Slide
1
Placebo Response
Nick Holford
University of Auckland
Slide
2
Clinical Pharmacology
=
Disease Progress + Drug Action
©NHG Holford, 2013 all rights reserved.
Slide
3
Components of a Disease
Progress Model
• Baseline Disease State
• Natural History
• Active Treatment Response
• Placebo Response
S(t) = S0 +Nat. Hx. + Active + Placebo
©NHG Holford, 2013 all rights reserved.
Disease progress models start with a baseline
disease status, S0.
The change from baseline in the absence of
drug treatment describes the natural history of
the disease (disease progression).
When drugs are used then the active effect of
the drug modifies disease status. In clinical
trials it is also necessary to consider the
placebo response as a separate component.
Some disease progress models are described
in Holford NHG, Mould DR, Peck CC. Disease
progress models. In: Atkinson A, editor.
Principles of Clinical Pharmacology. 2nd ed.
San Diego: Academic Press; 2007. p. 313-21.
More complex effects based on turnover
models have been described in Post TM,
Freijer JI, DeJongh J, Danhof M. Disease
system analysis: basic disease progression
models in degenerative disease. Pharm Res.
2005 Jul;22(7):1038-49.
Slide
4
Response to
Inactive Treatment
• PLACEBO
“I will please” -- Response improvement
• NOCEBO
“I will harm”
-- Response worsens
©NHG Holford, 2013 all rights reserved.
Slide
5
Placebo Response
HAM-D 17 point Hamilton Depression
HAM-D
20
10
0
2
4
6
8
Week
©NHG Holford, 2013 all rights reserved.
Slide
6
Placebo Response
“Constant input with first order elimination”
Tlag=Lag time
25
S0=Baseline
Drem=Remission
“Dose Rate”
HAM-D
20
15
Trem=Remission
Half-Life
10
0
14
28
42
56
70
84
Time (days)
©NHG Holford, 2013 all rights reserved.
98 112 126
Some clinical responses will show a natural
history pattern which approaches an
asymptote. For example, pain scores after
abdominal surgery typically decrease over a
few days and approach zero. The asymptote
may be non-zero as shown in the figure. This
illustrates the improvement in the Hamilton
Depression (HAM-D) rating scale after
administration of a placebo in an antidepressant clinical trial. It is a matter of
personal preference whether one calls this a
change due to disease progress or a change
due to placebo treatment. In this particular
case the two mechanisms are
indistinguishable.
Slide
7
Disease Progress and Placebo
Models for Depression Response
Models
Equations
Disease Progress
S (t ) = S 0
Placebo Response
Placebo(t ) = Drem ⋅ 1 − e − ln( 2) / Trem⋅(t −Tlag )
HAM-D Time Course
HAMD(t ) = S (t ) + Placebo(t )
(
)
An application of an exponential model with a
nonzero asymptote is shown here. The
disease progress model is assumed to remain
constant and the change with time is
attributed to a placebo response. An
exponential model with an asymptote of Drem
(the size of the remission expressed as the
placebo ‘dose’) and a half-life Trem (the halflife of remission induced by placebo) is used
to describe the placebo response. There is a
delay before the onset of the placebo effect
which can be described with Tlag (lag time).
©NHG Holford, 2013 all rights reserved.
Slide
8
The placebo response in anti-depressant trials
is not always monophasic. Sometimes it is
possible to discern a relapse (i.e. worsening of
HAM-D) during the trial. The relapse
component of the response can be described
by a simple change to the asymptotic
progress model.
Placebo
ID
2006
40
60
HAMD
10
-0
-0
20
40
60
20
40
60
-0
20
40
Days
2036
2044
2050
30
20
20
10
10
-0
-0
-0
40
60
-0
20
40
60
-0
20
40
60
20
10
-0
-0
20
40
60
-0
20
40
Days
Days
Days
Days
Days
2051
2062
2069
2071
2077
10
10
-0
10
-0
40
60
30
20
20
40
60
20
10
-0
-0
20
40
60
20
10
-0
-0
-0
-0
20
40
60
-0
20
40
Days
Days
Days
Days
Days
2081
2087
2092
2102
2107
10
60
Days
20
10
-0
40
HAMD
20
10
-0
30
30
HAMD
20
20
40
60
20
40
60
20
10
-0
-0
Days
20
10
-0
-0
-0
-0
20
Days
40
60
Days
-0
20
40
Days
©NHG Holford, 2013 all rights reserved.
Slide
9
Placebo Response Model
Bateman
“first order absorption and elimination”
Tlag
Remission
“Dose”
30
25
HAM-D
20
15
Relapse
Half-Life
10
Remission
Half-Life
5
0
0
50
100
150
Time (days)
©NHG Holford, 2013 all rights reserved.
60
30
HAMD
30
HAMD
30
60
30
HAMD
30
20
HAMD
20
HAMD
30
HAMD
30
60
30
HAMD
HAMD
HAMD
30
20
10
20
60
2033
30
-0
40
2030
-0
20
20
Days
10
-0
-0
-0
Days
20
20
10
-0
-0
20
Days
30
-0
2023
30
20
Days
HAMD
20
2017
30
20
10
-0
-0
HAMD
20
10
-0
HAMD
HAMD
HAMD
HAMD
20
10
HAMD
2013
30
30
HAMD
2004
30
200
250
300
60
Slide
10
A two exponential model with a biphasic
pattern is known as the Bateman function.
Placebo
Bateman Model
Drem ⋅ Krem
⋅ (e − Krel ⋅( t −Tlag ) − e − Krem⋅( t −Tlag ) )
( Krem − Krel )
HAMD(t ) = S 0 + Placebo(t )
Placebo(t ) =
S0 = Baseline HAM − D
Tlag = Placebo onset lag - time
Drem = Remission Dose
ln(2)
Trem
ln(2)
Krel =
Trel
Krem =
Trem = Remission Half − life
Trel = Relapse Half − life
©NHG Holford, 2013 all rights reserved.
Slide
11
Inverse Bateman
Placebo Response Profiles
30
Standard
Placebo
Response
25
HAM-D
20
15
Bigger
Remission
“Dose”
10
5
Faster 0
Remission
Half-life
0
50
100
150
200
250
Time (days)
©NHG Holford, 2013 all rights reserved.
Slide
12
What is the Time Course of
Placebo Response?
• Placebo Arm of Double Blind Randomized
Phase II Study of New Potential AntiDepressants
– Total 582 patients, 3864 observations
•
•
•
•
©NHG Holford, 2013 all rights reserved.
Drug X, Study A (154 patients)
Drug X, Study B (141 patients)
Drug Y, Study C (149 patients)
Drug Y, Study D (138 patients)
300
Slide
13
Time Course of Placebo
Response in Depression
Parameter
Estimate
Units
24
HAM-D
Baseline
Lag time
4.7
days
Remission amplitude
20.6
HAM-D
Remission half-life
60
days
Relapse half-life
280
days
iba_plaro_sdymixfix_s0sexwtsdyfix_tlwt_teme
©NHG Holford, 2013 all rights reserved.
Slide
14
Drug X
ID
40
60
40
20
40
60
HAMD
60
-0
20
40
Days
2036
2044
2050
60
20
-0
-0
20
40
60
20
10
10
20
40
60
20
10
-0
-0
-0
-0
20
40
60
-0
20
40
Days
Days
Days
Days
Days
2051
2062
2069
2071
2077
30
30
HAMD
20
20
20
20
10
10
10
10
-0
-0
-0
-0
40
60
-0
20
40
60
-0
20
40
60
20
10
-0
-0
20
40
60
-0
20
40
Days
Days
Days
Days
Days
2081
2087
2092
2102
2107
20
20
10
10
10
10
-0
-0
-0
-0
40
60
-0
20
Days
40
-0
60
20
40
60
20
10
-0
-0
20
Days
Days
60
30
30
20
HAMD
30
HAMD
HAMD
30
20
HAMD
30
60
30
HAMD
30
HAMD
30
60
30
HAMD
HAMD
20
-0
40
30
30
HAMD
HAMD
-0
20
40
2033
10
-0
20
2030
30
20
-0
-0
Days
10
-0
10
-0
-0
60
Days
20
20
10
-0
20
20
Days
30
-0
HAMD
10
-0
30
20
Days
HAMD
20
2023
30
20
-0
-0
HAMD
20
10
-0
HAMD
HAMD
HAMD
HAMD
20
2017
30
30
10
HAMD
2013
2006
2004
30
40
-0
60
20
Days
40
60
Days
Inverse Bateman
©NHG Holford, 2013 all rights reserved.
Slide
15
Drug Y
ID
5128
40
60
40
60
40
60
-0
20
40
HAMD
Days
5161
5168
40
60
30
20
20
40
60
-0
20
40
60
20
10
-0
-0
-0
20
10
10
-0
-0
20
40
60
-0
20
40
Days
Days
Days
Days
Days
5172
5178
5185
5187
5192
10
10
-0
10
-0
40
60
30
20
20
40
60
20
10
-0
-0
20
40
60
20
10
-0
-0
-0
-0
20
40
60
-0
20
40
Days
Days
Days
Days
Days
5195
5198
5207
5212
5216
30
20
30
20
20
10
10
10
10
-0
-0
-0
-0
40
60
Days
©NHG Holford, 2013 all rights reserved.
-0
20
40
Days
60
-0
20
40
Days
60
60
30
HAMD
20
HAMD
30
HAMD
30
60
30
HAMD
30
20
HAMD
20
HAMD
30
HAMD
30
60
30
HAMD
HAMD
HAMD
30
20
-0
-0
20
20
5155
10
-0
-0
-0
60
5150
30
20
40
5149
10
-0
20
Days
20
20
10
-0
-0
Days
HAMD
HAMD
20
20
Days
30
-0
10
-0
-0
30
20
Days
HAMD
20
5140
30
20
10
-0
-0
HAMD
20
10
-0
5135
30
HAMD
HAMD
HAMD
20
10
HAMD
5130
30
HAMD
5124
30
20
10
-0
-0
20
40
60
-0
20
Days
Inverse Bateman
40
Days
60
Slide
16
Relapse Mixture Model
• Assume some patients relapse (get worse
while on placebo treatment)
• Assume patients who do not relapse have
infinite relapse half-life
• Probability of patient having a relapse is
estimated using a mixture model
©NHG Holford, 2013 all rights reserved.
Slide
17
Relapse Probability
Study A
98%
Study B
45%
Study C
29%
Study D
18%
Why are relapse probabilities different?
iba_plaro_sdymixfix_s0sexwtsdyfix_tlwt_teme
©NHG Holford, 2013 all rights reserved.
Slide
18
Is It a Design Issue?
HAM-D Observation Times
Study B
24
18
12
6
0
0 14 28 42 56 70 84
OBS Day
Study C
Study D
24
24
18
18
12
12
6
6
0
0
0
28
56
84
112
OBS Day
©NHG Holford, 2013 all rights reserved.
140
168
196
0
28
56
84
112
OBS Day
140
168
196
224
Slide
19
Observation Effect Model
• Each HAM-D observation is a “dose” of
placebo
• Placebo “conc” rises and falls like oral drug
absorption model
• Placebo “conc” shortens remission and
relapse half-lives
©NHG Holford, 2013 all rights reserved.
Slide
20
Observation Effect
on Placebo Response
Parameter
Estimate
Placebo onset half-life
0.12 days
Placebo elimination half-life
31 days
Placebo effect on remission
-40%
Placebo effect on relapse
-64%
©NHG Holford, 2013 all rights reserved.
iba_plaro_sdymixfix_s0sexwtsdyfix_tlwt_teme
Slide
21
Disease Progression and
Placebo Response
• Requires assumption about shape of disease
progression (natural history)
• Commonly disease progression is linear
• Placebo (or nocebo) observed response will
be the sum of disease progression and the
placebo (nocebo) time course
©NHG Holford, 2013 all rights reserved.
Slide
22
Linear + Offset
(Symptomatic)
S (t ) = (S 0 + E (t ) ) + α ⋅ t
120
Status
110
100
Temporary Improvemen
90
Natural History
80
With any disease progress model it is possible
to imagine a drug action that is equivalent to a
change in the baseline parameter of the
model. This kind of effect on disease
produces a temporary offset. When treatment
is stopped the response to the drug washes
out and the status returns to the baseline. In
many cases it is reasonable to suppose that
the processes governing a delay in onset of
drug effect will also affect the loss of effect but
the offset effects of levodopa treatment in
Parkinson’s disease are one exception to this
assumption.
70
0
13
26
39
52
Time
Natural History
Offset Effect
©NHG Holford, 2013 all rights reserved.
Slide
23
Linear + Offset + Placebo
Griggs RC, Moxley RT, Mendell JR, Fenichel GM, Brooke MH, Pestronk A, et al. Prednisone in Duchenne
Dystrophy: A randomized, controlled trial defining the time course and dose response. Archives of Neurology
1991;48:383-88
©NHG Holford, 2013 all rights reserved.
Slide
24
DATATOP
ELLDOPA
TEMPO
©NHG Holford, 2013 all rights reserved.
Parkinson’s Disease
Inactive Treatment
Clinical Trials
• DATATOP cohort: early untreated PD patients to
determine
if
deprenyl
and/or
tocopherol
administration will prolong time before levodopa
rescue. Multicenter, randomized, double-blind,
placebo-controlled. 800 subjects. DATATOP cohort
followed up to 8 years (5). Tocopherol was shown to
be inactive so it has been included with placebo
treated patients as an inactive control treatment.
• ELLDOPA: effect of early or later levodopa treatment
on rate of PD progression. Multicenter, randomized,
dose-ranging,
double-blind,
placebo-controlled
washout design. 361 patients. 11 months.
• TEMPO: comparison of 1 mg/d and 2 mg/d of
Rasagiline in early PD patients not treated with
levodopa. Multicenter, randomized, double-blind,
delayed start design. 360 patients. 12 months.
Muscular dystrophy causes a progressive loss
of muscle strength. This graph shows the
author’s belief that the natural history is
essentially linear over 6 months. The effects
of two doses of prednisone demonstrate a
delayed onset of effect but no change in the
rate of progression after the maximum effect
is achieved. This seems to be an example of
an offset type of drug effect. The response to
placebo is also delayed but differs from
prednisone by loss of effect and return to the
natural history rate of progression. The
difference in time course of drug action,
placebo response and natural history
components allows these three phenomena to
distinguished.
Slide
25
Disease Progression And
Placebo/Nocebo in Parkinson’s Disease
70
60
UPDRS
50
40
30
20
10
0
0
0.5
1
1.5
2
2.5
3
3.5
Years
Nocebo
Placebo
Linear
Gompertz
©NHG Holford, 2013 all rights reserved.
Slide
26
Parkinson’s Disease Placebo and Nocebo
Parameter
POP_S0
POP_ALPHA
POP_PMAX
POP_TAB
FTEL
Probability
Description
Baseline UPDRS
Progression rate
Maximum 'placebo' benefit
'Placebo absorption' half-life
'Placebo elimination' half-life fraction of POP_TAB
Probability of positive response (PMAX)
Units Average RSE 2.5% ile
u
23.1
0.019 22.2
u/y
12.7
0.100 10.6
u
-5.09 -0.288 -8.22
day
202
0.438
111
x 100
0.805
2.64 0.005
.
0.162 0.298 0.066
97.5%
ile
24.0
15.6
-3.12
469
4.11
0.254
Pmax for placebo is negative to describe improvement
in response with inactive treatment
©NHG Holford, 2013 all rights reserved.
Slide
27
Placebo Response Summary
• A part of the disease progress model
• Usually requires an assumption about the
natural history
• May be a key part of the overall response to
treatment
• Quantitative models are helpful for
understanding active and inactive treatment
responses
©NHG Holford, 2013 all rights reserved.
Slide
28
Disease Progress, Placebo/Nocebo,
Termination Event
$PK
IF (MIXNUM.EQ.1) THEN ; Nocebo
FPmax=-FPOSPmax*FPOSET
ELSE
; Placebo
FPmax=1
ENDIF
; Peak response
PMAX=POP_PMAX*Fpmax*EXP(PPV_PMAX)
; nominal placebo ‘dose’
BPLA=PMAX*(Kab-Kel)/(Kab*(EXP(LOG(Kab/Kel)*Kel/(Kab-Kel))
- EXP(LOG(Kab/Kel)*Kab/(Kab-Kel)))
; Baseline disease status
A_0(1)=S0
$DES
;Disease status (UPDRS)
DDPRG=A(2) ; linear progression status
DPLA= (BPLA*Kab)/(Kab-Kel)*(EXP(Kel*T)-EXP(-Kab*T))
DSTAT=DDPRG+DPLA ; progression +
placebo
;Termination event hazard
DADT(1)=BASDRP*EXP(BUPD*DSTAT)
;Disease progression
DADT(2)=AL ; linear progression slope
©NHG Holford, 2013 all rights reserved.
$ERROR
CUMHAZ=A(1)
NH=A(2)
SRVT=EXP(-CUMHAZ); S(t)
IF (DVID.EQ.1) THEN
F_FLAG=0 ; Continuous ELS
Y = NH + PLA + ERRSD
ENDIF
IF (DVID.EQ.2.AND.DV.EQ.0) THEN ;
Censored
F_FLAG=1 ; Likelihood
Y=SRVT
ENDIF
IF (DVID.EQ.2.AND.DV.EQ.1) THEN ; Event
F_FLAG=1 ; Likelihood
Y=SRVZ-SRVT
ENDIF
IF (DVID.EQ.3) THEN
SRVZ=SRVT ;Save S(t) for start of
censor interval
ELSE
SRVZ=SRVZ ; Keep NM-TRAN happy
ENDIF