# Presentation: 042308

## Design of Type 1 Diabetes TrialNet Protocols 

- Mark Espeland

## How long should the treatment and follow-up period in trials be? Issues related to variance sources and latent structure

- Measured C-peptide as an indicator of current levels/status of C-peptide secretion
- Current levels/status of C-peptide secretion as an indicator of usual levels/status of C-peptide secretion
- Usual levels/status of C-peptide secretion as a measure of B-cell function

## Timeframe Issues

- DCCT confirms that treatments may have long-lasting but slowly detectable influences
- Impact of intensive therapy on atherosclerosis
- Validation of surrogates requires long follow-up times
- Relating change in surrogates with subsequent incidence of “hard” endpoints

## Can larger numbers of treatments be compared simultaneously with aggressive curtailment for futility? 

- Yes, if there is appropriate standardization with respect to protocols and inclusion
- Play-the-winner strategies for allocation of resources (e.g. participants and follow-up)
- Requires accelerated measurement protocols and intermediated outcomes
- Costs – if timeframes of effects vary, this may disenfranchise some interventions

## More Timeframe Issues

- Use of historical controls
- Network provides opportunities
- Standardization
- Homogeneity
- Potential for imbalances may have difficult issues
- Mismeasured covariates
- Timescales

## Yanez, et al. Statist Med 1998;17:2597-2606

- Use of baseline as a covariate in change models, if imbalances exist, may introduce considerable bias in relationships with change may be attributable to measurement error
- Example:  change in atherosclerosis in Cardiovascular Health Study

## Thiebaut ACM, Benichou J. Statist Med 2004;23:3803-3820.

- If imbalances exist, use of different timescales (e.g. age-based, time from randomization, time from diagnosis) may provide very different portrayals of relationships
- Example:  predictors of breast cancer

## Can short term trials be grafted onto long term trials – roll phase 2 patients into phase 3 studies? 

- Not unless formal probabilistic control is defined
- Phase 2 participants certainly can be followed to gain additional useful information

## Should trials be powered for large effect sizes or for more moderate effect sizes with monitoring guidelines that could terminate early for an unexpected large effect? 

## Effect Size

- Issue of clinical utility
- Moderate effect sizes are reasonable
- Trials powered only to detect large results may have intolerable Type II error

## Should trials be powered to rule out adverse effects? 

- No
- Phase 2 and Phase 4 contributions
- Multiple comparisons
- “Safety” indices may be a useful endpoint and/or guide to termination (e.g. WHI)

## Regulatory Standards

- “Regulatory standards should be based on the properties of the distribution of ... (“responses”).  At present, is only based on the expectation of this distribution ... “
*Longford N. Statist Med 1999;18:1467-74*

## Observed Outcomes

**Harm**

**Benefit**

## Homogenous Response

**Harm**

**Benefit**

**“****True” Responses**

**Measurement Error**

## No Measurement Error

**Harm**

**Benefit**

**Measurement Error**

**“****True” Reponses**

## Mixture Distribution:  Response and Error

**Harm**

**Benefit**

**Measurement Error**

**True Responses**

## “Clinical” Criteria for Surrogacy

- Boissel J-P, Collet J-P, Moleur P, Haugh M.  Surrogate endpoints: a basis for a rational approach. *Eur J Clin Pharm* 1992; 43: 235-244.

## Boissel Criteria for Surrogacy

- _Efficiency_  The surrogate marker should be relatively easy to evaluate, preferably by non-invasive means, and more readily available than the gold standard.  The time course of the surrogate should precede that of the endpoints so that disease and/or disease progression may be established more quickly via the surrogate.  In this manner, clinical trials based on surrogates should require fewer resources, less participant burden, and a shorter time frame.

## Boissel Criteria for Surrogacy

- _Linkage_ The quantitative and qualitative relationship between the surrogate marker and the clinical endpoint should be established based on epidemiological and clinical studies.  The nature of this relationship may be understood in terms of its pathophysiology or in terms of an expression of joint risk.

## Boissel Criteria for Surrogacy

- _Congruency_ The surrogate should produce parallel estimates of risk and benefit as endpoints.  Individuals with and without disease should exhibit differences in surrogate marker measurements.  In intervention studies, anticipated clinical benefits should be deducible from the observed changes in the surrogate marker.

## What happens when statisticians define surrogacy?

## Rule Out the Obvious

- “Perfect” surrogates do not exist
- Let S denote surrogate outcome
- Let T denote “true” outcome
- If S and T always provide the same answer (given linear models and normal distributions), it implies Corr(S,T) = _+_ 1.00

*Alonso A, et al. Biometrics 2004;60:724-8.*

## Develop Equations

- Let Z denote the intervention
- Let f( ) denote a “distribution”
- Implicit range
- Potential covariates
- Undefined functional form

## Prentice Criteria For Surrogates

- P1:  f(T|Z) ne f(T):  intervention affects the distribution of T
- P2:  f(S|Z) ne f(S):  intervention affects the distribution of S
- P3:  f(T|S) ne f(S):  so surrogate affects the distribution of T
- P4:  f(T|S,Z) = f(T|S) so that conditional on S, T is independent of Z

*Prentice R. Statist Med 1989;8:431-440.*
*Berger VW. Statist Med 2004;23:1571-8.*

## “Themes” of Prentice Definition:  Abstraction

- A surrogate may or may not be as efficient, cost effective, or burdensome as the true outcome.
- Problem is objective and mathematical

## “Themes” of Prentice Definition:  Localization

- Functions “f()” require definition
- Surrogacy may be limited in scope, timeframe, model, and cohort
- Covariates may be required
- Definition is dependent and specific to intervention
- No such thing as a “universal” surrogate

## “Themes” of Prentice Definition:  Dependent on Effect of Intervention

- P1:  f(T|Z) ne f(Z)
- Only applies when the intervention has an effect
- In an randomized trial, any baseline characteristic is a “surrogate” if the intervention has no effect

## “Themes” of Prentice Definition:  Impossible to “Validate”

- Difficult to confirm null:  conditional independence
- Impossible to anticipate intervention effect
- Impossible to generalize localization

## Impact of Prentice Definition

- No “non-trivial” surrogates exist
- No precise validation possible
- Methods developed to estimate proportion of “true” effect expressed by surrogate
- Unsatisfactory
- However, paradigm can be used to argue for surrogacy
- Espeland, et al. Carotid IMT in statin trials (in press)