1.
Case control study - Part 2
Dr. Rizwan S A, M.D.,
2.
Outline
Basic Concepts in the Assessment of Risk
Sample Size
Basic Method of Analysis
Multivariate Analysis
Nested Case-Control
3.
Basic Concepts in the Assessment of
Risk
Disease Occurrence
Relative Measures of Disease Occurrence
Cohort and Case-Control Sampling Schemes
Risk of Disease Attributable to Exposure
Exposure
Interpretation of Relative Risk
Cumulative Risk of Disease
Association and Testing for Significance
Relative Risk as a measure of the Strength Of
Association
Confounding
Interaction
Summary
4.
Disease Occurrence
•
Cumulative Incidence
Number of persons with disease onset during a specified
period
Number of persons at risk in the beginning of the period
• Incidence Rate
Number of new disease events in a specified period
The sum of the subjects disease free time of follow up during
this period
• Prevalence
Number of persons with a disease at a certain point intime
Number of persons in the population at that point in time
5.
Relative Measures of Disease Occurrence
Relative Risk: the ratio of the risk of disease in exposed
individuals to the risk of disease in non exposed
individuals.
Odds Ratio Ψ
The odds of an event can be defined as the ratio of the
number of ways the event can occur to the number of
ways the event cannot occur
Case Control study can’t determine IR of disease ass. with
+/- study exposure ,it can estimate the ratio of IR (RR)
in terms of Odds Ratio
•
6.
Figure A, Odds ratio (OR) in a cohort study. B Odds ratio (OR) in a case-control study.
7.
When Odds ratio a good estimate of
RR?
1. When the cases studied are representative, with regard to
history of exposure, of all people with the disease in the
population from which the cases were drawn.
2. When the controls studied are representative, with regard to
history of exposure, of all people without the disease in the
population from which the cases were drawn.
3. When the disease being studied does not occur frequently.
8.
The odds ratio is a good estimate of the
relative risk when a disease is infrequent.
The odds ratio is not a good
estimate of relative risk when a
disease is not infrequent.
10.
Cohort Sampling-Table
The incidence rates/relative risk/odds of dis. among
exposed /non exposed estimated from sample agree with
the values in target population but odds of exposure are
different in both.
11.
Case-Control sampling-Table
The proportion of incident cases among exposed /non
exposed individual in sample is different from target
population , but odds of exposure are same
12.
Risk of Disease Attributable to Exposure
Q.How much of the disease that occurs can be attributed to
a certain exposure?
A.The attributable risk,defined as the amount or proportion
of disease incidence (or disease risk) that can be
attributed to a specific exposure(δ)
OR
δ=p1-p2 =(R-1)p2≈(Ψ-1)p2
13.
Exposure-Specific Risk
IR for entire populations (p) are a weighted avg. of ExposureSpecific rates p1 and p2,
pe=M1/N
p=N1/N
p=p1pe +p2(1-pe)
p1=Rp2
p2=p/{Rpe+(1-pe)}
p̂2 = ̂p/{ ̂Ψ ̂pe+(1-̂pe)}
P̂1= ̂Ψp̂2
P(D/Ei)=P(Ei/D)P(D)/ P(Ei/D)P(D)+P(Ei/D̅)P(D̅)
The exp-sp prob of dis. can be determined given estimate of
overall probability of dis and proportion of cases and controls
in ith exp category.
14.
Etiologic Fraction –Table1
λ =proportion of all cases in the target population
attributable to exposure.
λ =N1-Np2/N1
λ= pe(R-1)/[pe(R-1)+1]
eg-Table
p2=p(1- λ); p1= Rp(1- λ)
15.
Exposure-table
Intensity dimension
Time dimension
Estimation of Population Exposure Rate From Control
Series
Control series must be representative of individual without dis. In
target population
Dis. must be rare.
Unconditional prob of ex in target population=weighted
avg of cond.prob of ex among dis. and non-dis.
P(E)= P(E/D)P(D)+P(E/D̅)P(D̅)
If P(D) ≈0,P(D̅) ≈1; P(E)=P(E/D̅) ,(rare- pê ,̂̂ Ψ )
λ̂= pê (̂̂Ψ -1)/[pê (̂̂ Ψ -1)+1]
17.
Relative risk as a measure of strength of
association
If X uncontrolled var. which doesn’t interact with E
accounts for all the risk due to E;R>1
• X must be R times more common among E/NE;
P(X/E)>RP(X/E̅)
• X must be as strong a risk facto as the E
•
Presence of multiple real causes reduces the apparent
relative risk for any one of them
18.
Interaction-Table
Effect modification tells us that the association between
exposure and disease is modified by a third factor.
When IR of a dis. in presence of 2 or > risk factors
differs from IR resulting from combination of their
individual effects-Interaction
◦ Synergism or Antagonism special case of Positive and Negative
Interaction .
◦ Additive
(p11-p00)=(p10-p00)+(p01-p00)
(Rxy-1)=(Rx-1)+(Ry-1)
◦ Multiplicative
p11/p00=(p10/p00)(p01/p00)
Rxy=RxRy
19.
Sample Size
Sample Size and Power for Unmatched Studies
Sample Size and Power with Multiple Control
per Case
Smallest detectable Relative Risk
Optimal Allocation
Adjustment for Confounding
Sample Size and Power for Pair-Matched
Studies
Sequential Case-Control Studies
Summary
20.
Sample size-Inroduction
Study should be large to avoid:
◦ Claiming that E is associated with D when it is not- α
◦ E is not associated with D when it is- β
Probability of finding the sampling estimate of RR(OR) differs
sig. from unity=1- β=Power
How many subjects for case control
study(matched/unmatched)?
◦
◦
◦
◦
Relative frequency of E among controls in target population-p0
Hypothesized RR associated with E of public health imp-R
Desired level of Significance- α
Desired study power, 1- β
31.
Optimal Allocation
Minimum cost for Fixed Power
32.
Adjustment for Confounding
Sample size for Case control study that use stratified
analysis to adjust for confounding must specify
◦ RR
◦ Estimated exposure rate among controls in each of k
strata po1,p02 etc
◦ Estimated proportion of cases in each strata f1,f2
◦ Significance- α
◦ power, 1- β
Eg-
35.
Sample Size and Power for Pair-Matched
Studies
Exposed (+) ,Unexposed (-)
Case, control(++)(+-)(--)(-+)
◦ For specified α,β no. of discordant pairs required for RR
36.
Sample Size and Power for Pair-Matched
Studies
37.
Sample Size and Power for Pair-Matched
Studies
38.
Sequential Case-Control Studies
Rather than waiting until a predetermined no. of cases and
controls have accumulated it proceeds as data become
available over time.
Sample size<for fixed sample size analysis.
Data collection continues until one either obtains a significant
case-control difference or until one reaches a predetermined
maximum no of stages , S.
eg
39.
Further consideration in estimating sample
size
Adjustment for Non response
◦ If rate of non response=r*100 percent,
◦ no of subjects to obtain final series size: na= n/1-r
◦ Eg-150/.85=177
Sub group analysis
41.
Multiple control per case
If c control per case n’≈(c+1)n/2c1
42.
Further consideration in estimating sample size
Dependence of sample size on parameter specification
43.
Further consideration in estimating sample size
Dependence of sample size on parameter specification
44.
Basic Method of Analysis
Unmatched Analysis of a Single 2*2 table
Adjustment for Confounding
Assessment of Individual and Joint Effects of Two
or More Variables
Test for Dose Response
Test-Based Control Limits
Matched Analysis with One Control Per Case
Matched Analysis with Two Control per Case
Matched Analysis with Three or more Control per
Case
Estimation of the Etiologic Fraction
46.
Adjustment for confounding
If OR-constant across subgroups/consistently
elevated/reduced=combine them to form a summary
estimate.
Summary Estimate as having been adjusted for effects of
variables used in stratification.
Methods for obtaining point estimates , test of
significance , CI for summary OR
◦ Mantel-Haenszel Method-weighted avg of individual OR
◦ Wolfes Method-constant OR across subgroup
49.
Assessment of Individual and Joint Effects
of Two or More Variables-tab
CI/test of sig=same
Test of heterogeneity and Confidence limits are
diff.
Adjustment for confounding-table`1
51.
Test for Dose Response-tab
Trend with Dose response
Trend with severity of dis.
Adjustment for comnfounding-tab
Test based confidence limits
68.
Confounder Score-tab
Each case and control is assigned a score that indicates
how ‘caselike’ that a person is estimated to be in absence
of exposure to study factor.
Each individual is assigned to one of strata
Stratum specific OR
Combined estimate by M-H method.
69.
Log linear Models
Approach to analyze Case-control data when all var. are
discrete-categorical/continuous have been stratified.
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