Regression Analysis in Trials

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

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Example data Pedometer trialCI Prof McMurdo
From trial of pedometersadvice 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
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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)

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Type of Analyses Pedometer trial
Advice only Pedometer Controls
Activity
Difference in means at 3 months
Baseline
3-months

1. Compare mean final activity with t-tests or ANOVA

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Type of Analyses Pedometer trial
Advice only Pedometer Controls
Activity
CHANGE between baseline and 3 months
Baseline
3-months
2. Subtract baseline from final and compare
CHANGE between groups with t-tests or ANOVA
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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 gt 0.8)
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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
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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
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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
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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)

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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 Contro
ls 62 123843.65 51090.5 110869.10 136818.19 To
tal 172 135490.95 53201.6 127483.52 143498.39
No significant difference but Pedometer arm
highest activity (p 0.076 ANOVA)
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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)
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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!
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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
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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
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Main analysis Pedometer trial
N.b. Pedom vs Control p0.117 Advice vs
Control p 0.014 Baseline AccelVM1a highly sig.
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Differences in baseline characteristics
Characteristics All (n 210) Randomised Group (6 missing) Randomised Group (6 missing) Randomised Group (6 missing)
Characteristics All (n 210) 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 ()        
Married 91 (43.3) 26 (38.2) 34 (50.0) 29 (42.6)
Widowed 96 (45.7) 36 (52.9) 22 (32.4) 33 (48.5)
Single 23 (10.9) 6 (8.8) 12 (17.6) 5 (7.4)
         
Used pedometer before, n ()        
No 196 (93.3) 63 (92.6) 64 (94.1) 63 (92.6)
Yes 14 (6.7) 5 (7.4) 4 (5.9) 5 (7.4)
         
Illness, n ()        
No 146 (69.5) 45 (66.2) 43 (63.2) 53 (77.9)
Yes 64 (30.5) 23 (33.8) 25 (36.8) 15 (22.1)
         
Daily stairs, n ()        
No 84 (40.0) 23 (33.8) 28 (41.2) 30 (44.1)
Yes 126 (60.0) 45 (66.2) 40 (58.8) 30 (55.9)
         
Stairs difficult, n ()        
No 143 (68.1) 48 (70.6) 48 (70.6) 45 (66.2)
Yes 67 (31.9) 20 (29.4) 20 (29.4) 23 (33.8)
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Differences in baseline characteristics
Characteristics All (n 210) Randomised Group (6 missing) Randomised Group (6 missing) Randomised Group (6 missing)
Characteristics All (n 210) 1 (n 68) 2 (n 68) 3 (n 68)
         
Season entered, n ()        
Winter 82 (39.0) 29 (42.6) 26 (38.2) 26 (38.2)
Spring 69 (32.9) 20 (29.4) 24 (35.3) 23 (33.8)
Summer 40 (19.0) 14 (20.6) 11 (16.2) 13 (19.1)
Autumn 19 (9.0) 5 (7.4) 7 (10.3) 6 (8.8)
         
Lives with, n ()        
Alone 113 (53.8) 39 (57.4) 31 (45.6) 38 (55.9)
With someone 2 (1.0) 29 (42.6) 37 (54.4) 30 (44.1)
         
Falls in last 3 months, n ()        
1st 3 months of study        
0 172 (81.9) 58 (85.3) 52 (76.5) 62 (91.2)
1 7 (3.3) 0 (0.0) 4 (5.9) 3 (4.4)
2 8 (3.9) 4 (5.9) 3 (4.4) 1 (1.5)
         
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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!

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Imbalance in baseline characteristics

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

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Pedometer trial Regression Analyses
Factors Regression Coefficients Regression Coefficients t p-value
Factors Beta Std. Error t p-value
Intercept 26613.5 49272.8 0.540 0.590
         
Pedometer Group vs. controls 10064.5 6030.6 1.669 0.097
Advice only vs. controls 18056.5 6242.3 2.893 0.004
All active vs. controls 13799.8 5270.2 2.618 0.010
         
Age -678.3 577.5 -1.175 0.242
Limb total at baseline 2070.0 1277.2 1.621 0.107
Stairs difficult 13081.2 6017.1 2.174 0.031
Total no. of drugs -1325.9 794.1 -1.670 0.097
Living Alone 6471.7 5323.2 1.216 0.226
Health Costs at baseline 13.11 8.52 1.539 0.126
Final regression model adjusting for a number of
baseline factors
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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!

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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
Geriatr Soc, 2010 58(11) 2099-106.
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Example with categorical outcome - Bells Palsy
Trial

• Background
• A multicentre factorial trial of the early
  administration of steroids and/or antivirals for
  Bells palsy
• What is Bells 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

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What the patient notices
I couldnt whistle. (Graeme Garden et al) Things
tasted odd my MacDonalds 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)
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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

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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

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Inclusion Criteria and Outcomes

• Inclusion criteria Adults (gt16), 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)

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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

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
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Posed portrait photographs at onset
eyebrows raised
eyes tightly closed
smiling
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Posed portrait photographs at 3 months
eyebrows raised
eyes tightly closed
smiling
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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!
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Results follow Randomisation - Aciclovir
Aciclovir No 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)
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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)
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Summary Bells

• 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

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Bells 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 Bells
palsy. NEJM 2007 357 1598-607
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Subgroup analysis
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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!

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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.

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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

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Summary

• Three examples of use of regression modelling in
  RCTs
• 1) Adjustment for baseline imbalances using
  logistic regression Bells Palsy
• 2) adjustment for baseline measure of primary
  outcome with multiple linear regression
  -Pedometer Trial

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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

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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.