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# Confidence Interval

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## Yip Terry

on 9 July 2013

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#### Transcript of Confidence Interval

The Z-test for 2 Proportions
Showing whether there is difference between the proportions of events in 2 groups

The Chi-square test for Association
Testing the association between the groups of feature and test result.
Incidence is different from prevalence
Measures the total number of cases of disease in a population

Incidence carries information about the risk of having the disease,
while prevalence indicates how widespread the disease is.
Incidence rate
The rate at which new clinical events occur in a population

The number of new events divided by the population at risk of an event in a specific time period

Sometimes it is the person-time at risk.
Correlation
Indicates whether two variables are associated
A value from -1 to 1
-1 representing perfectly negative correlation
1 representing perfectly positive correlation
Confidence Interval
Introduction
Confidence level (1-α)
The proportion of confidence intervals that cover the true parameter
i.e. a 95% C.I. is the interval that you are 95% certain contains the unknown population true value
Introduction
100(1-α)% confidence interval of the test statistic
The acceptance region of a 2-sided hypothesis test

If the test statistic is more extreme than the upper or lower bound of the confidence interval, H is rejected.

The significance level of the test is the complement of the confidence level.
Introduction
Calculators in Confidence Interval:
One sample proportion
Two sample proportions
Correlation
Single incidence rate
Relative Risk and Attributable Risk
Odds Ratios, ARR, RRR, NNT, PEER
Diagnostic Statistics
McNemar’s Test
One Sample Proportion
Proportion
The number of success divided by the sample size
The calculator gives a confidential interval for the estimate
Two sample proportions
Compare two proportions from independent samples
Provide a confidential interval.

Confidence intervals of difference not containing 0
There is a statistically significant difference between the
population proportions
Correlation
Introduction
Confidence interval (C.I.)
A range providing an interval estimate to true but unknown population parameter
Used to indicate the reliability of an estimate
Observed from the particular sample
Different from sample to sample in principle.
Single incidence rate
Single incidence rate
Relative Risk and Attributable Risk
Relative Risk
Ratio of incidence of disease in Exposed group to that in Non-exposed group from a cohort/prospective study
If Relative Risk is larger than 1 a positive association
If it is smaller than 1 a negative association.
Relative Risk and Attributable Risk
Attributable Risk
Amount of disease incidence which can be attributed to an exposure in a prospective study

Population Attributable Risk
Reduction in incidence if the whole population were unexposed, comparing with actual exposure pattern
Relative Risk and Attributable Risk
Relative Risk compares the risk of having a disease for not receiving a medical treatment against people receiving a treatment.
Or
the risk of having side effect in drug treatment against the people not receiving the treatment.
Relative Risk and Attributable Risk
Attributable Risk and Population Attributable Risk
Tell the amount of risk prevented if we do not have certain exposure.

Exposed group
The group of patients exposed to certain factors of interest such as a new treatment, age 45 or above or smoking for 10 years or above.
Odds Ratios, ARR, RRR, NNT, PEER
Odds Ratio (OR)
The ratio of the odds of the outcome in two groups in a retrospective study.
An estimate for the relative risk in a prospective study.
Odds Ratios, ARR, RRR, NNT, PEER
Absolute Risk Reduction (ARR)
Change in risk in the 2 groups and its inverse is the Number Needed to Treat (NNT).
Patient expected event rate (PEER)
Expected rate of events in a patient received no treatment or conventional treatment.
Odds Ratios, ARR, RRR, NNT, PEER
The Z-test for Odds Ratio shows whether the exposure affects the odds of outcome.
OR=1 means exposure has no effect on the odds of outcome.
OR>1 means exposure leads to higher odds of outcome and vice versa.
Odds Ratios, ARR, RRR, NNT, PEER
Diagnostic Statistics
Some terms in diagnostic statistics:
Sensitivity is the ability of the test to pick up what it is testing for and Specificity is ability to reject what it is not testing for.
Likelihood ratios determine how the test result changes the probability of certain outcomes and events.
Diagnostic Statistics
Pre-test and Post-test probabilities are the subjective probabilities of the presence of a clinical event or status before and after the diagnostic test.
For positive test, we find the positive post-test probability
For negative test, we find the negative post-test probability.
McNemar’s Test
McNemar’s Test
A test on a 2x2 contingency table
Check the marginal homogeneity of two dichotomous variables.
McNemar’s Test
It is used for data of the two groups coming from the same participants, i.e. paired data
E.g. Analyze people before and after the treatment in a population.
0
Reference: www.stat.yale.edu
Reference: www.leedefinancial.com
Correlation
The two variables
Come from random samples
Have a Normal distribution (or after transformation)

The confidence interval is a range which contains the true correlation with 100(1-α)% confidence.
Reference: v1shal.com
Reference: ccelearn.csus.edu
Reference: barbarabrenner.net
Reference: painconsortium.nih.gov
Reference: journal.publications.chestnet.org
Reference: www.toonpool.com
Reference: coolrisk.com
Reference: www.highrisefirefighting.co.uk
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