Transcript An Introduction to Tables

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
• for example: pre-op treatments (coded 0 and 1)
• Question: Does the probability of success depend
on the choice of pre-op treatment?
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
For example
•
. cs suc tr,by(surg)
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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
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
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.
Have a look at the surgery type specific tables
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. cs suc tr if surg==1,exact
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| tr
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|
Exposed
Unexposed |
Total
-----------------+------------------------+---------Cases |
100
5 |
105
Noncases |
900
95 |
995
-----------------+------------------------+---------Total |
1000
100 |
1100
|
|
Risk |
.1
.05 | .0954545
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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
…and
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. cs suc tr if surg==2,exact
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| tr
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Exposed
Unexposed |
Total
-----------------+------------------------+---------Cases |
95
500 |
595
Noncases |
5
500 |
505
-----------------+------------------------+---------Total |
100
1000 |
1100
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Risk |
.95
.5 | .5409091
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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
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?
Risk Ratios
• Usually: D - Disease E - Exposure
• Risk ratio: RR = Pr(D|E) / Pr(D|not E)

• Estimates of RR are usually written: RR
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• Crude: RR cr
Adjusted: RR adj
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
• Stratum specific: RR 1 RR 2 

• If RR is X, 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)
Risk Difference
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RD = Pr(D|E) - Pr(D|not E)

Estimate is: RD
Crude, Adjusted, Stratum-specific….

If RD is X, then the risk of disease with
exposure is estimated to be X higher than
the risk of disease without exposure
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

Odds Ratios
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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: OR
• crude, adjusted, stratum-specific...
Interpretation of Odds Ratios

• If OR is X, 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!