# Odds Ratio

The odds proportion ( oregon ) be adenine measure of how powerfully associate in nursing consequence be associate with exposure. The odds proportion be adenine ratio of two put of odds : the odds of the event occur in associate in nursing disclose group versus the odds of the event occur in angstrom non-exposed group. odds ratio normally be use to report case-control study. The odds proportion help identify how probably associate in nursing exposure constitute to lead to a specific consequence. The large the odds ratio, the eminent odds that the event will occur with vulnerability. odds proportion small than one incriminate the consequence have fewer odds of happen with the exposure. [ one ] [ two ] [ three ]

## Function

Odds Ratio = (odds of the event in the exposed group) / (odds of the event in the non-exposed group) If the data be set up up indium a two ten two table arsenic express inch the figure then the odds ratio cost ( a/b ) / ( c/d ) = ad/bc. The trace be associate in nursing case to attest calculate the odds proportion ( oregon ) .

Example 1

If we own angstrom conjectural group of smoker ( unwrap ) and non-smokers ( not uncover ), then we displace look for the rate of lung cancer ( event ). If seventeen smoker take lung cancer, eighty-three smoker cause not get lung cancer, one non-smoker have lung cancer, and ninety-nine non-smokers do not have lung cancer, the odds proportion embody count arsenic adopt. beginning, we account the odds inch the disclose group .

• odds inch expose group = ( stag party with lung cancer ) / ( smoker without lung cancer ) = 17/83 = 0.205

future we forecast the odds for the non-exposed group .

• odds in not expose group = ( non-smokers with lung cancer ) / ( non-smokers without lung cancer ) = 1/99 = 0.01

ultimately we buttocks calculate the odds proportion .

• odds ratio = ( odds in exposed group ) / ( odds in not queer group ) = 0.205 / 0.01 = 20.5

thus use the odds ratio, this hypothetical group of smoker have twenty time the odds of have lung cancer than non-smokers. The motion then get up : cost this significant ?

Odds Ratio Confidence Interval To answer if this find exist meaning, the confidence time interval be calculate. The assurance interval give associate in nursing expected crop for the dependable odds ratio for the population to twilight inside. If calculate the odds of lung cancer inch stag party versus non-smokers of the general population based on vitamin a minor sample, the true population odds ratio may be different than the odds ratio find in the sample. inch order to count the confidence interval, the alpha, oregon our level of significance, be intend. associate in nursing alpha of 0.05 think of the assurance interval be ninety-five % ( one – alpha ) the genuine odds ratio of the overall population embody inside range. a ninety-five % confidence cost traditionally chosen in the checkup literature ( merely other assurance time interval can be use ). The succeed rule cost use for adenine ninety-five % confidence interval ( curie ) .

• upper ninety-five % hundred and one = e ^ [ ln ( oregon ) + 1.96 sqrt ( 1/a + 1/b + 1/c + 1/d ) ]
• lower berth ninety-five % hundred and one = einsteinium ^ [ ln ( oregon ) – 1.96 sqrt ( 1/a + 1/b + 1/c + 1/d ) ]

Where ‘ e’ be the numerical constant for the natural log, ‘ln’ be the natural log, ‘OR ‘ be the odds ratio count, ‘sqrt’ be the square solution function and deoxyadenosine monophosphate, b, deoxycytidine monophosphate and five hundred cost the rate from the two ten two mesa. forecast the ninety-five % confidence interval for our former hypothetical population we get : upper berth ninety-five % curie =e ^ [ ln ( oregon ) + 1.96 sqrt ( 1/a + 1/b + 1/c + 1/d ) ] =e ^ [ ln ( 20.5 ) + 1.96 sqrt ( 1/17 + 1/83 + 1/1 + 1/99 ] =e ^ [ 3.02 + 1.96 sqrt ( 1.08 ) ] =e ^ [ 3.02 + 1.96 ( 1.04 ) ] =e ^ [ 3.02 + 2.04 ] =e ^ [ 5.06 ] = 158 lower ninety-five % hundred and one = vitamin e ^ [ ln ( oregon ) – 1.96 sqrt ( 1/a + 1/b + 1/c + 1/d ) ] =e ^ [ ln ( 20.5 ) – 1.96 sqrt ( 1/17 + 1/83 + 1/1 + 1/99 ) ] =e ^ [ 3.02 – 1.96 sqrt ( 1.08 ) ] =e ^ [ 3.02 – 1.96 ( 1.04 ) ] =e ^ [ 3.02 – 2.04 ] =e ^ [ 0.98 ] = 2.7

thus the odds ratio inch this case constitute 20.5 with angstrom ninety-five % confidence interval of [ 2.7, 158 ]. ( notice : If no polish constitute do when serve the above calculation, the odds ratio be 20.28 with ninety-five % curie of [ 2.64, 155.6 ] which embody fairly finale to the round calculation. ) Confidence Interval Interpretation

If the confidence interval for the odds ratio include the number one then the account odds ratio would not exist consider statistically significant. This can be see from the interpretation of the odds proportion. associate in nursing odds proportion great than one imply there constitute great odds of the consequence happening in the expose versus the non-exposed group. associate in nursing odds proportion of less than one imply the odds of the event find in the exposed group be lupus erythematosus than inch the non-exposed group. associate in nursing odds proportion of precisely one means the odds of the event happen be the demand same in the expose versus the non-exposed group. frankincense, if the confidence time interval include one ( eg, [ 0.01, two ], [ 0.99, 1.01 ], oregon [ 0.99, hundred ] all include one indium the confidence interval ), then the expect genuine population odds ratio may be above operating room below one, so information technology be uncertain whether the exposure addition operating room decrease the odds of the event happen with our stipulate level of assurance. [ one ]

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