1. Statistics for the Terrified Talk 4: Analysis of Clinical Trial data 30 th September 2010 Janet Dunn Louise Hiller

2. Data types What type of data do you have? Categorical2- levels More than 2 levels Ordered Non- ordered Continuous Normally distributed Non- normally distributed Time to event

3. Data types What type of data do you have? Categorical2- levels More than 2 levels Ordered Non- ordered Continuous Normally distributed Non- normally distributed Time to event

4. 2-level categorical (binary) data N (%)12Row total 1a (%)b (%)a+b 2c (%)d (%)c+d Column totala+cb+dn Variable 1 Variable 2 Frequency Table

5. 2-level categorical (binary) data - Test of association Null hypothesis: The 2 factors are independent Chi-squared test, with continuity correction  2 =11.4 p=0.0007  Treatment and gender are NOT independent N (%)12Row total Male55 (58%) 32 (33%) 87 Female40 (42%) 66 (67%) 106 Column total9598193 Treatment Gender

6. 2-level categorical (binary) data - Test of association Null hypothesis: The 2 factors are independent Commonly used with small numbers, Fisher’s exact test p=0.51  Treatment and gender are independent N (%)12Row total Male4 (10%) 6 (17%) 10 Female35 (90%) 30 (83%) 65 Column total393675 Treatment Gender

7. 2-level categorical (binary) data – Measure of agreement A measure of agreement between reviewers, above that expected by chance Kappa  =0.71 (95%CI 0.60-0.83)  There is good agreement between reviewers ResponseNo responseRow total Response 741286 No response 85058 Column total 8262144 Reviewer 1 Reviewer 2 Altman guidelines <0.20 poor 0.21 - 0.40 fair 0.41 - 0.60 moderate 0.61 - 0.80 good 0.81 - 1.00 very good

8. 2-level categorical (binary) data – Measure of agreement A measure of agreement between reviewers, above that expected by chance Kappa  =-0.04 (95%CI -0.24 - 0.15)  There is poor agreement between reviewers ResponseNo responseRow total Response 3525 60 No response 2515 40 Column total 6040100 Reviewer 1 Reviewer 2 Altman guidelines <0.20 poor 0.21 - 0.40 fair 0.41 - 0.60 moderate 0.61 - 0.80 good 0.81 - 1.00 very good

9. 2-level categorical (binary) data – Exploring patterns in the data Odds ratio (OR): the ratio of the odds of an event occurring in the 1 st gp to the odds of it occurring in the 2 nd gp OR=1 - event is equally likely to occur in both gps OR>1 - event is more likely to occur in 1 st gp OR<1 - event is less likely to occur in 1 st gp OR=4.1 (95%CI 2.2-7.9)  The odds of a male having a response are 4 times those of a female having a response YesNoRow total Male552075 Female4060100 Column total9580175 Response Gender

10. 2-level categorical (binary) data – Exploring patterns in the data Relative Risk (RR): the ratio of the risk of an event occurring in the 1 st gp to the risk of it occurring in the 2 nd gp RR=1 - event is equally likely to occur in both gps RR>1 - event is more likely to occur in 1 st gp RR<1 - event is less likely to occur in 1 st gp RR=1.7 (95%CI 0.64-4.50)  New trt patients are 1.7 times more likely to suffer an SAE than control patients YesNoRow total New trt108898 Control694100 Column total16182198 SAE suffered Treatment

11. Odds Ratio/Relative Risk plots 20.5

12. Exploring patterns in multivariate data - Logistic Regression A statistical modelling method that describes the relationship between a categorical response variable and 1 or more categorical and/or continuous variables e.g. Association between bearing grudges & medical conditions OR95%CIp Heart attack2.091.51 - 2.890.0001 High blood pressure1.471.27 - 1.710.0001 Heart disease1.641.24 - 2.180.001 Epilepsy0.860.55 - 1.380.59 Stroke0.990.66 - 1.490.96

13. Ordered categorical data – Test for trend Null hypothesis: No linear trend between groups Chi-squared tests for trend  2 =10.8 p=0.001  There is a linear trend between groups N (%)12Row total Mild17 (20%) 32 (38.5%) 49 Moderate29 (35%) 32 (38.5%) 61 Severe38 (45%) 19 (23%) 57 Column total8483167 Treatment Toxicity

14. Ordered categorical data – Test for trend (>2 rows & columns) Null hypothesis: No linear trend between rows and columns Chi-squared tests for trend  2 =7.1 p=0.008  There is a linear trend between rows & columns N (%)1mg2mg3mgRow total Mild30 (36%) 19 (23%) 18 (22%) 67 Moderate31 (37%) 32 (38.5%) 27 (33%) 90 Severe22 (27%) 32 (38.5%) 37 (45%) 91 Column total83 82248 Treatment dose Toxicity

15. Ordered categorical data – Measure of agreement A measure of agreement between reviewers, above that expected by chance CRPRSDRow total CR3012850 PR17322069 SD5223764 Column total526665183 Reviewer 1 Reviewer 2 Altman guidelines <0.20 poor 0.21 - 0.40 fair 0.41 - 0.60 moderate 0.61 - 0.80 good 0.81 - 1.00 very good Weighted kappa  =0.38 (95%CI 0.27-0.49)  There is fair agreement between reviewers

16. Non-ordered categorical data - Test of association Null hypothesis: The 2 factors are independent Chi-squared test  2 =0.51 p=0.78  Treatment and disease site are independent N (%)12Row total Head & Neck26 (23%)29 (26%)55 Limbs32 (28%)33 (30%)65 Body55 (49%)49 (44%)104 Column total113111224 Treatment Disease site

17. Non-ordered categorical data – Measure of agreement A measure of agreement between reviewers, above that expected by chance ABCRow total A3012850 B17322069 C5223764 Column total526665183 Reviewer 1 Reviewer 2 Altman guidelines <0.20 poor 0.21 - 0.40 fair 0.41 - 0.60 moderate 0.61 - 0.80 good 0.81 - 1.00 very good Kappa  =0.31 (95%CI 0.20-0.42)  There is fair agreement between reviewers

18. Categorical data – RECAP. LevelsTest of associationMeasure of agreement Exploring patterns in the data 2  2 test with continuity correction; Fisher’s exact test KappaOdds Ratio & Relative Risk; Logistic regression >2 (ordered)  2 test for trend Weighted kappa Not covered >2 (non-ordered)  2 test Kappa Not covered

19. Data types What type of data do you have? Categorical2- levels More than 2 levels Ordered Non- ordered Continuous Normally distributed Non- normally distributed Time to event

20. Normally distributed data Data forms a bell-shaped curve Non-significant Shapiro-Wilk test result

21. Mean & Standard Deviation graph Treatments Change over time in QOL (%)

22. Parametric tests Differences between means of 2 groups –T-tests Differences between means of >2 groups –ANOVA –Linear regression Correlation –Pearson’s correlation coefficient, r

23. Non-normally distributed data

24. Box and Whisker graphs Outliers (observations that lie outside of the 95% CIs) are sometimes plotted individually

25. Box and Whisker graphs Parallel box plots show the differences between groups

26. Non-parametric tests Differences between medians of 2 groups –Wilcoxon rank sum test Differences between medians of >2 groups –Kruskal-Wallis 1-way analysis of variance test Correlation –Spearman’s rank order correlation coefficient, 

27. Transforming data Can transform non-normally distributed data (e.g. logarithm, square root, reciprocal) to make create normally distributed data Then analyse transformed data using parametric methods

28. Data types What type of data do you have? Categorical2- levels More than 2 levels Ordered Non- ordered Continuous Normally distributed Non- normally distributed Time to event

29. Time-to-event data Why is this different to other continuous data? –Censoring TNO 1 2 3 4 5 6 KEY Randomisation date Date of event Censor date Time 20* 8 8* 14 1* 16*

30. What time? What event? Start date? –Diagnosis –Surgery Event? –Onset / worsening of pain –Hospital discharge –Death (OS) –Relapse (RFI/DFI/ Plateau) –Relapse or death (RFS/DFS) You need to know what you’re looking at to know how to interpret it / what to compare it to –Randomisation –Start/End of treatment

31. Time-to-event data analysis (‘Survival Analysis’) Can be used to measure time to any event –Arthritic joint remaining pain-free post steroid injections –Elderly patient with a fractured hip remaining in hosp. Calculate ‘survival’ time for each patient (some may be censored times) –Recruitment takes place over time so varying lengths of follow-up are expected Rank these times and calculate proportions alive at certain points, with due allowance for incomplete follow-up These proportions and times are plotted and overall distributions of curves compared

32. Time-to-event data Why is this different to other continuous data? –Censoring TNO 1 2 3 4 5 6 KEY Randomisation date Date of event Censor date Time 20* 8 8* 14 1* 16*

33. Kaplan-Meier Curves Median survival = 1.3 years Minimum & median FU indicate the maturity of the data

34. Kaplan-Meier Curves Numbers at Risk: ECMF 1189 1171 1120 1073 1020 965 826 606 380 196 53 CMF 1202 1178 1099 1024 957 888 759 564 352 176 55 78% 84%

35. Undesirable comparisons of survival rates

36. Statistical tests for time-to-event data Log-rank tests compare the overall distributions of the curves (  2 and p-value presented) –Null hypothesis: all curves are samples from populations with the same risk of the event –Compares the number of deaths observed on each treatment arm with the number expected under the null hypothesis that the 2 survival distributions are identical Cox proportional hazards model (Hazard Ratio, 95% CI’s and p-value presented) –Identifies which variables from a group of several are independently related to survival –In what order of importance –Gives you a measure of their relation to survival

37. Forest plots [Bars=95% confidence interval. Size of boxes can represent sample size]

38. Longitudinal data analysis A variable can be measured on the same patient over time (e.g. Baseline, 3 month, 6 month …) Can be any type of data (categorical, continuous)

39. Longitudinal data analysis – Summary Measures Change from Baseline in Global QOL CMF ECMF Change at 1 year (p=0.01) Change at 2 years (p=0.06) Improvement Deterioration TRT A TRT B

40. Longitudinal data analysis – Modelling Pulmonary function (TLCO score) over time Graphs show each patient as a separate line Solid line = Trt A pts Dashed line = Trt B pts Random effects modelling predicts the average patient score on each treatment arm

41. Cluster Randomised Trial data Patients within 1 cluster are often more likely to respond in a similar manner, and thus can not be assumed to act independently ICC = Intracluster Correlation Coefficient. A statistical measure of this dependence –Takes values between 0 and 1 –Higher values = greater between-cluster variation. e.g. Management within sites are consistent but, across different sites, there is wide variation Analysis must incorporate the effects of clustering i.e. the values of the ICC and design effect

42. Useful References Gore & Altman – Statistics in Practice Bland - An Introduction to Medical Statistics Altman - Practical Statistics for Medical Research Peto et al - Design and Analysis of Randomized Clinical- Trials Requiring Prolonged Observation of each patient –1/ Introduction and Design. British Journal of Cancer 1976. 34(6) 585-612 –2/ Analysis and Examples. British Journal of Cancer 1977. 35(1) 1-39