber-Carol988 Scad. JS

11 Proposed esmaor Uvarae compoud lkelhood uque mama p ep L β ep l l Mulvarae lkelhood fely may mama whe p > L β ep β ep β lr Idea: Mure of uvarae ad mulvarae lkelhood β a l a log L β alog L β, a [,] ˆ argma Specal case a : βˆ a se of p uverae esmaors call "compoud covarae esmaor"

12 Compoud shrkage esmaor : βˆ a argma a log L β alog L β a a β rue ˆβ Ifely may soluos for a mulvara e Co regresso { β L β maθ L θ} Rdge ad Lasso boh shrk oward zero

13 Proposo 2: our paper βˆ aˆ β, wh ˆ N Σ β a argma CV a. CV = Cross-Valdaed lkelhood of Verve & Houwelge 993 Plug- varace esmaor Σ A h a a Σ aˆ ˆ β aˆ a a a β A β{ V β / } A β a β V β h 2 β{ d CV a / da β U 2 } h β / a, where d CV a Esmag fuco of a, da a V β observed Fsher formao a β I β Score fuco *Reasoable performace eve whe p >. U a p

14 βˆ Numercal comparso s obaed by 4 mehods. Compoud covarae CC esmaor βˆ ˆ,..., ˆ, where ˆ p 2. Compoud shrkage CS esmaor a log L 3. Rdge esmaor log 4. Lasso esmaor log L L β alog L β / 2 β p p 2 β uvarae Co regresso esmaors * â or ˆ s obaed by cross-valdao Verve & Houwelge 993 Sa.Med.

15 Smulao se up Co model: h ep,, Cesorg: U,, moderae cesorg 54~63% Trag se {,, ;,, } Tesg se { * * ˆ * c Good progoss ; ˆ β β compoud covarae ˆ compoud shrkage β Rdge regresso Lasso *,, ;,, } Poor progoss P-value from a wo-sample Log-rak es Smaller P-value correspods o beer predco power Evaluao crero Bovelsa e al. 27 Boformacs: Meda P-value amog 5 replcaos c R compoud.co package Emura & Che 22 R pealzed package Goema 2

16 Table. Smulao resuls uder sparse cases. CC = compoud covarae, CS = compoud shrkage. LR-es = Log P-value for dscrmag poor / good paes. Scearo : Tag gee / Scearo 2: Gee pahway β.5,.5,,..., 98 CC CS Rdge Lasso Scearo LR-es Scearo2 LR-es β.8,...,.8, 5,..., 95 CC CS Rdge Lasso Scearo LR-es Scearo2 LR-es

17 Table 2. Smulao resuls uder No-sparse cases. CC = compoud covarae, CS = compoud shrkage. LR-es = Log P-value for dscrmag poor / good paes. Scearo : Tag gee / Scearo 2: Gee pahway β.2,...,.2,.2,...,.2,,..., 8 CC CS Rdge Lasso Scearo LR-es Scearo2 LR-es β.,...,., 5.,...,., 5,..., 7 CC CS Rdge Lasso Scearo LR-es Scearo2 LR-es Mosly, βˆ for Lasso

18 Smulao resuls: Summary Rdge s wors sparse cases Lasso s wors o-sparse cases Compoud covarae ad compoud shrkage performed smlar o or slghly beer ha Rdge Sce Rdge s repored as he bes mehod Bovelsad e al., 27; va Weerge e al., 29; Bovelsad ad Borga, 2 he compoud covarae ad compoud shrkage are compeve mehods

19 Daa: Lug cacer daa Che e al., 27 NEJM =25, p=672 β ˆ =63, p=97 Trag se compoud covarae compoud shrkage Rdge Lasso Predc Good progoss =62, p=97 es se {,...,62 } Poor progoss βˆ c wherec Good progoss ; s he meda of { βˆ βˆ c Poor progoss,,,..., }

20 Survval curves for Poor vs. Good progoss groups for =62 esg daa; p-value for Log-rak es

21 Survval curves for Poor, Medum, Good progoss groups for =62 esg daa; p-value for Log-rak red es Thak you for your aeo