Transcript Pedometer trial

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
• Practical analysis using SPSS
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
Type of Analyses –
Pedometer trial
1. Compare mean final activity with ttests 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)
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
Type of Analyses –
Pedometer trial
Advice only
Pedometer
Controls
Activity
CHANGE
between
baseline
and 3
months
Baseline
2.
3-months
Subtract baseline from final and compare
CHANGE between groups with t-tests or ANOVA
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 followup more likely to show significance
Regression approach more efficient
(unless correlation > 0.8)
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
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
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
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)
Pedometer trial –
1) Analysis of 3 months only
Descriptives
AccelVM2
N
Pedometer Group
58
Advice only 52
Controls
62
Total
172
Mean
145383.79
138343.81
123843.65
135490.95
SD
52585.7
54708.9
51090.5
53201.6
95% CI for Mean
131557.08 159210.50
123112.74 153574.87
110869.10 136818.19
127483.52 143498.39
No significant difference but Pedometer
arm highest activity (p = 0.076 ANOVA)
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)
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!
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
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
Main analysis – Pedometer
trial
N.b. Pedom vs Control p=0.117
Advice vs Control p = 0.014
Baseline AccelVM1a highly sig.
Differences in baseline
characteristics
Characteristics
Age in years, mean (SD)
All (n = 210)
Randomised Group (6 missing)
1 (n = 68)
2 (n = 68)
3 (n = 68)
77.28 (5.04)
77.15 (4.89)
77.56 (5.43)
76.96 (4.93)
Marital status, n (%)
Married
Widowed
Single
91 (43.3)
96 (45.7)
23 (10.9)
26 (38.2)
36 (52.9)
6 (8.8)
34 (50.0)
22 (32.4)
12 (17.6)
29 (42.6)
33 (48.5)
5 (7.4)
Used pedometer before, n (%)
No
Yes
196 (93.3)
14 (6.7)
63 (92.6)
5 (7.4)
64 (94.1)
4 (5.9)
63 (92.6)
5 (7.4)
146 (69.5)
64 (30.5)
45 (66.2)
23 (33.8)
43 (63.2)
25 (36.8)
53 (77.9)
15 (22.1)
84 (40.0)
126 (60.0)
23 (33.8)
45 (66.2)
28 (41.2)
40 (58.8)
30 (44.1)
30 (55.9)
143 (68.1)
67 (31.9)
48 (70.6)
20 (29.4)
48 (70.6)
20 (29.4)
45 (66.2)
23 (33.8)
Illness, n (%)
No
Yes
Daily stairs, n (%)
No
Yes
Stairs difficult, n (%)
No
Yes
Differences in baseline
characteristics
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)
113 (53.8)
39 (57.4)
31 (45.6)
38 (55.9)
2 (1.0)
29 (42.6)
37 (54.4)
30 (44.1)
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)
Lives with, n (%)
Alone
With someone
Falls in last 3 months, n (%)
1st 3 months of study
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!
Imbalance in baseline
characteristics
• Repeat the regression analysis
but adding baseline
characteristics as covariates in
the regression model
• What variables should you adjust
for?
Pedometer trial Regression
Analyses
Regression Coefficients
Factors
Final
regression
model
adjusting for
a number of
baseline
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
6471.7
5323.2
1.216
0.226
13.11
8.52
1.539
0.126
Living Alone
Health Costs at baseline
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!
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.
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
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)
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 costutility analyses alongside the clinical RCT
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
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)
Measurement of Primary
Outcome
Outcomes at 3 months and 9
months
I
However, if patient “cured”, this is,
H-B grading of 1, the individual
was no longer followed-up
II
Then,
IV
III
subjects not cured at 3 months
 data on baseline, 3 months
and 9 months post
randomisation
V
subjects cured at 3 months 
only have data at baseline and
3 months
VI
Normal symmetrical
function in all areas
Slight weakness
Slight asymmetry of
smile
Obvious weakness,
but not disfiguring
Obvious disfiguring
weakness
Motion barely
perceptible
Incomplete eye
closure, slight
movement corner
mouth
No movement, loss
of tone
Posed portrait photographs at onset
eyebrows raised
eyes tightly
closed
smiling
Posed portrait photographs at 3 months
eyebrows
raised
eyes tightly
closed
smiling
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!
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)
* Adjusted for age, sex, baseline H-B, interval from onset.
Results follow Randomisation Prednisolone
Prednisolone
No
Adjusted OR
Prednisolone
(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)
* Adjusted for age, sex, baseline H-B, interval from onset.
Proportion recovered (HB1) at 3m and 9m
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
OP
AP
OO
AO
0.1
0
0
3
6
months
:
:
:
:
84.3%
78.2%
63.1%
61.0%
(3m)
(3m)
(3m)
(3m)
9
96.1%
92.7%
85.2%
78.0%
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
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
Subgroup analysis
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!
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.
Issues with subgroup
analysis
• Interpretation of subgroup analyses still
contentious even if statistically correct
• Subgroup analyses will be underpowered
• Subgroup analyses tend to be overinterpretated by trialists (Pocock et al
2002)
• Biological plausibility needs to be considered
• Number should be limited due to problem of
multiple testing
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
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
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.