# Presentation: 045431

## Statistical issues in the validation of surrogate endpoints 

- With a focus on the evaluation of treatments for prostate cancer
- Stuart G. Baker, Sc.D.

## Hypothetical randomized trial with surrogate endpoint

- treatment B is better than treatment A
- Does this imply treatment B is better than treatment A  for true endpoint of death from prostate cancer?
- Assume, for now, no competing risk deaths –(only a minor adjustment for this approach)

|  | Same PSA | Elevated PSA |
| --- | --- | --- |
| Treatment A | 20 | 80 (80%) |
| Treatment B | 30  | 70 (70%) |

## Hypothetical effect of surrogate and treatment on prostate cancer death

|  | Same PSA | Elevated PSA |
| --- | --- | --- |
| Treatment A |          0 |     .50 |
| Treatment B |          0 |     .86 |

- Probability of prostate cancer death given treatment and  PSA

- Probability of prostate cancer death differs by treatment group

## Treatment A:  fewer prostate cancer deaths

|  | Same PSA | Elevated PSA |
| --- | --- | --- |
| Treatment A | 20 | 80 (80%) |
| Treatment B | 30  | 70  (70%) |

|  | Alive | Prostate cancer death |
| --- | --- | --- |
| Treatment A | 60 | 40 (40%) |
| Treatment B | 40  | 60  (60%) |

- Treatment A:  fewer prostate cancer deaths

- Treatment B:  fewer elevated PSA’s

- Different results for surrogate and true endpoints

- NEXT SLIDE:  GRAPHICAL VIEW

## Surrogate versus true endpoint

- Treatment B

**Fraction with elevated PSA**
**(surrogate)**

**Fraction with prostate CA death**
**(true)**

- Treatment A

**B**

**B**

-  **A**

**A**

- Treatment **A** better than **B **(in terms of elevated PSA)  Treatment **B** better than **A** (in terms of prostate CA death )

- 0

- 1

- 0

## Prentice Criterion-hypothesis testing

- Treatment B

**Fraction with elevated PSA**
**(surrogate)**

**Fraction with prostate CA death (true)**

- Treatment A

**B**

**B**

-  **A**

**A**

- If diagonal lines coincide:  If reject null under surrogate, reject null under true– true null implies surrogate null

- 0

- 1

- 0

## When the surrogate endpoint is weakly predictive of true endpoint

- Treatment B

**Fraction with elevated PSA**
**surrogate**

**Fraction with prostate CA death (true)**

- Treatment A

**B**

**B**

-  **A**

**A**

- Little information about the true endpoint

- 0

- 1

- 0

## Validation of surrogate endpoints

- (1) Fraction with prostate cancer death  among same or elevated PSA in **PREVIOUS** trials (with treatments similar to A or B)
- (2) Fraction with same and elevated PSA in **NEW** trial
- Use (1) and (2) to predict fraction with prostate cancer death in each treatment group of** ****NEW** trial
- Compare with observed prostate cancer deaths in **NEW**** trial**

## Validation of surrogate endpoint

- Treatment B

**Fraction with elevated PSA in ****new**** trial**

**Fraction with prostate CA death in ****new**** trial**

- Treatment A

**B**

**        ****B**

**        ****A**

**A**

- 0

- 1

- 0

- Estimate additional diagonal lines from **previous** trials

## What about deaths from competing risks?

- To predict effect of treatment on prostate cancer death,
- Deaths from unrelated causes are treated as missing at random (in binary example, just discard)
- Later multiply by probability of surviving unrelated causes of death
- If death from unrelated causes _differs_ by treatment group,
- An important harm that needs consideration
- Need  _another_ surrogate to predict death from unrelated causes

## Deaths from other causes (hypothetical)

| 
 | 

Alive | Unrelated deaths not due to treatment | Unrelated
deaths due to treatment | 

Related deaths | 
Prostatecancer
death |
| --- | --- | --- | --- | --- | --- |
| A | 20 | 20 | 20 | 4 | 36 |
| B |  10 | 20 |  10 | 6 | 54 |

**Unrelated deaths **_**not**_** due to treatment****  ****(e.g****. ****cardiovascular) – report separately**

**Unrelated deaths due to treatment  (e.g. infection)                   –report separately and predict with another surrogate**

**Related deaths –combine with prostate cancer death**

## Summary

- For validation of surrogate, need data from many previous trials of related treatments with same surrogate and true endpoints
- compare predicted and observed true endpoints in new trial
- If death from competing risk depends on the intervention, need another surrogate endpoint to predict probability of death from competing risk (and need validation)