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Resolving Conflicting Results Arising from a Pharmacometric and a Statistical Analysis - PPT Presentation

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

unique model slopes treatment model unique treatment slopes slope placebo pharmacometric statistical full day function sas initial effect objective

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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

Slide2

A 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

Slide3

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

Slide4

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.

Slide5

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

Slide6

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

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.

Slide7

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

t Value

> |t|

slope for placebo

0.08000

0.01746

4.58

<.0001

slope for treatment

0.09872

0.01241

7.95

<.0001

slope for treatment - slope for placebo

0.01873

0.02127

0.88

0.3811

,where TR=1 for treatment group, and TR=0 for placebo group.

Slide8

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.

Slide9

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

Slide10

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

0.0803

0.0986

1694.9

1756.2

61.3

4.9E-14

(df=2)

SAS Matched Model for 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)

Slide11

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

0.0803

0.0986

1694.9

1756.2

61.3

4.9E-14

(df=2)

SAS Matched Model for 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

Slide12

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

0.0803

0.0986

1694.9

1756.2

61.3

4.9E-14

(df=2)

SAS Matched Model for 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

Slide13

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

0.0803

0.0986

1694.9

1756.2

61.3

4.9E-14

(df=2)

SAS Matched Model for 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

Slide14

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

0.0803

0.0986

1694.9

1756.2

61.3

4.9E-14

(df=2)

SAS Matched Model for 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

Slide15

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

0.0803

0.0986

1694.9

1756.2

61.3

4.9E-14

(df=2)

SAS Matched Model for 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

Slide16

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.

Slide17

Acknowledgement

Dr. Robert Bies, UB

Dr.

Alan Breier, IU

Dr.

Michael Francis, IU

Ziheng Cheng, UB

Ziyi Yang, IU