Odds ratio, Relative risk, Attributable risk, Population attributable risk

Odds ratio (OR) is a measure of association between an exposure and an outcome. OR represents odds that an outcome will occur given a particular exposure, compared to the odds of outcome occurring in absence of that exposure. Odds ratios are most commonly used in case-control studies, however they can also be used in cross-sectional and cohort study designs as well (with some modifications and/or assumptions).

Odds ratios are used to compare relative odds of the occurrence of the outcome of interest (e.g. disease or disorder), given exposure to the variable of interest (e.g. health characteristic, aspect of medical history). The odds ratio can also be used to determine whether a particular exposure is a risk factor for a particular outcome, and to compare the magnitude of various risk factors for that outcome.

1.  OR=1 Exposure does not affect odds of outcome

2.  OR>1 Exposure associated with higher odds of outcome                        

3.  OR<1 Exposure associated with lower odds of outcome                    

Relative risk (RR): A synonym for risk ratio. However, the term is also commonly

used to refer to the rate ratio and even to the odds ratio (OR). To minimize confusion,

it may be better to avoid this term in favor of more specific terms.

Rate ratio The ratio of two rates; e.g., the rate in an exposed population divided by the rate

in an unexposed population.

Relative Risk (RR) = (incidence in exposed)/(incidence in non-exposed)

Attributable risk (AR) = (incidence in exposed - incidence in non-exposed)/(incidence in exposed)

Risk difference (RD) = (incidence in exposed - incidence in non-exposed)

Population attributable risk (PAR) = (incidence total- incidence in non-exposed)/(incidence total)

or PAR =  P_e (RR_e-1)  /  [1 + P_e (RR_e-1)]

where, Pe is prevalence of exposure

RRe is relative risk of that exposure

Ie - incidence in exposed

Iu - incidence in unexposed (non-exposed)

Ip - incidence total (exposed + nonexposed)

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Asymmetry test of EGGER

Asymmetry test of EGGER

•Linear regression approach to measure funnel plot asymmetry on the natural logarithm scale of the odds ratio

•The standard normal deviate (SND), defined as the odds ratio divided by its standard error, is regressed against the estimate's precision, the latter being defined as the inverse of the standard error 

•(regression equation: SND= a+ bxprecision)

•As precision depends largely on sample size, small trials will be close to zero on the × axis

•Null hypothesis –symmetry exists in the funnel plot

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Freeman-Tukey transform

•Freeman-Tukey transform

seek to adjust data to make the distribution more similar to a Normal distribution

•Was specifically designed for Poisson-like data, especially with a mean value >1. 

•The FT angular or arcsine transform was developed for Binomial-like data, in particular, data representing proportions or percentages.

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Duval and Tweedie’s Trim and Fill method

Duval and Tweedie’s Trim and Fill method

•Uses an iterative procedure to remove most extreme small studies from positive side of funnel plot, re-computing effect size at each iteration until funnel plot is symmetric about new effect size

•Yield an unbiased estimate of effect size

•Trimming also reduces variance of effects, yielding a too narrow C.I.

•Therefore algorithm then adds original studies back into analysis, and imputes a mirror image for each.

•This fill has no impact on point estimate but serves to correct the variance 

the black dots are studies added after the method...

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Publication Bias

Publication Bias:

•The publication or non-publication of research findings, depending on the nature and direction of the results (ref. Cochrane Handbook)

•Publication bias exists when the studies included in the analysis differ systematically from all the studies that should have been included.

•Typically, studies with larger than average effects are more likely to be published and this can lead to upward bias in the summary effect

•Publication bias is when studies with positive findings are more likely to be published 

•This means that any meta analysis or literature reviews based only on published data will be biased, so researchers should make sure to include unpublished reports in their data as well

Funnel Plot: 

•Plots of “trials’ effect estimates”against“sample size”

•Funnel plot is based on the fact that precision in estimating underlying treatment effect will increase as sample size of component studies increases

•Results from small studies will scatter widely at bottomofgraph, with spreadnarrowing among larger studies

•In absence of biasplot will resemble a symmetrical inverted funnel

•Conversely, if there is bias, funnel plots will often be skewed and asymmetrical

•Symmetry (or asymmetry) - visual examination(so it is subjective)

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How to calculate relative risk from odds ratio ?

Q. How to calculate relative risk from odds ratio ?

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Random and Fixed effect model

Random vs. fixed effect model 

PSM / COMMUNITY MEDICINE by Dr Abhishek Jaiswal is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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