Avoiding Bias Due to

Unmeasured Covariates

Alec Walker

1. Introduction

Disclosure

Alec Walker is a principal in World Health Information Science Consultants, LCC, a research and consulting firm whose clients include manufacturers or providers of health products and health-related services as well as public-private partnerships in the US.

None of the material in this short course relates to a product in which Dr. Walker has a financial interest.

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Confounders

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Confounders

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URandomization

Confounders

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URandomizationSelf-matching

Confounders

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URandomizationSelf-matchingProxies

Proxies

Confounders

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URandomizationSelf-matchingProxiesIntermediates

Proxies

Intermediates

Confounders

T D

URandomizationSelf-matchingProxiesIntermediates

Instruments

Proxies

Intermediates

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Disarming Unmeasured Covariates

Conditionally onUnmeasured covariates are uncorrelated with

Randomization Treatment

Self-matching Treatment (time-invariant covariates only)

Proxies Outcome or Treatment

Intermediates Outcome or Treatment

Instruments Treatment

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A “Classic” Example:Cimetidine and Gastric Cancer

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Does cimetidine cause stomach cancer? Case reports of de novo appearance in 1982 Colin-Jones et al looked at data from ongoing work

Persons treated with cimetidine in a 12-month window

Matched to a comparison person General practitioner Age Sex Seen for another condition

Examined the incidence of stomach cancer

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Excess cases during follow-upDiagnosed before cimetidine treatment startedDiagnosed within six months of starting cimetidine treatmentDiagnosed more than six months after starting cimetidine treatmentControlsCases of “early” cancer

Before study | Study period | After study

Diagnosed before cimetidine treatment startedDiagnosed within six months of starting cimetidine treatmentDiagnosed more than six months after starting cimetidine treatmentControlsCases of “early” cancer

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Colin-Jones et al. Cimetidine and gastric cancer: preliminary report from post-marketing surveillance study. Brit Med J 1982;285:1311-1313

Hypotheses to account for excess cancersColin-Jones and his coauthors suggested that Stomach cancer incidence was only an artifact

of treatment having come before diagnosis in disease was already present – The as-yet undetected disease caused the use of cimetidine and led to detected disease.

They hypothesized that the effect would disappear with longer follow-up.

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Excess persisted for years

Deathsfrom Year 1 2 3 4

Ex-pected

Malignant neoplasm of the stomach 45 12 5 3 3.5

Malignant neoplasm of the trachea, bronchus and lung

35 25 17 22 12.5

Diseases of the digestive system 33 21 20 10 5.0

Colin-Jones DG. Postmarketing surveillance of the safety of cimetidine: mortality during second, third, and fourth years of follow up. Brit Med J 1985;291:1084-8

Hypotheses to account for excess deaths Stomach cancer – The as-yet undetected disease

caused the use of cimetidine and led to detected disease.

Hypotheses to account for excess deaths Stomach cancer – The as-yet undetected disease

caused the use of cimetidine and led to detected disease.

Lung cancer – Shared determinants. Cigarette smoking predisposes to persistence of stomach ulcer, which in turn leads to cimetidine use. The smoking also causes lung cancer.

Hypotheses to account for excess deaths Stomach cancer – The as-yet undetected disease

caused the use of cimetidine and led to detected disease.

Lung cancer – Shared determinants. Cigarette smoking predisposes to persistence of stomach ulcer, which in turn leads to cimetidine use. The smoking also causes lung cancer.

GI disease – Conditions that motivated cimetidine use led to death.

Hypotheses to account for excess deaths Stomach cancer – The as-yet undetected disease

caused the use of cimetidine and led to detected disease.

Lung cancer – Shared determinants. Cigarette smoking predisposes to persistence of stomach ulcer, which in turn leads to cimetidine use. The smoking also causes lung cancer.

GI disease – Conditions that motivated cimetidine use led to death.

Under each of these hypotheses, cimetidine use was driven by unmeasured factors that also led to the outcomes. The argument was that cimetidine did not cause the deaths from GI disease, stomach cancer or lung cancer, but confounding created associations and the false appearance of causal relations.

But were any of these hypotheses correct? Stomach cancer – The as-yet undetected disease

caused the use of cimetidine and led to detected disease.

Lung cancer – Shared determinants. Cigarette smoking predisposes to persistence of stomach ulcer, which in turn leads to cimetidine use. The smoking also causes lung cancer.

GI disease – Conditions that motivated cimetidine use led to death.

Colin-Jones and colleagues could not know for sure. Had they used a different study design, an answer might have been clear.

Randomization

Randomization Treatment allocation is determined by a process That generates

An expectation of zero correlation between

treatment and predictors of outcome. The Predictors may be

Known or unknown to the experimenter Measured or unmeasured Measured poorly or well

Balance All characteristics other than treatment are balanced

in expectation Measured and unmeasured Predictors and correlates of predictors The intermediate states that later arise from these

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Balance All characteristics other than treatment are balanced

in expectation Measured and unmeasured Predictors and correlates of predictors The intermediate states that later arise from these

Unadjusted estimates are unbiased estimates of treatment effect Differences, ratios, more complex functions of Risk, rates, hazards, survival, … Costs, QoL, … Even of dependent happenings, like epidemics

(provided that exposure groups are not intermixed)

N Engl J Med. 2010 Apr 1;362(13):1192-202

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Delta = Treatment Effect

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Summary – Overview & Randomization Anything that leads to both treatment and the

outcome is a confounder. Confounders distort estimates of treatment effect. In observational studies there are many ways of

blocking the effect of confounders, as long as the confounders are perfectly known.

When confounders are unmeasured or unknown, conventional methods for control do not apply.

Study design can break the association between unmeasured confounders and treatment or outcome.

Randomization of the assignment of treatment to individuals mechanically breaks the association between confounder and treatment.

Alec Walker

Presentations in this series1. Overview

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

Avoiding Bias Due to

Unmeasured Covariates