avoiding bias due to unmeasured covariates

Presentations in this series1. Introduction2. Self-matching3. Proxies4. Intermediates5. Instruments6. Equipoise

Avoiding Bias Due toUnmeasured Covariates

Alec Walker

T D

U

T D

URandomization

T D

URandomizationSelf-matching

Celecoxibversus

Naproxen versus

No Treatment

PUBHospital

Admission

Celecoxib, Naproxen and GI Bleeding

in the treatment of pain

MD-perceived risk of peptic ulcer & bleeding (PUB)

True risk of PUB

Confounding by Contraindication

High risk for peptic ulcer and bleeding makes treatment with naproxen inadvisable. Celecoxib would be better. No treatment at all is safest.

Celecoxibversus

Naproxenversus

No Treatment

PUBHospital

Admission

MD-perceived risk of peptic ulcer & bleeding (PUB)

True risk of PUB

The physician’s belief, not the true risk, is what affects the choice of therapy.

Celecoxibversus

Naproxenversus

No Treatment

PUBHospital

Admission

MD-perceived risk of peptic ulcer & bleeding (PUB)

True risk of PUB

Celecoxib Ulcer

PUB

Celecoxib Ulcer

Celecoxib UlcerConfounded

Self-Matching

KeyCelecoxibNaproxen

No TherapyEvent X

X

X

Self-Matching

KeyCelecoxibNaproxen

No TherapyEvent X

X

X

When there is no event, there is no within-person comparison to be made, if we’re looking at relative risk.

Celecoxibversus

Naproxenversus

No Treatment

PUBHospital

Admission

MD-perceived risk of peptic ulcer & bleeding (PUB)

True risk of PUB

Matching on person means that all comparisons are within person and therefore at a common level of physician perception.

Celecoxibversus

Naproxenversus

No Treatment

PUBHospital

Admission

MD-perceived risk of peptic ulcer & bleeding (PUB)

True risk of PUB

Celecoxibversus

Naproxenversus

No Treatment

PUBHospital

Admission

MD-perceived risk of peptic ulcer & bleeding (PUB)

True risk of PUB

The time of observation needs to be sufficiently short that true risk and physician perception do not change.

Compare the Exposure at Case Occurrenceto Sampled Exposure(s) in the Past

Non-Cases Drop Out of Consideration

Uninformative Time Drops Out as Well

Case windo

w

Control windo

w

Case and Control Windows Case window: period preceding the event (GI

bleeding) during which the exposure (celecoxib, naproxen, no treatment) may have altered the risk

Control window(s): periods of the same length as, and not overlapping with, the case window that furthermore provide an estimate of the null-hypothesis probability of exposure for each case.

The core study technique is to identify cases, then ascertain exposure status in the case window and at earlier points in time – the control windows.

Estimating the Relative RiskCase

WindowControl Window

ExposedExposed Yes No

Yes f10

No f01

Place each case in the above table, according to exposure in the case window and the control window

Mantel-Haenszel odds ratio for matched sets Reduces to ratio of counts in discordant exposure windows (

f10 / f01 ) when there is one control Conditional logistic regression

When there are concurrent time-varying confounders Accommodates many-to-one matching of control and case

windows Concordant case-control windows are uninformative

Pharmacoepidemiology and Drug Safety 2011; 20: 763–771

Purpose This study aimed to evaluate risks of upper gastrointestinal (GI) adverse events across a variety of oral and parenteral coxibs and nonselective nonsteroidal anti‐inflammatory drugs (nsNSAIDs) in the general population of Taiwan.Methods In a case‐crossover study, all patients aged ≥20 years who were hospitalized for upper GI adverse events (peptic ulcer and bleeding; gastritis and duodenitis) in 2006 were identified ... For each patient, the case period was defined as 1–30 days and the control period as 31–60 days before the date of hospitalization. Outpatient pharmacy prescription database was searched for individual NSAID use during the case and control periods. A conditional logistic regression model was applied ...Results A total of 40 635 patients hospitalized for upper GI adverse events were included. The adjusted OR was 1.52 (95%CI: 1.27–1.82) for celecoxib and 2.56 (95%CI: 2.44–2.69) for oral nsNSAIDs…Conclusion Use of celecoxib and all nsNSAIDs studied was associated with a greater risk of upper GI toxicity as compared with nonuse…

Case Window

Control Window Exposed

Exposed Yes NoYes f10

No f01

Pharmacoepidemiology and Drug Safety 2011; 20: 763–771

Case Window

Control Window Exposed

Exposed Yes NoYes 413No f01

Pharmacoepidemiology and Drug Safety 2011; 20: 763–771

Case Window

Control Window Exposed

Exposed Yes NoYes 413No 232

Pharmacoepidemiology and Drug Safety 2011; 20: 763–771

Case Window

Control Window Exposed

Exposed Yes NoYes 413No 232

RRcrude = 413/232

= 1.78Pharmacoepidemiology and Drug Safety 2011; 20: 763–771

*Conditional logistic regression adjusted for important potential time‐varying confounding variables including selective serotonin reuptake inhibitors, other antidepressants, calcium channel blockers, nitrates, systemic corticosteroids, low‐dose aspirin, proton pump inhibitors, histamine 2 receptor blockers, and sucralfate.

Self-matched studies compare exposure at the time of an outcome event to the probability of exposure in the same person Calculated from the individuals own history Assuming the null hypothesis of no effect of exposure on

the risk of outcome. Unmeasured covariates that do not vary over time within

person do not confound the estimate of relative risk. Self-matched studies work well for intermittent exposures

whose associated risks rise and fall quickly Self-matched studies give mathematical meaning to the

question you might well hear from your doctor: “Were you doing anything unusual just before you got sick?”

Presentations in this series1. Overview

and Randomization2. Self-matching3. Proxies4. Intermediates5. Instruments

Avoiding Bias Due toUnmeasured Covariates

Alec Walker