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Statistical Considerations in Work Package 2
Michael Sweeting, Martin Law
Medical Research Council - Biostatistics Unit
December 13, 2011
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Introduction
Purpose:
To find an optimal long-term antibiotic treatment for COPD;
Primary objective is to reduce lower airway bacterial load over
a 13-week period;
To gather information on adherence and cost-effectiveness
(Work Packages 5 and 6).
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Introduction
Design:
Four treatment arms - three active treatments plus placebo;
Compare each treatment to placebo;
Single blind - treatment not known to patients or
microbiologist;
13 weeks on treatment - assessment at week 14.
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
What variables will be measured?
Primary endpoint:
Change in lower airway bacterial load (at baseline and 14
weeks);
Safety endpoints:
Bacterial resistance;
Adverse events;
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
What variables will be measured?
Secondary endpoints:
Spirometry (FEV1, FEV1 (% of predicted), FVC, FEV1/FVC);
Respiratory health status (SGRQ, daily diary cards);
General health status (EQ5D);
Number of exacerbations (diary cards);
Adherence to treatment (pill counts, MAQ-4, MAQ-8);
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Sample Size
Based on anticipated change in bacterial load counts and
anticipated correlation between baseline and post-treatment
counts (using previous study - fall of 1.88 log10 units/ml);
Sample size of 44 (per arm), 90% power, overall type I error
of α = 5%, test each treatment at p = 0.02, assume
correlation of 0.5;
Anticipating drop-out and non-compliance of ≤ 4% each,
sample size is inflated to 50 per arm - total sample size of
200.
Note: Study is not powered to detect differences between the
active treatments.
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Randomisation
Patients will be randomised online by SealedEnvelopeTM , using
random permuted blocks (RPBs) of differing sizes:
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Randomisation
Patients will be randomised online by SealedEnvelopeTM , using
random permuted blocks (RPBs) of differing sizes:
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Randomisation
Patients will be randomised online by SealedEnvelopeTM , using
random permuted blocks (RPBs) of differing sizes:
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Randomisation
Patients will be randomised online by SealedEnvelopeTM , using
random permuted blocks (RPBs) of differing sizes:
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Randomisation
Patients will be randomised online by SealedEnvelopeTM , using
random permuted blocks (RPBs) of differing sizes:
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Randomisation
Patients will be randomised online by SealedEnvelopeTM , using
random permuted blocks (RPBs) of differing sizes:
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Randomisation
Patients will be randomised online by SealedEnvelopeTM , using
random permuted blocks (RPBs) of differing sizes:
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Recruitment, blinding:
Recruitment period: Recruitment period is estimated to be
approximately 9 months;
Blinding: Trial is single-blinded: Patients are blinded to
treatment, but clinicians and statisticians are not. Microbiologists
will be blinded.
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Primary endpoint
Change in log (bacterial load) from baseline to end of treatment.
Intention-to-treat: Patients analysed as randomised;
Example of summary data :
log (bacterial load) Change
Baseline 14 weeks Mean (SD)
Drug A 7.0 5.0 -2.0 (1.0)
Drug B 6.8 5.8 -1.0 (2.2)
Drug C 7.1 4.0 -3.1 (1.5)
Placebo 7.0 6.7 -0.3 (0.5)
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Primary endpoint (2)
Multiple regression: The (log) counts will be analysed using
multiple regression, adjusting for
Baseline count;
Smoking status;
Disease severity.
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Secondary endpoints
Will be modelled using appropriate generalised linear models;
Hypotheses generating only;
Summary statistics: As primary outcome - mean, median, etc.;
Adjustments: For baseline values, treatment group,
confounders (as neccessary).
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Which drug will be taken forward?
We make a decision on the optimal treatment based on the criteria
below. Each criterion is given a weight – that is, some criteria are
deemed more important than others:
Efficacy (change in bacterial load counts) (weight = 2.0);
Adverse events (binary - yes / no) (weight = 1.5);
Bacterial resistance (binary - yes / no) (weight = 1.5);
Adherence (percentage of pills taken) (weight = 1.2);
Cost (fixed quantity) (weight = 1.0).
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Which drug will be taken forward?
Using Bayesian analysis, drugs will ranked on each criterion, with
an associated probability – e.g., “The probability that drug A ranks
1st for efficacy is 0.7”.
Note: Rank 1 is always associated with the superior treatment,
even if the criterion is “negative”, such as adverse events.
We combine each drug’s rankings, the probability of those rankings
being true and the weights to produce a utility score.
The treatment with the greatest utility score is concluded to be
optimal.
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Which drug will be taken forward?
Example:
Efficacy
P(rank is true)
Rank 1 2 3
Drug A 0.03 0.37 0.60
Drug B 0.06 0.55 0.39
Drug C 0.91 0.08 0.011 2 3
Drug ADrug BDrug C
Efficacy
Rank
Pro
babi
lity
0.0
0.2
0.4
0.6
0.8
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Which drug will be taken forward?
Example:
Adverse events
P(rank is true)
Rank 1 2 3
Drug A 0.17 0.79 0.04
Drug B 0.58 0.17 0.25
Drug C 0.25 0.04 0.711 2 3
Adverse Events
Rank
Pro
babi
lity
0.0
0.2
0.4
0.6
Drug ADrug BDrug C
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Which drug will be taken forward?
Efficacy (2) Adverse events (1.5)
P(rank is true) P(rank is true)
Rank 1 2 3 1 2 3
Drug A 0.03 0.37 0.60 0.17 0.79 0.04
Score:
10 - weight[ 1×P(rank 1) + 2×P(rank 2) + 3×P(rank 3) ] -
weight[ 1×P(rank 1) + 2×P(rank 2) + 3×P(rank 3) ]
Drug A:
10 − 2 [1 × 0.03 + 2 × 0.37 + 3 × 0.60] −1.5 [1 × 0.17 + 2 × 0.79 + 3 × 0.04] = 7.67
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Which drug will be taken forward?
Efficacy (2) Adverse events (1.5)
P(rank is true) P(rank is true)
Rank 1 2 3 1 2 3
Drug A 0.03 0.37 0.60 0.17 0.79 0.04
Score:
10 - weight[ 1×P(rank 1) + 2×P(rank 2) + 3×P(rank 3) ] -
weight[ 1×P(rank 1) + 2×P(rank 2) + 3×P(rank 3) ]
Drug A:
10 − 2 [1 × 0.03 + 2 × 0.37 + 3 × 0.60] −1.5 [1 × 0.17 + 2 × 0.79 + 3 × 0.04] = 7.67
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Which drug will be taken forward?
Efficacy (2) Adverse events (1.5)
P(rank is true) P(rank is true)
Rank 1 2 3 1 2 3
Drug A 0.03 0.37 0.60 0.17 0.79 0.04
Score:
10 - weight[ 1×P(rank 1) + 2×P(rank 2) + 3×P(rank 3) ] -
weight[ 1×P(rank 1) + 2×P(rank 2) + 3×P(rank 3) ]
Drug A:
10 − 2 [1 × 0.03 + 2 × 0.37 + 3 × 0.60] −1.5 [1 × 0.17 + 2 × 0.79 + 3 × 0.04] = 7.67
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Which drug will be taken forward?
Efficacy (2) Adverse events (1.5)
P(rank is true) P(rank is true)
Rank 1 2 3 1 2 3
Drug A 0.03 0.37 0.60 0.17 0.79 0.04
Drug B 0.06 0.55 0.39 0.58 0.17 0.25
Drug C 0.91 0.08 0.01 0.25 0.04 0.71
Drug A score = 7.67
Drug B score = 7.91
Drug C score = 11.48
We conclude that Drug C should be taken forward to Work
Package 3.
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Which drug will be taken forward?
Efficacy (2) Adverse events (1.5)
P(rank is true) P(rank is true)
Rank 1 2 3 1 2 3
Drug A 0.03 0.37 0.60 0.17 0.79 0.04
Drug B 0.06 0.55 0.39 0.58 0.17 0.25
Drug C 0.91 0.08 0.01 0.25 0.04 0.71
Drug A score = 7.67
Drug B score = 7.91
Drug C score = 11.48
We conclude that Drug C should be taken forward to Work
Package 3.
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Further analyses
Sensitivity analysis: Per-protocol or CACE analysis.
Per-protocol: Includes only patients who comply fully, taking
drug throughout follow-up.
CACE: Measure of causal effect of intervention. Includes only
patients who complied with active treatment or would have
complied with active treatment.
Why? Many patients may exacerbate and end treatment.
Per-protocol and CACE may answer questions regarding
effectiveness of regimes for patients who did not exacerbate.
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Further analyses (2)
Finally, the following subgroups will be assessed for their effect on
the primary endpoint:
Disease severity;
Exacerbation frequency;
Inhaled steroid use.
Again, these investigations will be hypotheses generating only.
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Discussion
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Appendix: Bayesisan calculations
Efficacy (2) Adverse events (1.5)
P(rank is true) P(rank is true)
Rank 1 2 3 1 2 3
Drug A 0.03 0.37 0.60 0.17 0.79 0.04
Drug B 0.06 0.55 0.39 0.58 0.17 0.25
Drug C 0.91 0.08 0.01 0.25 0.04 0.71
Drug A: 10 − 2 (1 × 0.03 + 2 × 0.37 + 3 × 0.60) −1.5 (1 × 0.17 + 2 × 0.79 + 3 × 0.04) = 7.67
Drug B: 10 − 2 (1 × 0.06 + 2 × 0.55 + 3 × 0.39) −1.5 (1 × 0.58 + 2 × 0.17 + 3 × 0.25) = 7.85
Drug C: 10 − 2 (1 × 0.91 + 2 × 0.08 + 3 × 0.01) −1.5 (1 × 0.25 + 2 × 0.04 + 3 × 0.71) = 11.49
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2
Appendix: Bayesisan calculations
Efficacy (2) Adverse events (1.5)
P(rank is true) P(rank is true)
Rank 1 2 3 1 2 3
Drug A 0.03 0.37 0.60 0.17 0.79 0.04
Drug B 0.06 0.55 0.39 0.58 0.17 0.25
Drug C 0.91 0.08 0.01 0.25 0.04 0.71
Drug A: 10 − 2 (1 × 0.03 + 2 × 0.37 + 3 × 0.60) −1.5 (1 × 0.17 + 2 × 0.79 + 3 × 0.04) = 7.67
Drug B: 10 − 2 (1 × 0.06 + 2 × 0.55 + 3 × 0.39) −1.5 (1 × 0.58 + 2 × 0.17 + 3 × 0.25) = 7.85
Drug C: 10 − 2 (1 × 0.91 + 2 × 0.08 + 3 × 0.01) −1.5 (1 × 0.25 + 2 × 0.04 + 3 × 0.71) = 11.49
Michael Sweeting, Martin Law Statistical Considerations in Work Package 2