Introduction Group Sequential Design Theory Commands Discussion

Group Sequential Clinical Trial Designs forNormally Distributed Outcome Variables

Michael Grayling James Wason Adrian Mander

Hub for Trials Methodology ResearchMRC Biostatistics Unit

Cambridge, UK

Stata UK Users Group Meeting, September 2017

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 1 / 20

Introduction Group Sequential Design Theory Commands Discussion

Outline

1 Introduction

2 Group Sequential Design Theory

3 Commands

4 Discussion

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 2 / 20

Introduction Group Sequential Design Theory Commands Discussion

Outline

1 Introduction

2 Group Sequential Design Theory

3 Commands

4 Discussion

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 3 / 20

Introduction Group Sequential Design Theory Commands Discussion

Randomised Controlled Trial Design

Choose a sample size that provides some level of statisticalpower for a target treatment effect.

Recruit the number of patients required.

Perform an analysis after all patients have been assessed.

Design, analysis, and reporting of such trials well characterised.

Incredibly effective way to assess the efficacy of a treatment.

But is this the best we can do?

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 4 / 20

Introduction Group Sequential Design Theory Commands Discussion

Randomised Controlled Trial Design

Choose a sample size that provides some level of statisticalpower for a target treatment effect.

Recruit the number of patients required.

Perform an analysis after all patients have been assessed.

Design, analysis, and reporting of such trials well characterised.

Incredibly effective way to assess the efficacy of a treatment.

But is this the best we can do?

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 4 / 20

Introduction Group Sequential Design Theory Commands Discussion

Randomised Controlled Trial Design

Choose a sample size that provides some level of statisticalpower for a target treatment effect.

Recruit the number of patients required.

Perform an analysis after all patients have been assessed.

Design, analysis, and reporting of such trials well characterised.

Incredibly effective way to assess the efficacy of a treatment.

But is this the best we can do?

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 4 / 20

Introduction Group Sequential Design Theory Commands Discussion

Randomised Controlled Trial Design

Choose a sample size that provides some level of statisticalpower for a target treatment effect.

Recruit the number of patients required.

Perform an analysis after all patients have been assessed.

Design, analysis, and reporting of such trials well characterised.

Incredibly effective way to assess the efficacy of a treatment.

But is this the best we can do?

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 4 / 20

Introduction Group Sequential Design Theory Commands Discussion

Randomised Controlled Trial Design

Choose a sample size that provides some level of statisticalpower for a target treatment effect.

Recruit the number of patients required.

Perform an analysis after all patients have been assessed.

Design, analysis, and reporting of such trials well characterised.

Incredibly effective way to assess the efficacy of a treatment.

But is this the best we can do?

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 4 / 20

Introduction Group Sequential Design Theory Commands Discussion

Randomised Controlled Trial Design

Choose a sample size that provides some level of statisticalpower for a target treatment effect.

Recruit the number of patients required.

Perform an analysis after all patients have been assessed.

Design, analysis, and reporting of such trials well characterised.

Incredibly effective way to assess the efficacy of a treatment.

But is this the best we can do?

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 4 / 20

Introduction Group Sequential Design Theory Commands Discussion

Adaptive Trial Design

Trials gather a lot of data during their progress!

What if we are unsure about the sample size to use?

What if the new treatment is harmful?

What if the new treatment works only in a subset of patients?

This is where adaptive trial design comes in.

Here discuss group sequential trials.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 5 / 20

Introduction Group Sequential Design Theory Commands Discussion

Adaptive Trial Design

Trials gather a lot of data during their progress!

What if we are unsure about the sample size to use?

What if the new treatment is harmful?

What if the new treatment works only in a subset of patients?

This is where adaptive trial design comes in.

Here discuss group sequential trials.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 5 / 20

Introduction Group Sequential Design Theory Commands Discussion

Adaptive Trial Design

Trials gather a lot of data during their progress!

What if we are unsure about the sample size to use?

What if the new treatment is harmful?

What if the new treatment works only in a subset of patients?

This is where adaptive trial design comes in.

Here discuss group sequential trials.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 5 / 20

Introduction Group Sequential Design Theory Commands Discussion

Adaptive Trial Design

Trials gather a lot of data during their progress!

What if we are unsure about the sample size to use?

What if the new treatment is harmful?

What if the new treatment works only in a subset of patients?

This is where adaptive trial design comes in.

Here discuss group sequential trials.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 5 / 20

Introduction Group Sequential Design Theory Commands Discussion

Adaptive Trial Design

Trials gather a lot of data during their progress!

What if we are unsure about the sample size to use?

What if the new treatment is harmful?

What if the new treatment works only in a subset of patients?

This is where adaptive trial design comes in.

Here discuss group sequential trials.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 5 / 20

Introduction Group Sequential Design Theory Commands Discussion

Adaptive Trial Design

Trials gather a lot of data during their progress!

What if we are unsure about the sample size to use?

What if the new treatment is harmful?

What if the new treatment works only in a subset of patients?

This is where adaptive trial design comes in.

Here discuss group sequential trials.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 5 / 20

Introduction Group Sequential Design Theory Commands Discussion

Group Sequential Trials

Can bring substantial administrative, ethical, monetary advan-tages.

Origins in industrial sampling and Wald’s SPRT.

First proposals were fully sequential, but this proved to be im-practical.

Idea therefore is to conduct analyses after particular landmarknumbers of patients recruited.

Trial may be stopped early to accept or reject null hypotheses.

Expected sample size typically reduced.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 6 / 20

Introduction Group Sequential Design Theory Commands Discussion

Group Sequential Trials

Can bring substantial administrative, ethical, monetary advan-tages.

Origins in industrial sampling and Wald’s SPRT.

First proposals were fully sequential, but this proved to be im-practical.

Idea therefore is to conduct analyses after particular landmarknumbers of patients recruited.

Trial may be stopped early to accept or reject null hypotheses.

Expected sample size typically reduced.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 6 / 20

Introduction Group Sequential Design Theory Commands Discussion

Group Sequential Trials

Can bring substantial administrative, ethical, monetary advan-tages.

Origins in industrial sampling and Wald’s SPRT.

First proposals were fully sequential, but this proved to be im-practical.

Idea therefore is to conduct analyses after particular landmarknumbers of patients recruited.

Trial may be stopped early to accept or reject null hypotheses.

Expected sample size typically reduced.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 6 / 20

Introduction Group Sequential Design Theory Commands Discussion

Group Sequential Trials

Can bring substantial administrative, ethical, monetary advan-tages.

Origins in industrial sampling and Wald’s SPRT.

First proposals were fully sequential, but this proved to be im-practical.

Idea therefore is to conduct analyses after particular landmarknumbers of patients recruited.

Trial may be stopped early to accept or reject null hypotheses.

Expected sample size typically reduced.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 6 / 20

Introduction Group Sequential Design Theory Commands Discussion

Group Sequential Trials

Can bring substantial administrative, ethical, monetary advan-tages.

Origins in industrial sampling and Wald’s SPRT.

First proposals were fully sequential, but this proved to be im-practical.

Idea therefore is to conduct analyses after particular landmarknumbers of patients recruited.

Trial may be stopped early to accept or reject null hypotheses.

Expected sample size typically reduced.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 6 / 20

Introduction Group Sequential Design Theory Commands Discussion

Group Sequential Trials

Can bring substantial administrative, ethical, monetary advan-tages.

Origins in industrial sampling and Wald’s SPRT.

First proposals were fully sequential, but this proved to be im-practical.

Idea therefore is to conduct analyses after particular landmarknumbers of patients recruited.

Trial may be stopped early to accept or reject null hypotheses.

Expected sample size typically reduced.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 6 / 20

Introduction Group Sequential Design Theory Commands Discussion

Outline

1 Introduction

2 Group Sequential Design Theory

3 Commands

4 Discussion

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 7 / 20

Introduction Group Sequential Design Theory Commands Discussion

Overview

Focus on the design of a two-arm group sequential trial testingfor superiority, with normally distributed outcomes.

Assume a maximum of L analysis planned, and that analysisl = 1, . . . , L takes place after n0l = ln and n1l = rln patientsevaluated in arms 0 and 1 respectively.

Suppose that Ydli ∼ N(µd, σ2d) for d = 0, 1.

Defining τ = µ1 − µ0, interest is in testing

H0 : τ ≤ 0, H1 : τ > 0.

Want overall type-I error-rate when τ = 0 of α, and power of1− β when τ = δ > 0.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 8 / 20

Introduction Group Sequential Design Theory Commands Discussion

Overview

Focus on the design of a two-arm group sequential trial testingfor superiority, with normally distributed outcomes.

Assume a maximum of L analysis planned, and that analysisl = 1, . . . , L takes place after n0l = ln and n1l = rln patientsevaluated in arms 0 and 1 respectively.

Suppose that Ydli ∼ N(µd, σ2d) for d = 0, 1.

Defining τ = µ1 − µ0, interest is in testing

H0 : τ ≤ 0, H1 : τ > 0.

Want overall type-I error-rate when τ = 0 of α, and power of1− β when τ = δ > 0.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 8 / 20

Introduction Group Sequential Design Theory Commands Discussion

Overview

Focus on the design of a two-arm group sequential trial testingfor superiority, with normally distributed outcomes.

Assume a maximum of L analysis planned, and that analysisl = 1, . . . , L takes place after n0l = ln and n1l = rln patientsevaluated in arms 0 and 1 respectively.

Suppose that Ydli ∼ N(µd, σ2d) for d = 0, 1.

Defining τ = µ1 − µ0, interest is in testing

H0 : τ ≤ 0, H1 : τ > 0.

Want overall type-I error-rate when τ = 0 of α, and power of1− β when τ = δ > 0.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 8 / 20

Introduction Group Sequential Design Theory Commands Discussion

Overview

Focus on the design of a two-arm group sequential trial testingfor superiority, with normally distributed outcomes.

Assume a maximum of L analysis planned, and that analysisl = 1, . . . , L takes place after n0l = ln and n1l = rln patientsevaluated in arms 0 and 1 respectively.

Suppose that Ydli ∼ N(µd, σ2d) for d = 0, 1.

Defining τ = µ1 − µ0, interest is in testing

H0 : τ ≤ 0, H1 : τ > 0.

Want overall type-I error-rate when τ = 0 of α, and power of1− β when τ = δ > 0.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 8 / 20

Introduction Group Sequential Design Theory Commands Discussion

Overview

Focus on the design of a two-arm group sequential trial testingfor superiority, with normally distributed outcomes.

Assume a maximum of L analysis planned, and that analysisl = 1, . . . , L takes place after n0l = ln and n1l = rln patientsevaluated in arms 0 and 1 respectively.

Suppose that Ydli ∼ N(µd, σ2d) for d = 0, 1.

Defining τ = µ1 − µ0, interest is in testing

H0 : τ ≤ 0, H1 : τ > 0.

Want overall type-I error-rate when τ = 0 of α, and power of1− β when τ = δ > 0.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 8 / 20

Introduction Group Sequential Design Theory Commands Discussion

Analysis

To test H0, the following test statistic is used after analysisl = 1, . . . , L

Zl =

1

n1l

l∑j=1

rn∑i=1

Y1jl −1

n0l

l∑j=1

n∑i=1

Y0jl

I1/2l ,

Il =

(σ2

0

n0l+σ2

1

n1l

)−1

.

Importantly (Z1, . . . , ZL) is multivariate normal with

E(Zl) = τI1/2l , l = 1, . . . , L,

Cov(Zl, Zk) = (Il/Ik)1/2, 1 ≤ l ≤ k ≤ L.

Means operating characteristics can be calculated analytically...

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 9 / 20

Introduction Group Sequential Design Theory Commands Discussion

Analysis

To test H0, the following test statistic is used after analysisl = 1, . . . , L

Zl =

1

n1l

l∑j=1

rn∑i=1

Y1jl −1

n0l

l∑j=1

n∑i=1

Y0jl

I1/2l ,

Il =

(σ2

0

n0l+σ2

1

n1l

)−1

.

Importantly (Z1, . . . , ZL) is multivariate normal with

E(Zl) = τI1/2l , l = 1, . . . , L,

Cov(Zl, Zk) = (Il/Ik)1/2, 1 ≤ l ≤ k ≤ L.

Means operating characteristics can be calculated analytically...

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 9 / 20

Introduction Group Sequential Design Theory Commands Discussion

Analysis

To test H0, the following test statistic is used after analysisl = 1, . . . , L

Zl =

1

n1l

l∑j=1

rn∑i=1

Y1jl −1

n0l

l∑j=1

n∑i=1

Y0jl

I1/2l ,

Il =

(σ2

0

n0l+σ2

1

n1l

)−1

.

Importantly (Z1, . . . , ZL) is multivariate normal with

E(Zl) = τI1/2l , l = 1, . . . , L,

Cov(Zl, Zk) = (Il/Ik)1/2, 1 ≤ l ≤ k ≤ L.

Means operating characteristics can be calculated analytically...

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 9 / 20

Introduction Group Sequential Design Theory Commands Discussion

Stopping Rules

...given choices for f1, . . . , fL and e1, . . . , eL. Use these in thefollowing stopping rules at analysis l = 1, . . . , L

If Zl ≥ el stop and reject H0.If Zl < fl stop and accept H0.otherwise continue to stage l + 1.

Then

P(Reject H0 | τ) =L∑

l=1

P(Reject H0 at stage l | τ),

= P(Z1 ≥ e1 | τ)

+L∑

l=2

P(f1 ≤ Z1 < e1, . . . , fl−1 ≤ Zl−1 < el−1, Zl ≥ el | τ).

Similar formulae for E(N | τ).Evaluate these formulae using mvnormal mata().

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 10 / 20

Introduction Group Sequential Design Theory Commands Discussion

Stopping Rules

...given choices for f1, . . . , fL and e1, . . . , eL. Use these in thefollowing stopping rules at analysis l = 1, . . . , L

If Zl ≥ el stop and reject H0.If Zl < fl stop and accept H0.otherwise continue to stage l + 1.

Then

P(Reject H0 | τ) =L∑

l=1

P(Reject H0 at stage l | τ),

= P(Z1 ≥ e1 | τ)

+L∑

l=2

P(f1 ≤ Z1 < e1, . . . , fl−1 ≤ Zl−1 < el−1, Zl ≥ el | τ).

Similar formulae for E(N | τ).Evaluate these formulae using mvnormal mata().

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 10 / 20

Introduction Group Sequential Design Theory Commands Discussion

Stopping Rules

...given choices for f1, . . . , fL and e1, . . . , eL. Use these in thefollowing stopping rules at analysis l = 1, . . . , L

If Zl ≥ el stop and reject H0.If Zl < fl stop and accept H0.otherwise continue to stage l + 1.

Then

P(Reject H0 | τ) =L∑

l=1

P(Reject H0 at stage l | τ),

= P(Z1 ≥ e1 | τ)

+L∑

l=2

P(f1 ≤ Z1 < e1, . . . , fl−1 ≤ Zl−1 < el−1, Zl ≥ el | τ).

Similar formulae for E(N | τ).Evaluate these formulae using mvnormal mata().

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 10 / 20

Introduction Group Sequential Design Theory Commands Discussion

Stopping Rules

...given choices for f1, . . . , fL and e1, . . . , eL. Use these in thefollowing stopping rules at analysis l = 1, . . . , L

If Zl ≥ el stop and reject H0.If Zl < fl stop and accept H0.otherwise continue to stage l + 1.

Then

P(Reject H0 | τ) =L∑

l=1

P(Reject H0 at stage l | τ),

= P(Z1 ≥ e1 | τ)

+L∑

l=2

P(f1 ≤ Z1 < e1, . . . , fl−1 ≤ Zl−1 < el−1, Zl ≥ el | τ).

Similar formulae for E(N | τ).Evaluate these formulae using mvnormal mata().

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 10 / 20

Introduction Group Sequential Design Theory Commands Discussion

Stopping Rules

...given choices for f1, . . . , fL and e1, . . . , eL. Use these in thefollowing stopping rules at analysis l = 1, . . . , L

If Zl ≥ el stop and reject H0.If Zl < fl stop and accept H0.otherwise continue to stage l + 1.

Then

P(Reject H0 | τ) =L∑

l=1

P(Reject H0 at stage l | τ),

= P(Z1 ≥ e1 | τ)

+L∑

l=2

P(f1 ≤ Z1 < e1, . . . , fl−1 ≤ Zl−1 < el−1, Zl ≥ el | τ).

Similar formulae for E(N | τ).Evaluate these formulae using mvnormal mata().

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 10 / 20

Introduction Group Sequential Design Theory Commands Discussion

Stopping Rules

...given choices for f1, . . . , fL and e1, . . . , eL. Use these in thefollowing stopping rules at analysis l = 1, . . . , L

If Zl ≥ el stop and reject H0.If Zl < fl stop and accept H0.otherwise continue to stage l + 1.

Then

P(Reject H0 | τ) =L∑

l=1

P(Reject H0 at stage l | τ),

= P(Z1 ≥ e1 | τ)

+L∑

l=2

P(f1 ≤ Z1 < e1, . . . , fl−1 ≤ Zl−1 < el−1, Zl ≥ el | τ).

Similar formulae for E(N | τ).Evaluate these formulae using mvnormal mata().

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 10 / 20

Introduction Group Sequential Design Theory Commands Discussion

Stopping Rules

...given choices for f1, . . . , fL and e1, . . . , eL. Use these in thefollowing stopping rules at analysis l = 1, . . . , L

If Zl ≥ el stop and reject H0.If Zl < fl stop and accept H0.otherwise continue to stage l + 1.

Then

P(Reject H0 | τ) =L∑

l=1

P(Reject H0 at stage l | τ),

= P(Z1 ≥ e1 | τ)

+L∑

l=2

P(f1 ≤ Z1 < e1, . . . , fl−1 ≤ Zl−1 < el−1, Zl ≥ el | τ).

Similar formulae for E(N | τ).Evaluate these formulae using mvnormal mata().

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 10 / 20

Introduction Group Sequential Design Theory Commands Discussion

Boundaries

Functional form assumed, then search to find group size andexact values for correct operating characteristics.

For example

el = Ce(l/L)Ω−1/2,

fl = δI1/2l − Cf (l/L)Ω−1/2.

Then take I1/2L = (Ce + Cf )/δ, to ensure eL = fL.

Search over Ce and Cf using optimize().

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 11 / 20

Introduction Group Sequential Design Theory Commands Discussion

Boundaries

Functional form assumed, then search to find group size andexact values for correct operating characteristics.

For example

el = Ce(l/L)Ω−1/2,

fl = δI1/2l − Cf (l/L)Ω−1/2.

Then take I1/2L = (Ce + Cf )/δ, to ensure eL = fL.

Search over Ce and Cf using optimize().

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 11 / 20

Introduction Group Sequential Design Theory Commands Discussion

Boundaries

Functional form assumed, then search to find group size andexact values for correct operating characteristics.

For example

el = Ce(l/L)Ω−1/2,

fl = δI1/2l − Cf (l/L)Ω−1/2.

Then take I1/2L = (Ce + Cf )/δ, to ensure eL = fL.

Search over Ce and Cf using optimize().

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 11 / 20

Introduction Group Sequential Design Theory Commands Discussion

Boundaries

Functional form assumed, then search to find group size andexact values for correct operating characteristics.

For example

el = Ce(l/L)Ω−1/2,

fl = δI1/2l − Cf (l/L)Ω−1/2.

Then take I1/2L = (Ce + Cf )/δ, to ensure eL = fL.

Search over Ce and Cf using optimize().

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 11 / 20

Introduction Group Sequential Design Theory Commands Discussion

Outline

1 Introduction

2 Group Sequential Design Theory

3 Commands

4 Discussion

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 12 / 20

Introduction Group Sequential Design Theory Commands Discussion

Commands

Six commands in total. Four for two-sided tests, and two forone-sided tests as discussed here.

One-sided tests as follows

powerFamily, [l(integer 3) delta(real 0.2)

alpha(real 0.05) beta(real 0.2)

sigma(numlist) ratio(real 1) Omega(real 0.5)

performance *]

triangular, [l(integer 3) delta(real 0.2) alpha(real 0.05)

beta(real 0.2) sigma(numlist) ratio(real 1)

performance *]

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 13 / 20

Introduction Group Sequential Design Theory Commands Discussion

Commands

Six commands in total. Four for two-sided tests, and two forone-sided tests as discussed here.

One-sided tests as follows

powerFamily, [l(integer 3) delta(real 0.2)

alpha(real 0.05) beta(real 0.2)

sigma(numlist) ratio(real 1) Omega(real 0.5)

performance *]

triangular, [l(integer 3) delta(real 0.2) alpha(real 0.05)

beta(real 0.2) sigma(numlist) ratio(real 1)

performance *]

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 13 / 20

Introduction Group Sequential Design Theory Commands Discussion

Example Output

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 14 / 20

Introduction Group Sequential Design Theory Commands Discussion

Example Output

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 15 / 20

Introduction Group Sequential Design Theory Commands Discussion

Example: Comparison

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 16 / 20

Introduction Group Sequential Design Theory Commands Discussion

Example: Comparison

300

400

500

600

700

800

E(N

|τ)

0.2

.4.6

.81

P(R

ejec

t H0|τ

)

-1 -.5 0 .5 1τ

P(Reject H0|τ) E(N|τ)

Power family with Ω = -0.25

300

400

500

600

700

800

E(N

|τ)

0.2

.4.6

.81

P(R

ejec

t H0|τ

)

-1 -.5 0 .5 1τ

P(Reject H0|τ) E(N|τ)

Power family with Ω = 0

300

400

500

600

700

800

E(N

|τ)

0.2

.4.6

.81

P(R

ejec

t H0|τ

)

-1 -.5 0 .5 1τ

P(Reject H0|τ) E(N|τ)

Power family with Ω = 0.25

300

400

500

600

700

800

E(N

|τ)

0.2

.4.6

.81

P(R

ejec

t H0|τ

)

-1 -.5 0 .5 1τ

P(Reject H0|τ) E(N|τ)

Triangular test

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 17 / 20

Introduction Group Sequential Design Theory Commands Discussion

Outline

1 Introduction

2 Group Sequential Design Theory

3 Commands

4 Discussion

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 18 / 20

Introduction Group Sequential Design Theory Commands Discussion

Discussion

Group sequential designs provide gains in efficiency, easy to find(at least in this case).

Key commands working.

Only considered design so far.

Only considered two-arm; multi-arm multi-stage designs of in-creasing interest.

An option to use simulation instead of integration would alsobe a good step.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 19 / 20

Introduction Group Sequential Design Theory Commands Discussion

Discussion

Group sequential designs provide gains in efficiency, easy to find(at least in this case).

Key commands working.

Only considered design so far.

Only considered two-arm; multi-arm multi-stage designs of in-creasing interest.

An option to use simulation instead of integration would alsobe a good step.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 19 / 20

Introduction Group Sequential Design Theory Commands Discussion

Discussion

Group sequential designs provide gains in efficiency, easy to find(at least in this case).

Key commands working.

Only considered design so far.

Only considered two-arm; multi-arm multi-stage designs of in-creasing interest.

An option to use simulation instead of integration would alsobe a good step.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 19 / 20

Introduction Group Sequential Design Theory Commands Discussion

Discussion

Group sequential designs provide gains in efficiency, easy to find(at least in this case).

Key commands working.

Only considered design so far.

Only considered two-arm; multi-arm multi-stage designs of in-creasing interest.

An option to use simulation instead of integration would alsobe a good step.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 19 / 20

Introduction Group Sequential Design Theory Commands Discussion

Discussion

Group sequential designs provide gains in efficiency, easy to find(at least in this case).

Key commands working.

Only considered design so far.

Only considered two-arm; multi-arm multi-stage designs of in-creasing interest.

An option to use simulation instead of integration would alsobe a good step.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 19 / 20

Introduction Group Sequential Design Theory Commands Discussion

References

1 Jennison C, Turnbull BW (2000) Group Sequential Methods with Applica-tions to Clinical Trials. Boca Raton, FL: Chapman & Hall/CRC.

2 Pampallona S, Tsiatis AA (1994) Group sequential designs for one-sidedand two-sided hypothesis testing with provision for early stopping in favorof the null hypothesis. Journal of Statistical Planning and Inference 42(1-2):19-35.

3 Whitehead J (1997) The Design and Analysis of Sequential Clinical Trials.Revised 2nd ed. Chichester: John Wiley & Sons.

M. J. Grayling (mjg211@cam.ac.uk) Group sequential trial designs MRC Biostatistics Unit 20 / 20