Most of the biologicals drug products are for the treatment of Cancer such as lung cancer, breast cancer or colorectal cancer. The efficacy endpoints for evaluation of the biological drug products in cancer trials are censored endpoints such as overall survival or progression-free survival. As a result, we extended the design and concept of parallel-line assay to assessment of equivalence between the biosimilar drug product and its corresponding innovative biologic drug based on the censored data. We derived the proposed procedure under the assumptions that the censored endpoint follow a single-parametric exponential distribution and the log-hazard can be modelled as a linear regression with the well-defined drug characteristic as the independent variable.
The empirical investigation by simulation studies demonstrates that the confidence intervals constructed by the proposed method provide sufficient converge probability. On the other hand, under the assumptions of the exponential distribution and the log-hazard linear regression, the proposed procedure can also adequately control the size at the nominal significance level. Furthermore, sufficient power can be provided if the sample size is moderate. For example, for the slope being -0.3 or -0.5, Δ=0, power exceed 0.9 even when sample size is 40 per group.
In this thesis we only consider the exponential parametric model which satisfies the
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proportional hazard assumption. In addition, we also assume that the relationship between the log-hazard and the well-defined drug characteristic is linear with a right and random censoring mechanism. More research is required to examine the impact of violating the assumptions on performance of the proposed procedure. On the other hand, extension of the proposed method to other parametric distributions such as Weibull or log-logistic distributions also requires more research. The cox proportion hazard is a semi-parametric method which does not assume a particular form of the mortality distribution for the censored data. It follows that the Cox proportional hazard model is more flexible and has widespread applications. However, the inference procedure for application of the parallel-line assay to evaluation of equivalence between the biosimilar drug products and the innovative product based on the proportional hazard requires further research.
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References
中文文獻：
沈明來(2000) , 生物檢定統計法 第一版, 九州圖書文物有限公司 台北市 台 灣
行政院衛生署 食品藥物管理局(2009) 藥品生體可用率及生體相等性試驗準則 林亞靚 (2010) 平行檢定法於生物製劑學名藥對等性評估之應用 台灣大學 張志熙 (2011) 羅吉斯回歸於生物相似性藥品對等性評估之應用 台灣大學 林治華、李元鳳、王蓉君(2011) 生物相似性藥品 Biosimilar 財團法人醫藥品查 驗中心 當代醫藥法規 RegMed Vol.3
生物仿製藥市場及發展概況
http://cdnet.stpi.narl.org.tw/techroom/market/bio/2009/bio_09_005.htm Accessed on 2013/05/03.
英文文獻：
Biosimilar and Biologic (2011), Wikipedia http://en.wikipedia.org/wiki/ “Biosimilar”
and “Biologic” Accessed on 2013/05/03
Chow, S. C. and Liu, J. P. (2010). Design and Analysis of Bioavailability and Bioequivalence Studies. 3rd ed. Marcel Dekker, Inc. New York, USA
Chow, S. C. and Liu, J. P. (2010). Statistical Assessment of Biosimilar Products. Journal of Biopharmaceutical Statistics, 20:10-30
(EMEA) 2001. Note for Guidance on the Investigation of Bioavailability and Bioequivalence, London, UK.
EMEA (2006a). Annex guideline on similar biological medicinal products containing biotechnology-derived proteins as drug substance – Non clinical and clinical issues – Guidance on similar medicinal products containing recombinant erythropoietins. The European Medicines Agency Evaluation of Medicines for Human Use.
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EMEA/CHMP/94526/05: London, United Kingdom.
EMEA (2006b). Annex guideline on similar biological medicinal products containing biotechnology-derived proteins as drug substance – Non clinical and clinical issues – Guidance on similar medicinal products containing recombinant granulocyte-colony stimulating factor. The European Medicines Agency Evaluation of Medicines for Human Use. EMEA/CHMP/31329/05: London, United Kingdom.
EMEA (2006c). Annex guideline on similar biological medicinal products containing biotechnology-derived proteins as drug substance – Non-clinical and clinical issues – Guidance on similar medicinal products containing somatropin. The European
Medicines Agency Evaluation of Medicines for Human Use. EMEA/CHMP/94528/05:
London, United Kingdom.
EMEA (2006d). Annex guideline on similar biological medicinal products containing biotechnology-derived proteins as drug substance – Non clinical and clinical issues – Guidance on similar medicinal products containing recombinant human insulin. The European Medicines Agency Evaluation of Medicines for Human Use.
EMEA/CHMP/32775/05: London, United Kingdom.
FDA (2001). Guidance on Statistical Approaches to Establishing Bioequivalence, Center for Drug Evaluation and Research, U.S. Food and Drug Administration, Rockville, MD.
FDA (2003). Guidance on Food-Effect Bioavailability and Fed Bio equivalence Studies, Center for Drug Evaluation and Research, U.S. Food and Drug Administration,
Rockville, MD.
FDA (2011a). Draft Guidance on Questions and Answers Regarding Implementation of Biologic Price Competition and Innovation Act of 2009. U.S. Food and Drug
Administration, Rockville, MD, U.S.A.
FDA (2011b). Draft Guidance on Scientific Considerations in Demonstrating
Biosimilarity to a Reference Product. U.S. Food and Drug Administration, Rockville, MD, U.S.A.
FDA(2011c). Draft Guidance on Quality Considerations in Demonstrating Biosimilarity to a Reference Protein Product. U.S. Food and Drug Administration, Rockville, MD, U.S.A.
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ICH (2005). Q5E Guideline on Comparability of Biotechnological/Biological Products Subject to Changes in Their Manufacturing Process. Center for Drug Evaluation and Research, Center for Biologics Evaluation and Research, the US Food and Drug Administration, Rockville, Maryland, USA
Kleinbaum, D.G. (1998), Survival Analysis, a Self-Learning Text. Biometrical Journal , 40: 107–108.
Lin J.R., Chow S.C., Chang C.H., Lin T.C. and Liu J.P. (2013) Application of the parallel line assay to assessment of biosimilar products based on binary endpoints.
Statistics in Medicine, 32 449-461.
Lawless, J. F. (2011). Statistical models and methods for lifetime data. Wiley-Interscience.
Schellekens, H. (2004). How similar do ‘biosimilar’ need to be? Nat Biotechnol, 22, 1357-1359.
Schuirmann, D. J. (1987). A Comparison of the Two One-Sided Tests Procedure and the Power Approach for Assessing the Equivalence of Average Bioavailability. Journal of Pharmacokinetics and Biopharmaceutics, Vol. 15, No. 6, 1987
Thomson Database of Pharmaceutical Invention (2007)
Webber K.O. (2007). Biosimilars: Are we there yet? Presented at Biosimilars 2007, George Washington University, Washington DC, USA.
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Appendix 1, Fortran Codes for Numerical Example
real*8 , allocatable :: Xs(:)real*8 , allocatable :: LifeR(:),CensR(:),LifeT(:),CensT(:) real*8 , allocatable ::
Datas(:,:),RTLCDatas(:,:),caR(:,:),caT(:,:),scaR(:),scaT(:),Tests(:,:),caC(:,:),scaC(:)
RatioT=CensRateT/(1-CensRateT) RatioR=CensRateR/(1-CensRateR) open(unit=15, file='Power_function.txt')
75 write(*,"(A,F4.1)") "The slope is ",BetaT0 write(15,"(A,F4.1)") "The slope is ",BetaT0 DO R=1,1
76
77
78
IF (0.0d0<=BetaTh-Z0025*StdBetahT .OR. BetaTh+Z0025*StdBetahT<=0.0d0 ) THEN
79
DO WHILE (ErrorBR0>0.000000001d0) DO J=1,TTS
80 IF (0.0d0<=BetaRh-Z0025*StdBetahR .OR. BetaRh+Z0025*StdBetahR<=0.0d0 ) THEN
Tests(N,2)=1 END IF
!write(*,"(4(2XF13.10))") AlphaTh,BetaTh,AlphaRh,BetaRh
!=======Common Slope Testing======
IF (Tests(N,1)==1 .AND. Tests(N,2)==1) THEN VarBetaRT=VarBetahR+VarBetahT
StdBetaRT=VarBetaRT**(0.5d0)
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!======Common Slope Model Newton-Raphson====
IF (Tests(N,3)==1) THEN
! LT,CT,Yt,DLT,Xt,LR,CR,Yr,DLR,Xr
caC(J,1)=DATAS(J,3)*DEXP(AlphaTh+BetaCh*DATAS(J,5)) !YtExp(At+BC*Xt) caC(J,2)=DATAS(J,8)*DEXP(AlphaRh+BetaCh*DATAS(J,10)) !YrExp(Ar+BC*Xr)
scaC(1))+scaC(5)*scaC(6)*(NumlifeR-scaC(2))-scaC(2)*scaC(5)*(scaC(3)+scaC(4)-82
IF (ErrorAR<0.000000001d0 .AND. ErrorAT<0.000000001d0 .AND.
ErrorBC<0.000000001d0) EXIT
! LT,CT,Yt,DLT,Xt,LR,CR,Yr,DLR,Xr
caC(J,1)=DATAS(J,3)*DEXP(AlphaTh+BetaCh*DATAS(J,5)) caC(J,2)=DATAS(J,8)*DEXP(AlphaRh+BetaCh*DATAS(J,10))
caC(J,5)=DATAS(J,3)*DATAS(J,5)*DEXP(AlphaTh+BetaCh*DATAS(J,5))
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Z0050**2*VarBetaCh)*((AlphaTh-AlphaRh)**2-84
Z0050**2*(VarAlphaCTh+VarAlphaCRh-2*CovATAR)))**(0.5))/(BetaCh**2-Z0050**2*VarBetaCh)
!DeltaU=((AlphaTh-AlphaRh)*BetaCh-Z0050**2*(CovATBC- CovARBC)+(((AlphaTh-AlphaRh)*BetaCh-Z0050**2*(CovATBC-CovARBC))**2-
(BetaCh**2-Z0050**2*VarBetaCh)*((AlphaTh-AlphaRh)**2- Z0050**2*(VarAlphaCTh+VarAlphaCRh-2*CovATAR)))**(0.5))/(BetaCh**2-Z0050**2*VarBetaCh)
!write(*,*) DeltaL,DeltaU
!write(15,*) DeltaL,DeltaU
!write(*,*) ' ' END IF
IF (-Delta<DeltaL .AND. DeltaU<Delta) THEN Tests(N,4)=1
END IF END IF
WRIT(*,"((1XF4.1),A,(1XF6.4))") AlphaT0/BetaT0,' ',SUM(Tests(:,4))/SimuN WRITE(15,"((1XF4.1),A,(1XF6.4))") AlphaT0/BetaT0,' ',SUM(Tests(:,4))/SimuN deallocate(LifeT,CensT,LifeR,CensR)
deallocate(DATAS)
deallocate(caT,caR,scaT,scaR,caC,scaC) deallocate(Tests)
deallocate(Xs) END DO !Q END DO !P END DO !O END DO !R END DO !T END DO !U end program
Appendix 2, Fortran Codes for Selection of Dose
85 real*8 , allocatable :: Xs(:)
real*8 , allocatable :: LifeR(:),CensR(:),LifeT(:),CensT(:) real*8 , allocatable ::
Datas(:,:),RTLCDatas(:,:),caR(:,:),caT(:,:),scaR(:),scaT(:),Tests(:,:),caC(:,:),scaC(:)
write(*,*) "Input the censored rate, assuming the two censored rates are equil: "
read(*,*) CensRateT CensRateR=CensRateT
!CensRateT=0.2d0
!CensRateR=0.2d0
RatioT=CensRateT/(1-CensRateT) RatioR=CensRateR/(1-CensRateR) open(unit=15, file='Power_function.txt')
86 write(*,"(A,F4.1)") "The slope is ",BetaT0 write(15,"(A,F4.1)") "The slope is ",BetaT0 DO R=3,3
!write(*,"(A,F3.1,A,F3.1,A)") "The minimun hazard is ",Haza,". The maximun hazard is ",Hazb,"."
!write(15,"(A,F3.1,A,F3.1,A)") "The minimun hazard is ",Haza,". The maximun hazard is ",Hazb,"."
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! write(10,'(f11.8,2Xf11.8,2Xf11.8,2XF2.0,2XF11.8)') DATAS(I,1:5)
! END DO
TTSS=DFLOAT(TTS) NlifeT=SUM(DATAS(:,4))
88
89
IF (0.0d0<=BetaTh-Z0025*StdBetahT .OR. BetaTh+Z0025*StdBetahT<=0.0d0 ) THEN
90
DO WHILE (ErrorBR0>0.000000001d0) DO J=1,TTS
91 IF (0.0d0<=BetaRh-Z0025*StdBetahR .OR. BetaRh+Z0025*StdBetahR<=0.0d0 ) THEN
Tests(N,2)=1 END IF
!write(*,"(4(2XF13.10))") AlphaTh,BetaTh,AlphaRh,BetaRh
92
!=======Common Slope Testing======
IF (Tests(N,1)==1 .AND. Tests(N,2)==1) THEN VarBetaRT=VarBetahR+VarBetahT
!======Common Slope Model Newton-Raphson====
IF (Tests(N,3)==1) THEN
caC(J,1)=DATAS(J,3)*DEXP(AlphaTh+BetaCh*DATAS(J,5)) !YtExp(At+BC*Xt) caC(J,2)=DATAS(J,8)*DEXP(AlphaRh+BetaCh*DATAS(J,10)) !YrExp(Ar+BC*Xr)
93
IF (ErrorAR<0.000000001d0 .AND. ErrorAT<0.000000001d0 .AND.
ErrorBC<0.000000001d0) EXIT END DO
!write(*,"(3(2XF13.10))") AlphaTh,AlphaRh,BetaCh
!======Relative Potency======
DO J=1,TTS
caC(J,1)=DATAS(J,3)*DEXP(AlphaTh+BetaCh*DATAS(J,5)) caC(J,2)=DATAS(J,8)*DEXP(AlphaRh+BetaCh*DATAS(J,10))
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Z0050**2*VarBetaCh)*((AlphaTh-AlphaRh)**2-95
IF (-Delta<DeltaL .AND. DeltaU<Delta) THEN Tests(N,4)=1
END IF END IF
WRITE(*,"((1XF4.1),A,(1XF6.4))") AlphaT0/BetaT0,' ',SUM(Tests(:,4))/SimuN WRITE(15,"((1XF4.1),A,(1XF6.4))") AlphaT0/BetaT0,' ',SUM(Tests(:,4))/SimuN
Appendix 3, Fortran Code for Simulation
Program
96 real*8 , allocatable :: Xs(:)
real*8 , allocatable :: LifeR(:),CensR(:),LifeT(:),CensT(:) real*8 , allocatable ::
Datas(:,:),RTLCDatas(:,:),caR(:,:),caT(:,:),scaR(:),scaT(:),Tests(:,:),caC(:,:),scaC(:)
write(*,*) "Input the censored rate, assuming the two censored rates are equil: "
read(*,*) CensRateT CensRateR=CensRateT
!CensRateT=0.2d0
!CensRateR=0.2d0
RatioT=CensRateT/(1-CensRateT) RatioR=CensRateR/(1-CensRateR) open(unit=15, file='Power_function.txt')
97
write(*,"(A,F4.1)") "The slope is ",BetaT0 write(15,"(A,F4.1)") "The slope is ",BetaT0 DO R=1,5
!write(*,"(A,F3.1,A,F3.1,A)") "The minimun hazard is ",Haza,". The maximun hazard is ",Hazb,"."
!write(15,"(A,F3.1,A,F3.1,A)") "The minimun hazard is ",Haza,". The maximun hazard is ",Hazb,"."
98
! write(10,'(f11.8,2Xf11.8,2Xf11.8,2XF2.0,2XF11.8)') DATAS(I,1:5)
! END DO
99
100
IF (0.0d0<=BetaTh-Z0025*StdBetahT .OR. BetaTh+Z0025*StdBetahT<=0.0d0 ) THEN
101
DO WHILE (ErrorBR0>0.000000001d0) DO J=1,TTS
102 IF (0.0d0<=BetaRh-Z0025*StdBetahR .OR. BetaRh+Z0025*StdBetahR<=0.0d0 ) THEN
Tests(N,2)=1 END IF
!write(*,"(4(2XF13.10))") AlphaTh,BetaTh,AlphaRh,BetaRh
!=======Common Slope Testing======
IF (Tests(N,1)==1 .AND. Tests(N,2)==1) THEN VarBetaRT=VarBetahR+VarBetahT
StdBetaRT=VarBetaRT**(0.5d0)
103
!======Common Slope Model Newton-Raphson====
IF (Tests(N,3)==1) THEN
caC(J,1)=DATAS(J,3)*DEXP(AlphaTh+BetaCh*DATAS(J,5)) !YtExp(At+BC*Xt) caC(J,2)=DATAS(J,8)*DEXP(AlphaRh+BetaCh*DATAS(J,10)) !YrExp(Ar+BC*Xr)
104
IF (ErrorAR<0.000000001d0 .AND. ErrorAT<0.000000001d0 .AND.
ErrorBC<0.000000001d0) EXIT END DO
!write(*,"(3(2XF13.10))") AlphaTh,AlphaRh,BetaCh
!======Relative Potency======
DO J=1,TTS
caC(J,1)=DATAS(J,3)*DEXP(AlphaTh+BetaCh*DATAS(J,5)) caC(J,2)=DATAS(J,8)*DEXP(AlphaRh+BetaCh*DATAS(J,10))
caC(J,5)=DATAS(J,3)*DATAS(J,5)*DEXP(AlphaTh+BetaCh*DATAS(J,5)) caC(J,6)=DATAS(J,8)*DATAS(J,10)*DEXP(AlphaRh+BetaCh*DATAS(J,10))
caC(J,7)=DATAS(J,3)*(DATAS(J,5)**2)*DEXP(AlphaTh+BetaCh*DATAS(J,5))+DA TAS(J,8)*(DATAS(J,10)**2)*DEXP(AlphaRh+BetaCh*DATAS(J,10))
105
CovARBC)+(((AlphaTh-AlphaRh)*BetaCh-Z0050**2*(CovATBC-CovARBC))**2-106
IF (-Delta<DeltaL .AND. DeltaU<Delta) THEN Tests(N,4)=1 Power is ', SUM(Tests(:,4))/SimuN
!ELSE
!WRITE(*,"(A,(1XF6.4),A,(1XF6.4))") 'Coverage
probility=',SUM(Tests(:,I+4))/SimuN,' Size is ', SUM(Tests(:,4))/SimuN
!WRITE(15,"((1XF6.4),A,(1XF6.4))") SUM(Tests(:,I+4))/SimuN,' Size is ', SUM(Tests(:,4))/SimuN
!ENDIF
!ENDIF
!END DO
!write(15,"(F)") SUM(Tests(:,4))/SimuN
WRITE(*,"((1XF4.1),A,(1XF6.4))") AlphaT0/BetaT0,' ',SUM(Tests(:,4))/SimuN WRITE(15,"((1XF4.1),A,(1XF6.4))") AlphaT0/BetaT0,' ',SUM(Tests(:,4))/SimuN
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end program