measuring associations between exposure and outcomes chapter 3, szklo and nieto
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Measuring Associations Between Measuring Associations Between Exposure and OutcomesExposure and Outcomes
Chapter 3, Szklo and Nieto
Measures of Association can be Measures of Association can be based on:based on:
Absolute differences Between Groups (e.g., disease risk among exposed – disease risk among unexposed)
Relative differences or ratios Between Groups (e.g., disease risk ratio or relative risk: disease risk in exposed/disease risk in unexposed)
Absolute differencesAbsolute differences
Public Health activitiesPreventive activitiesMeasure of association when the outcome
of interest is continuous Examples: PAR , Mean Differences
Relative differences or ratiosRelative differences or ratios
For discrete variableTo assess causal associationsExamples: Relative Risk/Rate,
Relative odds
Types of VariablesTypes of Variables
Discrete/categorical– Dichotomous, binary
• Absolute Difference?• Relative Difference
Continuous– Difference between
means
Cohort StudyCohort Study
Diseased
Non-diseased
Totals: Risk odds
Exposure
Exposed a b a+b a / a+b a / b
Unexposed c d c+d c /c+d c / d
Totals:
Disease
a+c b+d a+b+c+d
Odds in Exposed and UnexposedOdds in Exposed and Unexposed
Odds in exposed=( a / a+b) / 1- (a / a+b )
=(a / a+b) / (b / a+b) = a/bOdds in unexposed=( c / c+d) / 1- (c / c+d )
=(c / c+d) / (d / c+d) = c/d
Relative RiskRelative Risk
RR= a / a+b / c / c+d
OR= a / b / c / d = a*d / b*cOdds ratio is a cross-product ratio
Rare Disease - MIRare Disease - MI
MI Free of MI Totals:
Exposure
High Blood
Pressure
180 9820 10000
Normal
Pressure
30 9970 10000
Probability + =q + = 180/10000 = 0.0180
Probability - = q - = 30/10000 = 0.0030
Odds dis +
= 180/9820 = 0.01833
Odds dis -
= 30/9970 = 0.00301
RR=6 OR=6.09
Common Disease – Vaccine ReactionsCommon Disease – Vaccine Reactions
Local
Reactions
Free of
Reactions
Totals:
Exposure
Vaccinated 650 1920 2570
Placebo 170 2240 2240
RR = 650 / 2570 / 170 / 2410 = 0.2529 / 0.0705 = 3.59
OR = 650 / 1920 / 170 / 2240 = 0.3385 / 0.0759 = 4.46
Built – in biasBuilt – in bias
OR =( q + / 1 - q +) / (q - / 1 - q –)
= q + / q - * (1 - q - / 1- q + ) = RR * (1 - q - / 1- q + )
Built – in biasBuilt – in bias
Use of the odds ratio as an estimate of the relative risk biases it in a direction opposite to the null hypothesis.
(1 - q - / 1- q + ) defines the bias responsible for the discrepancy between the RR & OR.
When the disease is relatively rare , this bias is negligible.
When the incidence is high, the bias can be substantial.
OR is a valuable measure of OR is a valuable measure of association :association :
1. It can be measured in case – control studies. 2. It is directly derived from logistic regression
models 3. The OR of an event is the exact reciprocal of
the OR of the nonevent. (survival or death OR both are informative)
4. when the baseline risk is not very small, RR can be meaningless.
Cross-sectional StudiesCross-sectional Studies
In the stationary population:Prevalent RR= Prev+ / prev-
= ( q+ * Dur+ * (1- prev+)) / ( q- * Dur- * (1- prev-))
PPR = RR x dur+ x {1-prev+}
dur- {1-prev-}
Cross-sectional StudiesCross-sectional Studies
A point prevalence ratio may be able to estimate the relative risk depending on – the ratio of the durations of disease among
• the exposed with disease+
• the unexposed with disease-
– the ratio of the values• 1-prevalence among the exposed+
• 1-prevalence among the unexposed-
The two bias factors that differentiate the PRR from the relative risk:
1. Dur+/Dur- survival or duration bias
2. (1- prev+/ 1- prev -) complement bias
1 & 2 (S.B) Incidence – prevalence bias
We can estimate RR in cross sectional study when the exposure don’t modify the duration of the disease and the disease is rare.
Since (1- prev+/ 1- prev -)< 1:
PRR underestimates RR
We should consider temporality
Case-Control StudyCase-Control Study
The OR of disease and the OR of exposure are mathematically equivalent.
In case control study we calculate the OR of exposure as it’s algebraically identical to the OR of disease.
OR exp = a /c / b/ d = a*d/ b*c = a / b / c / d = OR dis
Case-Control StudyCase-Control Study
The fact that the OR exp is identical to the OR dis
explains why the interpretation of the odds ratio in case control studies is prospective.
Odds Ratio as an Estimate of the Odds Ratio as an Estimate of the Relative Risk:Relative Risk:
The disease under study has low Incidence thus resulting in a small built-in bias : OR is an estimate of RR
The case – cohort approach allows direct estimation of RR by OR and does not have to rely on rarity assumption.
When the OR is used as a measure of association in itself, this assumption is obviously is not needed
Calculation of the OR when there are Calculation of the OR when there are more than two exposure categoriesmore than two exposure categories
To calculate the OR for different exposure categories , one is chosen as the reference category (biologically or largest sample size)
Cases of Craniosynostosis and normal Cases of Craniosynostosis and normal Control according to maternal ageControl according to maternal age
Maternal age
Cases Controls Odds exp in case
Odds exp in control
OR
<20 12 89 12/12 89/89 1
20-24 47 242 47/12 242/89 1.44
25-29 56 255 56/12 255/89 1.63
>29 58 173 58/12 173/89 2.49
When the multilevel exposure variable is ordinal, it may be of interest to perform a trend test
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