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- CONFIDENCE INTERVAL Dr.RENJ U
- OVERVIEW INTRODUCTION CONFIDENCE INTERVAL CONFIDENCE LEVEL CONFIDENCE LIMITS HOW TO SET? FACTORS – SET SIGNIFICANCE APPLICATIONS
- INTRODUCTIO N Statistical parameter Descriptive statistics : Describe what is there in our data Inferential statistics : Make inferences from our data to more general conditions
- Inferential statistics Data taken from a sample is used to estimate a population parameter Hypothesis testing (P-values) Point estimation (Confidence intervals)
- POINT ESTIMATE Estimate obtained from a sample Inference about the population Point estimate is only as good as the sample it represents Random samples from the population - Point estimates likely to vary
- ISSUE ??? Variation in sample statistics
- SOLUTION Estimating a population parameter with a confidence interval
- CONFIDENCE INTERVAL A range of values so constructed that there is a specified probability of including the true value of a parameter within it
- CONFIDENCE LEVEL Probability of including the true value of a parameter within a confidence interval Percentage
- CONFIDENCE LIMITS Two extreme measurements within which an observation lies End points of the confidence interval Larger confidence – Wider
- A point estimate is a single number A confidence interval contains a certain set of possible values of the parameter Point Estimate Lower Confidence Limit Upper Confidenc e Limit Width of confidenceinterval
- HOW TO SET
- CONCEPTS NORMAL DISTRIBUTION CURVE MEAN ( µ ) STANDARD DEVIATION (SD) RELATIVE DEVIATE (Z)
- NORMAL DISTRIBUTION CURVE
- Perfect symmetry Smooth Bell shaped Mean (µ) Median Mode SD(σ) - 1 Area - 1 0
- RELATIVE DEVIATE (Z) Distance of a value (X) from mean value (µ) in units of standard deviation (SD) Standard normal variate
- Z =x – µ SD
- CONFIDENCE LIMITS From µ - Z(SD) To µ + Z(SD)
- CONFIDENCE INTERVAL
- FACTORS – TO SET CI Size of sample Variability of population Precision of values
- SAMPLE SIZE Central Limit Theorem “Irrespective of the shape of the underlying distribution, sample mean & proportions will approximate normal distributions if the sample size is sufficiently large” Large sample – Narrow CI
- SKEWED DISTRIBUTION
- VARIABILITY OF POPULATION
- POPULATION STATISTICS Repeated samples Different means Standard normal curve Bell shape Smooth Symmetrical
- POPULATION STATISTICS
- Population mean (µ) Standard error - Sampling (SD/√n) Z = x – µ SD/√n Confidence limits From µ - Z(SE) To µ + Z(SE)
- 95% 95% sample means are within 2 SD of population mean
- PRECISION OF VALUES Greater precision Narrow confidence interval Larger sample size
- PRECISION OF VALUES
- SIGNIFICANCE
- 95% Significance Observed value within 2 SD of true value
- CONFIDENCE INTERVAL AND Α ERROR Type I error Two groups Significant difference is detected Actual – No difference exists False Positive
- Confidence level is usually set at 95% (1– ) = 0.95
- MARGIN OF ERROR n σ zME α/ 2 x
- Margin of error Reduce the SD (σ↓) Increase the sample size (n↑) Narrow confidence level (1 – ) ↓
- P VALUE 95% CI corresponds to hypothesis testing with P <0.05
- SIGNIFICANC E If CI encloses no effect, difference is non significant
- P value – Statistical significance Confidence Interval – Clinical significance
- APPLICATIONS CLINICAL TRIALS
- Margin of error Increase the sample size Reduce confidence level Dynamic relation Confidence intervals and sample size
- EXAMPLE Series of 5 trials Equal duration Different sample sizes To determine whether a novel hypolipidaemic agent is better than placebo in preventing stroke
- Smallest trial 8 patients Largest trial 2000 patients ½ of the patients in each trial – New drug All trials - Relative risk reduction by 50%
- QUESTION S In each individual trial, how confident can we be regarding the relative risk reduction Which trials would lead you to recommend the treatment unequivocally to your patients
- MORE CONFIDENT - LARGER TRIALS CI - Range within which the true effect of test drug might plausibly lie in the given trial data
- Greater precision Narrow confidence intervals Large sample size
- THERAPEUTIC DECISIONS Recommend for or against therapy ?
- Minimally Important Treatment Effect Smallest amount of benefit that would justify therapy Points
- Uppermost point of the bell curve Observed effect Point estimate Observed effect
- Tails of the bell curve Boundaries of the 95% confidence interval Observed effect
- TRIAL 1
- TRIAL 2
- CI overlaps the smallest treatment benefit Not Definitive Need narrower Confidence interval Larger sample size
- TRIAL 3
- TRIAL 4
- CI overlaps the smallest treatment benefit Not Definitive Need narrower Confidence interval Larger sample size
- CONFIDENCE INTERVALS FOR EXTREME PROPORTIONS Proportions with numerator – 0 Proportions approaching - 1 Proportions with numerators very close to the corresponding denominators
- NUMERATOR - 0 Rule of 3 Proportion – 0/n Confidence level – 95% Upper boundary – 3/n
- EXAMPL E 20 people – Surgery None had serious complications Proportion 0/20 3/n – 3/20 15%
- PROPORTIONS APPROACHING - 1 Translate 100% into its complement
- EXAMPL E Study on a diagnostic test 100% sensitivity when the test is performed for 20 patients who have the disease. Test identified all 20 with the disease as positive – 100% No falsely negatives – 0%
- 95% Confidence level Proportion of false negatives - 0 /20 3/n rule Upper boundary - 15% (3 /20 ) Sensitivity Lower boundary Subtract this from 100% 100 – 15 = 85%
- NUMERATORS VERY CLOSE TO THE DENOMINATORS Rule Numerator X 1 5 2 7 3 9 4 10
- 95% Confidence level Upper boundary –
- CONCLUSION Confidence interval Confidence level Confidence limits 95% Observed value within 2 SD Population statistics
- THANK YOU

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