Regression Analysis in Trials:

Baseline Variables Peter T. Donnan

Professor of Epidemiology and Biostatistics

ObjectivesObjectives

•Understand when to use Understand when to use regression modelling in trialsregression modelling in trials

•Regression for adjustment for Regression for adjustment for baseline value of primary outcomebaseline value of primary outcome

•Regression for imbalanceRegression for imbalance•Regression for subgroup analysesRegression for subgroup analyses•Practical analysis using SPSSPractical analysis using SPSS

Example data Pedometer Example data Pedometer trialtrial

CI Prof McMurdoCI Prof McMurdoFrom trial of pedometers+advice From trial of pedometers+advice vs advice vs controls in sedentary vs advice vs controls in sedentary elderly women i.e. 3 arm trialelderly women i.e. 3 arm trialFollow-up at 3 and 6 monthsFollow-up at 3 and 6 monthsMain outcome measure of activity Main outcome measure of activity from accelerometer counts at 3 from accelerometer counts at 3 monthsmonths210 randomised / 170 at 3 210 randomised / 170 at 3 monthsmonths

Type of Analyses – Type of Analyses – Pedometer trialPedometer trial

1.1. Compare mean final activity with Compare mean final activity with t-tests or ANOVAt-tests or ANOVA

2.2. Subtract baseline from final and Subtract baseline from final and compare CHANGE between groups compare CHANGE between groups with t-tests or ANOVA (sometimes with t-tests or ANOVA (sometimes as %)as %)

3.3. Compare mean final activity with Compare mean final activity with t-test adjusting for baseline t-test adjusting for baseline activity (Regression or ANCOVA)activity (Regression or ANCOVA)

Type of Analyses – Type of Analyses – Pedometer trialPedometer trial

1.1. Compare mean final activity with t-tests or Compare mean final activity with t-tests or ANOVAANOVA

Acti

vity

Acti

vity

Baseline 3-months

Difference in means at 3 months

Advice onlyPedometerControls

Type of Analyses – Type of Analyses – Pedometer trialPedometer trial

2.2. Subtract baseline from final and compare Subtract baseline from final and compare CHANGE between groups with t-tests or ANOVACHANGE between groups with t-tests or ANOVA

Acti

vity

Acti

vity

Baseline 3-months

CHANGE between baseline and 3 months

Advice onlyPedometerControls

Problems with CHANGE or Problems with CHANGE or % CHANGE% CHANGE

Regression to the mean – low Regression to the mean – low baseline values correlated with baseline values correlated with high changehigh changeIf low correlation between If low correlation between baseline measure and follow-up baseline measure and follow-up then using CHANGE will add then using CHANGE will add variation and follow-up more variation and follow-up more likely to show significancelikely to show significanceRegression approach more Regression approach more efficient (unless correlation > efficient (unless correlation > 0.8)0.8)

Pedometer trial Pedometer trial Regression AnalysesRegression Analyses

Fit model with baseline measure as Fit model with baseline measure as covariate and indicator variable for arm covariate and indicator variable for arm of trial (A vs. B)of trial (A vs. B)

Follow-up score = constant + a x baseline score + Follow-up score = constant + a x baseline score + b b x armx arm

Where b represents the difference Where b represents the difference between the two arms of the trial i.e. between the two arms of the trial i.e. the intervention ‘effect’ adjusted for the intervention ‘effect’ adjusted for the baseline value the baseline value

Pedometer trial Pedometer trial Regression AnalysesRegression Analyses

Best analysis is regression model (or Best analysis is regression model (or ANCOVA)ANCOVA)Linear regression as outcome continuous Linear regression as outcome continuous Primary Outcome 3 mnth activity – Primary Outcome 3 mnth activity – AccelVM2AccelVM2Want to compare Pedom Vs. control Want to compare Pedom Vs. control (GRP1) and Advice vs. control (GRp2) – (GRP1) and Advice vs. control (GRp2) – so create 2 dummy variables so create 2 dummy variables Important adjustment variable is the Important adjustment variable is the baseline baseline AccelVM1aAccelVM1a

Example data – Example data – Pedometer trialPedometer trial

Read in data ‘SPSS Study Read in data ‘SPSS Study databse.sav’ databse.sav’ Main outcome is:Main outcome is:3 mnth activity – 3 mnth activity – AccelVM2AccelVM2Baseline activity – Baseline activity – AccelVM1aAccelVM1a

Trial arm represented by two Trial arm represented by two dummy variables:dummy variables: Grp1Grp1 = Pedom. = Pedom. Vs. controlVs. control

Grp2Grp2 = Advice vs. = Advice vs. control control

Example data – Example data – Pedometer trialPedometer trial

Carry out the three ways of Carry out the three ways of analysing the outcomeanalysing the outcome1.1.Final 3 months activity only Final 3 months activity only (AccelVM2)(AccelVM2)2.2.Change between 3 months activity Change between 3 months activity and baseline and baseline (DiffVM_3mn)(DiffVM_3mn)3.3.Regression on 3 months activity Regression on 3 months activity (AccelVM2) (AccelVM2) adjusting for baseline adjusting for baseline activity activity (AccelVM1a)(AccelVM1a)

Pedometer trial – Pedometer trial – 1) Analysis of 3 months 1) Analysis of 3 months

onlyonly

No significant difference but No significant difference but Pedometer arm highest activity (p Pedometer arm highest activity (p = 0.076 ANOVA)= 0.076 ANOVA)

DescriptivesAccelVM2 N Mean SD 95% CI for MeanPedometer Group 58 145383.79 52585.7 131557.08 159210.50Advice only 52 138343.81 54708.9 123112.74 153574.87

Controls 62 123843.65 51090.5 110869.10 136818.19Total 172 135490.95 53201.6 127483.52 143498.39

Pedometer trial – 2) Pedometer trial – 2) Analysis of CHANGE 3 Analysis of CHANGE 3

months months

Significant difference but Advice Significant difference but Advice CHANGE greatest (p = 0.042 CHANGE greatest (p = 0.042 ANOVA)ANOVA)

Diffvm_3mnN Mean Std.

DeviationPedometer Group 58 5504.3 34010.2

Advice only 52 13305.337084.9Controls 61 -2290.3 29020.9

Total 171 5096.0 33733.1

Pedometer trial -Analysis Pedometer trial -Analysis of CHANGE 3 months + of CHANGE 3 months +

Run-in Run-in After run-in period Pedometer group started After run-in period Pedometer group started highest and so Advice group started lowest and highest and so Advice group started lowest and rose most!rose most!

Pedometer trial –Notes on analysis Pedometer trial –Notes on analysis of PERCENTAGE CHANGE 3 months of PERCENTAGE CHANGE 3 months

Analysis by %CHANGE similar Analysis by %CHANGE similar problems to analysis of CHANGE problems to analysis of CHANGE but….. but….. also creates non-normality and does also creates non-normality and does NOT allow for imbalance at baseline NOT allow for imbalance at baseline (Vickers, 2001)(Vickers, 2001)Still o.k. to calculate results as % Still o.k. to calculate results as % change for presentation purposes but change for presentation purposes but analysisanalysis is more efficient as adjusted is more efficient as adjusted regressionregression

Pedometer trial – Pedometer trial – 3) regression analysis adjusting 3) regression analysis adjusting

for baseline for baseline

3) Regression on 3) Regression on 3 months activity 3 months activity adjusting for adjusting for baseline activity baseline activity and two dummy and two dummy variables variables representing representing trial arm trial arm contrasts contrasts

Main analysis – Main analysis – Pedometer trialPedometer trial

N.b. Pedom vs Control N.b. Pedom vs Control p=0.117p=0.117 Advice vs Control p = Advice vs Control p = 0.0140.014 Baseline AccelVM1a highly Baseline AccelVM1a highly sig.sig.

Characteristics All (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 (%)         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)

Differences in baseline Differences in baseline characteristicscharacteristics

Characteristics All (n = 210)

Randomised Group (6 missing)

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)         

Differences in baseline Differences in baseline characteristicscharacteristics

• Despite randomisation there are some Despite randomisation there are some characteristics that are not BALANCED characteristics that are not BALANCED across the three arms of the trialacross the three arms of the trial

• More likely to get imbalance in smaller More likely to get imbalance in smaller trialstrials

• One solution is to adjust for these One solution is to adjust for these imbalances in regression of final imbalances in regression of final outcomeoutcome

• Alternatives are to use Alternatives are to use STRATIFICATION, or MINIMISATION STRATIFICATION, or MINIMISATION when allocating eligible subjects to when allocating eligible subjects to treatment in designtreatment in design

• n.b. do NOT test for differences across n.b. do NOT test for differences across arms as not primary hypothesis!arms as not primary hypothesis!

Imbalance in baseline Imbalance in baseline characteristicscharacteristics

• Repeat the regression Repeat the regression analysis but adding baseline analysis but adding baseline characteristics as covariates characteristics as covariates in the regression modelin the regression model

• What variables should you What variables should you adjust for?adjust for?

Imbalance in baseline Imbalance in baseline characteristicscharacteristics

Pedometer trial Regression Pedometer trial Regression AnalysesAnalyses

Final Final regression regression model model adjusting adjusting for a for a number of number of baseline baseline factorsfactors

• Regression adjustment most Regression adjustment most appropriate methodappropriate method

• Significant advice only vs. ControlsSignificant advice only vs. Controls• Pedometer approaching significancePedometer approaching significance• Perhaps run-in should be counted as Perhaps run-in should be counted as

part of intervention part of intervention butbut protocol protocol stipulated comparison of change stipulated comparison of change between baseline and 3 months between baseline and 3 months ignoring the run-inignoring the run-in

• Be careful how analysis is framed in Be careful how analysis is framed in protocol!protocol!

Summary Pedometer Summary Pedometer Trial Trial

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

Pedometer Trial Pedometer Trial paperpaper

Example with categorical Example with categorical outcome - Bell’s Palsy outcome - Bell’s Palsy TrialTrial

Background A multicentre factorial trial of the early A multicentre factorial trial of the early administration of steroids and/or administration of steroids and/or antivirals for Bell’s palsyantivirals for Bell’s palsy

What is Bell’s Palsy?What is Bell’s Palsy? BP is an acute unilateral paralysis of BP is an acute unilateral paralysis of

the facial nervethe facial nerve Its cause is unknown; it affects Its cause is unknown; it affects

between 25 to 30 people per 100,000 between 25 to 30 people per 100,000 population per annum; most common population per annum; most common within 30 and 45 years oldwithin 30 and 45 years old

higher prevalence in: pregnant women, higher prevalence in: pregnant women, diabetes, influenza, upper respiratory diabetes, influenza, upper respiratory ailmentailment

What the patient What the patient noticesnotices

I couldn’t whistle. (I couldn’t whistle. (Graeme Garden et alGraeme Garden et al))

Things tasted odd: my MacDonald’s tasted Things tasted odd: my MacDonald’s tasted awful. (awful. (BELLS pt, EdinburghBELLS pt, Edinburgh))

My food fell out of my mouth. (My food fell out of my mouth. (BELLS pt, BELLS pt, DundeeDundee))

I winked at my husband. He jumped. I winked at my husband. He jumped. ((BELLS pt, MontroseBELLS pt, Montrose))

Background and Background and AimAim

2003: in UK 36% were treated with 2003: in UK 36% were treated with steroids; 19% were referred to Hospital steroids; 19% were referred to Hospital and 45% were untreatedand 45% were untreated

Most recover well but up to 30% had Most recover well but up to 30% had poor recovery:poor recovery:

Facial disfigurementFacial disfigurement Psychological difficultiesPsychological difficulties Facial pain Facial pain

To conduct a cost-effectiveness and To conduct a cost-effectiveness and cost-utility analyses alongside the cost-utility analyses alongside the clinical RCTclinical RCT

RCT DesignRCT Design A randomised 2 x 2 factorial designA randomised 2 x 2 factorial design To assess: prednisolone (steroids) and/or To assess: prednisolone (steroids) and/or

acyclovir (antiviral) commenced within 72 acyclovir (antiviral) commenced within 72 hours of onset of BP result in the same level hours of onset of BP result in the same level of disability and pain after 9 months as of disability and pain after 9 months as treatment with placebo.treatment with placebo.

Patient randomised received 2 identical Patient randomised received 2 identical preparations for 10 days simultaneously:preparations for 10 days simultaneously:

Prednisolone (50 mg per day) + placeboPrednisolone (50 mg per day) + placebo Acyclovir (2000 mg per day) + placeboAcyclovir (2000 mg per day) + placebo Prednisolone + Acyclovir Prednisolone + Acyclovir Placebo + placeboPlacebo + placebo

Inclusion Criteria and Inclusion Criteria and OutcomesOutcomes

Inclusion criteria: Adults (>16), no Inclusion criteria: Adults (>16), no identifiable cause unilateral facial identifiable cause unilateral facial nerve weakness seen within 72 hours nerve weakness seen within 72 hours of onsetof onsetOutcome measures:Outcome measures:

1. House-Brackman grading system2. Health Utility Index Mark III3. Chronic pain grade4. Costs (PC, LoS, outpatient visits,

medications)

Measurement of Measurement of Primary OutcomePrimary Outcome

Outcomes at 3 months and 9 Outcomes at 3 months and 9 monthsmonthsHowever, if patient “cured”, However, if patient “cured”, this is, H-B grading of 1, the this is, H-B grading of 1, the individual was no longer individual was no longer followed-upfollowed-upThen,Then,

subjects not cured at 3 subjects not cured at 3 months months data on baseline, data on baseline, 3 months and 9 months 3 months and 9 months post randomisationpost randomisationsubjects cured at 3 months subjects cured at 3 months only have data at only have data at baseline and 3 monthsbaseline 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 mouthVI No movement, loss

of tone

eyebrows raised

eyes tightly closed

smiling

Posed portrait photographs at onset

eyebrows raised

eyes tightly closed

smiling

Posed portrait photographs at 3 months

Results follow Results follow Randomisation – No Randomisation – No

significant interactionssignificant interactionsPrednisolone x Aciclovir interaction at 3 monthsPrednisolone x Aciclovir interaction at 3 months

p = 0.32p = 0.32

Prednisolone x Aciclovir interaction at 9 monthsPrednisolone x Aciclovir interaction at 9 monthsp = 0.72p = 0.72

Two trials for the price of one!Two trials for the price of one!

* Adjusted for age, sex, baseline H-B, interval from onset.* Adjusted for age, sex, baseline H-B, interval from onset.

Results follow Results follow Randomisation - AciclovirRandomisation - Aciclovir

Aciclovir No Aciclovir

Adjusted OR (95% CI)*

H-B I3 months

71.2% 75.7% 0.86 (0.55, 1.34)

H-B I9 months

85.4% 90.8% 0.61 (0.33, 1.11)

* Adjusted for age, sex, baseline H-B, interval from onset.* Adjusted for age, sex, baseline H-B, interval from onset.

Results follow Results follow Randomisation - Randomisation -

PrednisolonePrednisolonePrednisolone

No Prednisolone

Adjusted OR (95% CI)*

H-B I3 months

83.0% 63.6% 2.44 (1.55, 3.84)

H-B I9 months

94.4% 81.6% 3.32 (1.72, 6.44)

00.10.20.30.40.50.60.70.80.91

0 3 6 9

prop

orti

on r

ecov

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months

Proportion recovered (HB1) at 3m and 9m

OP : 84.3% (3m) 96.1% (9m) AP : 78.2% (3m) 92.7% (9m) OO : 63.1% (3m) 85.2% (9m) AO : 61.0% (3m) 78.0% (9m)

Summary Bell’sSummary Bell’s• Recovery at 9 months Recovery at 9 months

– 78% Acyclovir78% Acyclovir– 85% Placebo85% Placebo– 96% Prednisolone recover96% Prednisolone recover

•NNT 6 at 3 monthsNNT 6 at 3 months•NNT 8 at 9 monthsNNT 8 at 9 months

• The basis for sensible discussion of treatment The basis for sensible discussion of treatment options with patientsoptions with patients

• The type of study which is difficult to do The type of study which is difficult to do without a primary care research networkwithout a primary care research network

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

Bell’s Palsy Trial Bell’s Palsy Trial paperpaper

Subgroup Subgroup analysisanalysis

• No mention of subgroup analysis in No mention of subgroup analysis in protocolprotocol

• After testing initial primary After testing initial primary hypothesis, test separately if results hypothesis, test separately if results differ by: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 Bound to find something significant by

chance alone (Type I error) and then chance alone (Type I error) and then report!report!

IncorrectIncorrect approach to approach to subgroup analysissubgroup analysis

• Must be Must be pre-specifiedpre-specified in the protocol in the protocol and SAP prior to data lockand SAP prior to data lock

• Test if results differ by subgroup by Test if results differ by subgroup by fitting the appropriate interaction fitting the appropriate interaction term in a regression modelterm in a regression model

• E.g. E.g. Treatment arm (0,1) x Gender Treatment arm (0,1) x Gender (0,1)(0,1)

• If statistically significant then present If statistically significant then present results separately by group but results separately by group but strength of evidence needs strength of evidence needs interpretation.interpretation.

CorrectCorrect approach to approach to subgroup analysissubgroup analysis

• Interpretation of subgroup analyses Interpretation of subgroup analyses still contentious even if statistically still contentious even if statistically correctcorrect

• Subgroup analyses will be Subgroup analyses will be underpoweredunderpowered

• Subgroup analyses tend to be over-Subgroup analyses tend to be over-interpretated by trialists (Pocock et al interpretated by trialists (Pocock et al 2002)2002)

• Biological plausibility needs to be Biological plausibility needs to be consideredconsidered

• Number should be limited due to Number should be limited due to problem of multiple testingproblem of multiple testing

Issues with subgroup Issues with subgroup analysisanalysis

SummarySummary• Three examples of use of Three examples of use of

regression modelling in RCTsregression modelling in RCTs• 1) Adjustment for baseline 1) Adjustment for baseline

imbalances using logistic imbalances using logistic regression – Bell’s Palsyregression – Bell’s Palsy

• 2) adjustment for baseline measure 2) adjustment for baseline measure of primary outcome with multiple of primary outcome with multiple linear regression -Pedometer Triallinear regression -Pedometer Trial

SummarySummary

• 3) Adding interaction terms to test for 3) Adding interaction terms to test for subgroup differences in treatment subgroup differences in treatment effecteffect

• Regression analysis type could be Regression analysis type could be linear (continuous outcome), logistic linear (continuous outcome), logistic (binary outcome, Cox (survival (binary outcome, Cox (survival outcome) or counts (Poisson)outcome) or counts (Poisson)

• All easily fitted in SPSS or other All easily fitted in SPSS or other statistical softwarestatistical software

ReferencesReferences

• 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.