When to Treat Prostate Cancer Patients Based on their PSA Dynamics

Transcription

1 When o Tea Posae Cance Paens Based on he PSA Dynamcs CLARA day on opeaons eseach n cance eamen & opeaons managemen Novembe 7 00 Mael S. Lave PhD Man L. Pueman PhD Sco Tyldesley M.D. Wllam J. Mos M.D

2 CIHR Team fo Opeaons n Qualy Cance Cae Oncologss Admnsaos Sascans Faculy Reseaches Pos-doc fellows PhD Sudens BCCA UBC Opeaons Reseach Pofessonals lave@umch.edu

3 Oulne The clncal poblem: Posae Cance Modelng PSA dynamcs Makng he decson: When should each paen sa hs adaon heapy eamen? Conclusons Fuue wok

4 Posae Cance Summay Sascs In 008: 4700 Canadan dagnosed wh posae cance 4300 ded of he dsease (Canadan Cance Socey 008 BCCA esponsble fo he delvey of all adoheapy eamen n BC: Man Type of Teamen Receved by Posae Cance Paens n BC lave@umch.edu

5 Combnng Homone and Radoheapy Hgh sk localzed posae cance paens ae ofen eaed wh homone heapy po o he adoheapy eamen - Goal: save umou cells of esoseone (man felze esulng n umou egesson Paens monoed peodcally - PSA (blood es used o pedc egesson Maxmal umo egesson pobably occus when PSA eaches s nad level (Gleave La Banca and Goldebeg Key assumpon - The nad s he deal me o sa RT Challenge: Cances egess a dffeen aes (dffcul o pedc lave@umch.edu

6 Tumou Regesson as a Funcon Tumo of PSA Tumou Sze PSA RT Tme lave@umch.edu

7 Tumou Regesson as a Funcon of PSA Tumou Sze RT Tumou Sze RT Tme Tme Tumou Sze RT Tme lave@umch.edu

8 Tadeoffs Toleance Responsveness Why sa RT now? Avod pogesson Rsk of cells becomng essan Toxcy of homone heapy Why wa? Maxmum educon of umo sze unde homone heapy Moe nfomaon

9 Cuen Poocol Hgh-nemedae o hgh sk paen? Offe neoadjuvan homone heapy po o adaon heapy Sa adaon heapy f: 8 monhs of homone heapy have been eceved o PSA levels sa o se o PSA ng/ml o PSA < 0.05 ng/ml afe 4 monhs lave@umch.edu

10 Ou Goal Impove modelng of PSA knecs and esmaon of fuue PSA knecs Povde a fomal decson makng appoach and ool o deemne when a paen should begn adaon heapy eamen lave@umch.edu

11 PSA Knecs PSA S vs s mee PSA nad Tme ln( PSA = α β γ v v ~ N(0 V lave@umch.edu

12 Descpon of he Poblem Populaon N((αβγR {(α β γ R }??? Tme PSA ln( PSA = α β γ v v ~ N(0 V lave@umch.edu

13 Dynamcally Changng Nad Esmaes Tme o Mnmum PSA eadngs Max esponse 00 PSA 0 New PSA eadng Maxmum Response Tme fom NAH sa (days 0. ln( PSA = α β γ v v ~ N(0 V lave@umch.edu

14 Descpon of he Poblem (Con. Populaon N((αβγR Cluse N((α β γ R Cluse N((α β γ R Cluse 3 N((α 3 β 3 γ 3 R 3 {(α β γ R }??? P j??? Tme PSA ln( PSA = α β γ v v ~ N(0 V lave@umch.edu

15 Fomulaon Inal Belefs (based on Populaon Chaacescs Obseve PSA Updae Cuve Paamees Esmae Nad

16 Modelng Inal Belefs F egesson cuve fo each paen Cluse paens F egesson fo each cluse Esmae pobably of a paen beng n a cluse lave@umch.edu

17 Daa Souce 63 paens fom a pospecve andomzed al All nemedae sk posae cance paens (PSA < 40 wh no measass on sagng: - Ehe a PSA> 0 o Gleason gade 7 o sage T3a All eceved 8 monhs of homones befoe he adaon All saed on luenzng homone-eleasng homone wh monh of nonseodal anandogen All had PSA and esoseone eadngs evey monhs befoe adoheapy lave@umch.edu

18 Tumo Knecs X( = numbe of andogen dependen cells Y( = numbe of andogen ndependen cells N( = oal numbe of cells = X( Y( Whou homone eamen: dn( d = ( g a N( N( = Ce ( g a Wh homone eamen: dn( gn( an( d PSA N( ln( PSA (/ g a = α β γ N( = Ce lave@umch.edu

19 Modelng Inal Belefs F egesson cuve fo each paen Cluse paens ln( PSA = α β γ d ln( PSA d β = γ = β γ = 0 v v ~ N(0 V PSA vs me F egesson fo each cluse Esmae pobably of a paen beng n a cluse gven baselne values PSA nad nad Tme lave@umch.edu

20 Modelng Inal Belefs Cluseed based on mn PSA and nad 3 goups: Goup Goup Goup 3 nad (days 7 4 >>40 mn PSA Pobably 7% 0% 8% lave@umch.edu

21 Modelng Inal Belefs PSA 0 PSA vs Tme (Goup Weghng egesson paamees Measuemen eo 0. Tme fom NAH sa PSA vs Tme (Goup 0 PSA vs Tme (Goup 3 PSA PSA Tme fom NAH sa 0.0 Tme fom NAH sa lave@umch.edu

22 Modelng Inal Belefs Logsc egesson: Pobably n Goup : EXP(.3-0.6*PSA = EXP( *PSAEXP(.3-0.6*PSA Pobably n Goup : EXP( *PSA = EXP( *PSAEXP(.3-0.6*PSA Pobably n Goup 3: = (Pobably n Goup (Pobably n Goup lave@umch.edu

23 Fomulaon Inal Belefs (based on Populaon Chaacescs Obseve PSA Updae Cuve Paamees Esmae Nad

24 Tmelne Obseve PSA Updae cuve paamees Don Sa Sa RT? Receve Obseve eamen PSA Updae cuve paamees ζ Sae Updang (Kalman Fleng P(eang a he gh me lave@umch.edu

25 Model Assumpons Dsubances and nal sae veco ae nomally dsbued Model s me-homogeneous Eos ae empoally and muually ndependen lave@umch.edu

26 Obsevaon Equaon: Sae Equaon: Updang Equaons: 0 ; (0 ~ = = W W N w w θ θ Cuve Updae V F R F Q R F F Q R R R F Y F Q R ' ' ' ] [ = = = θ θ θ v PSA Y V N v v F Y ' ln( (0 ~ = = = γ β α θ = = 3 ln( ln( ln( ln( ; ' ( * ( ; ' ( * ( ( k k PSA PSA PSA PSA dy Q F f k P dy Q F f P P ε ε ε ε θ θ Pobably funcon of a nomal dsbuon

27 Dsbuon of Tme of Nad nad = -β/γ whee ( β γ ~ N ( β γ ; As P(γ >0 Dsbuon of me of nad Rao of coelaed Nomal andom vaables F( Relave fequency nad 60% 50% 40% 30% = 0% 0% 0% γ 0 ( β Tme of nad >=70 e π u du (Hnkley969 lave@umch.edu

28 Clncally Implemenable Polces Cuen polcy Sa RT when he cumulave pobably of havng eached he nad s geae han a heshold Sa RT when he pobably of eang a he nad s geae han a heshold lave@umch.edu

29 Cumulave Pecenage of Paens who Would Have Saed RT unde Dffeen Decson Rules

30 The Tool

31 The Tool

32 Cuen Reseach Develop MDP models o deemne opmal sa me when o ake he nex eadng when o change homone heapy dug Valdae model a ohe ses and wh ohe daa Undeake a clncal al o measue benefs of poposed paen adaped poocol lave@umch.edu

33 Summay Used cluseng echnques o capue dffeen ypes of PSA pogessons Developed an eave way o updae he esmaes of he dsbuon of he nad By usng a heshold o decde whehe o sa RT we wee able o denfy eale when he nad s eached lave@umch.edu

34 The Bg Pcue

35 Demand modelng Paen Specfc Populaon Based Posae Cance Beas Cance Lung Cance NHL Coloecal Cance Ohe No Mono Hgh poy Tea? Yes Use Consaned Resouces Clncal Tal Daa Bes Pacces

36 Thank you!

37 MDP Model Dscee me fne hozon MDP Acon: Sa adaon heapy Don sa adaon heapy Sae: α θ = β γ Paamee means ; R Paamee covaances lave@umch.edu

38 MDP Model Maxmze Pobably of Teang whn ζ of he Nad = ( ( ; ( max ( nad R v R R P R P R v θ θ θ θ ζ θ = γ β α θ = R ( = F ( ( ( ( V Q = ( ( ' ~ Q F N Y θ ( du e u ( ( 4 ( ζ ζ β ζ γ β γ π Sa RT [ ] ( Y R Y dp R F Q R F R F Y Q R F v ( ' ' θ θ θ Don Sa RT

39 Issues Involved n Solvng he MDP Connuous sae space Paally obsevable sae space Rewad funcon: ao of coelaed Nomal andom vaables lave@umch.edu