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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? 2 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 3 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 4 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 5 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 6 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 7 Example 1: Crosstabulation Analyse Descriptive statistics Crosstabs 8 Statistics and display 9 Output Males more likely than females to achieve the target P<0.001 10 Testing for trend When one of the classes is ordinal: Deprivation score Age group Severity of disease More sensitive Chi-squared tests are available 11 Example 2: Test of trend Association Trend Pre-eclamplsia is associated with parity P=0.001 The linear trend is significant P<0.001 12 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 13 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 14 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 15 Dependent data: Example 3 Cholesterol measured on two occasions Baseline After treatment Analyse Compare means Paired sample t test Assuming … Checked distribution Plausibly Normal 16 Dependent data Cholesterol reduced after treatment From 6.09 (0.036) to 3.67 (0.200) P<0.001 17 Independent data: Example 4 Cholesterol measured at baseline Males Females Analyse Compare means Independent samples t test 18 Independent data 19 Independent data Baseline cholesterol different in males and females Males 5.83 (0.048) Females 6.36 (0.051) P<0.001 20 Comparing sample variances Think! If SDs are unequal, does it make sense to compare means? 21 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 22 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 23 One-way ANOVA: Example 5 Is baseline cholesterol related to BMI? Analyse General linear model Univariate 24 One-way ANOVA: Model 25 One-way ANOVA: Contrasts 26 Contrasts All pairwise combinations Bonferroni Specific comparisons Contrasts From the previous - Difference From the first From the last Simple Trend Linear Non-linear 27 One-way ANOVA: Profile plots 28 One-way ANOVA: Post-hoc 29 One-way ANOVA: Options 30 One-way ANOVA: Output 31 One-way ANOVA: Output 32 One-way ANOVA: Output 33 One-way ANOVA: Plot 34 Two-way ANOVA Two factors Time Post-surgery review Gender Ethnicity 35 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 36 Factor or covariate? Factors are categorical variables Otherwise they are covariates 37 Two-way ANOVA: Example 6 Is baseline cholesterol related to BMI? Gender? 38 Two-way ANOVA: Output 39 Survival Time between entry to study and subsequent event Death Full recovery Recurrence of disease Readmission to hospital Dislocation of joint 40 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 41 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 42 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 43 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 44 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 45 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 46 Example 7 Does survival from surgery to death vary with Dukes’ score? 47 Define time and event 48 Define factor(s) and test 49 Select options 50 Output 51 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? 52 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? 53