an introduction to tables
DESCRIPTION
An Introduction to Tables. Confounding and Effect Modification Interpretation and Choices. Population characteristics. p = Probability of an event of interest for example: Probability of successful post op probability is thought to be ‘conditional’ on factors of interest - PowerPoint PPT PresentationTRANSCRIPT
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An Introduction to Tables
Confounding and Effect Modification
Interpretation and Choices
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Population characteristics
• p = Probability of an event of interest• for example: Probability of successful post op• probability is thought to be ‘conditional’ on
factors of interest• for example: pre-op treatments (coded 0 and 1)
• Question: Does the probability of success depend on the choice of pre-op treatment?
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But the patients receive a several different operations
• Surgery types are then coded 1 and 2• Question: Does our previous question depend on
the type of surgery?• i.e. Does the comparison between treatments (with
regard to the probability of success) depend on the type of surgery?
• This is addressing whether surgery type is an effect modifier
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For example
• . cs suc tr,by(surg)
• surg | RR [95% Conf. Interval] M-H Weight• -----------------+-------------------------------------------------• 1 | 2 .8342841 4.79453 4.545455 • 2 | 1.9 1.759944 2.051202 45.45455 • -----------------+-------------------------------------------------• Crude | .3861386 .3348359 .4453018 • M-H combined | 1.909091 1.71543 2.124615• -------------------------------------------------------------------• Test of homogeneity (M-H) chi2(1) = 0.026 Pr>chi2 = 0.8724
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Notice:
• The surgery group specific risk ratios are nearly equal. (2 is ‘close’ to 1.9)
• The test of the null hypothesis of no effect modification (in Stata, it is called the test for homogeneity) has a p-value of 0.8724
• So, on the basis of this test, there is no evidence that surgery type is an effect modifier (0.386 is not ‘close’ to
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Since there is no evidence that surgery type is an effect modifier:
• We can assess whether surgery type is a confounder
• We compare the ‘crude’ estimate of the risk ratio with the ‘adjusted’ estimate of the risk ratio ( 0.386 is not ‘close’ to 1.909)
• So, there is ‘evidence’ that surgery type is a confounder.
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Have a look at the surgery type specific tables
• . cs suc tr if surg==1,exact
• | tr |• | Exposed Unexposed | Total• -----------------+------------------------+----------• Cases | 100 5 | 105• Noncases | 900 95 | 995• -----------------+------------------------+----------• Total | 1000 100 | 1100• | |• Risk | .1 .05 | .0954545• | |• | Point estimate | [95% Conf. Interval]• |------------------------+----------------------• Risk difference | .05 | .0034122 .0965878 • Risk ratio | 2 | .8342841 4.79453 • Attr. frac. ex. | .5 | -.1986325 .791429 • Attr. frac. pop | .4761905 |• +-----------------------------------------------• 1-sided Fisher's exact P = 0.0667• 2-sided Fisher's exact P = 0.1503
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…and• . cs suc tr if surg==2,exact
• | tr |• | Exposed Unexposed | Total• -----------------+------------------------+----------• Cases | 95 500 | 595• Noncases | 5 500 | 505• -----------------+------------------------+----------• Total | 100 1000 | 1100• | |• Risk | .95 .5 | .5409091• | |• | Point estimate | [95% Conf. Interval]• |------------------------+----------------------• Risk difference | .45 | .3972264 .5027736 • Risk ratio | 1.9 | 1.759944 2.051202 • Attr. frac. ex. | .4736842 | .4318 .512481 • Attr. frac. pop | .0756303 |• +-----------------------------------------------• 1-sided Fisher's exact P = 0.0000• 2-sided Fisher's exact P = 0.0000
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The previous 2 displays highlight the importance of looking at the actual data
• Should the surgery specific risk ratios be offered? • Look at the p-values in each group• Look at the width of the confidence intervals in
each group.• Is a test for homogenity enough here?
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Risk Ratios
• Usually: D - Disease E - Exposure• Risk ratio: RR = Pr(D|E) / Pr(D|not E)• Estimates of RR are usually written:
• Crude: Adjusted:
• Stratum specific:
• we can say that the risk of disease with exposure is estimated to be X times the risk of disease without exposure (with a p-value and/or a CI)
RR
cr
RR adj
RR
2RR
1RR
X,RR isIf
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Risk Difference
• RD = Pr(D|E) - Pr(D|not E)
• Estimate is:
• Crude, Adjusted, Stratum-specific….
• then the risk of disease with exposure is estimated to be X higher than the risk of disease without exposure
RD
,XRD isIf
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Odds
• Odds(E|D) = Pr(E|D)/Pr(not E|D)
• for example, if Pr(E|D) = 2/3, then odds(E|D) = 2
• notice: odds risk
• odds can be any positive number
• risk (is a probability) and must be between 0 and 1
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Odds Ratios
• OR = odds(E|D)/odds(E|not D)• most useful in case-control studies• OR can be any positive number• log(OR) = logit can be any number (positive or
negative)• logits provide a ‘natural’ outcome for modelling• estimates written:• crude, adjusted, stratum-specific...
OR
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Interpretation of Odds Ratios
• we can say that the odds of exposure with disease is estimated to be X times the odds of exposure without disease (with a p-value and/or a CI)
• But we can also say that the odds of disease with exposure is estimated to be X times the odds of disease without exposure (with a p-value and/or a CI)
• Odds ratio’s magic property!
X,OR isIf