Epidemiology

Basics & Definition

Epidemiology

Odds in statistics and Odds in a horse race

Collider bias

Data distribution

Statistical test

Regression model

Multivariate analysis

Marginal effects

Prediction and decision

Table-related commands in STATA

Missing data and imputation

Bradford Hill Criteria for assuming causality

	In terms of the association between exposure and outcome, exposure is more likely to be causal if ....
1. Strength of association	the stronger the association is.
2. Consistency	in the more varieties settings the association is observed.
3. Specificity	the more specific the exposure is, i.e., the exposure is associated with only single outcome.
4. Temporality	the exposure comes first and the outcome appears after the exposure
5. Biological gradient	the more (or less) exposure is associated with more frequent outcome (exposure dose dependent).
6. Plausibility	the mechanism between the exposure and the outcome can be explained according to biological body of knowledge.
7. Coherence	the mechanism between the exposure and the outcome can be proven by certain medical testings.
8. Experiment	some intervention to the exposure can change frequency and/or extent of the outcome.
9. Analogy	another similar exposure is associated with another similar outcome.

Classification of Bias

Catalogue of Bias

Major classification		Specific name	Description	Affecting design
Selection bias	Sample is not properly representative of population	Ascertainment bias	Inappropriate definition of population	Any observational design
		Healthy worker effect	Current employees are more likely to be healthy than general population and ex-employees	Cohort, esp. historical
		Detection bias	Diagnostic procedures are different between case and control	Case-control
		Attrition bias (Loss to follow-up)	needless to explain	Cohort Clinical trial
		Non-response bias	a.k.a. Healthy volunteer effect; Voluntary participants are not representative of population	Any observational design
		Language bias	Medical articles written in languages unfamiliar to researchers are more likely to be ignored	Meta-analysis Systematic review
		Publication bias	Researches with negative results are more likely to be unpublished	Meta-analysis Systematic review
Information bias (Measurement bias)	Observation is not properly conducted	Non-differential misclassification bias	Failure to properly measure exposure/outcome and inappropriate allocations of groups in the same weight for both underestimate effect size (decrease power)	Any design
		Differential misclassification bias	Failure to properly measure exposure/outcome and inappropriate allocations of groups in different weights in-between under- or overestimate effect size	Any design
		└Recall bias	└(subcategory of differential misclassification) Participants are more likely to recall their memory in skewed way according to their outcome status	Any design
		└Reporting bias	└(subcategory of differential misclassification) Participants are more (or less) likely to report their exposure according to their outcome status	Any design
		Observer/interviewer bias	Observers/interviewers are more likely to observe/draw interviews toward exposure according to case outcome status	Any design
		Ecological fallacy		Ecological design
		Regression to the mean	Extreme observations in initial investigations will be toward true population value in later investigations	Cohort Clinical trial
		Hawthorne effect	Observation itself can affect outcome	Clinical trial
		Lead-time bias	Screening trial can diagnose outcome even in its earlier latent period which fallaciously show longer survival	Screening trial
Confounding	Third factors affect both of exposure and outcome	Confounding may occur even in RCT if randomization process is inappropriate (as systematic error) or randomly allocated groups are heterogenous by chance (as random error)

Difference between Population and Sample

Accuracy and Precision

Definition

Accuracy	Closeness of observed values to true population values AKA 'Trueness'	=Validity
Precision	Closeness of observed values to each other among sample	=Reliability

Accuracy in [math]\displaystyle{ x }[/math]-axis, Precision in [math]\displaystyle{ y }[/math]-axis
*In this example, μ is sample mean, not the population mean

Precision in [math]\displaystyle{ x }[/math]-axis, Accuracy in [math]\displaystyle{ y }[/math]-axis

Tips in Case-control design

Sampling (selection bias)

Case sampling	Control sampling
Incident case for outcome with short duration or poor survival Prevalent case for rare or chronic outcome	The same inclusion criteria as case except for outcome itself
Population-based case from surveillance, registry, death certificates, etc. easy to define population	Population-based control random sampling from the same population random-digit dialing, population registry, etc. For occupation-based case, beware of healthy worker effect and select control from similar occupation with the same exposure as the population
Hospital-based case from hospital difficult to define population	Hospital-based control sampling from the same hospital must be exposed at the same extent as the population
	Population-based control Only when assumable that all patients from the population visit the hospital and patients from other than population never visit the hospital
Matching increases precision of observations, i.e. increases power Matching does not decrease bias Matching masks the effect of matching variables themselves Overmatching makes extents of exposure of both groups too similar, which leads to decrease power Matching with age and sex only is a better way 1:n matching (n>1) increases power 1:4 is maximum; more matching brings no more benefit

Measurement (Information bias)

Observer bias	To mask case/control status to observers
Recall bias	To use memory aids To mask research question/hypothesis to participants

Sampling

Simple random sampling (SRS)

Standard Error with Finite Population Correction in SRS

The formula [math]\displaystyle{ SE = \frac{\sigma}{\sqrt{N}} }[/math] assume that samples are selected from infinite population with replacement (allowing repetitive sampling of the same individuals).

In reality, sampling is made from finite population without replacement (not allowing repetitive sampling of the same individuals).

When sampling from finite population without replacement, if fraction [math]\displaystyle{ \frac{n}{N} }[/math] > 5% (0.05), [math]\displaystyle{ SE }[/math] will be too large.

Repeating sampling from finite population of size of [math]\displaystyle{ N }[/math] by sample size of [math]\displaystyle{ n_i }[/math] decreases population size at every sampling:

population size at [math]\displaystyle{ m }[/math]^th sampling = [math]\displaystyle{ N - \sum_{i=1}^m {n_i} }[/math]

If the fraction [math]\displaystyle{ \frac{n}{N} }[/math] > 5% (0.05), [math]\displaystyle{ SE }[/math] should be corrected by Finite Population Correction.

Standard Error corrected by Finite Population Correction when [math]\displaystyle{ \frac{n}{N} }[/math] > 5% (0.05)
[math]\displaystyle{ Finite\ Population\ Correction\ (FPC) = \sqrt{\frac{N-n}{N-1}} }[/math]
[math]\displaystyle{ Corrected\ SE = FPC \times SE = \sqrt{\frac{N-n}{N-1}} \cdot \frac{\sigma}{\sqrt{N}} }[/math]

Two-stage (multi-stage) sampling

In case of two-stage sampling:

1. Randomly sample primary sampling units (PSUs) (clusters) with probability proportional to size (PPS)
   1. larger size of PSUs (clusters) are more likely to be selected
2. Randomly sample second-stage units (SSUs) (individuals) with the same number of individuals within PSUs (clusters)
   1. individuals in smaller size of PSUs are more likely to be selected
   2. final individual probability to be sampled is equivalent in entire population because of balancing probabilities between PSUs and SSUs

Stratified random sampling

To increase precision of estimates in heterogeneous groups in sample, separated (stratified) random sampling from each group in population can be chosen.

In stratified random sampling, sampling fractions in strata can be varied, e.g., sample size of minority groups can be larger than majority groups.