5 Overview of Trial Designs

Parallel group design

different groups of patients are studied concurrently (in parallel). Patients receive a single therapy (or combination of therapies) $⟶$ estimate of treatment effect is based upon a between-subject comparison.

Paired design

patient receives both treatment for example, matching parts of anatomy (e.g. limbs, eyes, kin etc) $⟶$ estimate of treatment effect is based upon within-subject comparison. (symmetry can be problematic!)

Crossover design

patients receive a sequence of treatments; the order determined by randomisation $⟶$ estimate of treatment effect based upon ’within-subject’ comparisons.

Sequential designs

aim to stop trials early. Sequential analyses: strict -/ group sequential.

Factorial designs

study all possible treatment combinations, for example, placebo/control, A, B and AB. Allow for investigation of interactions.

Adaptive designs

aim to address ethical issues: proportion of patients receiving inferior treatment diminishes (ethics).

Zelen’s design

problems with informed consent: randomise patient to standard/experimental treatment. Treat standard group as if not in the trial $\to$ seek consent from experimental group and analyse as randomised.

Equivalence trials

aim to show treatments are as efficacious but fewer side effects: comparing new to standard.

Non-inferiority trials

one-sided equivalence trials.

Systematic review

(perhaps with meta analysis): studies which combine trial results qualitatively or quantitatively.

Advantages

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  Within-subject comparisons: patients act as their own control $\to$ elimination of between-patient variation
  

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  Sample size is smaller: same number of observations with fewer patients
  

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  Precision increased: can achieve the same degree precision in estimation with fewer observations.
  

Further reading (Senn 1993, Sec. 1.3)

Disadvantages of Cross-Over Trials (Senn 1993, Sec. 1.4)

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  drop outs: patients may withdraw
  

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  only suitable for certain indications
  

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  period by treatment interaction: the treatment effect is not constant over time
  

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  carry-over effect: “Carry-over is the persistence […] of a treatment applied in one period in a subsequent period of treatment.”
  

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  inconvenience to patients: several treatments, longer total time under observation (sometimes advantage!)
  

• •

  analysis is more complex: pairs of measurement; may be systematic differences between periods.
  

What may be done about carry-over? (Senn 1993, Sec. 1.8)

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  wash-out period:

  “A wash-out period is a period in a trial during which the effect of a treatment given previously is believed to disappear. If no treatment is given during the wash-out period then the wash-out is passive. If a treatment is given during the wash-out period than the wash-out is active.”

• •

  example for active wash-out: 4 weeks under each of two treatments, but only second two weeks as observation period.

Where are cross-over trials useful? (Senn 1993, Sec. 1.5)

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  chronic diseases which are relatively stable (e.g. asthma)

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  other examples: rheumatism, migraine, moderate hypertension, epilepsy

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  single-dose trials (PK/PD) rather than long-term trials

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  drugs with rapid, reversible effects rather than ones with persistent effects.

Various types of cross-over design exist but we shall focus upon the so-called $\mathrm{𝟐}\times \mathrm{𝟐}$ design:

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  two treatment, two period cross-over

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  two sequences: 1) AB and 2) BA

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  also called AB/BA design (more specific)

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  in the following normally distributed endpoint considered

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  Motivating example: asthma trial.

Example (Senn 1993, Sec. 3.1)

Reference: Graff-Lonnevig V, Browaldh L (1990) Clinical and Experimental Allergy 20: 429-432.

The objective is to compare the effects of formoterol (exp) and salbutamol (std).

Patients

13 children (aged 7 to 14 y) with moderate to severe asthma.

Single-dose trial

200 $\mu$ g subatomic, 12 $\mu$g formoterol: bronchodilators.

Primary endpoint

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  peak expiratory flow (PEF, [l/min]): a measure lung function

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  several measurements during the first 12 hours after drug intake

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  measurements after 8 hours considered here.

Drop-outs

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  NOTE patient 8 dropped out after first period

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  not mentioned by Graff-Lonnevig V, Browaldh L (1990)!

Design

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  randomised (randomisation procedure?): order of treatments assigned at random the sequence group

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  double-blind: double-dummy technique

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  two treatment, two period cross-over (AB/BA design)

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  wash-out period of at least one day.

Unnumbered Figure: Link

Unnumbered Figure: Link

A simple analysis: ignoring the effect of period. (Senn 1993, Sec.3.2, 3.3)

Method

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  calculate the so called “cross-over differences” (formoterol-salbutamol) for each subject

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  perform a one-sample t-test for the differences (i.e. a paired t-test).

Assumptions

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  normally distributed differences

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  expectation(diff) = true treatment effect.

Mean: $\overline{d}=45.4$, standard deviation: ${\widehat{\sigma }}_d=40.6$, df: $n-1=12$
test statistic

$$t=\sqrt{n}\frac{\overline{d}}{{\widehat{\sigma }}_d}=\sqrt{13}\frac{45.4}{40.6}=4.0$$

confidence interval

$$[\overline{d}-t_{n-1,1-\alpha /2}{\widehat{\sigma }}_d/\sqrt{n};\overline{d}+t_{n-1,1-\alpha /2}{\widehat{\sigma }}_d/\sqrt{n}]$$

$$=[45.4-2.2\cdot 11.3;45.4+2.2\cdot 11.3]=[21;70]$$

p-value: $p=0.0017$

Conclusion/comments?

“factors that might cause the differences not to be distributed at random about the true treatment effect”

• •

  period effect (e.g. hay fever: pollen count)

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  period by treatment interaction

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  carry-over

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  patient by treatment interaction: cannot be investigated in AB/BA design

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  patient by period interaction.

Let $\mu$ denote the expectation for treatment B,
$\tau$ denote the treatment effect (treatment A - treatment B)
$\pi$ denote period effect (period 2 - period 1).
Then we can express the expected values for the AB/BA design:

Sequence	Period 1	Period 2
AB	$\mu +\tau$	$\mu +\pi$
BA	$\mu$	$\mu +\tau +\pi$

Treatment effect

1. 1.

   Compute the expected period differences

   $${\overline{d}}_i,i=1,2$$

   for each sequence group (1:(AB), 2:(BA)):

   $${\overline{d}}_1=\tau -\pi ,{\overline{d}}_2=-\tau -\pi$$

2. 2.

   subtract the expected period differences:

   $${\overline{d}}_1-{\overline{d}}_2=(\tau -\pi )-(-\tau -\pi )=2\tau$$

3. 3.

   divide by 2 to yield $\tau$.
   

and the period effect……

1. 1.

   Compute the expected period differences for each sequence group:

   $${\overline{d}}_1=\tau -\pi ,{\overline{d}}_2=-\tau -\pi$$

2. 2.

   sum the expected period differences:

   $${\overline{d}}_1+{\overline{d}}_2=(\tau -\pi )+(-\tau -\pi )=-2\pi$$

3. 3.

   divide by -2 to yield $\pi$.

Comments?

Adjusting for a period effect (Senn 1993; Sec.3.5) using cross-over differences. So-called Hills-Armitage approach.
“basic estimators”

• •

  definition (Senn 1993, p 43) ‘A basic estimator of a given treatment contrast is the given contrast calculated for an individual.’

• •

  here: difference at 8 hours in the PEF under formoterol and salbutamol (formoterol - salbutamol).

Calculate basic estimators $d_{ij}$ for each individual.

Calculate means ${\overline{d}}_i$ and std dev $s_i$ of basic estimators for both sequence groups $i=1,2$.

Estimate the treatment effect: $\overline{d}=({\overline{d}}_1+{\overline{d}}_2)/2$.

Test statistic

$$t=\frac{\overline{d}}{{\widehat{\sigma }}_{\overline{d}}}$$

with

$${\widehat{\sigma }}_{\overline{d}}=\sqrt{\frac{1}{4}\left(\frac{1}{n_1}+\frac{1}{n_2}\right)s^2}$$

and

$$s^2=((n_1-1)s_1^2+(n_2-1)s_2^2)/(n-2).$$

Confidence Interval

$$[\overline{d}-t_{n-2,1-\alpha /2}\cdot {\widehat{\sigma }}_{\overline{d}};\overline{d}+t_{n-2,1-\alpha /2}\cdot {\widehat{\sigma }}_{\overline{d}}].$$

Means and std dev of basic estimates

sequence	n	${\overline{d}}_i$	$s_i$
for/sal	7	30.7	33.0
sal/for	6	62.5	44.7

test statistic

$t=46.6/10.8=4.3$

confidence interval

$[46.6\pm 2.2\cdot 10.8]=[23;70]$

p-value

p=0.001

Comments?

Subtract sequence group means as opposed to summing them and divide by -2.

n.b the standard error is the same for the treatment and period effect: why?

n.b You can work with either the period differences or the cross-over differences but need to use appropriate formulas!

What is the association between the ’period-differences’ (period 1 - period 2) and the cross-over differences? (treatment A - treatment B, say)

where

• •

  ${\lambda }_1$ and ${\lambda }_2$ carry-over effects ($\mu$, $\tau$, and $\pi$ as above)

• •

  How could you/can use the cell means to estimate carry over effects?

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  only the difference between ${\lambda }_1$ and ${\lambda }_2$ identifiable

• •

  based upon differences between sequences.

Testing for carry-over

• •

  estimate is based upon ’between-patient’ variation $\Rightarrow$ low power of test

• •

  the carry over effect is confounded with period-treatment interaction in $AB/BA$ design

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  two-stage procedure $\Rightarrow$ biased estimator of treatment effect.

$\Rightarrow$ do not test for carry-over!

Conclusion (Senn 1993, p 69)

‘No help regarding this problem is to be expected from the data. The solution lies entirely in design.’

Further reading: Senn (1993), Senn (1997).

Three types of baseline measurements

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  taken before first treatment

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  taken after completion of first treatment, before start of second

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  taken after completion of second treatment.

Further reading: Senn (1993), Section 3.15.

• •

  Senn S (1993) Cross-over trials in clinical research. Wiley, Chichester.

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  Senn S (1997) Statistical issues in drug development. Wiley, Chichester.

• •

  Jones B, Kenward MG (1990) Design and analysis of cross-over trials. Chapman & Hall, London.

• •

  Senn S et al. An incomplete blocks cross-over in asthma. In: Vollmar J, Hothorn LA (eds). Cross-over clinical trials. Gustav Fischer Verlag, Stuttgart.

‘Randomised Consent Design’

Procedure

• •

  randomise patients to standard or experimental treatment

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  standard group treated as if not in trial

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  experimental group is offered exp. treatment, but can have standard

• •

  analysis according to randomisation.

Purpose: avoid problems associated with getting informed consent
Is this ethical?

Further reading

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  Zelen M (1979) NEJM 300, 1242-1245.

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  Zelen M (1982) Cancer Treatment Reports 66, 1095-1100.

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  Zelen M (1990) Statistics in Medicine 9, 645-656.