# Presentation: 424080

## A Perspective on Exposure -Response Relationships

**Robert T.O’Neill,  Ph.D.**
**Director, Office of Biostatistics**
**CDER, FDA**

**To be presented at the American Association of Pharmaceutical Scientists, June 3-5,2002, Arlington , Virginia**

## Outline of talk

**Some principles to keep in mind**
**Time, duration of exposure, and dose - it role in estimation of effects and modeling it**
**Exposure - response for clinical safety and toxicity - a problem seeking solution**
**Subgroup effects, covariates, expected vs. systematic variation**
**Concluding remarks**

## Basic principles

**Is response due to exposure or associated with exposure**
**What are the confounders of response, ie other things that may be responsible for observed effects**
**A prognostic factor can be predictive and confounding at the same time**
**Comparative dose (exposure) - response of two independent groups assumes comparability of confounders - the reason for randomization**

## Causal models, associations, randomization

**Exposure as a random variable (in RCT’s it is usually fixed and a grouping variable)**
**Exposure as an intermediate variable  (marker) on the clinical outcome chain**
**Fixed covariates (age, gender) related to exposure outcome (time dependent)**
**Fixed covariates (age, gender) related to clinical outcome (time dependent)**
**Similar, different, no relationships (time)**

## When do we distinguish between associations and causality:More often for efficacy, less often for safety outcomes

**Assume causality and estimate the functional relationships between individual patient level exposures (dose) and responses ( outcomes)**

## Criteria for Causal Association

**Temporal Relationship**
**Strength of the association**
**Dose response relationship**
**Biological plausibility**
**Consistency with other knowledge**
**   ****Replication of the findings**

**Notes:**
Cartoon of risk by time

## Recommendations for dose adjustments - up or downWhat is the evidence for effect caused by dose

## If a patient does not respond to 10 mg, increase the dose to 20 mgIf a patient experiences an adverse event at 30 mg, reduce the dosage to 20mg

## When future response to a new exposure is conditioned on prior response to prior exposure

- 20mg

- 10mg

- placebo

**Response rate**

**Dose**

- 40%

-  30%

- 10%

- Randomize N subjects to one of 3 groups

**When future response to a new exposure is conditioned on prior response to prior exposure**

## You need another design to conclude causality

- 10mg

- 20mg

- 20mg

- 10mg

- placebo

**Response rate**

**Dose**

- 40%

-  30%

- 10%

- Randomize N subjects to one of 3 groups

**Response rate**

**You need another design to conclude causality**

## Randomized vs. non-randomized studies

**Randomized studies**
**dose is fixed or regimen is assigned**
**dose, exposure is not an outcome**
**exposure is an outcome after a randomized assignment of dose - now more like a surrogate marker - influenced by the individual covariates and the processing of site specific exposures which can be genomic, proteonomic related**
**Observational studies**
**Analysis of RCT which does not account for the randomization, like test drug exposure cohort, combining data from two or more exposure cohorts in separate studies**

##  A comment on design of exposure - response studies

**Traditional assigned dose, dose response studies**
**few studies demonstrate dramatic dose response especially for clinical efficacy endpoints whose relationship to initial or ongoing dosing is distant**
**How, where and when is exposure measured**
**site of action, metabolite, inducer, prohibitor, for which response and which pathway - multiplicity of models and choice of which as that associated with ‘intended’ and ‘unintended‘ effects**

## Response

**Clinical endpoint, surrogate endpoint, surrogate marker,  biomarker - all different**
**At a single time point**
**A  curve at a point in time, or a curve as a function of time**
**A repeated measure symptom score**
**Non-comparative: eg. Proportion responding by time T;   risk per unit of time**
**Comparative: eg. Relative risk of responding by time T (the hazard ratio)**

## Aspects of response

**Delay**
**Onset**
**Duration**
**Mixture response models**
**An estimated R% of patients respond in the first week, of whom C% continue to respond until time T; RxC%**

## Which types of exposures are best characterized

**Acute single dose**
**Chronic multiple dose steady state**

## Which types of response are best characterized

**Those occurring near in time to exposure**
**Those occurring distant in time from initial and or chronic exposure - probably not**

## Individual dose response curves

**Expose all individuals to all doses, regardless of each individual’s response to each dose**
**Possible when ethical, and no safety issue**
**What do you do when patients cannot tolerate higher doses - informative censoring impacts estimation of individual and population (averaged) dose response curves**
**  ****The role of cumulative time and cumulative dose  - the real problem**

## Responses that are both time and dose related

**Adverse reactions**
**Cure rates**
**Absorbing events (death)**
**G.I. Events**
**cardiovascular events**

## Patient time line graph for clinical trial data, AE’s, med. exposures, labs, outcomes

**Exposure history of test treatment - time course**

**Time of occurrence and duration of ADE’s**

**Exposure history of concomitant medications -time course**

**Lab data**

**Primaryoutcome**

**Patient time line graph for clinical trial data, AE’s, med. exposures, labs, outcomes**

**Seriousevent**

## Slide 20

## Exposure-response relationships for safety outcomes

## Integrated safety analysisExposure -response relationships are an important aspect

**Often is an epidemiological exercise**
**Randomization is broken to calculate estimates**
**May combine data from two or more studies, or subgroups to estimate relationships**
**Caution in how one combines data**
**Examining response for cohorts exposed to fixed dose ; , not comparisons of dose groups controlling for patient comparability**

## Dose-duration -response relationships and effects over time

## Why ?

**relationship between exposure and beneficial and/or adverse effects of a drug are essential to determining efficacy, safety and risk/benefit**

## Dose Response: Relating Drug Toxicity To Dose Of Drug Administered And Received

- <date/time>

**Dose Response: ****Relating Drug Toxicity To Dose Of Drug Administered And Received**

** ****Fixed dose treatment groups where subjects are assigned and stay on a fixed dose for the study duration**
** ****Dosing patterns for individual patients varies (or is modified) over the duration of study follow-up.**
** ****Sometimes, the earlier exposure period of the trial involves a dose escalation or titration period for several weeks before a dose is settled on.  **

## Example

- <date/time>

**Example**

**907 subjects exposed in clinical studies to an anti-psychotic drug in which ****23 subjects are observed to have seizures**** as the adverse event of concern.**
**Subjects are titrated early in the trial's conduct and over the course of the full trial subjects have different cumulative levels of exposure. Since dose is changed during the study, the relationship of study duration, exposure duration, dose, and time to dropout becomes complicated.**
**Issue: Can a margin of safety for the drug be determined such that it can be administered at a dose which is not associated with a high incidence of seizures. **

## Example (cont)

- <date/time>

**Example (cont)**

**Subjects at risk are categorized as to three dose levels of exposure to drug namely, low, medium and high on the basis of:**
**the mean or average dose they were on for the duration of study**
**the mean dose excluding the titration period**
**the maximum daily dose they were on (assuming the drug spiking effects may be responsible for side effects). **
**Subjects who experienced a seizure were categorized according to:**
**actual dose they were on at the time of the seizure**
** ****mean dose they were on at the time of the seizure**
** ****maximum daily dose they were on at the time of the seizure**

## Dose Toxicity Relationships According to Categorizationof Dose at Risk and Dose at Time of Seizure

- <date/time>

**Dose Toxicity Relationships According to Categorization****of Dose at Risk and Dose at Time of Seizure**

_**Categorization**__**	**__**Low**__**	**__**Medium**__**	**__**High**__**	**__**Total**_
**Actual dose/Mean dose**** ****	****3/526****	****	****5/281****	****15/100****	**** 23/907****	****0.6%****	****	****1.8%****	****15.0%****	****2.5%**
**Actual dose/Mean dose**** ****	****3/374****	****   5/343****	****15/190****	****23/907 ****(Excluded Titration) ****	****0.8%****	****	****1.5%****	****7.9%****	****2.5%**
**Mean dose/Mean dose**** ****	****5/374****	****	****11/374****	****7/190****	****23/907 ****(****Excluded Titration****) ****	**** ****1.3%        2.9%     3.6%****%****	****2.5%**
**Max. daily dose/****	****3/268****	****	****4/275****	****16/364****	****23/907 ****(****Excluded Titration****) ****	****1.1%        1.5%       4.4%****	****2.5%**

## Metrics of risk : Quantifying adverse event rates

**Crude rate  R = X / N**
**Occurrences per unit time of exposure - constant hazard rate; delayed events**
**Life table or cumulative rates**
**Hazard rates and functions**
**Competing risks - death , GI bleeding**
**Accounting for differential exposure time -acute and chronically administered drugs**

## Exposure-response relationship for safety outcomes

## Time to event responses:The hazard rate

## DURATION OF EXPOSURE PATTERN

**O'Neill RT 1988**

**DURATION OF EXPOSURE PATTERN**
**FOR SUBJECT FOLLOW UP**

## FREQUENCY OF OCCURRENCE OF 30

**ADVERSE EVENTS: 3 PATTERNS**

**O'Neill RT 1988**

## ESTIMATED CUMULATIVE ADVERSE EVENTS FOR 

**ESTIMATED CUMULATIVE ADVERSE EVENTS FOR **
**THREE PATTERNS OF ADVERSE EVENTS OCCURRENCE**

**O'Neill RT 1988**

## HAZARD FUNCTIONS FOR THREE PATTERNS

**OF DRUG-INDUCED CLINICAL EVENTS**

**O'Neill RT 1988**

*** OR  RISK PER UNIT TIME**

**MONTHS FROM INITIAL DRUG EXPOSURE**

***HAZARD RATE**

**0**

**1**

**2**

**3**

**4**

**5**

**6**

**7**

**8**

**9**

**10**

**11**

**12**

**DECREASING**

**DELAYED (INCREASING)**

**CONSTANT**

## Relative risks that are time dependent

**RR = I(T) / I(C) - proportional hazards, constant hazard ratios**
**RR (t) = I(T; t) / I(C; t) - non-proportional hazard ratios**
**RR and RR (t) are not the same and need to be evaluated to demonstrate they are not**
**This point is critical to the combining of relative risk estimates from two or more heterogenous studies of different durations (D), with different controls  (e.g. the Vioxx - Naproxen comparisons) [D****1 ****< D****2  ****< D****3**** ]**

## NEJM 2000;343:1520-8.

**NEJM 2000;343:1520-8.**

## Cumulative incidence of primary safety endpoint

- Decreasing patients
- exposed over time

## An Example

**An Example**

## Reported as .4%in the original article -best estimate is 1.8%for 12 months exposure

## Hazard Function Estimates

##  An Example of Combining Adverse Event Rates From Three Trials : The Issue of  taking time into account

**Trial****	****	****Measure****	****	****	**** 1****	**** 2****	****  3**
**    ****1****	****	****No. with event****	****	****	****  5**
**	****	****No. exposed****	****	****	****500**
**	****	****Cumulative rate****	****	****0.01**
**	****	****Crude rate =                     5/500 = 0.01**
**    ****2****	****	****No. with event****	****	****	****  2****	****  2**
**	****	****No. exposed****	****	****	****200****	****100**
**	****	****Cumulative rate****	****	****0.01****	****0.03**
**	****	****Crude rate =                      4/200 = 0.02**
**    ****3****	****	****No. with event****	****	****	****  1****	****  1****	****  1**
**	****	****No. exposed****	****	****	****100****	**** 50****	**** 25**
**	****	****Cumulative rate****	****              0.01       0.03****	**** 0.069**
**	****	****Crude rate =                       3/100 = 0.03**

**Months of Exposure**

##  An Example of Combining Adverse Events From Three Trials : The Issue of  taking time into accountThe  Combined Studies

**Combined ****	****Measure****	****	****	**** 1****	**** 2****	****  3**
**    ****	****	****No. with event****	****	****	****  8            3             1**
**	****	****No. exposed****	****	****	****800       150          25**
**	****	****Cumulative rate****	****	****0.01      0.03       0.69**
**	****	****Crude rate =                    12/800 = 0.015**
**    **

**Months of Exposure**

**3 Studies**

## Subgroups: Issues  of Design and Analysis

**What are the questions of interest for a clinical trial?**
**Effects in all subgroups**
**Effects of equal size in all subgroups**
**No effect overall, but effects in some subgroups**
**Overall effect, but no effects in some subgroups**
**Overall effect is the average of different, but true effects in all subgroups**
**Does the same dose produce same size effects in all subroups?**

## Type 1 and Type 2 Errors Associated With Subgroup Analysis

**Chances of missing a treatment effect in a specific subgroup: a function of  the sample size (power to detect a constant treatment effect) in each of the subgroups**
**Chances of falsely concluding a treatment effect exists in a subgroup when there is no treatment effect: a function of the number of individual subgroup analyses**

## Chance Variation When The Null Hypothesis is True

## Subgroup Comparisons

**The potential to inflate the probability of a false positive conclusion in some subgroup**
**When there is ****no**** effect in any any subgroup, the chance of at least one statistically significant result is a function of k, the number of subgroups e.g. for k = 9 and ******** = .05, the chance of at least one statistically significant result is**

**1 - (1 - .05)****9**** = .37**

**2         subgroups****	****.10**
**4         subgroups****	****.185**
**6         subgroups****	****.264**

## Chance Variation When The Alternative Hypothesis is True

## Four Subgroups

**Male**

**< Age 40**

**> Age 40**

**Female**

**Equal sample size 2N in each subgroup**

**< Age 40**

**> Age 40**

## Expected Treatment Effects Among Four Subgroups Rank Ordered From Smallest to Largest

****** ****= 0.05****	****	******** = .10**

****** ****= 0.05****	****	******** = .20**

## Expected Difference in Treatment Effect Between the Largest and Smallest Subgroup

****** ****= 0.05****	****	******** = .10**

****** ****= 0.05****	****	******** = .20**

## Using population pk to estimate exposure to support observed  clinical gender effect differences that are not statistically different Data analysis, bias and its impact on conclusions

## Slide 53

## Slide 54

## Slide 55

## Slide 56

## Slide 57

## Slide 58

## Concluding remarks

**Examining and estimating exposure response relationships: a critical objective**
**Distinguish your goals of inference**
**Recognize difference between causality and association for exposure - response relationships**
**Most safety assessment is observational in nature - exposure response is  basic goal**
**Many areas where improvement needed**