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How strong is strong. Confidence intervals for measures of associations FETP India. Competency to be gained from this lecture. Calculate the confidence intervals of the measure of association that corresponds to a study design . Confidence intervals for measures of associations.

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how strong is strong

How strong is strong

Confidence intervals for measures of associations

FETP India

competency to be gained from this lecture
Competency to be gained from this lecture

Calculate the confidence intervals of the measure of association that corresponds to a study design

confidence intervals for measures of associations
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
key areas
Key areas
  • Cohort studies (cumulative incidence)
  • Cohort studies (incidence density)
  • Case control studies
risk among exposed and unexposed in a cohort study
Risk among exposed and unexposed in a cohort study

Ill Non ill Total

Exposed a b L1

Non exposed c d L0

Total a+c b+d L1 + L0

Risk among exposed : R1 = a/L1

Risk among unexposed : R0 = c/L0

Cumulative risk cohorts

slide7
Risk of anthrax among persons exposed and unexposed to slaughtering cows, Sarkarpara, Murshidabad, West Bengal

Ill Non ill Total

Exposed 20 4 24

Non exposed 25 247 272

Total 45 251 296

Risk among exposed : R1 = a/L1= 83%

Risk among unexposed : R0 = c/L0 = 9%

Relative risk = 83% / 9% = 9.1

Cumulative risk cohorts

interpretation of the relative risk
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

formula of the 95 confidence interval
Formula of the 95% confidence interval
  • Confidence interval of relative risk
  • Formula of the variance

Cumulative risk cohorts

slide10
Risk of anthrax among persons exposed and unexposed to slaughtering cows, Sarkarpara, Murshidabad, West Bengal

Ill Non ill Total

Exposed 20 4 24

Non exposed 25 247 272

Total 45 251 296

Cumulative risk cohorts

slide11
Risk of anthrax among persons exposed and unexposed to slaughtering cows, Sarkarpara, Murshidabad, West Bengal

Ill Non ill Total

Exposed 20 4 24

Non exposed 25 247 272

Total 45 251 296

Lower limit:

Upper limit:

Cumulative risk cohorts

interpretation of the 95 confidence interval of the relative risk
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

calculation of a relative rate in a cohort study
Calculation of a relative rate in a cohort study

Events Person-years Rate

Exposed a PT1 Rate1

Non exposed c PT0 Rate0

Total a+c PT Rate

Relative rate = Rate1/Rate0 = (a/PT1) / (c/PT0)

Incidence density cohorts

calculation of a relative rate in a cohort study15
Calculation of a relative rate in a cohort study

Events Person-years Rate

Exposed 32 12,000 Rate1

Non exposed 20 15,000 Rate0

Total a+c 27,000 Rate

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

interpretation of the relative rate
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

formula of the 95 confidence interval17
Formula of the 95% confidence interval
  • Confidence interval of relative rate
  • Formula of the variance

Incidence density cohorts

calculation of a relative rate in a cohort study18
Calculation of a relative rate in a cohort study

Events Person-years Rate

Exposed 32 12,000 Rate1

Non exposed 20 15,000 Rate0

Total a+c 27,000 Rate

Incidence density cohorts

calculation of a relative rate in a cohort study19
Calculation of a relative rate in a cohort study

Events Person-years Rate

Exposed 32 12,000 Rate1

Non exposed 20 15,000 Rate0

Total a+c 27,000 Rate

Lower limit:

Upper limit:

interpretation of the 95 confidence interval of the relative rate
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

odds ration in a case control study
Odds ration in a case control study

Cases Controls Total

Exposed a b N/A

Non exposed c d N/A

Total a+c b+d N/A

OR = ad/bc

Case control studies

slide23
Consumption of pump A water among cholera cases and controls, Barwai, Bhopal, Madhya Pradesh, India, 2006

Cases Controls Total

Exposed 37 26 N/A

Non exposed 3 14 N/A

Total 40 40 N/A

OR = ad/bc = (37x14)/ (3x26) = 6.6

Case control studies

interpretation of the odds ratio
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

formula of the 95 confidence interval25
Formula of the 95% confidence interval
  • Confidence interval of odds ratio
  • Formula of the variance

Case control studies

slide26
Consumption of pump A water among cholera cases and controls, Barwai, Bhopal, Madhya Pradesh, India, 2006

Cases Controls Total

Exposed 37 26 N/A

Non exposed 3 14 N/A

Total 40 40 N/A

Case control studies

slide27
Consumption of pump A water among cholera cases and controls, Barwai, Bhopal, Madhya Pradesh, India, 2006

Cases Controls Total

Exposed 37 26 N/A

Non exposed 3 14 N/A

Total 40 40 N/A

Lower limit:

Upper limit:

Case control studies

interpretation of the 95 confidence interval of the odds ratio
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

formula for the test based 95 confidence intervals for larger studies
Formula for the test-based 95% confidence intervals (For larger studies)
  • Cohort study
  • Case control study
take home messages
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