Period Effect in a 2x2 Crossover Trial: The Change Follows the Period, Not the Drug

อ่านฉบับภาษาไทย (Thai version)

Abstract

A period effect is a change in the outcome caused by when it is measured, not by which treatment is given. In a randomised 2x2 crossover trial, one group takes treatment A in period 1 and B in period 2 (sequence AB), and the other takes B and then A (sequence BA), so each participant acts as their own control. If both sequences improve by a similar amount in period 2, the common factor is not the drug, because the period-2 drug is B in one sequence and A in the other; the common factor is period 2 itself. In a chronic pain example, mean pain falls from 8 to 5 in both sequences, and neither drug alone explains the fall. A treatment effect follows the drug, a period effect follows the time period, and a carry-over effect depends on the treatment given in the previous period. This article separates the four effects of a crossover trial, treatment, period, carry-over and sequence, and gives one diagnostic question for each.

Visual summary of the period effect in a 2x2 crossover trial: sequences AB and BA both improve from a mean pain score of 8 to 5 in period 2, so the change follows the period, not the drug. — Visual summary. Hand example: mean pain scores of 8 in period 1 and 5 in period 2 in both sequences.

Both groups felt better in period 2

A pain clinic runs a randomised crossover trial of two treatments for chronic pain, A and B. Every participant takes both treatments, one in each study period: half in the order A then B, half in the order B then A.

When the pain scores come in, both groups report less pain in the second period. The group that switched to B improved. The group that switched to A improved by about the same amount.

It is tempting to say that B works in the first group and A works in the second. Before anyone credits either drug, the team has to ask a simpler thing: what did the two groups have in common in period 2? The drug was different. The time was the same.

Crossover trials and the four effects to separate

A crossover trial is a clinical trial in which each participant receives more than one treatment during different study periods. In a randomised 2x2 crossover trial, participants are allocated to one of two treatment sequences:

Sequence AB: treatment A in Period 1, then treatment B in Period 2.
Sequence BA: treatment B in Period 1, then treatment A in Period 2.

Because the same participant receives both treatments, the participant can act as their own control: the comparison of A with B is a within-participant comparison.

However, crossover trials introduce several special effects that must be distinguished: the treatment effect, period effect, sequence effect and carry-over effect [1, 2]. This article starts with the period effect, because it is the one most easily mistaken for a treatment effect.

What is a period effect?

A period effect occurs when the outcome changes because of when the measurement is made, rather than because of which treatment is being given.

The 2x2 crossover: which treatment each sequence receives in each period.
Sequence	Period 1	Period 2
AB	A	B
BA	B	A

When both sequences improve in Period 2

Suppose participants in both sequences improve during Period 2, regardless of whether they receive treatment A or treatment B.

Look down the Period 2 column of the table. Sequence AB is taking B there; sequence BA is taking A. The common factor is not the treatment.

The common factor is that they are all being measured in Period 2. Therefore, this pattern suggests a period effect.

A simple example: chronic pain

Average pain scores in a crossover study comparing treatments A and B for chronic pain (hand example; higher scores mean more pain).
Sequence	Period 1	Period 2
AB	8 while receiving A	5 while receiving B
BA	8 while receiving B	5 while receiving A

Reading the pain example

Both groups improve

Both groups improve from a pain score of 8 to 5, a fall of 3 points in each sequence.
The Period 2 treatment in AB

In sequence AB, the Period 2 treatment is B.
The Period 2 treatment in BA

In sequence BA, the Period 2 treatment is A.
Neither drug explains it

The same improvement happens under B in one sequence and under A in the other. Therefore, neither A nor B alone explains the improvement.

Result: The pattern instead suggests that something related to Period 2 itself influenced the outcome.

Read inside sequence AB alone, the fall from 8 to 5 would be credited to B. Read inside sequence BA alone, the same fall would be credited to A. Only the two sequences side by side show that the improvement follows the period.

Why can a period effect occur?

A period effect reflects changes associated with time rather than with the treatment assignment.

Participants may differ between Period 1 and Period 2 because their clinical state or the circumstances of the study have changed over time. The same participant, measured later in the trial, is not in exactly the same situation as at the start, and that change can move the outcome whichever treatment is being taken.

Period effect versus treatment effect

A treatment effect occurs when outcomes systematically differ according to which treatment is received. For example:

outcomes are consistently better with A than with B,
regardless of whether A is given in Period 1 or in Period 2.

A period effect, in contrast, occurs when:

Period 2 is systematically different from Period 1,
regardless of whether the treatment in Period 2 is A or B.

The two are mirror images. A treatment effect stays with the drug when the drug moves between periods; a period effect stays with the period when the drug in that period changes.

Period effect versus carry-over effect

These two concepts are commonly confused, because both show up in Period 2.

A carry-over effect occurs when the effect of the treatment from an earlier period persists into the following treatment period. Crossover trials therefore commonly require an appropriate washout period, a treatment-free interval between the periods, to reduce residual treatment effects [1, 2]. The crossover design and analysis guide covers how the washout is planned.

For example:

AB participants may still experience residual effects of A when they start B.
BA participants may still experience residual effects of B when they start A.

Therefore, carry-over depends on what treatment was given previously.

A period effect does not. It appears in Period 2 whichever treatment came before.

Key distinction: one question for each effect

These are distinct components that should be considered when interpreting crossover trials [1, 2].
Effect	Main question
Treatment effect	Which treatment was received?
Period effect	In which period was the outcome measured?
Carry-over effect	What treatment was given in the previous period?
Sequence effect	Does treatment order, AB versus BA, matter?

Recognising a period effect in a trial report

A crossover trial report may describe its results like this:

Outcomes improve during Period 2 by a similar amount in both treatment sequences, regardless of which treatment is administered.

That one sentence is enough to recognise the pattern, if it is read step by step.

The reasoning, step by step

Step 1

Sequence AB receives B in Period 2.
Step 2

Sequence BA receives A in Period 2.
Step 3

Both groups improve.
Step 4

Therefore, the improvement does not consistently follow A or B.
Step 5

The improvement follows Period 2.

Result: The most likely explanation is a period effect.

Four questions to ask of any crossover result

When reading the results of a crossover trial, ask:

Does the difference follow the treatment? Think treatment effect.
Does the difference follow Period 1 versus Period 2? Think period effect.
Does it depend on the treatment received previously? Think carry-over effect.
Does AB behave differently from BA because of treatment order? Think sequence effect.

Pitfalls

Crediting a Period 2 improvement to the Period 2 drug

Inside one sequence, the improvement in Period 2 coincides with the switch of treatment, so it is read as the effect of the treatment taken in Period 2.

Fix: Look at both sequences together. If AB and BA show a similar Period 2 shift, consider a period effect before attributing the difference to treatment.
Calling a period effect carry-over, or carry-over a period effect

Both concern what happens in Period 2, so the two are commonly confused.

Fix: Ask what the change depends on. Carry-over depends on what treatment was given in the previous period; a period effect does not, and appears in Period 2 whichever treatment is given.

Glossary

crossover trial (การศึกษาแบบไขว้): A clinical trial in which each participant receives more than one treatment during different study periods.
sequence (ลำดับการรักษา): The order in which a participant receives the treatments; in a 2x2 crossover, AB or BA.
within-participant comparison (การเปรียบเทียบภายในผู้เข้าร่วม): A comparison of one participant's outcome under one treatment with the same participant's outcome under the other, so the participant acts as their own control.
treatment effect (ผลของการรักษา): A systematic difference in outcome according to which treatment is received, whichever period it is given in.
period effect (ผลของช่วงเวลา): The effect of time or study period on the outcome, independent of treatment.
carry-over effect (ผลตกค้าง): An effect of an earlier period's treatment that persists into the following treatment period.
washout period (ช่วงล้างยา): A treatment-free interval between periods that reduces residual effects of the earlier treatment.
sequence effect (ผลของลำดับ): A difference between the AB and BA groups that comes from the order in which the treatments are given.

References

Senn S. Cross-over trials in clinical research. 2nd ed. Wiley; 2002. https://doi.org/10.1002/0470854596
Jones B, Kenward MG. Design and analysis of cross-over trials. 3rd ed. Chapman and Hall/CRC; 2014. https://doi.org/10.1201/b17537

Key takeaways

A period effect is an outcome difference attributable to the study period rather than to the assigned treatment.
If both the AB and BA sequences change similarly in Period 2, suspect a period effect.
A treatment effect follows the treatment itself.
A carry-over effect reflects residual effects of a previous treatment.
In crossover trials, the treatment, period, sequence and carry-over effects must be conceptually separated for correct interpretation.

Related in the wiki: [[treatment-by-time-interaction-longitudinal-trials]] [[crossover-trials-design-analysis-guide]] [[mixed-model-series-guide]]