How strong is strong Confidence intervals for measures of associations FETP India.
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Transcript of How strong is strong Confidence intervals for measures of associations FETP India.
![Page 1: How strong is strong Confidence intervals for measures of associations FETP India.](https://reader036.fdocuments.us/reader036/viewer/2022062417/551b6ed5550346a10a8b484c/html5/thumbnails/1.jpg)
How strong is strong
Confidence intervals for measures of associations
FETP India
![Page 2: How strong is strong Confidence intervals for measures of associations FETP India.](https://reader036.fdocuments.us/reader036/viewer/2022062417/551b6ed5550346a10a8b484c/html5/thumbnails/2.jpg)
Competency to be gained from this lecture
Calculate the confidence intervals of the measure of association that
corresponds to a study design
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Confidence intervals for measures of associations
• Exact method (Requires computer) Provides largest confidence intervals Maximizes the beta error
• Semi-exact (Taylor’s series) Based on the variance of the Log of the measure
of association Described in this lecture
• Test-based (Miettinen) Based on the Chi-square Provides the most narrow confidence interval Maximizes the power
![Page 4: How strong is strong Confidence intervals for measures of associations FETP India.](https://reader036.fdocuments.us/reader036/viewer/2022062417/551b6ed5550346a10a8b484c/html5/thumbnails/4.jpg)
Key areas
• Cohort studies (cumulative incidence)• Cohort studies (incidence density)• Case control studies
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Cohort study for calculation of cumulative incidence
Cumulative risk cohorts
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Ill Non ill Total
Exposed a b L1
Non exposed c d L0
Total a+c b+d L1 + L0
Risk among exposed and unexposed
in a cohort study
Risk among exposed : R1 = a/L1
Risk among unexposed : R0 = c/L0Cumulative risk cohorts
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Ill Non ill Total
Exposed 20 4 24
Non exposed 25 247 272
Total 45 251 296
Risk of anthrax among persons exposed and unexposed to
slaughtering cows, Sarkarpara, Murshidabad, West Bengal
Risk among exposed : R1 = a/L1= 83%
Risk among unexposed : R0 = c/L0 = 9%
Relative risk = 83% / 9% = 9.1Cumulative risk cohorts
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Interpretation of the relative risk
• Those exposed to cow slaughtering have a risk of illness that is 9.1 greater than those who were not exposed
• The sample size is limited• Could this association be an effect of
chance alone? Calculation of the confidence interval
Cumulative risk cohorts
![Page 9: How strong is strong Confidence intervals for measures of associations FETP India.](https://reader036.fdocuments.us/reader036/viewer/2022062417/551b6ed5550346a10a8b484c/html5/thumbnails/9.jpg)
€
RR=RR* e±1.96 ( )Var lnRR
€
Var(ln RR) =1a−
1a+ b
+1c−
1c+ d
Formula of the 95% confidence interval
• Confidence interval of relative risk
• Formula of the variance
Cumulative risk cohorts
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Ill Non ill Total
Exposed 20 4 24
Non exposed 25 247 272
Total 45 251 296
Risk of anthrax among persons exposed and unexposed to
slaughtering cows, Sarkarpara, Murshidabad, West Bengal
€
Var(ln RR) =120
−1
20 + 4+
125
−1
25 + 272=0.0446
Cumulative risk cohorts
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Ill Non ill Total
Exposed 20 4 24
Non exposed 25 247 272
Total 45 251 296
Risk of anthrax among persons exposed and unexposed to
slaughtering cows, Sarkarpara, Murshidabad, West Bengal
€
RRL =9.1* e−1.96 0.0446
=6.0
€
RRU =9.1* e+1.96 0.0446
=14
Lower limit:
Upper limit:Cumulative risk cohorts
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Interpretation of the 95% confidence interval of the relative risk
• Those exposed to cow slaughtering have a risk of illness that is 9.1 greater than those who were not exposed
• While this estimate is based upon a sample, there is a 95% probability that the real relative risk lies between 6.0 and 14
• The same formula applies for analytical cross sectional studies
Cumulative risk cohorts
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Cohort study for calculation of incidence density
Incidence density cohorts
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Events Person-years Rate
Exposed a PT1 Rate1
Non exposed c PT0 Rate0
Total a+c PT Rate
Calculation of a relative rate in a cohort study
Relative rate = Rate1/Rate0 = (a/PT1) / (c/PT0)
Incidence density cohorts
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Events Person-years Rate
Exposed 32 12,000 Rate1
Non exposed 20 15,000 Rate0
Total a+c 27,000 Rate
Calculation of a relative rate in a cohort study
Rate1 = 32/ 12,000 = 2.6 per 1,000 PY
Rate0 = 20/ 15,000 = 1.33 per 1,000 PY
Relative rate = 2.6/ 1.33 = 1.95 Incidence density cohorts
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Interpretation of the relative rate
• Those exposed have a rate of illness that is 1.95 greater than those who were not exposed
• The sample size is limited• Could this association be an effect of
chance alone? Calculation of the confidence interval
Incidence density cohorts
![Page 17: How strong is strong Confidence intervals for measures of associations FETP India.](https://reader036.fdocuments.us/reader036/viewer/2022062417/551b6ed5550346a10a8b484c/html5/thumbnails/17.jpg)
• Confidence interval of relative rate
• Formula of the variance
Formula of the 95% confidence interval
€
RR=RR* e±1.96 Var(lnRR)
€
Var(ln RR) =1a+1c
Incidence density cohorts
![Page 18: How strong is strong Confidence intervals for measures of associations FETP India.](https://reader036.fdocuments.us/reader036/viewer/2022062417/551b6ed5550346a10a8b484c/html5/thumbnails/18.jpg)
Events Person-years Rate
Exposed 32 12,000 Rate1
Non exposed 20 15,000 Rate0
Total a+c 27,000 Rate
Calculation of a relative rate in a cohort study
€
Var(ln RR) =132
+120
=0.0812
Incidence density cohorts
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Events Person-years Rate
Exposed 32 12,000 Rate1
Non exposed 20 15,000 Rate0
Total a+c 27,000 Rate
Calculation of a relative rate in a cohort study
€
RRL =1.95 * e−1.96 0.0812
=1.12
€
RRU =1.95 * e+1.96 0.0812
=3.41
Lower limit:
Upper limit:
![Page 20: How strong is strong Confidence intervals for measures of associations FETP India.](https://reader036.fdocuments.us/reader036/viewer/2022062417/551b6ed5550346a10a8b484c/html5/thumbnails/20.jpg)
Interpretation of the 95% confidence interval of the relative rate
• Those exposed have a rate of illness that is 1.95 greater than those who were not exposed
• While this estimate is based upon a sample, there is a 95% probability that the real relative rate lies between 1.1 and 3.4
Incidence density cohorts
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Case control study for calculation of odds ratios
Case control studies
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Cases Controls Total
Exposed a b N/A
Non exposed c d N/A
Total a+c b+d N/A
Odds ration in a case control study
OR = ad/bc
Case control studies
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Cases Controls Total
Exposed 37 26 N/A
Non exposed 3 14 N/A
Total 40 40 N/A
Consumption of pump A water among cholera cases and controls, Barwai, Bhopal, Madhya Pradesh,
India, 2006
OR = ad/bc = (37x14)/ (3x26) = 6.6
Case control studies
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Interpretation of the odds ratio
• The odds of exposure to the pump water is 6.6 higher for cholera cases than for controls
• Since the disease is rare, we infer that the risk of cholera is 6.6 higher for those who drank water from the pump
• The sample size is limited• Could this association be an effect of
chance alone? Calculation of the confidence interval
Case control studies
![Page 25: How strong is strong Confidence intervals for measures of associations FETP India.](https://reader036.fdocuments.us/reader036/viewer/2022062417/551b6ed5550346a10a8b484c/html5/thumbnails/25.jpg)
• Confidence interval of odds ratio
• Formula of the variance
Formula of the 95% confidence interval
€
OR=OR* e±1.96 Var(lnOR)
€
Var(ln OR) =1a+1b+1c+1d
Case control studies
![Page 26: How strong is strong Confidence intervals for measures of associations FETP India.](https://reader036.fdocuments.us/reader036/viewer/2022062417/551b6ed5550346a10a8b484c/html5/thumbnails/26.jpg)
Cases Controls Total
Exposed 37 26 N/A
Non exposed 3 14 N/A
Total 40 40 N/A
Consumption of pump A water among cholera cases and controls, Barwai, Bhopal, Madhya Pradesh,
India, 2006
€
Var(ln RR) =137
+126
+13+
114
=0.457
Case control studies
![Page 27: How strong is strong Confidence intervals for measures of associations FETP India.](https://reader036.fdocuments.us/reader036/viewer/2022062417/551b6ed5550346a10a8b484c/html5/thumbnails/27.jpg)
Cases Controls Total
Exposed 37 26 N/A
Non exposed 3 14 N/A
Total 40 40 N/A
Consumption of pump A water among cholera cases and controls, Barwai, Bhopal, Madhya Pradesh,
India, 2006
€
ORL =6.6 * e−1.96 0.457
=1.76
€
ORU =6.6 * e+1.96 0.457
=25
Lower limit:
Upper limit:Case control studies
![Page 28: How strong is strong Confidence intervals for measures of associations FETP India.](https://reader036.fdocuments.us/reader036/viewer/2022062417/551b6ed5550346a10a8b484c/html5/thumbnails/28.jpg)
Interpretation of the 95% confidence interval of the odds ratio
• Those exposed to the water from pump A have a risk of illness that is 6.6 greater than those who were not exposed
• While this estimate is based upon a sample, there is a 95% probability that the real relative risk lies between 1.76 and 25
Case control studies
![Page 29: How strong is strong Confidence intervals for measures of associations FETP India.](https://reader036.fdocuments.us/reader036/viewer/2022062417/551b6ed5550346a10a8b484c/html5/thumbnails/29.jpg)
Formula for the test-based 95% confidence intervals (For larger
studies)
€
RR=RR1±1.96 χ 2
€
OR=OR1±1.96 χ 2
• Cohort study
• Case control study
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Take home messages
• The 95% confidence interval generates a range of measures of association within which 95% of the values will fall
• Three main methods are available, with an increasing degree of risk of alpha error (and decreasing degree of risk of beta error)
• Statistical calculators (e.g., Epi-Info Statcalc) allow these calculations from a 2x2 table