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# Case control study - Part 2

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### Case control study - Part 2

1. 1. Case control study - Part 2 Dr. Rizwan S A, M.D.,
2. 2. Outline      Basic Concepts in the Assessment of Risk Sample Size Basic Method of Analysis Multivariate Analysis Nested Case-Control
3. 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. 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. 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. 6. Figure A, Odds ratio (OR) in a cohort study. B Odds ratio (OR) in a case-control study.
7. 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. 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.
9. 9. Table
10. 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. 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. 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. 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. 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. 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] 
16. 16. Interpretation of Relative Risk-table
17. 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. 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. 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. 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
21. 21. Sample Size and Power for Unmatched Studies
22. 22. Sample Size and Power for Unmatched Studies
23. 23. Sample Size and Power for Unmatched Studies
24. 24. Sample Size and Power with Multiple Control per Case-With unequal controls per case
25. 25. Sample Size and Power with Multiple Control per Case-With unequal controls per case
26. 26. Sample Size and Power with Multiple Control per Case-With unequal controls per case
27. 27. Smallest detectable Relative Risk  Given fixed n,a,p0;what is smallest R can be detected with specified power?
28. 28. Optimal Allocation  Equal Case-control cost
29. 29. Optimal Allocation  Unequal cost: Max power for fixed total cost
30. 30. Unequal cost: Max power for fixed total cost
31. 31. Optimal Allocation  Minimum cost for Fixed Power
32. 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. 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. 36. Sample Size and Power for Pair-Matched Studies
37. 37. Sample Size and Power for Pair-Matched Studies
38. 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. 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
40. 40. Sub group analysis
41. 41.  Multiple control per case If c control per case n’≈(c+1)n/2c1
42. 42. Further consideration in estimating sample size Dependence of sample size on parameter specification
43. 43. Further consideration in estimating sample size  Dependence of sample size on parameter specification
44. 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
45. 45. Unmatched Analysis of a Single 2*2 table
46. 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
47. 47.  Mantel-Haenszel method
48. 48. Test for Heterogeneity of OR
49. 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. 51. Test for Dose Response-tab  Trend with Dose response Trend with severity of dis. Adjustment for comnfounding-tab  Test based confidence limits  
52. 52. *-
53. 53. Matched Analysis with One Control Per Case
54. 54. Matched Analysis with One Control Per Case-*   Test for sig and CI Probability of exposed case is estimated by p=b/b+c
55. 55. Matched Analysis with Two Control Per Case
56. 56. Test of sig ,CI
57. 57. Matched Analysis with Three /more Control Per Case
58. 58. Estimation of the Etiologic Fraction  Unmatched study with dichotomous E
59. 59. Multivariate Analysis       Logistic Regression For Case-Control Studies Estimation of Logistic Parameter Application Of Logistic Regression Matched Analysis Confounder Score Log linear Models
60. 60. Introduction  Analysis concerned with the variability of a Dependent variable related to multiple Explanatory var.
61. 61. Logistic Regression For Case-Control Studies
62. 62. Estimation of Logistic Parameter  Discriminant Analysis ◦ to isolate relevant risk factors in a logistic model by tests of sig
63. 63. Maximum Likelihood Estimation To estimate the actual magnitude of parameters or probability of events under the logistic model.
64. 64.  CI and Test of Sig.
65. 65. Application Of Logistic Regression
66. 66. Application Of Logistic Regression
67. 67. Matched Analysis Matched  Unmatched analysis of Matched data? 
68. 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. 69. Log linear Models  Approach to analyze Case-control data when all var. are discrete-categorical/continuous have been stratified.
70. 70. Thank You