statistical analysis - nihr meeting - 13th dec 2011

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).


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.


What variables will be measured?

Primary endpoint:

Change in lower airway bacterial load (at baseline and 14

weeks);

Safety endpoints:

Bacterial resistance;

Adverse events;


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);


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.


Randomisation

Patients will be randomised online by SealedEnvelopeTM , using

random permuted blocks (RPBs) of differing sizes:


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.


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)


Primary endpoint (2)

Multiple regression: The (log) counts will be analysed using

multiple regression, adjusting for

Baseline count;

Smoking status;

Disease severity.


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).


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).



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.



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



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



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





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.


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.


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.


Discussion


Appendix: Bayesisan calculations



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


statistical analysis - nihr meeting - 13th dec 2011

Devices & Hardware

sealedenvelope tm

bacterial load counts

optimal treatment

log bacterial load

treatment group

treatment arms

treatment assessment

treatment pill counts