「Epidemiology」の版間の差分

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[[File:Accuracy and Precision 2.gif|frame|400px|Accuracy in <math>x</math>-axis, Precision in <math>y</math>-axis]]
Accuracy in <math>x</math>-axis, Precision in <math>y</math>-axis
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<nowiki>*</nowiki>In this example, &mu; is sample mean, not the population mean
 
<nowiki>*</nowiki>In this example, &mu; is sample mean, not the population mean
  
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Precision in <math>x</math>-axis, Accuracy in <math>y</math>-axis
 
  
 
==Tips in Case-control design==
 
==Tips in Case-control design==

2023年2月17日 (金) 12:28時点における版

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

Disease frequency measurement

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

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{ 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.