Philip Akude – MSc, Reza Mahjoub – PhD, Mike Paulden – MSc, Christopher McCabe – PhD
University of Alberta
CADTH
April 12, 2016
 This study was conducted under the PACEOMICS project, funded by Genome
Canada, Genome Quebec, Genome Alberta and the Canadian Institutes for Health
Research (CIHR).
 The following authors are funded by PACEOMICS project: Philip Akude, Reza
Mahjoub, and Michael Paulden.
 Christopher McCabe is funded by the University of Alberta, Faculty of Medicine
and Dentistry.
 Background
 Objective
 General model description
 Simplified model with probability of response set
exogenously
 Optimal cut-offs for the general model under perfect
information
 Conclusions
HTA for treatment technologies are increasingly required to have randomized
controlled trial evidence of efficacy.

Test technologies are frequently adopted on the basis of evidence of laboratory
validity and clinical test performance.

The ascent of personalised medicine, specifically test guided therapies is
bringing these two evidentiary traditions together.

Stakeholders of personalized medicine product seek a coherent framework to
appraise these technologies.

 Develop methods for combining evidence on the test(s) and treatment components
of co-dependent technologies, and to identify the cost effective cut offs on the test
components for pre-specified values of the willingness to pay for health.
Genotypic
Test
(Test d)
Positive?
Yes
TP?
Yes
Therapy
Responder
Test
(Test π)
Π≥ΠC
No
FP
No
No
Treatme
nt
Test π
Stand.
Care
TN
No
Treatme
nt
Yes
Phenotypic
Test
(Test u)
UR≥UC
No
Stand.
Care
Yes
New Tx
U i : Health benefit (phenotype) resulting from the new treatment or standard care, U i  1,
i  {R, N , S R  Responding, N  Non-responding, S  Standard Care}
U i : Expected health benefit, i  {R, N , S}
Ci : Cost of treatment/standard care per unit time, i  {R, N , S}
Ci : Expected cost, i  {R, N , S}
Ctj : Cost of test, j  {d ,  , u}
 j : Error in test measurment;  j ~ N (0,  j ), j { , u};
Uˆ R : Observed health benefit(phenotypic expression) for a responding patient; Uˆ R  U R   u
ˆ : Estimated probability of response, 
ˆ   


g : Inverse of CE ratio
1. The patient population heterogeneous with respect
to the “success rate”, i.e., Π:
 Fπ(π)=Pr{Π≤π} is CDF of Π and fπ(π) is PDF of Π
2. The patient population heterogeneous with respect
to their phenotypic expression for patients who
respond to treatment, i.e., UR:
 Fu(uR)=Pr{UR ≤ uR} is CDF of UR and fu(uR) is PDF of UR
Uˆ R  U C
Test u
U R  UC
ˆ 

C
Test 
U R  1  u  U R  UC
Uˆ R  U R   u
Uˆ R  U C
  1      c
  C
ˆ   


U R  UC

Phelps & Mushlin Framework
p
Test d
U R  UC
ˆ 

C
FN
U SN  g (CSN  Ctd )
†
FP
q
Uˆ R  U C
Uˆ R  U C
Sick
f
1 p
U R  g (CR  Ctd  Ct  Ctu )
Stand. Care
U S  g (CS  Ctd  Ct  Ctu )
Stand. Care
U S  g (CS  Ctd  Ct )
New Tx
U R  g (CR  Ctd  Ct  Ctu )
  C    
E  NBTP 
Do Not Treat
New Tx
U R  UC u
ˆ 

C
TP
U S  g (CS  Ctd  Ct  Ctu )
U R  1  u  U R  UC
Uˆ R  U R   u
U R  1  u  U R  UC
Uˆ R  U R   u
Uˆ R  U C
  1      c
U R  UC   u
  C
Uˆ R  U C
ˆ   


Test 2
U R  UC
U HN  g (CHN  Ctd  Ct )
Stand. Care U  g (C  C  C  C )
S
S
td
t
tu
New Tx
U R  g (CR  Ctd  Ct  Ctu )
Stand. Care
U S  g (CS  Ctd  Ct  Ctu )
U R  1  u  U R  UC
Uˆ R  U R   u
Healthy
Uˆ R  U C
U R  UC  u
1 f
ˆ 

C
TN
1 q
  C    
Do Not Treat
U HN  g (CHN  Ctd )
Not Responding
1 
Stand. Care
†
U R  g (CR  Ctd  Ct  Ctu )
Stand. Care
U R  UC  u
Uˆ R  U C
Responding
New Tx
U S  g (CS  Ctd  Ct )
FP patients will be correctly diagnosed as TN as a result of second tes
Same tree as on responding
• Π exogenous
• Imperfect information (error in measurement)
• One test for magnitude of response UR
Uˆ R  U C
Test u
U R  UC
Uˆ R  U R   u
Uˆ R  U C
Uˆ R  U C
Phelps & Mushlin Framework
U R  UC
Uˆ R  U R   u
E  NBTP 
Stand. Care
New Tx
U R  1  u  U R  UC
Uˆ R  U C
Stand. Care
U R  UC  u
Sick
f
Uˆ R  U C
FN
Do Not Treat
1 p
Test 1
U R  1  u  U R  UC
U R  UC  u

TP
p
New Tx
FP
U SN  g (CSN  Ctd )
U R  UC
Uˆ R  U R   u
Test u
q
U R  1  u  U R  UC
Uˆ R  U C
Uˆ R  U C
Healthy
U R  UC
TN
1 q
Do Not Treat
U HN  g (CHN  Ctd )
Uˆ R  U R   u
U R  UC  u
U R  g (CR  Ctd  Ctu )
U S  g (CS  Ctd  Ctu )
U N  g (C N  Ctd  Ctu )
U S  g (CS  C td Ctu )
New Tx
U R  1  u  U R  UC
Uˆ R  U C
U S  g (CS  Ctd  Ctu )
Stand. Care
U R  UC  u
1 
1 f
New Tx
U R  g (CR  Ctd  Ctu )
Stand. Care
U N  g (C N  Ctd  Ctu )
U S  g (CS  Ctd  Ctu )


uR   

E  NBTP    
uR 1


uR   


uR 1


uR 


uR 1
U
u
R
 U N  g (CR  CN )
N  gCN

U S  gCS
 g  Ctd  Ctu .

u uR UC
u uR 1

u 
u uR UC

u uR UC
u uR 1

 
f u  u  d  u   f uR uR  duR

 
fu  u  d  u   f uR uR  duR

fu  u  d  u  f uR uR  duR

E  NBTP  uR 1
FOC:

K  fu uR  U C  f uR uR  duR  0,
uR  0
U C


where K    uR  U N  g  CR  CN    U S  U N  g  CS  CN .





Example:
Us
UN
CN
CR
CS
π
U C*  0.461
0.69
0.35
$
1,245
$
$
1,245
15,958
0.6
U R ~  (2.7, 0.3) 
Mean=0.9 and Stand. Deviation=0.15
 u ~ N (0, 0.1)
Note that under perfect information, U C*  0.51.
Test u
Test 
• No error in measurement
U R  UC
ENBTP
TP
  C
p
Sick
f
Do Not Treat
1 p
FP†
Stand. Care
U S  g (CS  Ctd  Ct  Ctu )

Phelps & Mushlin Framework
Test 1
U R  g (CR  Ctd  Ct  Ctu )
  C
U R  UC
FN
New Tx
Test 2
q
U SN  g (CSN  Ctd )
Stand. Care
U R  UC
New Tx
U R  UC
Stand. Care
U S  g (CS  Cd  Ct )
U N  g (C N  Ctd  Ct  Ctu )
  C
U HN  g  (CHN  Ctd  Ct )
U S  g (CS  Ctd  Ct  Ctu )
Not Responding
1 
Healthy
1 f
TN
1 q
Do Not Treat
  C
Stand. Care
U HN  g (CHN  Ctd )
†
U S  g (CS  Ctd  Ct )
FP patients will be correctly diagnosed as TN as a result of second t
E  NBTP    
1
C

C

1

C
0
C
0
E  NBTP   
1

0
UC
 uR  g  (CR  Ctd  Ct  Ctu )  fuR (uR )duR  
S
U
S

 g  (CS  Ctd  Ct  Ctu )  f uR (u R )du R f ( )d 
 U S  g  (CS  Ctd  Ct )  f ( )d
1   

1
UC
U N  g  (CN  Ctd  Ct  Ctu )  fuR (uR )duR  
UC

U
S

 g  (CS  Ctd  Ct  Ctu )  f uR (u R )du R f ( )d
1    U S  g  (CS  Ctd  Ct )  f ( )d
   u
U
UC

1
C UC
C

1
R

 g  (CR  Ctd  Ct  Ctu )   1    U N  g  (C N  Ctd  Ct  Ctu )  f uR (u R ) f ( )du R d 
 g  (CS  Ctd  Ct )  f ( )d   
1
C

UC

U
S

 g  (CS  Ctd  Ct  Ctu )  f uR (u R )du R f ( )d 
E  NBTP     
1
UC
  u
R

 g (CR  Ctd  Ct  Ctu )   1    U N  g (C N  Ctd  Ct  Ctu )  f uR (u R )du R
U S  g (CS  Ctd  Ct )  
UC

U
S
 g (CS  Ctd  Ct  Ctu )  f uR (u R )du R
FOC to find the optimal phenotypic cut off, U C* :

 E  NBTP   
U C
U C*  U N  g (CR  C N ) 
Net benefits from new Tx
U


1
S
 0
 U N  g (CS  C N ) 
Net benefits from Stand. Care
  uR  gCR   1  U N  gCN   U S  gCS





UC* is equal to the clinical expression for a responding patient, at
which the payer becomes indifferent between the new treatment and
the standard care.
To find the optimal cut-off probability of response  *C :
FOC :
E  NBTP 
 C
0
At  C   *C :

1
U C* ( *C )
 u
*
C
R
 gCR   1  
*
C
 U
N

 gC N )  f uR (u R )du R  gCtu  
1
U C* ( *C )
U
S
 gCS  f uR (u R )du R
 This study develops a formal decision analytic
framework for the economic evaluation of
personalised medicine co-dependent technologies.
 The method presented offers decision makers the
impact a changing cost effectiveness threshold has on
the optimal cut-off value for co-dependent
technologies.
 The optimal test cut-off must be set at the point where
the marginal payoff from new treatment is equal to the
marginal payoff from standard care.