Comparing groups

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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

Wot Test?
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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
• Plt0.001

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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 P0.001
• The linear trend is significant Plt0.001

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Small numbers
Now youve wrecked it!

• Chi-squared not appropriate
• In a 2 by 2 table (i.e. 1 dof)
• Total frequency lt20
• Total frequency between 20 and 40, and smallest
  expected frequency lt5
• In tables with more than 1 dof
• More than one fifth of cells have expected
  frequency lt5
• Any cell has expected frequency lt1
• Yates correction for 2 by 2 table (i.e. 1 dof)
• When Chi-squared not appropriate

• Dont 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 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 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 data
Cholesterol reduced after treatment From 6.09
(0.036) to 3.67 (0.200) Plt0.001
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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)
• Plt0.001

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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
• 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

• 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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Whats 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 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-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
• 1Disease free, 2Recurrence, 3Death
• 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?
• 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?