Sihang Liu PhD Candidate University at Buffalo School of Pharmacy and Pharmaceutical Sciences A phase 1b2a adaptive clinical trial of a selective estrogen beta receptor ER β agonist for its preliminary effects in cognitive function in schizophrenia ID: 915675
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Slide1
Resolving Conflicting Results Arising from a Pharmacometric and a Statistical Analysis of the Cognitive Effects of a Selective Estrogen Receptor Beta Agonist (LY500307) in Schizophrenic Patients
Sihang Liu
Ph.D. Candidate
University at Buffalo
School of Pharmacy and Pharmaceutical Sciences
Slide2A phase 1b/2a adaptive clinical trial of a selective estrogen beta receptor (ER-β) agonist for its preliminary effects in cognitive function in schizophrenia.
8-week randomized, double-blind, placebo-controlled, dose ranging, parallel group study.Ninety-four patients were randomized across the four treatment arms: placebo N=2925 mg/day N=1075 mg/day N=29
150 mg/day N=26.
Patient Evaluations: MATRICS Consensus Cognitive Battery (MCCB) Fronto-parietal functional activation during N-back performance (N-back)
Personal and Social Performance Scale (PSP) Adjusted Score
etc.
Background of the Clinical Trial
Slide33
Background of the Analysis
Clinical Trial Data
Pharmacometric Team
Statistical Team
The treatment group is superior to the placebo group in endpoints including: MCCB, N-back, PSP, etc.
No significant difference between the two groups in above endpoints.
NONMEM
SAS
Slide44
The MATRICS Consensus Cognitive Battery (MCCB)
Widely used in international trials examining cognitive function in
patients with schizophrenia (Nuechterlein et al., 2008).
The test consists of:
Speed of processing Attention/vigilance
Working memoryVerbal memory
Visual learningReasoning and problem solving Social cognition
MCCB overall composite T-score
ranges from 0 to 81, where a higher score indicates a better cognitive function.
MCCB was assessed at week 0, 4, and 8.
Nuechterlein
, K. H. et al. (2008). The MATRICS Consensus Cognitive Battery, Part 1: Test selection, reliability, and validity. American Journal of Psychiatry, 165(2), 203-213.
Kern, R. S. et al. (2008). The MATRICS Consensus Cognitive Battery, Part 2: Co-norming and standardization. American Journal of Psychiatry, 165(2), 214-220.
Slide55
Initial Model Strategy Proposed by the Pharmacometric Team
Full model
,where TR=1, PL=0 for treatment group, and TR=0, PL=1 for placebo group.
Backward elimination and likelihood ratio test
Removal of the treatment slope, OFV 61.2 (p<0.0001, df=2) points.
Removal of the placebo slope, OFV 24.5 (p<0.0001, df=2) points.
Model predicted MCCB composite score change at the 8-week endpoint
20% increase in the treatment group
16% increase in the placebo group
Equivalent Statistical expression of the full model
Slide66
Initial Model Proposed by the Statistical Team
Model with random intercept:
For the
-th subject at
-th measurement occasion, we have
where
Equivalent pharmacometric expression:
Result:
The slope for treatment is not significantly different from the slope for placebo.
Estimates
Label
Estimate
Standard Error
DF
t Value
Pr > |t|
slope for placebo
0.07976
0.01653
165
4.83
<.0001
slope for treatment
0.09852
0.01176
165
8.38
<.0001
slope for treatment - slope for placebo
0.01876
0.02010
165
0.93
0.3519
,where TR=1 for treatment group, and TR=0 for placebo group.
7
Second Model Proposed by the Statistical Team
After the first round of communication, the statistical team proposed the second model
with random intercept and random slope
in the full model.
For the
-th subject at
-th measurement occasion, the full model is:
Equivalent pharmacometric expression:
The slope for treatment is not significantly different from the slope for placebo
Result:
Estimates
Label
Estimate
Standard Error
DF
t Value
Pr
> |t|
slope for placebo
0.08000
0.01746
82
4.58
<.0001
slope for treatment
0.09872
0.01241
82
7.95
<.0001
slope for treatment - slope for placebo
0.01873
0.02127
82
0.88
0.3811
,where TR=1 for treatment group, and TR=0 for placebo group.
8
Investigat
ing the Difference
Differences in setting the inter-individual variability (IIV) structure/random slopes:
The pharmacometric model made the following assumptions on IIV structure:
Shared IIV for baseline
Unique IIV terms for the
and
The default options in SAS (proc mixed) is to assume the random slopes equal to zero or treat the “random slopes” as a whole term in the model, which means all the slopes in the model would share the same normal distribution and use only one random slope term in the model.
Differences in constructing the reduced model:
The pharmacometric model reduce the treatment slope to zero
The statistical model reduce the difference between treatment slope and placebo slope to zero.
9
Modified backward elimination
Full model: Unique Treatment Slope and Placebo Slope
Reduced Model 1: Shared Slope Between Treatment and Placebo
Reduced Model 2: Baseline Only
Remove treatment effect
Remove shared slope
OFV 2.4 (p=0.3, df=2) points
OFV 73.4 (p<0.0001, df=2) points
Slide1010
Summary of the Comparisons
Model
Full Model setting for treatment and placebo slopes
Reducing Treatment Effect
Placebo Slope
(1/day)
Treatment
Slope
(1/day)
Full model Objective Function Value
Reduced Model Objective Function
Value
P-value of LRT for treatment Effect
(df)
Initial Pharmacometric Model (P1)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1282.0
61.2
4.9E-14
(df=2)
Second Pharmacometric Model (P2)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1223.1
2.3
0.32
(df=2)
Initial Statistical Model (S1)
Unique slopes
No IIV
0.0798
0.0985
1697.5
1698.4
0.9
0.35
(df=1)
Second Statistical Model (S2)
Unique slopes
Shared IIV
0.0800
0.0987
1696.5
1697.3
0.8
0.38
(df=1)
SAS Matched Model for P1
Same with P1
Same with P1
0.0803
0.0986
1694.9
1756.2
61.3
4.9E-14
(df=2)
SAS Matched Model for P2
Same with P2
Same with P2
0.0803
0.0986
1694.9
1697.3
2.4
0.30
(df=2)
Model
Full Model setting for treatment and placebo slopes
Reducing Treatment Effect
Placebo Slope
(1/day)
Treatment
Slope
(1/day)
Full model Objective Function Value
Reduced Model Objective Function
Value
P-value of LRT for treatment Effect
(df)
Initial Pharmacometric Model (P1)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1282.0
61.2
4.9E-14
(df=2)
Second Pharmacometric Model (P2)
Unique slopes
Unique IIVs
0.0792
0.09841220.81223.12.30.32(df=2)Initial Statistical Model (S1)Unique slopesNo IIV0.07980.09851697.51698.40.90.35(df=1)Second Statistical Model (S2)Unique slopesShared IIV0.08000.09871696.51697.30.80.38(df=1)SAS Matched Model for P1Same with P1Same with P10.08030.09861694.91756.261.34.9E-14(df=2)SAS Matched Model for P2Same with P2Same with P20.08030.09861694.91697.32.40.30(df=2)
Slide1111
Summary of the Comparisons
Model
Full Model setting for treatment and placebo slopes
Reducing Treatment Effect
Placebo Slope
(1/day)
Treatment
Slope
(1/day)
Full model Objective Function Value
Reduced Model Objective Function
Value
P-value of LRT for treatment Effect
(df)
Initial Pharmacometric Model (P1)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1282.0
61.2
4.9E-14
(df=2)
Second Pharmacometric Model (P2)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1223.1
2.3
0.32
(df=2)
Initial Statistical Model (S1)
Unique slopes
No IIV
0.0798
0.0985
1697.5
1698.4
0.9
0.35
(df=1)
Second Statistical Model (S2)
Unique slopes
Shared IIV
0.0800
0.0987
1696.5
1697.3
0.8
0.38
(df=1)
SAS Matched Model for P1
Same with P1
Same with P1
0.0803
0.0986
1694.9
1756.2
61.3
4.9E-14
(df=2)
SAS Matched Model for P2
Same with P2
Same with P2
0.0803
0.0986
1694.9
1697.3
2.4
0.30
(df=2)
Model
Full Model setting for treatment and placebo slopes
Reducing Treatment Effect
Placebo Slope
(1/day)
Treatment
Slope
(1/day)
Full model Objective Function Value
Reduced Model Objective Function
Value
P-value of LRT for treatment Effect
(df)
Initial Pharmacometric Model (P1)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1282.0
61.2
4.9E-14
(df=2)
Second Pharmacometric Model (P2)
Unique slopes
Unique IIVs
0.0792
0.09841220.81223.12.30.32(df=2)Initial Statistical Model (S1)Unique slopesNo IIV0.07980.09851697.51698.40.90.35(df=1)Second Statistical Model (S2)Unique slopesShared IIV0.08000.09871696.51697.30.80.38(df=1)SAS Matched Model for P1Same with P1Same with P10.08030.09861694.91756.261.34.9E-14(df=2)SAS Matched Model for P2Same with P2Same with P20.08030.09861694.91697.32.40.30(df=2)
Slide1212
Summary of the Comparisons
Model
Full Model setting for treatment and placebo slopes
Reducing Treatment Effect
Placebo Slope
(1/day)
Treatment
Slope
(1/day)
Full model Objective Function Value
Reduced Model Objective Function
Value
P-value of LRT for treatment Effect
(df)
Initial Pharmacometric Model (P1)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1282.0
61.2
4.9E-14
(df=2)
Second Pharmacometric Model (P2)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1223.1
2.3
0.32
(df=2)
Initial Statistical Model (S1)
Unique slopes
No IIV
0.0798
0.0985
1697.5
1698.4
0.9
0.35
(df=1)
Second Statistical Model (S2)
Unique slopes
Shared IIV
0.0800
0.0987
1696.5
1697.3
0.8
0.38
(df=1)
SAS Matched Model for P1
Same with P1
Same with P1
0.0803
0.0986
1694.9
1756.2
61.3
4.9E-14
(df=2)
SAS Matched Model for P2
Same with P2
Same with P2
0.0803
0.0986
1694.9
1697.3
2.4
0.30
(df=2)
Model
Full Model setting for treatment and placebo slopes
Reducing Treatment Effect
Placebo Slope
(1/day)
Treatment
Slope
(1/day)
Full model Objective Function Value
Reduced Model Objective Function
Value
P-value of LRT for treatment Effect
(df)
Initial Pharmacometric Model (P1)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1282.0
61.2
4.9E-14
(df=2)
Second Pharmacometric Model (P2)
Unique slopes
Unique IIVs
0.0792
0.09841220.81223.12.30.32(df=2)Initial Statistical Model (S1)Unique slopesNo IIV0.07980.09851697.51698.40.90.35(df=1)Second Statistical Model (S2)Unique slopesShared IIV0.08000.09871696.51697.30.80.38(df=1)SAS Matched Model for P1Same with P1Same with P10.08030.09861694.91756.261.34.9E-14(df=2)SAS Matched Model for P2Same with P2Same with P20.08030.09861694.91697.32.40.30(df=2)
Slide1313
Summary of the Comparisons
Model
Full Model setting for treatment and placebo slopes
Reducing Treatment Effect
Placebo Slope
(1/day)
Treatment
Slope
(1/day)
Full model Objective Function Value
Reduced Model Objective Function
Value
P-value of LRT for treatment Effect
(df)
Initial Pharmacometric Model (P1)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1282.0
61.2
4.9E-14
(df=2)
Second Pharmacometric Model (P2)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1223.1
2.3
0.32
(df=2)
Initial Statistical Model (S1)
Unique slopes
No IIV
0.0798
0.0985
1697.5
1698.4
0.9
0.35
(df=1)
Second Statistical Model (S2)
Unique slopes
Shared IIV
0.0800
0.0987
1696.5
1697.3
0.8
0.38
(df=1)
SAS Matched Model for P1
Same with P1
Same with P1
0.0803
0.0986
1694.9
1756.2
61.3
4.9E-14
(df=2)
SAS Matched Model for P2
Same with P2
Same with P2
0.0803
0.0986
1694.9
1697.3
2.4
0.30
(df=2)
Model
Full Model setting for treatment and placebo slopes
Reducing Treatment Effect
Placebo Slope
(1/day)
Treatment
Slope
(1/day)
Full model Objective Function Value
Reduced Model Objective Function
Value
P-value of LRT for treatment Effect
(df)
Initial Pharmacometric Model (P1)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1282.0
61.2
4.9E-14
(df=2)
Second Pharmacometric Model (P2)
Unique slopes
Unique IIVs
0.0792
0.09841220.81223.12.30.32(df=2)Initial Statistical Model (S1)Unique slopesNo IIV0.07980.09851697.51698.40.90.35(df=1)Second Statistical Model (S2)Unique slopesShared IIV0.08000.09871696.51697.30.80.38(df=1)SAS Matched Model for P1Same with P1Same with P10.08030.09861694.91756.261.34.9E-14(df=2)SAS Matched Model for P2Same with P2Same with P20.08030.09861694.91697.32.40.30(df=2)
Slide1414
Summary of the Comparisons
Model
Full Model setting for treatment and placebo slopes
Reducing Treatment Effect
Placebo Slope
(1/day)
Treatment
Slope
(1/day)
Full model Objective Function Value
Reduced Model Objective Function
Value
P-value of LRT for treatment Effect
(df)
Initial Pharmacometric Model (P1)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1282.0
61.2
4.9E-14
(df=2)
Second Pharmacometric Model (P2)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1223.1
2.3
0.32
(df=2)
Initial Statistical Model (S1)
Unique slopes
No IIV
0.0798
0.0985
1697.5
1698.4
0.9
0.35
(df=1)
Second Statistical Model (S2)
Unique slopes
Shared IIV
0.0800
0.0987
1696.5
1697.3
0.8
0.38
(df=1)
SAS Matched Model for P1
Same with P1
Same with P1
0.0803
0.0986
1694.9
1756.2
61.3
4.9E-14
(df=2)
SAS Matched Model for P2
Same with P2
Same with P2
0.0803
0.0986
1694.9
1697.3
2.4
0.30
(df=2)
Model
Full Model setting for treatment and placebo slopes
Reducing Treatment Effect
Placebo Slope
(1/day)
Treatment
Slope
(1/day)
Full model Objective Function Value
Reduced Model Objective Function
Value
P-value of LRT for treatment Effect
(df)
Initial Pharmacometric Model (P1)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1282.0
61.2
4.9E-14
(df=2)
Second Pharmacometric Model (P2)
Unique slopes
Unique IIVs
0.0792
0.09841220.81223.12.30.32(df=2)Initial Statistical Model (S1)Unique slopesNo IIV0.07980.09851697.51698.40.90.35(df=1)Second Statistical Model (S2)Unique slopesShared IIV0.08000.09871696.51697.30.80.38(df=1)SAS Matched Model for P1Same with P1Same with P10.08030.09861694.91756.261.34.9E-14(df=2)SAS Matched Model for P2Same with P2Same with P20.08030.09861694.91697.32.40.30(df=2)
Slide1515
Summary of the Comparisons
Model
Full Model setting for treatment and placebo slopes
Reducing Treatment Effect
Placebo Slope
(1/day)
Treatment
Slope
(1/day)
Full model Objective Function Value
Reduced Model Objective Function
Value
P-value of LRT for treatment Effect
(df)
Initial Pharmacometric Model (P1)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1282.0
61.2
4.9E-14
(df=2)
Second Pharmacometric Model (P2)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1223.1
2.3
0.32
(df=2)
Initial Statistical Model (S1)
Unique slopes
No IIV
0.0798
0.0985
1697.5
1698.4
0.9
0.35
(df=1)
Second Statistical Model (S2)
Unique slopes
Shared IIV
0.0800
0.0987
1696.5
1697.3
0.8
0.38
(df=1)
SAS Matched Model for P1
Same with P1
Same with P1
0.0803
0.0986
1694.9
1756.2
61.3
4.9E-14
(df=2)
SAS Matched Model for P2
Same with P2
Same with P2
0.0803
0.0986
1694.9
1697.3
2.4
0.30
(df=2)
Model
Full Model setting for treatment and placebo slopes
Reducing Treatment Effect
Placebo Slope
(1/day)
Treatment
Slope
(1/day)
Full model Objective Function Value
Reduced Model Objective Function
Value
P-value of LRT for treatment Effect
(df)
Initial Pharmacometric Model (P1)
Unique slopes
Unique IIVs
0.0792
0.0984
1220.8
1282.0
61.2
4.9E-14
(df=2)
Second Pharmacometric Model (P2)
Unique slopes
Unique IIVs
0.0792
0.09841220.81223.12.30.32(df=2)Initial Statistical Model (S1)Unique slopesNo IIV0.07980.09851697.51698.40.90.35(df=1)Second Statistical Model (S2)Unique slopesShared IIV0.08000.09871696.51697.30.80.38(df=1)SAS Matched Model for P1Same with P1Same with P10.08030.09861694.91756.261.34.9E-14(df=2)SAS Matched Model for P2Same with P2Same with P20.08030.09861694.91697.32.40.30(df=2)
Slide1616
Communications
This work illustrates the importance of communicating the model structures and assumptions being evaluated.
Understanding exactly what the other side is doing is the fundamental step in resolving conflicting analytical results.
Detailed communication on multiple levels including terms, parameters, model structures, model estimation method, construction of test statistics, etc. is critical to fully understand the similarities and differences between the two approaches.
The comprehensive comparison and communication facilitated learning and comprehension for pharmacometricians and statisticians.
Slide1717
Acknowledgement
Dr. Robert Bies, UB
Dr.
Alan Breier, IU
Dr.
Michael Francis, IU
Ziheng Cheng, UB
Ziyi Yang, IU