1. Regression Analysis in Trials: Baseline Variables Peter T. Donnan Professor of Epidemiology and Biostatistics

2. Objectives Understand when to use regression modelling in trials Understand when to use regression modelling in trials Regression for adjustment for baseline value of primary outcome Regression for adjustment for baseline value of primary outcome Regression for imbalance Regression for imbalance Regression for subgroup analyses Regression for subgroup analyses Practical analysis using SPSS Practical analysis using SPSS

3. Example data Pedometer trial CI Prof McMurdo From trial of pedometers+advice vs advice vs controls in sedentary elderly women i.e. 3 arm trial Follow-up at 3 and 6 months Main outcome measure of activity from accelerometer counts at 3 months 210 randomised / 170 at 3 months

4. Type of Analyses – Pedometer trial 1.Compare mean final activity with t- tests or ANOVA 2.Subtract baseline from final and compare CHANGE between groups with t-tests or ANOVA (sometimes as %) 3.Compare mean final activity with t-test adjusting for baseline activity (Regression or ANCOVA)

5. Type of Analyses – Pedometer trial 1.Compare mean final activity with t-tests or ANOVA Activity Baseline3-months Difference in means at 3 months Advice only Pedometer Controls

6. Type of Analyses – Pedometer trial 2.Subtract baseline from final and compare CHANGE between groups with t-tests or ANOVA Activity Baseline3-months CHANGE between baseline and 3 months Advice only Pedometer Controls

7. Problems with CHANGE or % CHANGE Regression to the mean – low baseline values correlated with high change If low correlation between baseline measure and follow-up then using CHANGE will add variation and follow- up more likely to show significance Regression approach more efficient (unless correlation > 0.8)

8. Pedometer trial Regression Analyses Fit model with baseline measure as covariate and indicator variable for arm of trial (A vs. B) Follow-up score = constant + a x baseline score + b x arm Where b represents the difference between the two arms of the trial i.e. the intervention ‘effect’ adjusted for the baseline value

9. Pedometer trial Regression Analyses Best analysis is regression model (or ANCOVA) Linear regression as outcome continuous Primary Outcome 3 mnth activity – AccelVM2 Want to compare Pedom Vs. control (GRP1) and Advice vs. control (GRp2) – so create 2 dummy variables Important adjustment variable is the baseline AccelVM1a

10. Example data – Pedometer trial Read in data ‘SPSS Study databse.sav’ Main outcome is: 3 mnth activity – AccelVM2 Baseline activity – AccelVM1a Trial arm represented by two dummy variables:Grp1 = Pedom. Vs. control Grp2 = Advice vs. control

11. Example data – Pedometer trial Carry out the three ways of analysing the outcome 1.Final 3 months activity only (AccelVM2) 2.Change between 3 months activity and baseline (DiffVM_3mn) 3.Regression on 3 months activity (AccelVM2) adjusting for baseline activity (AccelVM1a)

12. Pedometer trial – 1) Analysis of 3 months only No significant difference but Pedometer arm highest activity (p = 0.076 ANOVA) Descriptives AccelVM2 N Mean SD 95% CI for Mean Pedometer Group 58145383.79 52585.7131557.08159210.50 Advice only 52138343.81 54708.9123112.74153574.87 Controls 62123843.65 51090.5110869.10136818.19 Total172135490.95 53201.6127483.52143498.39

13. Pedometer trial – 2) Analysis of CHANGE 3 months Significant difference but Advice CHANGE greatest (p = 0.042 ANOVA) Diffvm_3mn NMeanStd. Deviation Pedometer Group58 5504.334010.2 Advice only5213305.337084.9 Controls61 -2290.329020.9 Total1715096.033733.1

14. Pedometer trial -Analysis of CHANGE 3 months + Run-in After run-in period Pedometer group started highest and so Advice group started lowest and rose most!

15. Pedometer trial –Notes on analysis of PERCENTAGE CHANGE 3 months Analysis by %CHANGE similar problems to analysis of CHANGE but….. also creates non-normality and does NOT allow for imbalance at baseline (Vickers, 2001) Still o.k. to calculate results as % change for presentation purposes but analysis is more efficient as adjusted regression

16. Pedometer trial – 3) regression analysis adjusting for baseline 3) Regression on 3 months activity adjusting for baseline activity and two dummy variables representing trial arm contrasts

17. Main analysis – Pedometer trial N.b. Pedom vs Control p=0.117 Advice vs Control p = 0.014 Advice vs Control p = 0.014 Baseline AccelVM1a highly sig. Baseline AccelVM1a highly sig.

18. CharacteristicsAll (n = 210) Randomised Group (6 missing) 1 (n = 68)2 (n = 68)3 (n = 68) Age in years, mean (SD)77.28 (5.04)77.15 (4.89)77.56 (5.43)76.96 (4.93) Marital status, n (%) Married91 (43.3)26 (38.2)34 (50.0)29 (42.6) Widowed96 (45.7)36 (52.9)22 (32.4)33 (48.5) Single23 (10.9)6 (8.8)12 (17.6)5 (7.4) Used pedometer before, n (%) No196 (93.3)63 (92.6)64 (94.1)63 (92.6) Yes14 (6.7)5 (7.4)4 (5.9)5 (7.4) Illness, n (%) No146 (69.5)45 (66.2)43 (63.2)53 (77.9) Yes64 (30.5)23 (33.8)25 (36.8)15 (22.1) Daily stairs, n (%) No84 (40.0)23 (33.8)28 (41.2)30 (44.1) Yes126 (60.0)45 (66.2)40 (58.8)30 (55.9) Stairs difficult, n (%) No143 (68.1)48 (70.6) 45 (66.2) Yes67 (31.9)20 (29.4) 23 (33.8) Differences in baseline characteristics

19. CharacteristicsAll (n = 210) Randomised Group (6 missing) 1 (n = 68)2 (n = 68)3 (n = 68) Season entered, n (%) Winter82 (39.0)29 (42.6)26 (38.2) Spring69 (32.9)20 (29.4)24 (35.3)23 (33.8) Summer40 (19.0)14 (20.6)11 (16.2)13 (19.1) Autumn19 (9.0)5 (7.4)7 (10.3)6 (8.8) Lives with, n (%) Alone113 (53.8)39 (57.4)31 (45.6)38 (55.9) With someone2 (1.0)29 (42.6)37 (54.4)30 (44.1) Falls in last 3 months, n (%) 1 st 3 months of study 0172 (81.9)58 (85.3)52 (76.5)62 (91.2) 17 (3.3)0 (0.0)4 (5.9)3 (4.4) 2+8 (3.9)4 (5.9)3 (4.4)1 (1.5) Differences in baseline characteristics

20. Despite randomisation there are some characteristics that are not BALANCED across the three arms of the trial Despite randomisation there are some characteristics that are not BALANCED across the three arms of the trial More likely to get imbalance in smaller trials More likely to get imbalance in smaller trials One solution is to adjust for these imbalances in regression of final outcome One solution is to adjust for these imbalances in regression of final outcome Alternatives are to use STRATIFICATION, or MINIMISATION when allocating eligible subjects to treatment in design Alternatives are to use STRATIFICATION, or MINIMISATION when allocating eligible subjects to treatment in design n.b. do NOT test for differences across arms as not primary hypothesis! n.b. do NOT test for differences across arms as not primary hypothesis! Imbalance in baseline characteristics

21. Repeat the regression analysis but adding baseline characteristics as covariates in the regression model Repeat the regression analysis but adding baseline characteristics as covariates in the regression model What variables should you adjust for? What variables should you adjust for? Imbalance in baseline characteristics

22. Pedometer trial Regression Analyses Final regression model adjusting for a number of baseline factors Factors Regression Coefficients tp-value BetaStd. Error Intercept26613.549272.80.5400.590 Pedometer Group vs. controls 10064.56030.61.6690.097 Advice only vs. controls18056.56242.32.8930.004 All active vs. controls13799.85270.22.6180.010 Age-678.3577.5-1.1750.242 Limb total at baseline2070.01277.21.6210.107 Stairs difficult13081.26017.12.1740.031 Total no. of drugs-1325.9794.1-1.6700.097 Living Alone6471.75323.21.2160.226 Health Costs at baseline13.118.521.5390.126

23. Regression adjustment most appropriate method Regression adjustment most appropriate method Significant advice only vs. Controls Significant advice only vs. Controls Pedometer approaching significance Pedometer approaching significance Perhaps run-in should be counted as part of intervention but protocol stipulated comparison of change between baseline and 3 months ignoring the run-in Perhaps run-in should be counted as part of intervention but protocol stipulated comparison of change between baseline and 3 months ignoring the run-in Be careful how analysis is framed in protocol! Be careful how analysis is framed in protocol! Summary Pedometer Trial

24. McMurdo MET, Sugden J, Argo I, Boyle P, Johnston DW, Sniehotta FF, Donnan PT. Do pedometers increase physical activity in sedentary older women? A randomised controlled trial. J Am Geriatr Soc, 2010; 58(11): 2099-106. Pedometer Trial paper

25. Example with categorical outcome - Bell’s Palsy Trial Background A multicentre factorial trial of the early administration of steroids and/or antivirals for Bell’s palsy  A multicentre factorial trial of the early administration of steroids and/or antivirals for Bell’s palsy What is Bell’s Palsy? What is Bell’s Palsy? BP is an acute unilateral paralysis of the facial nerve BP is an acute unilateral paralysis of the facial nerve Its cause is unknown; it affects between 25 to 30 people per 100,000 population per annum; most common within 30 and 45 years old Its cause is unknown; it affects between 25 to 30 people per 100,000 population per annum; most common within 30 and 45 years old higher prevalence in: pregnant women, diabetes, influenza, upper respiratory ailment higher prevalence in: pregnant women, diabetes, influenza, upper respiratory ailment

26. What the patient notices I couldn’t whistle. (Graeme Garden et al) Things tasted odd: my MacDonald’s tasted awful. (BELLS pt, Edinburgh) My food fell out of my mouth. (BELLS pt, Dundee) I winked at my husband. He jumped. (BELLS pt, Montrose)

27. Background and Aim 2003: in UK 36% were treated with steroids; 19% were referred to Hospital and 45% were untreated Most recover well but up to 30% had poor recovery: Most recover well but up to 30% had poor recovery: Facial disfigurement Facial disfigurement Psychological difficulties Psychological difficulties Facial pain Facial pain To conduct a cost-effectiveness and cost- utility analyses alongside the clinical RCT

28. RCT Design A randomised 2 x 2 factorial design To assess: prednisolone (steroids) and/or acyclovir (antiviral) commenced within 72 hours of onset of BP result in the same level of disability and pain after 9 months as treatment with placebo. To assess: prednisolone (steroids) and/or acyclovir (antiviral) commenced within 72 hours of onset of BP result in the same level of disability and pain after 9 months as treatment with placebo. Patient randomised received 2 identical preparations for 10 days simultaneously: Patient randomised received 2 identical preparations for 10 days simultaneously: Prednisolone (50 mg per day) + placebo Prednisolone (50 mg per day) + placebo Acyclovir (2000 mg per day) + placebo Acyclovir (2000 mg per day) + placebo Prednisolone + Acyclovir Prednisolone + Acyclovir Placebo + placebo Placebo + placebo

29. Inclusion Criteria and Outcomes Inclusion criteria: Adults (>16), no identifiable cause unilateral facial nerve weakness seen within 72 hours of onset Outcome measures: 1.House-Brackman grading system 2.Health Utility Index Mark III 3.Chronic pain grade 4.Costs (PC, LoS, outpatient visits, medications)

30. Measurement of Primary Outcome Outcomes at 3 months and 9 months However, if patient “cured”, this is, H-B grading of 1, the individual was no longer followed-up Then, subjects not cured at 3 months  data on baseline, 3 months and 9 months post randomisation subjects cured at 3 months  only have data at baseline and 3 months INormal symmetrical function in all areas IISlight weakness Slight asymmetry of smile IIIObvious weakness, but not disfiguring IVObvious disfiguring weakness VMotion barely perceptible Incomplete eye closure, slight movement corner mouth VINo movement, loss of tone

31. eyebrows raisedeyes tightly closed smiling Posed portrait photographs at onset

32. eyebrows raised eyes tightly closed smiling Posed portrait photographs at 3 months

33. Results follow Randomisation – No significant interactions Prednisolone x Aciclovir interaction at 3 months p = 0.32 Prednisolone x Aciclovir interaction at 9 months p = 0.72 Two trials for the price of one!

34. * Adjusted for age, sex, baseline H-B, interval from onset. Results follow Randomisation - Aciclovir AciclovirNo Aciclovir Adjusted OR (95% CI)* H-B I 3 months 71.2%75.7% 0.86 (0.55, 1.34) H-B I 9 months 85.4%90.8% 0.61 (0.33, 1.11)

35. * Adjusted for age, sex, baseline H-B, interval from onset. Results follow Randomisation - Prednisolone Prednisolone No Prednisolone Adjusted OR (95% CI)* H-B I 3 months 83.0%63.6% 2.44 (1.55, 3.84) H-B I 9 months 94.4%81.6% 3.32 (1.72, 6.44)

37. Summary Bell’s Recovery at 9 months Recovery at 9 months – 78% Acyclovir – 85% Placebo – 96% Prednisolone recover NNT 6 at 3 months NNT 6 at 3 months NNT 8 at 9 months NNT 8 at 9 months The basis for sensible discussion of treatment options with patients The basis for sensible discussion of treatment options with patients The type of study which is difficult to do without a primary care research network The type of study which is difficult to do without a primary care research network

38. Sullivan FM, Swan RC, Donnan PT, Morrison JM, Smith BH, McKinstry B, Vale L, Davenport RJ, Clarkson JE, Daly F. Early treatment with prednisolone or acyclovir and recovery in Bell’s palsy. NEJM 2007; 357: 1598-607 Bell’s Palsy Trial paper

39. Subgroup analysis

40. No mention of subgroup analysis in protocol No mention of subgroup analysis in protocol After testing initial primary hypothesis, test separately if results differ by: After testing initial primary hypothesis, test separately if results differ by: Males vs females, Age groups, Males vs females, Age groups, Baseline severity, Baseline severity, Deprivation status, Deprivation status, High / low BP, High / low BP, Etc……..ad infinitum! Etc……..ad infinitum! Bound to find something significant by chance alone (Type I error) and then report! Bound to find something significant by chance alone (Type I error) and then report! Incorrect approach to subgroup analysis

41. Must be pre-specified in the protocol and SAP prior to data lock Must be pre-specified in the protocol and SAP prior to data lock Test if results differ by subgroup by fitting the appropriate interaction term in a regression model Test if results differ by subgroup by fitting the appropriate interaction term in a regression model E.g. Treatment arm (0,1) x Gender (0,1) E.g. Treatment arm (0,1) x Gender (0,1) If statistically significant then present results separately by group but strength of evidence needs interpretation. If statistically significant then present results separately by group but strength of evidence needs interpretation. Correct approach to subgroup analysis

42. Interpretation of subgroup analyses still contentious even if statistically correct Interpretation of subgroup analyses still contentious even if statistically correct Subgroup analyses will be underpowered Subgroup analyses will be underpowered Subgroup analyses tend to be over- interpretated by trialists (Pocock et al 2002) Subgroup analyses tend to be over- interpretated by trialists (Pocock et al 2002) Biological plausibility needs to be considered Biological plausibility needs to be considered Number should be limited due to problem of multiple testing Number should be limited due to problem of multiple testing Issues with subgroup analysis

43. Summary Three examples of use of regression modelling in RCTs Three examples of use of regression modelling in RCTs 1) Adjustment for baseline imbalances using logistic regression – Bell’s Palsy 1) Adjustment for baseline imbalances using logistic regression – Bell’s Palsy 2) adjustment for baseline measure of primary outcome with multiple linear regression -Pedometer Trial 2) adjustment for baseline measure of primary outcome with multiple linear regression -Pedometer Trial

44. Summary 3) Adding interaction terms to test for subgroup differences in treatment effect 3) Adding interaction terms to test for subgroup differences in treatment effect Regression analysis type could be linear (continuous outcome), logistic (binary outcome, Cox (survival outcome) or counts (Poisson) Regression analysis type could be linear (continuous outcome), logistic (binary outcome, Cox (survival outcome) or counts (Poisson) All easily fitted in SPSS or other statistical software All easily fitted in SPSS or other statistical software

45. References Analysing controlled trials with baseline and follow-up measurements. Vickers AJ, Altman DG. BMJ 2001; 323: 1123-4 The use of percentage change from baseline as an outcome in a controlled trial is statistically inefficient: a simulation study. Vickers A. BMC Medical Research Methodology 2001; 1: 6. Subgroup analysis, covariate adjustment and baseline comparisons in clinical trial reporting: current practice and problems. Pocock SJ, Assmann SE, Enos LE, Kasten LE. Statist Med 2002; 21: 2917-2930.