Confounding

1
Confounding

• Confounding is an apparent association between
  disease and exposure caused by a third factor not
  taken into consideration
• A confounder is a variable that is associated
  with the exposure and, independent of that
  exposure, is a risk factor for the disease

2
Examples

• Study A found an association between cigar
  smoking and baldness
• The study was confounded by age
• Study B found a protective effect between animal
  companions and heart attack
• The study may be confounded by the fact that pets
  require care and pet owners were more active or
  able to physically care for them
• The study may also be confounded by the fact that
  those who can tolerate pets are more easy-going
  (Type B personalities)
• Study C found improved perinatal outcomes for
  birthing centers when compared to hospitals
• The study may be confounded by highly motivated
  volunteers who select the birthing center option

3
Testing for Confounding

• Obtain a crude outcome measure (crude death rate,
  crude birth rate, overall odds ratio or relative
  risk)
• Repeat the outcome measure controlling for the
  variable (age-adjusted rate, gender- specific
  odds ratio or relative risk)
• Compare the two measures the estimate of the two
  measures will be different if the variable is a
  confounder

4
Testing for Confounding (cont.)
Age
Expected
Std Pop
ASR/1,000
Pop At Risk
Cancer Deaths
Young
60,500
1.00
5,000
5
56,120
140,300,000
0.40
25,000
10
Middle
171,419
25,700,000
6.67
15,000
Old
100
288,039
XXXX
45,000
115
Total
226,500,000
1980 Population of the U.S., where Young
0-18, Middle 19-64, Old 65
Crude Rate Total Deaths / Pop At Risk 115
/ 45,000 2.56 / 1,000
AAR Sum of Expected / Total in Std Pop
1.27 / 1,000
AGE IS A CONFOUNDER FOR DEATH FROM CANCER
5
Controls for Confounding

• Controls for confounding may be built into the
  design or analysis stages of a study
• Design stage
• Randomization (For Experimental Studies)
• Restriction (Allow only those into the study who
  fit into a narrow band of a potentially
  confounding variable)
• Matching (Match cases and controls on the basis
  of the potential confounding variables
  especially age and gender)
• Cases and controls can be individually matched
  for one or more variables, or they can be group
  matched
• Matching is expensive and requires specific
  analytic techniques
• Overmatching or unnecessary matching may mask
  findings

6
Controls for Confounding (cont)

• Analysis Stage
• Stratification
• Multivariate Analysis Multiple Linear
  Regression, Logistic Regression, Proportional
  Hazards Model

7
Testing for Effect Modification (Interaction
among variables)

• When the incidence rate of disease in the
  presence of two or more risk factors differs from
  the incidence rate expected to result from their
  individual effects
• The effect can be greater than would be expected
  (positive interaction, synergism) or less than
  would be expected (negative interaction,
  antagonism)

8
Effect Modification (Interaction), cont.

• To assess interaction
• Is there an association?
• If so, is it due to confounding?
• If not, are there differences in strata formed on
  the basis of a third variable?
• If so, interaction or effect modification is
  present
• If not, there is no interaction or effect
  modification

9
The prevalence of osteoarthritisis 50 among
females at age 65. Are Ca supplements beginning
at age 50 helpful?
Those with treatment had 84 less disease at age
65
10
Did smoking confound the Ca treatment?
No Disease
Disease
Non-smokers
340
320
20
Ca
RR0.12
160
80
80
Ca-
500
400
100
No Disease
Disease
Smokers
160
130
30
Ca
RR0.24
340
70
270
Ca-
500
200
300
11
Was treatment for smokers modified by alcohol?
No Disease
Disease
100
75
25
Ca
RR0.30
300
50
250
Ca-
400
125
275
Smokers who drink
No Disease
Disease
60
55
5
Ca
RR0.17
40
20
20
Ca-
Smokers who do not drink
100
75
25
12
Assessing the Relationship Between a Possible
Cause and an Outcome

• OBSERVED ASSOCIATION

2. Could it be due to confounding or effect
modification?
1. Could it be due to selection or information
bias?
NO
NO
3. Could it be a result of the role of chance?
PROBABLY NOT
4. Could it be causal?
Apply guidelines and make judgment
13
Evaluating an Association

• How can we be sure that what we have found is a
  true association to build a case for cause?
• Epidemiologists go through a 3 step process
• Examine the methodology for bias
• Examine the analysis for confounding and effect
  modification
• Examine the results for statistical significance

14
Inferential Statistics

• Allow for making predictions, estimations or
  inferences about what has not been observed based
  on what has (from a sample) through hypothesis
  testing

15
Inferential Statistics

• Requires testing a hypothesis
• Ho null hypothesis
• No effect or no difference
• Ha research (alternative) hypothesis
• There is an effect or difference

16
Statistical Significance

• I believe that Treatment A is better than
  Treatment B. Why not test my research
  hypothesis? Why test the null hypothesis?
• H0 Treatment A Treatment B
• The research hypothesis requires an infinite
  number of statistical tests
• If we test the null hypothesis, we only have to
  perform one test, that of no difference

17
Steps in Hypothesis Testing (cont.)

• A statistical association tells you the
  likelihood the result you obtained happened by
  chance alone
• A strong statistical association does not show
  cause!
• Every time we reject the null hypothesis we risk
  being wrong
• Every time we fail to reject the null hypothesis
  we risk being wrong

18
Examples of Hypothesis Testing

• We calculated age-adjusted rates for San
  Francisco and San Jose and compared them
• Ho AAR1 AAR2
• Ha There is a statistically significant
  difference between the age-adjusted rates of San
  Francisco and San Jose

19
Hypothesis Testing (cont.)

• We calculated odds ratios and relative risks
• Ho OR 1 (or RR 1)
• Ha There is a statistically significant
  difference between cases and controls (or between
  the exposed and unexposed)

20
Hypothesis Testing (cont.)

• We calculated the SMR for farmers
• Ho SMR 100
• Ha There is a statistically significant
  difference between the cohort and the control
  population

21
Steps in Hypothesis Testing

• Assume the null hypothesis is true
• Collect data and test the difference between the
  two groups
• The probability that you would get these results
  by chance alone is the p-value
• If the p-value is low (chance is an improbable
  explanation for the result), reject the null
  hypothesis

22
Null Hypothesis

• H0 Treatment A (single-dose treatment for UTI)
  Treatment B (multi-dose treatment for UTI)
• Set alpha at .05 (1 in 20 chance of a Type I
  Error)
• You calculate a p-value (the probability that
  what you found was by chance) of .07
• You fail to reject the null hypothesis
• The difference between the groups was not
  statistically significant
• Are the findings clinically important?

23
Null Hypothesis

• There is nothing magical about an alpha of .05 or
  .01
• There are situations where an alpha of .20 is
  acceptable
• The size of the p-value does not indicate the
  importance of the results
• The p-value tells us the probability that we have
  made a mistake that we rejected the null
  hypothesis and claimed a difference when there
  was none
• Results may be statistically significant but be
  clinically unimportant
• Results that are not statistically significant
  may still be important

24
Confidence Interval

• Sometimes we are more concerned with estimating
  the true difference than the probability that we
  are making the right decision (p-value)
• The .95 confidence interval provides the interval
  in which the true value is likely to be found 95
  percent of the time
• If the confidence limit contains 0 or 1 (the
  value of no difference) we cannot reject the null
  hypothesis
• Larger sample sizes yield smaller confidence
  intervals more confidence in the results

25
Are these rates statistically significantly
different from each other? The 95 confidence
intervals tell you.

• AAR1 346.9 (SE 2.5) (344.4, 349.4)
• AAR2 327.8 (SE 14) (313.8, 341.8)

26
AAR1 was statistically significantly higher than
AAR2What about these?

• SMR 112 (99, 125)
• RR 3.4 (1.2, 5.6)

27
Every time we use inferential statistics we risk
being wrong
28
Null Hypothesis H0 Treatment A Treatment B
29
Ways to be wrong

• TYPE I ERROR rejecting the null when the null
  is true there is no difference
• TYPE II ERROR failing to reject the null when
  the null is false there is a difference

30
Power of the Test

• Beta (the probability of a Type II Error) is
  important if we dont want to miss an effect
• We can reduce the risk of Type II Error by
  improving the power of the test
• Power The likelihood you will detect an effect
  of a particular size based on a particular number
  of subjects

31
Power of the Test

• Power is influenced by
• The significance level (probability of a Type I
  Error) you set for the hypothesis test
• The size of the difference you wish to detect
• The number of subjects in the study

32
Subjects in the Study

• More subjects allows for determining smaller
  differences
• More subjects yields smaller confidence intervals
• More subjects cost more money
• More subjects increases the complexity of the
  project
• Do you need more subjects?

33
Maybe! Balance the Following

• Finding no significant difference in a small
  study tells us nothing
• Finding a significant difference in a small study
  may not be able to be replicated because of
  sampling variation
• Finding no significant difference in a large
  study tells us treatments or outcomes are
  essentially equivalent
• Finding a significant difference in a large study
  reveals a true difference, but the findings may
  not be clinically important

34
How Do I Figure Out What to Do?

• Go to the literature to estimate the incidence or
  prevalence of the disease (or rate of recovery)
  in the control population OR
• Estimate the exposure (treatment, screening) in
  the control population
• Determine what difference you wish to detect
  between the control and study populations
• Select an alpha the risk of finding an effect
  when there really isnt one (usually .05 or .01)
• Select a power level the probability of finding
  an effect when there really is one (usually .80
  or .90)
• Calculate or use sample size tables to determine
  how many subjects you will need

35
Finally, can you get that many subjects with your
budget, time, and logistical constraints?

• If not, the study is probably not worth doing
  unless you will accept a lower power or a larger
  alpha

36
Sample Size for a Clinical Trial
H0 Treatment A Treatment B
(1-tail vs. 2-tail test, by which we wish to test
increased or decreased survival with Treatment B)
Sample Size Required for Each Group
Survival with Treatment B
Survival with Treatment A
Power
Significance Level
.05 1-tail
280
.80
10 increase or decrease
30
356
.80
10 increase or decrease
30
.05 2-tail
73
.80
20 increase or decrease
30
.05 1-tail
92
.80
20 increase or decrease
30
.05 2-tail
37
Sample Size for a Clinical Trial
H0 Treatment A Treatment B
(1-tail test, varying the significance level,
power and difference we wish to detect)
Sample Size Required for Each Group
Significance Level
Survival with Treatment B
Survival with Treatment A
Power
280
10 difference
.80
30
.05
73
20 difference
388
10 difference
.90
30
.05
101
20 difference
10 difference
455
.80
30
.01
118
20 difference
590
10 difference
.90
30
.01
20 difference
153