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Researches with negative results are more likely to be unpublished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=Validity and Precision=Reliability
Definition
Accuracy
Validity
Closeness of observed values to true population values
AKA 'Trueness'
Precision
Reliability
Closeness of observed values to each other among sample
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
Confounding and Effect modification
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{ 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:
Randomly sample primary sampling units (PSUs) (clusters) with probability proportional to size (PPS)
larger size of PSUs (clusters) are more likely to be selected
Randomly sample second-stage units (SSUs) (individuals) with the same number of individuals within PSUs (clusters)
individuals in smaller size of PSUs are more likely to be selected
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.
