[PPT] - Group Sequential Clinical Trial Designs for Normally Distributed PowerPoint Presentation

SLIDE 1

Introduction Group Sequential Design Theory Commands Discussion

Group Sequential Clinical Trial Designs for Normally Distributed Outcome Variables

Michael Grayling James Wason Adrian Mander

Hub for Trials Methodology Research MRC 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

SLIDE 2

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

SLIDE 3

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

SLIDE 4

Introduction Group Sequential Design Theory Commands Discussion

Randomised Controlled Trial Design

Choose a sample size that provides some level of statistical power 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

SLIDE 5

Introduction Group Sequential Design Theory Commands Discussion

Randomised Controlled Trial Design

Choose a sample size that provides some level of statistical power 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

SLIDE 6

Introduction Group Sequential Design Theory Commands Discussion

Randomised Controlled Trial Design

Choose a sample size that provides some level of statistical power 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

SLIDE 7

Introduction Group Sequential Design Theory Commands Discussion

Randomised Controlled Trial Design

Choose a sample size that provides some level of statistical power 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

SLIDE 8

Introduction Group Sequential Design Theory Commands Discussion

Randomised Controlled Trial Design

Choose a sample size that provides some level of statistical power 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

SLIDE 9

Introduction Group Sequential Design Theory Commands Discussion

Randomised Controlled Trial Design

Choose a sample size that provides some level of statistical power 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

SLIDE 10

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

SLIDE 11

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

SLIDE 12

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

SLIDE 13

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

SLIDE 14

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

SLIDE 15

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

SLIDE 16

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 landmark numbers 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

SLIDE 17

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 landmark numbers 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

SLIDE 18

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 landmark numbers 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

SLIDE 19

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 landmark numbers 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

SLIDE 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 landmark numbers 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

SLIDE 21

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 landmark numbers 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

SLIDE 22

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

SLIDE 23

Introduction Group Sequential Design Theory Commands Discussion

Overview

Focus on the design of a two-arm group sequential trial testing for superiority, with normally distributed outcomes. Assume a maximum of L analysis planned, and that analysis l = 1, . . . , L takes place after n0l = ln and n1l = rln patients evaluated in arms 0 and 1 respectively. Suppose that Ydli ∼ N(µd, σ2

d) 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 of 1 − β when τ = δ > 0.

M. J. Grayling (mjg211@cam.ac.uk)

Group sequential trial designs MRC Biostatistics Unit 8 / 20

SLIDE 24

Introduction Group Sequential Design Theory Commands Discussion

Overview

Focus on the design of a two-arm group sequential trial testing for superiority, with normally distributed outcomes. Assume a maximum of L analysis planned, and that analysis l = 1, . . . , L takes place after n0l = ln and n1l = rln patients evaluated in arms 0 and 1 respectively. Suppose that Ydli ∼ N(µd, σ2

d) 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 of 1 − β when τ = δ > 0.

M. J. Grayling (mjg211@cam.ac.uk)

Group sequential trial designs MRC Biostatistics Unit 8 / 20

SLIDE 25

Introduction Group Sequential Design Theory Commands Discussion

Overview

Focus on the design of a two-arm group sequential trial testing for superiority, with normally distributed outcomes. Assume a maximum of L analysis planned, and that analysis l = 1, . . . , L takes place after n0l = ln and n1l = rln patients evaluated in arms 0 and 1 respectively. Suppose that Ydli ∼ N(µd, σ2

d) 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 of 1 − β when τ = δ > 0.

M. J. Grayling (mjg211@cam.ac.uk)

Group sequential trial designs MRC Biostatistics Unit 8 / 20

SLIDE 26

Introduction Group Sequential Design Theory Commands Discussion

Overview

Focus on the design of a two-arm group sequential trial testing for superiority, with normally distributed outcomes. Assume a maximum of L analysis planned, and that analysis l = 1, . . . , L takes place after n0l = ln and n1l = rln patients evaluated in arms 0 and 1 respectively. Suppose that Ydli ∼ N(µd, σ2

d) 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 of 1 − β when τ = δ > 0.

M. J. Grayling (mjg211@cam.ac.uk)

Group sequential trial designs MRC Biostatistics Unit 8 / 20

SLIDE 27

Introduction Group Sequential Design Theory Commands Discussion

Overview

Focus on the design of a two-arm group sequential trial testing for superiority, with normally distributed outcomes. Assume a maximum of L analysis planned, and that analysis l = 1, . . . , L takes place after n0l = ln and n1l = rln patients evaluated in arms 0 and 1 respectively. Suppose that Ydli ∼ N(µd, σ2

d) 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 of 1 − β when τ = δ > 0.

M. J. Grayling (mjg211@cam.ac.uk)

Group sequential trial designs MRC Biostatistics Unit 8 / 20

SLIDE 28

Introduction Group Sequential Design Theory Commands Discussion

Analysis

To test H0, the following test statistic is used after analysis l = 1, . . . , L Zl =   1 n1l

l

j=1

rn

i=1

Y1jl − 1 n0l

l

j=1

n

i=1

Y0jl   I1/2

l

, Il = σ2 n0l + σ2

1

n1l −1 . Importantly (Z1, . . . , ZL) is multivariate normal with E(Zl) = τI1/2

l

, 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

SLIDE 29

Introduction Group Sequential Design Theory Commands Discussion

Analysis

To test H0, the following test statistic is used after analysis l = 1, . . . , L Zl =   1 n1l

l

j=1

rn

i=1

Y1jl − 1 n0l

l

j=1

n

i=1

Y0jl   I1/2

l

, Il = σ2 n0l + σ2

1

n1l −1 . Importantly (Z1, . . . , ZL) is multivariate normal with E(Zl) = τI1/2

l

, 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

SLIDE 30

Introduction Group Sequential Design Theory Commands Discussion

Analysis

To test H0, the following test statistic is used after analysis l = 1, . . . , L Zl =   1 n1l

l

j=1

rn

i=1

Y1jl − 1 n0l

l

j=1

n

i=1

Y0jl   I1/2

l

, Il = σ2 n0l + σ2

1

n1l −1 . Importantly (Z1, . . . , ZL) is multivariate normal with E(Zl) = τI1/2

l

, 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

SLIDE 31

Introduction Group Sequential Design Theory Commands Discussion

Stopping Rules

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

If Zl ≥ el stop and reject H0. If Zl < fl stop and accept H0.

therwise 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

SLIDE 32

Introduction Group Sequential Design Theory Commands Discussion

Stopping Rules

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

If Zl ≥ el stop and reject H0. If Zl < fl stop and accept H0.

therwise 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

SLIDE 33

Introduction Group Sequential Design Theory Commands Discussion

Stopping Rules

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

If Zl ≥ el stop and reject H0. If Zl < fl stop and accept H0.

therwise 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

SLIDE 34

Introduction Group Sequential Design Theory Commands Discussion

Stopping Rules

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

If Zl ≥ el stop and reject H0. If Zl < fl stop and accept H0.

therwise 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

SLIDE 35

Introduction Group Sequential Design Theory Commands Discussion

Stopping Rules

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

If Zl ≥ el stop and reject H0. If Zl < fl stop and accept H0.

therwise 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

SLIDE 36

Introduction Group Sequential Design Theory Commands Discussion

Stopping Rules

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

If Zl ≥ el stop and reject H0. If Zl < fl stop and accept H0.

therwise 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

SLIDE 37

Introduction Group Sequential Design Theory Commands Discussion

Stopping Rules

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

If Zl ≥ el stop and reject H0. If Zl < fl stop and accept H0.

therwise 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

SLIDE 38

Introduction Group Sequential Design Theory Commands Discussion

Boundaries

Functional form assumed, then search to find group size and exact values for correct operating characteristics. For example el = Ce(l/L)Ω−1/2, fl = δI1/2

l

− Cf(l/L)Ω−1/2. Then take I1/2

L

= (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

SLIDE 39

Introduction Group Sequential Design Theory Commands Discussion

Boundaries

Functional form assumed, then search to find group size and exact values for correct operating characteristics. For example el = Ce(l/L)Ω−1/2, fl = δI1/2

l

− Cf(l/L)Ω−1/2. Then take I1/2

L

= (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

SLIDE 40

Introduction Group Sequential Design Theory Commands Discussion

Boundaries

Functional form assumed, then search to find group size and exact values for correct operating characteristics. For example el = Ce(l/L)Ω−1/2, fl = δI1/2

l

− Cf(l/L)Ω−1/2. Then take I1/2

L

= (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

SLIDE 41

Introduction Group Sequential Design Theory Commands Discussion

Boundaries

Functional form assumed, then search to find group size and exact values for correct operating characteristics. For example el = Ce(l/L)Ω−1/2, fl = δI1/2

l

− Cf(l/L)Ω−1/2. Then take I1/2

L

= (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

SLIDE 42

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

SLIDE 43

Introduction Group Sequential Design Theory Commands Discussion

Commands

Six commands in total. Four for two-sided tests, and two for

ne-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

SLIDE 44

Introduction Group Sequential Design Theory Commands Discussion

Commands

Six commands in total. Four for two-sided tests, and two for

ne-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

SLIDE 45

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

SLIDE 46

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

SLIDE 47

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

SLIDE 48

Introduction Group Sequential Design Theory Commands Discussion

Example: Comparison

300 400 500 600 700 800 E(N|τ) .2 .4 .6 .8 1 P(Reject H0|τ)

1
.5

.5 1 τ P(Reject H0|τ) E(N|τ)

Power family with Ω = -0.25

300 400 500 600 700 800 E(N|τ) .2 .4 .6 .8 1 P(Reject H0|τ)

1
.5

.5 1 τ P(Reject H0|τ) E(N|τ)

Power family with Ω = 0

300 400 500 600 700 800 E(N|τ) .2 .4 .6 .8 1 P(Reject H0|τ)

1
.5

.5 1 τ P(Reject H0|τ) E(N|τ)

Power family with Ω = 0.25

300 400 500 600 700 800 E(N|τ) .2 .4 .6 .8 1 P(Reject H0|τ)

1
.5

.5 1 τ 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

SLIDE 49

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

SLIDE 50

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 also be a good step.

M. J. Grayling (mjg211@cam.ac.uk)

Group sequential trial designs MRC Biostatistics Unit 19 / 20

SLIDE 51

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 also be a good step.

M. J. Grayling (mjg211@cam.ac.uk)

Group sequential trial designs MRC Biostatistics Unit 19 / 20

SLIDE 52

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 also be a good step.

M. J. Grayling (mjg211@cam.ac.uk)

Group sequential trial designs MRC Biostatistics Unit 19 / 20

SLIDE 53

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 also be a good step.

M. J. Grayling (mjg211@cam.ac.uk)

Group sequential trial designs MRC Biostatistics Unit 19 / 20

SLIDE 54

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 also be a good step.

M. J. Grayling (mjg211@cam.ac.uk)

Group sequential trial designs MRC Biostatistics Unit 19 / 20

SLIDE 55

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-sided and two-sided hypothesis testing with provision for early stopping in favor

f 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