Statistics for the Terrified:Trial Design and Sample Size

Andrea MarshallMark Williams

Learning Objectives

By the end of this session you will be aware of

• The different types of trial designs and why we use them

• Importance of sample size and requirements needed to be able calculate it

• Types of statistical errors

• Statistical power

Clinical Trial

• A prospective experiment • Designed to assess the effect of one or more

interventions in a group of patients

Phases of Research

Phase II Studies

• Generally small studies • 1 or more interventions • Provide initial assessment of efficacy

• Identify promising new interventions for further evaluation and screen out ineffective interventions

• Not able to compare interventions

Choice of control

• Uncontrolled – no control – may be useful for small phase II studies looking to show a intervention is feasible or effective

• Historical control – trial compares patients treated with new intervention with earlier series of patients – but may not be truly comparable

• Controlled trial –intervention is compared to standard in patients over the same period of time

• Matched controls – patients allocated to intervention are matched to those on the standard intervention according to specific characteristics

Types of Phase III trial design

• Parallel group• Factorial• Cross-over• Cluster-randomised• Adaptive designs

Parallel group design

• Most simple design• Compares at least one intervention with the standard

in patients at the same time• Can consider two or more arms - i.e. have 2 or more

intervention options but have to be confident can get enough patients

• Patients on each arm are similar and only the allocated interventions differ

• Allocation to trial arms is made at random

Example - Parallel group design

• SARAH trial: Assessing the effectiveness of exercise programme over and above usual care

Sample: People with Rheumatoid Arthritis

of the hand

Usual Care

Usual care + Exercise

Factorial design

• Allows more than 1 question to be answered using the same patients and therefore less patients are needed

• If interested in two types of therapy• Alternative to running 2 parallel group trials instead

Sunscreen anyone?

Factorial design (2)

1. Looking at role of suncreen, i.e. Suncreen versus no sunscreen

2. Looking at role of betacarotene,

i.e. betacarotene versus no betacaroteneSample

(n=1620)

Suncreen(n=810)

Control(n=810)

Sample(n=1620)

Betacarotene(n=810)

Control(n=810)

Factorial design (4) Example

1. Looking at role of sunscreen

2. Looking at role of Betacarotene

Sample(n=1621)

Placebo tabs only (n=393)

Betacarotene tabs only (n=416)

Sunscreen + placebo tabs

(n=408)

Sunscreen + betacarotene tabs (n=404)

No sunscreen (n=809) BC and Placebo tabs only

Sunscreen (n=812)Sunscreen+BC and Sunscreen+placebo

No BC (n=801) Sunscreen+placebo and

placebo tabs only

BC (n=820)Sunscreen+BC and BC tabs

only

Crossover designs

• Patients are allocated to a sequence of two or more interventions

• Classified by number of interventions allocated to each patient – i.e. 2-period crossover = each person receives each of

the 2 interventions in a random order

Treatment A

Washout

period

Treatment

BSample Trea

tment B

Washout

Period

Treatment A

Crossover designs (2)

• Limited to situations where:– Disease is chronic and stable– Different interventions can be administered to same

patient for a short period of time – Patients return to the same state afterward each

intervention s to avoid a carry over effect • Wash out period should be long enough for complete

reversibility of intervention effect• Generally fewer patients required as interventions

evaluated within the same patients

Cross over design (3)- example

• Sleep apnoea victim?• Engleman et al (1999) Randomised placebo-

controlled cross-over trial of CPAP for mild sleep apnea/hypopnea syndrome

CPAP

Washout

period

Placebo tabs

Placebo tabs

Washout

Period

CPAP

Sample

Cluster design

• Patients within any one cluster are often more likely to respond in a similar manner

• Intervention is delivered to or affects groups• E.g. Group exercise program

• Intervention is targeted at health professionals• E.g. Educational regarding disease management

• Contamination between individuals

Cluster design (2) E.g. OPERA

Care Homes

Intervention – Physical

activation programme

Control – Depression Awareness

Adaptive designs

• Ability to modify the study without undermining the validity and integrity of the trial

• Can save time and money • Need short-term evaluable• Possible modifications include:-

– Re-estimating sample size– Stopping trial early– Dropping interventions– Changing the eligibility criteria

Size of trial

• Important to determine precisely at the design stage• Minimum number of subjects

– To reliably answer the question– Avoid patients unnecessarily receiving an inferior

treatment• Want trials to have

– High chance of detecting clinically important differences– Small chance of observing differences when they do not

exist

Sample Size

• In order to calculate the required sample size we need to know:– Trial design

– Primary outcome and how it will be analysed

– Hypothesis being tested – superiority/non-inferiority/equivalence

– Significance level (generally set to 5%)

– Power (generally 80-90%.)

Additional information

– What is expected on the standard arm (based on previous trials or experience)

– Size of a clinically relevant difference

– Expected dropout/loss to follow-up rate

Primary outcome

• Ideally only one• Must be pre-defined• Validated• Most clinically relevant outcome • Able to provide convincing evidence to answer the

primary objective

Types of primary outcomes

• Binary – yes/no, – E.g. toxicity suffered or response to intervention

• Continuous– E.g. Quality of life scores from the SF-12

• Time to event – E.g. Overall survival or time to hospital discharged

Difference/Superiority trials

• To determine the effectiveness of a new intervention relative to a control

• Need to know what is a clinically relevant improvement/difference

• If no statistically significant difference, then cannot conclude interventions are equivalent only that NOT sufficient evidence to prove a difference

“Absence of evidence is not evidence of absence”

Non-inferiority trials

• To determine if new intervention is no worse (by a certain amount) than control but maybe associated with e.g. less severe toxicity or better quality of life

• Need to know the largest difference to be judged clinically acceptable

• One sided test as only looking at whether no worse• Generally need more patients than superiority trials

Equivalence trials

• Trying to show that a new intervention only differs by a clinically unimportant difference

• Need to know the size of equivalence margin, i.e. a difference which is clinically unimportant

• Two sided test• Generally need more patients than superiority trials

Errors

• Type I error () – chance of detecting a difference when there is none

• Type II error ( ) – chance of failing to detect a difference when it DOES exists

• Power (1-) – chance of detecting the difference if it DOES exists

From data analysis

Truth

No difference There is a difference

Fail to detect a difference Correct decision Type II error (b)

Detected a difference Type I error (a) Correct decision1-b Power

Sample size calculations

Important to • Allow for dropouts/loss to follow-up in calculations• Investigate sensitivity of sample size estimates to

deviations from assumptions used• Be able to answer secondary outcomes

• Proportion of successes on control arm (P0)

• Difference you want to detect or the proportion (P1) expected with the new intervention

• E.g. With 5% two-sided significance level (=0.05 ),80% power for standard 2-arm parallel group trial with a 1:1 allocation and P0 = 0.25 and P1 = 0.40, i.e. 15% absolute differences in proportion of responsesSample size required is 152 patients in each arm giving a minimum total of 304 patients

Sample size for binary outcome

Changes to the assumptions

• Numbers given are for the sample size in each arm

Difference P0 P1 Power

80% 90% 95%

15% 0.25 0.40 152 203 251

10% 0.25 0.35 329 440 543

5% 0.25 0.30 1251 1674 2070

15% 0.30 0.45 163 217 268

10% 0.30 0.40 356 477 589

5% 0.30 0.35 1377 1843 2278

• Difference you want to detect in the means of the outcome and Standard deviation (SD)

• E.g. In MINT, – 1% two-sided significance level (=0.01 ),– 90% Power– To detect a difference of 3 points on the Neck

Disability Index with an estimated SD of 8 Sample size required is 211 patients in each arm

giving a minimum total of 422 patients

Sample size for continuous outcome

Sample size for continuous outcome

• Or standardised difference/effect size – difference in means divided by the SD– small (0.2), median (0.3) or large (0.6)

Standardised difference

80% 90%

0.2 394 5270.3 176 2350.4 100 1330.5 64 860.6 45 60

Sample size for time to event outcome• Survival rate at a particular time-point, e.g. 2 years,

or the median survival time (time at which 50% of patients have experienced the event) for those on the control arm

• Difference wanting to detect• Also can depend on

– Expected recruitment rate

– Duration of follow-up after recruitment closes

Sample size for time to event outcome (2)E.g. In COUGAR-2, • To detect a 2 month improvement in median overall

survival from 4 months on the control arm to 6 months on the intervention arm

• 5% two-sided significance level (=0.05 ),90% Power

• 2 year recruitment period with analysis 6 months after completed recruitmentSample size required is 146 patients in each arm giving a minimum total of 292 patients

Sample size for cluster trials

• Need to inflate sample size for the primary outcome to take into account clustering by the Design effect

– n = average number to be recruited per cluster– ρ = Intracluster correlation coefficient (ICC)

• Statistical measure for the level of between cluster variation

• Values between 0 and 1 (higher values represent greater between cluster variability)

• 0.05 is often used

Sample size for cluster trials (2)

• Number of clusters– Better to have more clusters than a large number of

patients in fewer clusters– Even if the overall number of patients is large if the

number of clusters is inadequate the trial will be underpowered• E.g. Trials with 2 clusters equivalent to a trial with 2

patients– Absolute minimum of 4 clusters per arm

• E.g. In OPERA – Clusters: Residential and nursing accommodation (RNH)– Control = depression awareness programme

versus Intervention = exercise programme– Primary Outcome = Proportion of residents depressed at end

of trial (Geriatric depression scale 15 score <5)– Clinical important benefit = 15% reduction from 40% for

controls to 25% for the intervention– 80% power and 5% significance level – Allocation of 1.5 controls to 1 intervention

A total sample size of 343 is needed for a patient randomised trial

Sample size for cluster trials (3) Example

Sample size for cluster trials (4)

• To adjust for clustering – ICC=0.05 – Average cluster size =15Design effect = 1.7So Total sample size = 343 * 1.7 = 583

• A total sample size of 583 patients with assessments at end of the trial is needed (233 in intervention arm and 350 in control arm)

• At least 39 clusters (RNH) are required (=583/15)

• Effect of varying ICC and number of patients per cluster

Sample size for cluster trials (5)

Total number without clustering

ICC Number per cluster

Design effect

Total with clustering

Number of clusters

343 0.05 15 1.7 583 39

343 0.05 50 2.45 840 17

343 0.15 15 2.1 720 48

343 0.15 50 7.35 2521 50

Summary

• Phase of clinical trial depends on evidence already acquired

• Phase III trials = RCT• Trial design depends on

– Outcome and questions to be answered– Number and type of Interventions being compared– Unit of allocation and controlling of bias

• Bigger sample sizes gives us increased confidence in our results (but there is a limit!)

• Always consult a statistician!!!

Quiz

How many arms can a parallel group trial have?

0%

43%

0%

57%1. 12. 23. 34. 2 or more

Which type of trial would you need a washout period incorporated into the design?

0%7%

93%

0%

1. Parallel design2. Factorial design3. Cross-over design4. Cluster design

Which type of trial is likely to require the largest sample size?

Phas

e I t

rial

Phas

e II

trial

Phas

e III

(par

...

Phas

e III

(clu

...

4%

70%

26%

0%

1. Phase I trial2. Phase II trial3. Phase III (parallel) trial4. Phase III (cluster) trial

What is the generally acceptedminimum level of power for a trial?

60%

70%

80%

90%

4% 7%

89%

0%

1. 60%2. 70%3. 80%4. 90%

Which of the following information do you NOT need to calculate the sample size for a binary outcome?

33%

17%

8%

42%

1. Clinically relevant difference2. Standard deviation3. Power4. Significance level

If sample size to detect 10% differences in a binary outcome with 5% significance level and 80% power is not obtainable, how could you decrease the sample size required?

Det

ect d

iffer

e...

Use

85%

pow

er

Use

1%

sig

nifi...

All

of the

abo...

None

of above

46%

0%

19%

31%

4%

1. Detect differences of 15%2. Use 85% power3. Use 1% significance level4. All of the above5. None of above

If wanting to detect with a continuous outcome: Trial A: difference in means of 5, SD = 10 Trial B: difference in means of 4, SD = 8 Trial C: Standardised difference of 0.5would you need ... ?

More

pat

ients

...

More

pat

ients

...

More

pat

ients

...

Sam

e fo

r all

t...

9%

50%

18%23%

1. More patients with Trial A2. More patients with Trial B3. More patients with Trial C4. Same for all trials

References

• The handbook of clinical trials and other research Ed. Alan Earl-Slater

• Sample size tables for clinical studies. Machin, Campbell, Fayer and Pinol.

Questions?