# Presentation: 290372

## SAMPLE SIZE CONSIDERATIONSIN TrialNet:POPPII -1 and Other StudiesJohn M. LachinTrialNet Coordinating CenterThe Biostatistics CenterThe George Washington Universisy

**SAMPLE SIZE CONSIDERATIONS****IN TrialNet:*****POPPII -1 and Other Studies*****John M. Lachin****TrialNet Coordinating Center****The Biostatistics Center****The George Washington Universisy**

## TrialNet STUDIES

**BETA CELL MASS**

**DIABETES**

**“****PRE”-DIABETES**

**GENETIC**
**PREDISPOSITION**

**INSULITIS**
**BETA CELL INJURY**

***PREVENTION ***
***OF T1DM    ***

***PRESERVATION OF***
***BETA CELL FUNCTION***

**TrialNet STUDIES**

***PREVENTION OF AUTOIMMUNITY***

## TrialNet Objectives

***Preserve Insulin Secretory Capacity (Beta Cell Function) in Newly Diagnosed T1DM***
***Prevent Diabetes Onset in Auto-immune Positive First Degree Relatives***
***Understand the Pathophysiology of Beta Cell Destruction***

***TrialNet***

## TrialNet STRATEGY

***Evaluate new therapies in new onset T1DM***
**	****Preliminary assessment of safety**
**	****Assessment of effectiveness in preservation of Beta cell function (C-peptide)**
**	****If satisfactory benefit:risk then evaluate effectiveness for prevention of T1DM**

***TrialNet***

## TrialNet DILEMMA

***Preservation of Beta cell function***
**	****No physiologic (biochemical, immunologic) marker for biologic effects on mechanisms leading to Beta cell destruction**
**	****	****Proof of concept can not be established at Phase II**
***Prevention of T1DM***
**	****No physiologic marker for biological effects on mechanisms leading to Beta cell destruction and onset of T1DM**
***Phase II studies must use a clinical effect as the outcome***

***TrialNet***

## C-PEPTIDE AS A MEASURE OF BETA CELL FUNCTION

***A direct measure of insulin secretory capacity***
**	****Co-secreted with insulin in equimolar concentrations**
**	****Not rapidly excreted:**
**	****	****30 min plasma half-life vs 4 min for insulin**
***Measurable in response to a glucose stimulus***
**	****Mixed Meal Tolerance Test (MMTT)**
**	****	****Liquid “meal” (Boost) following overnight fast**
**	****	****Timed collections over 2 or 4 hours**
**	****	****Various summary measures: peak, AUC, mean**

***TrialNet***

## CLINICAL BENEFITS OF PRESERVATION OF BETA CELL FUNCTION (C-PEPTIDE )

***DIABETES CONTROL AND COMPLICATIONS TRIAL***
**	****Measurable C-peptide present 1 - 15 years after onset**
**	****Higher C-peptide levels associated with**
**	****	****Improved glucose control**
**	****	****Reduced risk of complications, after adjusting for**
**	****	****	****level of control**
**	****	****Reduced risk of hypoglycemia (coma/siezure)**

***TrialNet***

## C-peptide As an Outcome Measure

***Timed Collections***
**	****2 hour test: 0, 30, 60, 90, 120 min**
***Summary Measures***
**	****Peak post-stimulus – nmol/l**
**	****Area Under the Curve (AUC) – trapezoidal rule**

| AUC = | 30(X0 + X30)/2 + 30(X30 + X60)/2 + 30(X60 + X90)/2 + 30(X90 + X120)/2 |
| --- | --- |

***TrialNet***

## C-peptide As an Outcome Measure

***Timed Collections***
**	****2 hour test: 0, 30, 60, 90, 120 min**
***Summary Measures***
**	****Peak post-stimulus – nmol/l**
**	****Area Under the Curve (AUC) – trapezoidal rule**

| AUC = | 30(X0 + X30)/2 + 30(X30 + X60)/2 + 30(X60 + X90)/2 + 30(X90 + X120)/2 |
| --- | --- |

|         = | 15(X0 + 2X30 + 2X60 + 2X90 + X120) |
| --- | --- |

***TrialNet***

## C-peptide As an Outcome Measure

***Timed Collections***
**	****2 hour test: 0, 30, 60, 90, 120 min**
***Summary Measures***
**	****Peak post-stimulus – nmol/l**
**	****Area Under the Curve (AUC) – trapezoidal rule**

| Weighted Mean = | AUC | = | X0 + 2X30 + 2X60 + 2X90 + X120 | (nmol/l) |
| --- | --- | --- | --- | --- |
|  | 120  |  | 8 |  |

| AUC = | 30(X0 + X30)/2 + 30(X30 + X60)/2 + 30(X60 + X90)/2 + 30(X90 + X120)/2 |
| --- | --- |

|          = | Weighted Mean * 120 (120 nmol/l minutes)  |
| --- | --- |

|         = | 15(X0 + 2X30 + 2X60 + 2X90 + X120) |
| --- | --- |

***TrialNet***

## C-peptide AUC and Weighted MeanA Typical Subject

- 0

- 0.2

- 0.4

- 0.6

- 0.8

- 1

- 0

- 30

- 60

- 90

- 120

**Time in minutes**

**C-peptide (nmol/l)**

***TrialNet***

**Weighted Mean = 0.555 nmol/l**

**C-peptide AUC and Weighted Mean*****A Typical Subject***

**AUC = 66.6 (120 nmol/l minutes)**

## C-peptide Analyses

***MMTT Schedule (POPPII-1)***
**	****0, 3, 6, 12, 18, 24 months of treatment**
**	****30, 36, 42, 48 months post-treatment**
***Possible Primary Outcomes***
**	****Means at 1 y, 2 y**
**	****Proportions with preserved C-peptide at 1 y, 2 y**
**	****Longitudinal (repeated measures) analysis**
**	****Hazard rate (risk) of an event over time (survival analysis)**

***TrialNet***

## Evaluation of Outcomes

***Metabolic Outcomes Committee***
**TNCC assembled data set from 9 prior studies with data up to 2 y.**
**Evaluated sample sizes needed for each of these types of analyses**
**40% Effect Size (difference between groups) deemed meaningful**
**	**

***TrialNet***

## C-peptide Skewed DistributionMMTT Peak Values

***Density***

***Peak/Stimulated C-peptide***

**Age < 12 y**

**Age 12 - 17 y**

**Age **_**>**_** 18 y**

**C-peptide Skewed Distribution*****MMTT Peak Values***

##  = 0.05 (two-sided),  = 0.15, Power = 0.85
 = 40% difference between groups (means, hazards, etc.)
	  Adjusted for age, gender and baseline C-peptide value
Difference in Mean in C-Peptide Between Groups
		Weighted (AUC) Mean: 
			No Exclusions, n = 113 / group
			Age ≥ 12 y, Baseline C-peptide > 0.2 pmol/l, n = 82 / group
Difference in Mean Slope of Change in AUC (or mean) over time
		2 y follow-up with 4 post-tx MMTTs, n = 78 / group
Difference in Hazard Rates
		1 y recruitment, 3 y study, 5% losses per year
			50% reduction in C-peptide from baseline, n = 128 / group
			C-peptide < 0.2 pmol/l, n = 130 / group

**C-peptide Sample Size Calculations**

** ****= 0.05 (two-sided), ********** = 0.15, Power = 0.85**
** ****= 40% difference between groups (means, hazards, etc.)**
**	****  ****Adjusted for age, gender and baseline C-peptide value**
***Difference in Mean in C-Peptide Between Groups***
**	****	****Weighted (AUC) Mean: **
**	****	****	****No Exclusions, *****n***** = 113 / group**
**	****	****	****Age ****≥ 12 y, Baseline C-peptide > 0.2 pmol/l****, *****n***** = 82 / group**
***Difference in Mean Slope of Change in AUC (or mean) over time***
**	****	****2 y follow-up with 4 post-tx MMTTs, *****n***** = 78 / group**
***Difference in Hazard Rates***
***	******	*****1 y recruitment, 3 y study, 5% losses per year**
**	****	****	****50% reduction in C-peptide from baseline, *****n***** = 128 / group**
**	****	****	****C-peptide < 0.2 pmol/l, *****n***** = 130 / group**

## Study Group General Recommendation
		Primary Outcome: Time to C-peptide < 0.2 pmol/ml
		40% risk reduction
POPPII-1 Study
		n = 130 / group (3 groups) unacceptable risk
		Maximum acceptable n = 60 per group
			85% power to detect a 60% risk reduction
		Changed outcome to difference in means at 2 y
			85% power to detect a 57% mean difference
				(adjusted for 3 tests)

**C-peptide Sample Size Calculations**

***Study Group General Recommendation***
**	****	*****Primary Outcome:***** Time to C-peptide < 0.2 pmol/ml**
**	****	****40% risk reduction**
***POPPII-1 Study***
**	****	*****n***** = 130 / group (3 groups) unacceptable risk**
**	****	****Maximum acceptable *****n***** = 60 per group**
**	****	****	****85% power to detect a 60% risk reduction**
**	****	****Changed outcome to difference in means at 2 y**
**	****	****	****85% power to detect a 57% mean difference**
**	****	****	****	****(adjusted for 3 tests)**

## 2 years recruitment, 4 year total duration
All treated for 2 years
Continue follow-up to study end
		1 – 2 y follow-up off treatment
		2 – 4 y total follow-up
Objectives of continued follow-up
		Assess long term adverse effects
		Assess long term benefits of an initial 2 year 				period of treatment

**POPPII-1 STUDY PLAN**

**2 years recruitment, 4 year total duration**
**All treated for 2 years**
**Continue follow-up to study end**
**	****	****1 – 2 y follow-up off treatment**
**	****	****2 – 4 y total follow-up**
**Objectives of continued follow-up**
**	****	****Assess long term adverse effects**
**	****	****Assess long term benefits of an initial 2 year ****	****	****	****	****period of treatment**

## Full scale trial designed to detect 40% effect with
Early stopping if effect > 40% using -spending group sequential design
Early stopping if effect size < 40% using futility boundary 
Study group preferred not to commit to a full-scale trial regardless of high probabilities of stopping early for large or negligible effect sizes

**OTHER APPROACHES CONSIDERED**

**Full scale trial designed to detect 40% effect with**
**Early stopping if effect > 40% using ********-spending group sequential design**
**Early stopping if effect size < 40% using futility boundary **
**Study group preferred not to commit to a full-scale trial regardless of high probabilities of stopping early for large or negligible effect sizes**

## Sample size of 40 / group determined arbitrarily
Power to detect mean difference is described, 
	85% power to detect a 70% difference in mean C-peptide
But principal objective is safety after 1 y of treatment

**ANTI-CD20 IN NEW ONSET**

**Sample size of 40 / group determined arbitrarily**
**Power to detect mean difference is described, **
**	****85% power to detect a 70% difference in mean C-peptide**
**But principal objective is safety after 1 y of treatment**

## DESIGN OF THE ORAL INSULIN TRIAL

***A Study of Diabetes Prevention in Pre-Diabetes***
***	******	*****Confirm a subgroup finding in the prior DPT-1**
**	****	**** ****oral insulin trial**
***Maximum Sample Size (Duration) Design***
**	****	****Determine N under specific assumptions**
**	****	****Determine plan (duration) to provide that N**
**	****	****N *****expected***** to provide desired level of power**

***TrialNet***

## 	Determine the total Information required to provide desired 	power 1 -  to detect a desired effect .
	Continue the study until this level of information is attained.
	Power is guaranteed regardless of the actual study characteristics, e.g.:
			Control group hazard rate 
			Rate of recruitment
			Recruitment Interval 
			Total Duration
			Losses to follow-up   

**	****Continue the study until this level of information is attained.**
**	****Power is guaranteed regardless of the actual study characteristics, e.g.:**
**	****	****	****Control group hazard rate ******
**	****	****	****Rate of recruitment**
**	****	****	****Recruitment Interval **
**	****	****	****Total Duration**
**	****	****	****Losses to follow-up***** *****  **

***TrialNet***

**Maximum Information Design**

## Specify the desired significance level , one or two-sided, and corresponding Z-value, Z1-.
Specify the desired level of power 1 -  and Z1- 
Specify the risk reduction  that is desired to detect, or the minimal relevant effect of interest.
Hazard Ratio: HR = E / C
		E = Experimental Treatment group rate
		 C  = Control group hazard rate (fraction/year)
Risk reduction  = 100*(1 – HR)

**Specify the desired level of power 1 - ******** and *****Z******1-********* **
**Specify the risk reduction ******** that is desired to detect, or the minimal relevant effect of interest.**
**Hazard Ratio: *****HR = ************E ******/ ************C***
***	******	************E****** = Experimental Treatment group rate***
***	******	****** ************C ****** = Control group hazard rate (fraction/year)***
**Risk reduction ******** = 100*(1 – *****HR*****)**

***TrialNet***

**Maximum Information Design*****Event-Time Data***

## Information required to provide power  1 -  to detect a risk reduction  using a test at level  is computed as

**	**

***TrialNet***

**Maximum Information Design*****Event-Time Data***

**For example, to detect a ****** = **45% risk reduction *****(HR***** = 0.55) with 85% power and a one-sided test at the 0.05 level, the required information is**
**	**

## The actual information obtained at any point during the study is a function of
		DE = number of events in the treated group
		DC = number of events in the control group
		DT = total number of events
The measure of information is provided by

**	****	*****D******E****** = number of events in the treated group***
***	******	******D******C****** = number of events in the control group***
***	******	******D******T****** = total number of events***
**The measure of information is provided by**

***TrialNet***

**Maximum Information Design*****Event-Time Data***

**The study continues until attained *****I***** equals *****I*****(********,********)**

## The total duration of the trial is unknown. 
However, projections can be made using the same types of assumptions that provide the basis for a sample size calculation in a maximum duration design.
These projections can be updated as the trial progresses.

**However, *****projections***** can be made using the same types of assumptions that provide the basis for a sample size calculation in a maximum duration design.**
**These projections can be updated as the trial progresses.**

***TrialNet***

**Maximum Information Design*****Event-Time Data***

## Consider two treatments E1 and E2 versus control C.
Three pairwise comparisons
	 E1 versus C,    E2 versus C, 	   E1 versus E2
A single study could be more efficient than two separate studies of E1 versus C and E2 versus C
For all three tests require p < 0.05/3 = 0.0167 to ensure that overall  = 0.05.
BUT is this adjustment necessary?

***Three pairwise comparisons***
***	****** ******E******1***** versus *****C,    E******2***** versus *****C, ******	******   E******1***** versus *****E******2***
**A single study *****could***** be more efficient than two separate studies of *****E******1***** versus *****C *****and *****E******2***** versus *****C***
**For all three tests require *****p***** **_**<**_** 0.05/3 = 0.0167 to ensure that overall ******** = 0.05.**
***BUT***** is this adjustment necessary?**

***TrialNet***

**Multiple Treatment Design**

## Objectives:
	Determine whether either E1 or E2 is effective.
		E1 versus C, E2 versus C, each one-sided
	Determine whether E1 or E2 is more effective
		E1 versus E2, two-sided
		Poor power
			E1 – C, HR = 0.55 (45% risk reduction)
			E2 – C, HR = 0.70 (30% risk reduction)
			E1 – E2, HR = 0.55/0.70 = 0.79 (21% risk red.)
		Huge study required

**	****Determine whether **_***either***_** *****E******1***** **_***or***_** *****E******2***** is effective.**
**	****	*****E******1***** versus *****C, E******2***** versus *****C, *****each one-sided**
**	****Determine whether *****E******1***** or *****E******2***** is **_***more***_** effective**
**	****	*****E******1***** versus *****E******2*****, two-sided**
**	****	****Poor power**
**	****	****	*****E******1***** – *****C*****, *****HR***** = 0.55 (45% risk reduction)**
**	****	****	*****E******2***** – *****C*****, *****HR***** = 0.70 (30% risk reduction)**
**	****	****	*****E******1***** – *****E******2, ******HR***** = 0.55/0.70 = 0.79 (21% risk red.)**
**	****	****Huge study required**

***TrialNet***

**Multiple Treatment Design**

## Recommendation:
	Design to determine whether either E1 or E2 is effective.
		E1 versus C, E2 versus C, one-sided
	For H treatments, k = H comparisons
		require p < 0.05/H
	Single study more efficient than 2 studies

**	****Design to determine whether **_***either***_** *****E******1***** **_***or***_** *****E******2***** is effective.**
**	****	*****E******1***** versus *****C, E******2***** versus *****C*****, one-sided**
**	****For *****H***** treatments, *****k = H *****comparisons**
**	****	****require *****p ***_***<***_*** 0.05/H***
***	*****Single study more efficient than 2 studies**

***TrialNet***

**Multiple Treatment Design**

## Required information:
		85% power,  = 0.05 (one-sided)
		45% risk reduction
		H = 2, required I(,) = 25.1
		Recruit over 3 y, N = 225
Two Studies
		Total duration = 4.0 y for EACH study
Single study
		Total duration = 4.9 y for a SINGLE study

**	****	****85% power, ******** = 0.05 (one-sided)**
**	****	****45% risk reduction**
**	****	*****H***** = 2, required *****I*****(********,********) = 25.1**
**	****	****Recruit over 3 y, N = 225**
**Two Studies**
**	****	****Total duration = 4.0 y for *****EACH***** study**
**Single study**
**	****	****Total duration = 4.9 y for *****a SINGLE***** study**
**	****	**** **

***TrialNet***

**Multiple Treatment Design**

## Start with E1 versus C, then later add E2 versus C

***TrialNet***

**Emerging Therapies**

***E******1***** versus *****C, *****use ****	****(*****E******1***** + *****E******1(2)*****) vs. (*****C******1***** + *****C******1(2)*****), or**
**	****	***** ******	******	******	*****(*****E******1***** + *****E******1(2)*****) vs. (*****C******1***** + *****C******1(2) *****+ *****C******2*****)**
***E******2***** versus *****C, *****use ****	****(*****E******2***** + *****E******2(1)*****) vs. (*****C******1***** + *****C******2 (1)*****), or**
**	****	****	****	****	****(*****E******2***** + *****E******2(1)*****) vs. (*****C******1***** + *****C******2 (1) *****+ *****C******2*****)****	**

## Start with small studies to explore effects, but still using diabetes onset as the outcome.

**	**

***TrialNet***

**Small Studies**

**To detect a 45% risk reduction with 85% power *****I***** = 25 is required.**
**As *****I***** decreases, power decreases to unacceptable levels except for large risk reductions of 60% or more. **
**	**

## Start with small studies search for a silver bullet.
How likely is one to exist among the therapies under consideration?
If unlikely, then small studies will be inconclusive. 
If start with a larger study:
	Study will likely be terminated early by DSMB if 	silver bullet exists.
	If not, then would still have good power to detect	 meaningful effects.

**How likely is one to exist among the therapies under consideration?**
**If unlikely, then small studies will be inconclusive. **
**If start with a larger study:**
**	****Study will likely be terminated early by DSMB if ****	****silver bullet exists.**
**	****If not, then would still have good power to detect****	**** meaningful effects.**

***TrialNet***

**Silver Bullet Hypothesis**