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?