Transcript Comparing groups (new window)

Comparing groups
Research questions
Is outcome of birth related to
deprivation?
 Are surgical and conservative
treatments equally effective in
resolving schapoid lunate fractures?
 Does survival from diagnosis to death
vary with Dukes’ score?

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Issues in comparing groups

Type of data
 Categorical


Ordered
Unordered
 Continuous
 Survival

Dependence of observations
 Different
case
 Same cases or matched cases

Number of groups
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So – WOT test?

Categorical data
 Chi squared
 Test of association
 Test of trend

Continuous data
 Normal (plausibly!)
 Two groups
 t tests
 More than two groups
 ANOVA

Survival data
 Logrank
test
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Categorical data

Are males and females equally likely to
meet targets to reduce cholesterol?
 Test
of association
 Example 1

Does the proportion of mothers developing
pre-eclampsia vary by parity (birth order)?
 Test
of trend
 Example 2
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Hypotheses to be tested


H0: Males and females equally likely to
meet targets to reduce cholesterol
H1: Males and females not equally likely to
meet targets to reduce cholesterol
 Two-sided

test
H2: Males are less likely to meet targets to
reduce cholesterol
 One
sided test
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The test statistic

Used to decide whether the null hypothesis is:
 Accepted
 Rejected
in favour of the alternative

Value calculated from the data

Significance assessed from known distribution
of the test statistic
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Example 1: Crosstabulation
Analyse
 Descriptive
statistics
 Crosstabs

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Statistics and display
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Output

Males more likely than females to achieve the target

P<0.001
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Testing for trend

When one of the classes is ordinal:
 Deprivation
score
 Age
group
 Severity of disease

More sensitive Chi-squared tests are
available
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Example 2: Test of trend
Association
Trend


Pre-eclamplsia is associated with parity P=0.001
The linear trend is significant P<0.001
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Small
numbers
Now you’ve
wrecked it!

Chi-squared not appropriate:
 In
a 2 by 2 table (i.e. 1 dof)
 Don’t
panic!!!!!
 Total frequency <20
 Total frequency between 20 and 40, and smallest
 SPSS
will
sort
out
these
details
expected frequency <5
tables with
than 1 dofto tell you
Return
amore
message

In



More than one fifth of cells have expected frequency
<5
Any cell has expected frequency <1
Yates’ correction for 2 by 2 table (i.e. 1 dof)
 When
Chi-squared not appropriate
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Splitting the test statistic

To assess the contribution of one
category to overall significance
 Corresponding
row or column removed
 Test statistic recalculated
 New test statistic no longer significant

The category concerned is responsible for the
effect
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Comparing two means

Dependent
 Same

person
Measured on two occasions

Cholesterol
 Baseline
 After treatment
 Measured

Matching on factors known to affect outcome


on two matched cases
Age, BMI
Independent
 Different

people
Cholesterol at baseline in males and females
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Dependent data: Example 3

Cholesterol measured on two occasions
 Baseline
 After

treatment
Analyse
 Compare
means
 Paired sample t test

Assuming …


Checked distribution
Plausibly Normal
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Dependent data
Cholesterol reduced after treatment
From 6.09 (0.036) to 3.67 (0.200)
P<0.001
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Independent data: Example 4

Cholesterol measured at baseline
 Males
 Females

Analyse
 Compare
means
 Independent samples t test
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Independent data
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Independent data




Baseline cholesterol different in males and
females
Males 5.83 (0.048)
Females 6.36 (0.051)
P<0.001
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Comparing sample variances

Think!
 If
SDs are unequal, does it make sense to
compare means?
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Comparing more than 2 groups






ANOVA
Total variance = V
Between groups variance = B
Within groups variance = W
Ratio = B/W
No differences between groups
 Ratio

=1
Higher the ratio
 Larger
differences between groups
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One-way ANOVA

One factor

Smoking status


BMI category


Underweight, normal, pre-obese, obese
School type


Never, current, former
Grammar, Independent, Comprehensive
Tests are:


Global between-group differences
Specific comparisons

e.g. all groups against the first

Contrasts
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One-way ANOVA: Example 5




Is baseline cholesterol related to BMI?
Analyse
General linear model
Univariate
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One-way ANOVA: Model
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One-way ANOVA: Contrasts
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Contrasts

All pairwise combinations
 Bonferroni

Specific comparisons
 Contrasts

 From
the previous - Difference
 From
the first
 From
the last
Simple
Trend
 Linear
 Non-linear
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One-way ANOVA: Profile plots
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One-way ANOVA: Post-hoc
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One-way ANOVA: Options
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One-way ANOVA: Output
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One-way ANOVA: Output
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One-way ANOVA: Output
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One-way ANOVA: Plot
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Two-way ANOVA

Two factors
 Time

Post-surgery review
 Gender
 Ethnicity
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Within- and between-subject factors

Within-subjects factors
 Side
(left, right)
 Review
(pre-treatment, post-treatment)
 Treatment

(in a cross-over study)
Between-subjects factors
 Gender
 BMI
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Factor or covariate?

Factors are categorical variables

Otherwise they are covariates
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Two-way ANOVA: Example 6

Is baseline cholesterol related to
 BMI?
 Gender?
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Two-way ANOVA: Output
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Survival

Time between entry to study and
subsequent event
 Death
 Full
recovery
 Recurrence of disease
 Readmission to hospital
 Dislocation of joint
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What’s the problem?

Impossible to wait until all members of
the study have experienced the event
 Some
might leave the study before the
event occurred


Censored events

Survival time unknown
Times not Normally distributed
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Survival methods

Life table
 Events


One year, three year, five year post-op review

Survival times are inexact
Kaplan-Meier
 Time

are grouped into intervals
at which event occurred known

Time to mobility during hospital stay

Survival times are exact
Comparing groups
 Logrank
test
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Outcomes from analysis

Life table (life table)
 One

Survival table (Kaplan-Meier)
 One

row for each interval
row for each event or censored observation
Time to survival
 Mean,

median, quartiles, SE
Survival curve
 Probability

of no event by time t
Hazard curve
 Probability
of event by time t
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Comparing survival in groups

Log-rank
 Test
of survival experience of all groups
 Groups


have the same survival curve
Survival is comparable for all groups
Trend
 If
groups are ordinal a trend test might be
appropriate
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Cox regression


Used to investigate effect of continuous
variables on survival time
 Age
at diagnosis on time to death
 BMI
on time to dislocation
Estimates hazard ratio
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Data for analysis

Time to survival
 Time
to event (if event occurred)
 Time to end of study (censored event)

Status
 Identifies
cases in which the event has
happened
 Can be multiple


1=Disease free, 2=Recurrence, 3=Death
Group
 Treatment
regime
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Example 7
 Does
survival from surgery to death
vary with Dukes’ score?
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Define time and event
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Define factor(s) and test
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Select options
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Output
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Summary





Are males and females equally likely to
meet targets to reduce cholesterol?
Does the proportion of mothers developing
pre-eclampsia vary by parity (birth order)?
Does cholesterol change following
treatment?
Is cholesterol the same in males and
females?
Does survival from surgery to death vary
with Dukes’ score?
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Summary

Are males and females equally likely to meet targets to
reduce cholesterol?


Does the proportion of mothers developing pre-eclampsia
vary by parity (birth order)?


Chi test for trend
Does cholesterol change following treatment?


Chi test for global differeces
Paired t test
Is cholesterol the same in males and females?
Independent groups t test
Is baseline cholesterol related to BMI?
 ANOVA



Does survival from surgery to death vary with Dukes’ score?
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