Confidence interval
-
Upload
dr-renju-s-ravi -
Category
Health & Medicine
-
view
41 -
download
1
Transcript of Confidence interval
CONFIDENCE INTERVAL
Dr.RENJU
OVERVIEW INTRODUCTION
CONFIDENCE INTERVAL
CONFIDENCE LEVEL
CONFIDENCE LIMITS
HOW TO SET?
FACTORS – SET
SIGNIFICANCE
APPLICATIONS
INTRODUCTION
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 interval
A point estimate is a single number A confidence interval contains a certain set of possible values of the parameter
Point EstimateLower Confidence Limit
UpperConfidence Limit
Width of confidence interval
HOW TO SET
CONCEPTS
NORMAL DISTRIBUTION CURVE
MEAN ( µ )
STANDARD DEVIATION (SD)
RELATIVE DEVIATE (Z)
NORMAL DISTRIBUTION CURVE
Perfect symmetrySmoothBell shaped
Mean (µ)MedianMode
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
σzME 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
SIGNIFICANCE
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%
QUESTIONS 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
EXAMPLE 20 people – Surgery None had serious complications
Proportion 0/20 3/n – 3/20 15%
PROPORTIONS APPROACHING - 1
Translate 100% into its complement
EXAMPLE 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 52 73 94 10
95% Confidence level
Upper boundary –
CONCLUSION
Confidence interval
Confidence level
Confidence limits
95%
Observed value within 2 SD
Population statistics
THANK YOU