# Case-control study 3: Bias and confounding and analysis Preben Aavitsland.

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Case-control study 3: Bias and confounding and analysis Preben Aavitsland

Contents Monday 1 –Design: Case-control study as a smarter cohort study –The odds ratio Tuesday 2 –Choosing cases and controls –Power calculation Wednesday –Case-control studies in outbreaks Thursday 3 –Bias and confounding –Matching –Analysis

Summary of the case-control study Study causal effects of exposures (risk factors, preventive factors) on disease Define cases Find source population Select controls that are representative of source population Ask cases and controls the same questions about exposures Compare exposure ratios between cases and controls, OR = a/b / c/d

Calculating the odds ratio (OR) Cross product ratio: ad / bc = a/b / c/d

Can we believe the result? Having a dogTBE OR = RR = 4.5

What can be wrong in the study? Random error Results in low precision of the epidemiological measure measure is not precise, but true 1 Imprecise measuring 2 Too small groups Systematic errors (= bias) Results in low validity of the epidemiological measure measure is not true 1 Selection bias 2 Information bias 3 Confounding

Random errors

Systematic errors

Errors in epidemiological studies Error Study size Systematic error (bias) Random error (chance)

Random error Low precision because of –Imprecise measuring –Too small groups Decreases with increasing group size Can be quantified by confidence interval

Estimation When we measure OR, we estimate a point estimate –Will never know the true value Confidence interval indicates precision or amount of random error –Wide interval low precision –Narrow interval high precision OR = 4.5 (2.0 – 10)

OR and confidence interval Shows magnitude of the causal effect Shows direction of the effect –OR > 1 increases risk (risk factor) –OR > 1 decreases risk (preventive factor) Shows the precision around the point estimate Condition: no systematic errors Forget about p-values! No advantages.

Larger study narrower interval Use Episheet

Systematic error Does not decrease with increasing sample size Selection bias Information bias Confounding

Selection bias Error because the association exposure disease is different for participants and non- participants in the study Errors in the –procedures to select participants –factors that influence participation

Examples of selection bias Self-selection bias Healthy worker effect Non-response Refusal Loss to follow-up

Can we believe the result? Having a dogTBE OR = IRR = 4.5 Cases were interviewed in the hospital. Controls were interviewed by phone to their home in the evening. But then, many dog-owners would be walking their dog… OR=ad / bc

Preventing selection bias Same selection criteria High response-rate High rate of follow-up

Information bias Error because the measurement of exposure or disease is different between the comparison groups. Errors in the –procedures to measure exposure –procedures to diagnose disease

Examples of information bias Diagnostic bias Recall bias Researcher influence

Can we believe the result? Having a dogTBE OR = IRR = 4.5 Cases were so eager to find an explanation for their disease that they included their neighbours dog when they were asked whether they had a dog… OR=ad / bc

Misclassification True Differential Non- differential

Non-differential misclassification Same degree of misclassification in both cases and controls OR will be underestimated –True value is higher If no causal effect found, ask: –Could it be due to non-differential misclassification?

Preventing information bias Clear definitions Good measuring methods Blinding Standardised procedures Quality control

Confunding - 1 Mixing of the effect of the exposure on disease with the effect of another factor that is associated with the exposure. EksposureDisease Confounder

Confounding - 2 Key term in epidemiology Most important explanation for associations Always look for confounding factors SurgeonPost op inf. Op theatre I

Criteria for a confounder 1 A confounder must be a cause of the disease (or a marker for a cause) 2 A confounder must be associated with the exposure in the source population 3 A confounder must not be affected by the exposure or the disease UmbrellaLess tub. Class 1 3 2

Downs syndrome by birth order

Find confounders Second, third and fourth child are more often affected by Downs syndrome. Many childrenDowns Maternal age

Downs syndrome by maternal age

Downs syndrome by birth order and maternal age groups

Find confounders The Norwegian comedian Marve Fleksnes once stated: I am probably allergic to leather because every time I go to bed with my shoes on, I wake up with a headache the next morning. Sleep shoesHeadache Alcohol

Find confounders A study has found that small hospitals have lower rates of nosocomial infections than the large university hospitals. The local politicians use this as an argument for the higher quality of local hospitals. Small hospFew infections Well patients

Controlling confounding In the design Restriction of the study Matching In the analysis Restriction of the analysis Stratification Multivariable regression

Restriction Restriction of the study or the analysis to a subgroup that is homogenous for the possible confounder. Always possible, but reduces the size of the study. UmbrellaLess tub. Class Lower class

Restriction We study only mothers of a certain age Many childrenDowns 35 year old mothers

Matching Selection of controls to be identical to the cases with respect to distribution of one or more potential confounders. Many childrenDowns Maternal age

Disadvantages of matching Breaks the rule: Control group should be representative of source population –Therefore: Special matched analysis needed –More complicated analysis Cannot study whether matched factor has a causal effect More difficult to find controls

Why match? Random sample from source population may not be possible Quick and easy way to get controls –Matched on social factors: Friend controls, family controls, neighbourhood controls –Matched on time: Density case-control studies Can improve efficiency of study Can control for confounding due to factors that are difficult to measure

Should we match? Probably not, but may: If there are many possible confounders that you need to stratify for in analysis

Stratified analysis Calculate crude odds ratio with whole data set Divide data set in strata for the potential confounding variable and analyse these separately Calculate adjusted (OR mh ) odds ratio If adjusted OR differs (> 10-20%) from crude OR, then confounding is present and adjusted OR should be reported

Stratification

Multivariable regression Analyse the data in a statistical model that includes both the presumed cause and possible confounders Measure the odds ratio OR for each of the exposures, independent from the others Logistic regression is the most common model in epidemiology

Controlling confounding In the design Restriction of the study Matching In the analysis Restriction of the analysis Stratification Multivariable methods

What can be wrong in the study? Random error Results in low precision of the epidemiological measure measure is not precise, but true 1 Imprecise measuring 2 Too small groups Systematic errors (= bias) Results in low validity of the epidemiological measure measure is not true 1 Selection bias 2 Information bias 3 Confounding

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