Transcript Session2 - Mater Research

Statistics for clinical
research
An introductory course
Session 2
Comparing two groups
Previous session
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Normal distribution
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Standard Deviation (of measurements)
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Standard Error (of the mean)
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Confidence Interval of measurements
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Confidence Interval of the mean
Main overview
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Dealing with both Means and Proportions
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Two groups will be compared
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Effect Size along with its Confidence
Interval (C.I.) will be calculated from data
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Remember the C.I. tells us about the
uncertainty of the effect size
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The different calculations for effect sizes
Means
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Means calculated from measured data
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Standard Deviation (of Measurements)
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Standard Error (of the Mean)
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Effect Size = Difference in Means
Proportions
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Proportion
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Binary outcome (e.g. yes/no)
Number between 0 and 1
2x2 table
Group 1
Group 2
Positive
p1
p2
Negative
n1
n2
Effect sizes
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Risk Difference (RD); Relative Risk (RR);
Odds Ratio (OR)
Comparing two groups
Two proportions
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Risk Difference
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Number Needed to Treat
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Relative Risk
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Odds Ratio
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Fisher’s Exact Probability
Two means
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The t-distribution
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Difference between means
Risk Difference
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Risk is a proportion (number between 0
and 1)
Each group incorporate its own risk
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Group 1: 15 people are given money…
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Happy
= 12
Not happy = 3
Total
= 15
Risk of happiness = 12/15 = 0.8
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Group 2: 10 people are not given money…
Happy
=5
Not happy = 5
Total
= 10
Risk of happiness = 5/10 = 0.5
Risk Difference
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Risk Difference (RD) is the risk of
one group subtracted from the risk
of the other group
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RD = 0.8 – 0.5 = 0.3
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Excel file “TwoGroups.xls”
Comparing two groups
Two proportions
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Risk Difference
Number Needed to Treat
Relative Risk
Odds Ratio
Fisher’s Exact Probability
Two means
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The t-distribution
Difference between means
Number Needed to Treat
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NNT = 1 / Risk Difference
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If RD = 0.21 (21%), then need to treat
100 to prevent 21 adverse events
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NNT = 1 / 0.21 = 5 (rounded up)
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5 need to be treated to prevent 1
additional adverse event
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Excel file “TwoGroups.xls”
Comparing two groups
Two proportions
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Risk Difference
Number Needed to Treat
Relative Risk
Odds Ratio
Fisher’s Exact Probability
Two means
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The t-distribution
Difference between means
Relative Risk (RR)
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Risk is a proportion
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Each of the two groups has its own risk
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Relative Risk (RR) is the ratio of two risks
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RR is mostly used for cohort studies
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Ratios do not have a Normal distribution
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log(RR) has a Normal distribution
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Confidence interval calculations require a
Normal distribution
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Excel file “TwoGroups.xls”
Relative Risk (RR)
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If Confidence Interval…
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Contains 1: No difference in
outcome between two groups
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<1: Less risk in group 1
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>1: Greater risk in group 1
Comparing two groups
Two proportions


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Risk Difference
Number Needed to Treat
Relative Risk
Odds Ratio
Fisher’s Exact Probability
Two means

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The t-distribution
Difference between means
Odds Ratio (OR)
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Odds – the number who have an event
divided by the number who do not
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Odds of an event occurring is obtained for
both groups
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OR mostly used for case-control studies
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Ratios are not Normally distributed
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log(OR) has a Normal distribution
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Confidence Interval calculations require a
Normal distribution
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Extra: Logistic regression is typically used to
adjust odds ratios to control for potential
confounding by other variables
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Excel file “TwoGroups.xls”
Odds Ratio (OR)
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If Confidence Interval…
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Contains 1: No difference in
outcome between two groups
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<1: Odds in group 1 significantly
less
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>1: Odds in group 1 significantly
greater
Comparing two groups
Two proportions
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Risk Difference
Number Needed to Treat
Relative Risk
Odds Ratio
Fisher’s Exact Probability
Two means
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The t-distribution
Difference between means
Fisher’s Exact Test
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Determines if significant associations
exist between group and outcome
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Used when sample sizes are small
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i.e. cell count < 5 in a 2x2 table
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Alternative to the Chi-Square test
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Test only provides a p-value (no C.I.)
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Probability of observing a result more
extreme than that observed
Comparing two groups
Two proportions
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Risk Difference
Number Needed to Treat
Relative Risk
Odds Ratio
Fisher’s Exact Probability
Two means
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The t-distribution
Difference between means
The t-distribution
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Population SD is unknown and
is estimated from the data
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Blue curve = Normal
distribution
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Green = t-distribution with 1
degree of freedom (df)
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Red = t-distribution, 2 df
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Underlying theory of the t-test
Comparing two groups
Two proportions
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Risk Difference
Number Needed to Treat
Relative Risk
Odds Ratio
Fisher’s Exact Probability
Two means

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The t-distribution
Difference between means
Difference between means
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Two sample t-test is used to test the
difference between two means
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Measurements must be considered
Normally distributed
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Quite powerful. A decision can be
made with a small sample size…much
smaller than when compared to
proportions
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Excel file “TwoGroups.xls”
Forest Plot
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Plot effect sizes with confidence intervals
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Useful in comparing multiple effect sizes
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Go to applet on website:
http://www.materrsc.org/Course/CI_Diff.html
Additional topics
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Normality tests (e.g. Shapiro-Wilk)
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Test for equality of variances (e.g.
Bartlett’s test)
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t-test for unequal variances
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Paired t-test for dependent samples
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Comparing more than two groups
(e.g. one-way ANOVA)
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Nonparametric tests