comparing groups
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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?. Issues in comparing groups. Type of data - PowerPoint PPT PresentationTRANSCRIPT
Comparing groups
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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 scoreAge groupSeverity of disease
More sensitive Chi-squared tests are available
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Example 2: Test of trend
Pre-eclamplsia is associated with parity P=0.001 The linear trend is significant P<0.001
Trend
Association
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Now you’ve wrecked it!Small numbers
Chi-squared not appropriate: In a 2 by 2 table (i.e. 1 dof)
Total frequency <20 Total frequency between 20 and 40, and smallest
expected frequency <5 In tables with more than 1 dof
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
Don’t panic!!!!!SPSS will sort out these details
Return a message to tell you
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Splitting the test statistic
To assess the contribution of one category to overall significanceCorresponding row or column
removedTest statistic recalculatedNew 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 on two matched cases Matching on factors known to affect outcome
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 dataCholesterol 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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Baseline cholesterol different in males and females
Males 5.83 (0.048) Females 6.36 (0.051) P<0.001
Independent data
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Comparing sample variances
Think! If SDs are unequal, does it make sense to
compare means?
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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
Comparing more than 2 groups
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One-way ANOVA One factor
Smoking status Never, current, former
BMI category Underweight, normal, pre-obese, obese
School type 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
GenderEthnicity
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Within- and between-subject factors
Within-subjects factorsSide (left, right)Review (pre-treatment, post-
treatment)Treatment (in a cross-over study)
Between-subjects factorsGenderBMI
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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 eventDeathFull recoveryRecurrence of diseaseReadmission to hospitalDislocation of joint
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What’s the problem?
Impossible to wait until all members of the study have experienced the eventSome 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 are grouped into intervals One year, three year, five year post-op review Survival times are inexact
Kaplan-Meier Time 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 row for each interval Survival table (Kaplan-Meier)
One 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-rankTest 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 timeAge at diagnosis on time to deathBMI 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
happenedCan be multiple
1=Disease free, 2=Recurrence, 3=Death
GroupTreatment 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? Chi test for global differeces
Does the proportion of mothers developing pre-eclampsia vary by parity (birth order)? Chi test for trend
Does cholesterol change following treatment? 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?