Comparing groups

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Research questions Does outcome of birth vary with

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 equally likely to

meet targets to reduce cholesterolTwo-sided test

H2: Males are less likely to meet targets to reduce cholesterolOne 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 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 Cholesterol measured at baseline

Males Females

Analyse Compare means Independent samples t test

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Independent dataBaseline cholesterol different in males and females

Males 5.83 (0.048) to 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? Techniques include:

Transformation of observationsFormulae for degrees of freedom

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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 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: Output

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One-way ANOVA: Plot

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Two-way ANOVA Two factors

BMI groupGenderTime

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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: Output

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Two-way ANOVA: Output

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Survival Time between entry to study and

subsequent eventDeathFull recoveryRecurrence of diseaseReadmissionDislocation of joint

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What’s the problem? Impossible to wait until all

members of the study have experienced the eventSome may 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-MeierTime at which event occurred known

Time to mobility during hospital stay Survival times are exact

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Estimates of survival Probability

Of survival to some given time Survival time

Median or mean Confidence intervals for survival

ProbabilitiesTimes

Survival curves

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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 Group

Treatment regime

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Data for analysis: Example 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 Group

Treatment regime

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Outcomes from analysis Survival table (Kaplan-Meier)

one row for each event or censored observation Life table (life table)

one row for each interval Time to survival

Mean, median, quartiles, SE Survival curve

probability of no event by time t Hazard curve

probability of event at time t

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Comparing survival in groups Survival probabilities or times are

point estimatespr(5yr survival) = 0.80±0.05 for

Group 1 pr(5yr survival) = 0.75±0.10 for

Group 2 Survival curves can be compared

Groups have the same survival curve Survival is comparable for both groups

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Comparing survival curves Log-rank

survival experience of all groups is comparable

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 timeBMI on time to dislocationage at diagnosis on time to death

Estimates regression coefficients

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Define time and event

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Define factor(s) and test

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Define time and event

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Select options

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Output