ERRORS, CONFOUNDING, and INTERACTION Hamid Heidarian PhD of Epidemiology Assistant Professor at Mashhad University of Medical Sciences heidarianh@mums.ac.ir

خطا، مخدوش کنندگی و برهمکنش

ارزشیابی مداخله 1 2 مشاهده داده اطلاعات 3 10 بينش 4 9 ایجاد فرضیه 5 Epidemiological Sequence cycle 10 ارزشیابی بينش 4 9 مداخله ایجاد فرضیه 5 انجام مطالعه تجربی استنتاج علمی آزمون فرضیه 8 7 6 3

آیا همبستگی مشاهده شده در نمونه = همبستگی در جامعه است؟ خیر: خطای تصادفی خطای سیستماتیک بلی: آیا همبستگی = اثر است؟ مخدوش شدگی

خطای تصادفی

فارسی ! خطای تصادفی واریانس دقت اطمینان یا پایایی قابلیت تکرار English -/+ فارسی ! Random error - خطای تصادفی Variance واریانس Precision + دقت Reliability اطمینان یا پایایی Repeatability قابلیت تکرار Reproducibility قابلیت بازتولید

What Is Random Error? Any factors that randomly affect results Random error adds variability to the data but does not affect average Sampling and measurement errors can produce random error.

Random Error Frequency The distribution of X with no random error X

Random Error The distribution of X with random error Frequency The distribution of X with no random error X

Random Error The distribution of X with random error Frequency The distribution of X with no random error Notice that random error doesn’t affect the average, only the variability around the average. X

Association in Reality There are tow types of random errors: Association in Reality Association in Study + - correct Type one Type two

Indices of reliability Qualitative variables: Percent agreement Kappa statistic Quantitative variables: Correlation graph and coefficients Intraclass correlation coefficient Mean difference and paired t-test Coefficient of variability Bland-Altman plot

How to reduce random error How to reduce random error? Increase the sample size How to explain random error? Statistics: Confidence Interval P-value

Systematic Error

English -/+ فارسی ! Systematic error - خطای منظم Bias تورش validity + اعتبار- اعتماد - روایی - نااریبی

The average of hypothetically infinite number of results differ from the true value. Systematic error does affect the average Sampling and measurement errors can produce systematic Error.

Systematic Error Frequency The distribution of X with no systematic error X

Systematic Error The distribution of X with systematic error Frequency The distribution of X with no systematic error X

Systematic Error The distribution of X with systematic error Frequency The distribution of X with no systematic error Notice that systematic error does affect the average; we call this a bias. X

Selection bias Selection Bias: is present when individuals have different probabilities of being included in the study according to relevant study characteristics: namely the exposure and the outcome of interest Selection bias is a systematic error in the selection of study subjects – cases or controls in a case-control study, exposed or unexposed in a cohort study Examples of selection bias Self-selection bias self-referral non-response bias healthy worker effect Prevalence-incidence bias (Neyman’s bias) Medical surveillance bias diagnostic bias Berkson’s bias (admission rate)

REFERENCE POPULATION Diseased + - + - Exposed STUDY SAMPLE + - + - Exposed The book illustrates this in Figure 4.2, where exposed cases have a higher probability of being selected for the study than other categories of individuals. They describe a type of selection bias called “medical surveillance bias”. In a case-control study examining the association between oral contraceptive use to diabetes (a disease with “an important” subclinical component”) Since oral contraceptive use is likely to be associated with greater medical surveillance due to a higher than normal frequency of medical encounters, women who use OC’s are more likely to be diagnosed with diabetes than other women (not using OC’s). In a study comparing cases of diabetes and controls without diabetes, a spurious association with OC’s and diabetes may occur. The effect of selection bias on the direction of measure of association is a function of which cell’s in a n x k table (eg., 2 x 2)) is/are subject to a spuriously higher or lower probability of selection. STUDY SAMPLE

Avoiding and detecting selection bias In case-control studies, Choose controls from the same “study-base” as cases. In cohort studies, the rate of loss to follow-up indicates the potential for selection bias. Comparison of the characteristics of those lost to follow-up with those persons remaining under follow-up, may indicate the potential consequences of any selection bias. the approach to case and control selection signals the potential for selection bias. Studies based around particular institutions or facilities, i.e., a hospital, are particularly susceptible.

Information Bias Information Bias: results from a systematic error in measurement thus leading to misclassification (in exposure or outcome category). tendency for individuals selected for inclusion in the study to be erroneously placed in different exposure/outcome categories, thus leading to misclassification. Results from either imperfect definitions of study variables or flawed data collection procedures. These errors result in misclassification of exposure and/or outcome status for a significant proportion of study participants

REFERENCE POPULATION Cases Control Misclassification of EXPOSURE Diseased + - + - Exposed Cases Control STUDY SAMPLE

REFERENCE POPULATION Misclassification of OUTCOME Diseased + - + + - + - Disease Exposed + - STUDY SAMPLE

Information Bias These errors result in misclassification of exposure and/or outcome status Terms: validity (sensitivity and specificity) refer to classification of both disease and exposure status

Information bias could be either Non-differential or Differential

Sensitivity and Specificity=100% No Misclassification Sensitivity or Specificity<100% They are not equal in comparison groups They are equal in comparison groups Differential Misclassification Non-differential Misclassification

Internal Validity External Validity (generalizability)

Accuracy = validity + reliability

Confounding

Is Association = Effect?

Confounding is: association measure ≠ effect measure

Counterfactual or Potential Outcome Definition of effect measure: If we can imagine the experience of a cohort over the same interval under two different conditions, then we can ask what the incidence rate of any outcome would be under two different conditions.

Confounding IAe IAu IAe IBu

Criteria for a Confounding Factor A Confounding factor must be a extraneous risk factor for the disease. A Confounding factor must be associated with the exposure under study in the source population. A Confounding factor must not be affected by the exposure or the disease.

E D C

Confounding is not a all or none situation There are Negative, positive and qualitative confounding

Ways to deal with confounding: Randomization Matching Restriction Stratification Modeling

Interaction Synonyms: Effect modification Heterogeneity of effect

There are two definitions for interaction:

When the incidence rate of disease in the presence of two or more risk factors differs from the incidence rate expected to result from their individual effects. The effect can be greater than what we would expect (positive interaction, synergism) or less Than what we would expect (negative interaction, antagonism).

The problem is to determine what we would expect to result from the individual effects of the exposures (additive vs multiplicative model).

2. when the magnitude of a measure of association (between exposure and disease) meaningfully differs according to the values of the third variable.

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