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Regression Analysis in Trials

Regression Analysis in Trials. Peter T. Donnan Professor of Epidemiology and Biostatistics. Objectives. Understand when to use regression modelling in trials Regression for adjustment for baseline value of primary outcome Regression for imbalance Regression for subgroup analyses

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Regression Analysis in Trials

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

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

  3. Example data Pedometer trialCI Prof McMurdo From trial of pedometers+advicevs 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 Compare mean final activity with t-tests or ANOVA Subtract baseline from final and compare CHANGE between groups with t-tests or ANOVA (sometimes as %) Compare mean final activity with t-test adjusting for baseline activity (Regression or ANCOVA)

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

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

  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 Final 3 months activity only (AccelVM2) Change between 3 months activity and baseline (DiffVM_3mn) Regression on 3 months activity (AccelVM2) adjusting for baseline activity (AccelVM1a)

  12. Pedometer trial – 1) Analysis of 3 months only Descriptives AccelVM2 N Mean SD 95% CI for Mean Pedometer Group 58 145383.79 52585.7 131557.08 159210.50 Advice only 52 138343.81 54708.9 123112.74 153574.87 Controls 62 123843.65 51090.5 110869.10 136818.19 Total 172 135490.95 53201.6 127483.52 143498.39 No significant difference but Pedometer arm highest activity (p = 0.076 ANOVA)

  13. Pedometer trial – 2) Analysis of CHANGE 3 months Diffvm_3mn N Mean Std. Deviation Pedometer Group 58 5504.3 34010.2 Advice only 52 13305.3 37084.9 Controls 61 -2290.3 29020.9 Total 171 5096.0 33733.1 Significant difference but Advice CHANGE greatest (p = 0.042 ANOVA)

  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.Pedomvs Control p=0.117 Advice vs Control p = 0.014 Baseline AccelVM1a highly sig.

  18. Differences in baseline characteristics

  19. Differences in baseline characteristics

  20. Imbalance in baseline characteristics • 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 • 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 • n.b. do NOT test for differences across arms as not primary hypothesis!

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

  22. Pedometer trial Regression Analyses Final regression model adjusting for a number of baseline factors

  23. Summary Pedometer Trial • Regression adjustment most appropriate method for analysing change • Significant advice only vs. Controls • 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 • Be careful how analysis is framed in protocol!

  24. Pedometer Trial paper 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 GeriatrSoc, 2010; 58(11): 2099-106.

  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 • What is Bell’s Palsy? • 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 • 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: • Facial disfigurement • Psychological difficulties • 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. • Patient randomised received 2 identical preparations for 10 days simultaneously: • Prednisolone (50 mg per day) + placebo • Acyclovir (2000 mg per day) + placebo • Prednisolone + Acyclovir • Placebo + placebo

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

  30. Measurement of PrimaryOutcome • 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 I Normal symmetrical function in all areas II Slight weakness Slight asymmetry of smile III Obvious weakness, but not disfiguring IV Obvious disfiguring weakness V Motion barely perceptible Incomplete eye closure, slight movement corner mouth VI No movement, loss of tone

  31. Posed portrait photographs at onset eyebrows raised eyes tightly closed smiling

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

  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. Results follow Randomisation - Aciclovir * Adjusted for age, sex, baseline H-B, interval from onset.

  35. Results follow Randomisation - Prednisolone * Adjusted for age, sex, baseline H-B, interval from onset.

  36. Summary Bell’s • Recovery at 9 months • 78% Acyclovir • 85% Placebo • 96% Prednisolone recover • NNT 6 at 3 months • NNT 8 at 9 months • 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

  37. Bell’s Palsy Trial paper 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

  38. Subgroup analysis

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

  40. Correct approach to subgroup analysis • 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 • 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.

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

  42. Summary • Three examples of use of regression modelling in RCTs • 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

  43. Summary • 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) • All easily fitted in SPSS or other statistical software

  44. 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.

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