# Example 2

## Effect of a 5-HT_{4} partial agonist on attentional deficit in rats, animals used as their own control (crossover design)

View experiment diagram | Use this diagram as a template

5-HT_{4} agonists are currently being developed as candidate treatments for Alzheimer’s disease. While the effect of this family of compounds on cognition has been demonstrated, no tests had been conducted specifically to assess their effects on attention. To investigate this, this experiment is conducted to assess the effect of a 5-HT_{4} partial agonist on attentional deficit in rats, using the five-choice serial reaction time task.

Rats are trained over a number of sessions (around 30) to react to a visual stimulus. The rear wall of the test chamber contains five holes, which can be illuminated from behind. To receive a food reward, a rat had to learn to poke its nose into a (randomly) illuminated hole. Each animal is shown 100 visual stimuli in 100 trials and the total number of incorrect trials is recorded for each animal.

Because the compounds wash out quickly and produce no adverse effects, each animal can be used as its own control and hence will receive the 5HT_{4} agonist and its vehicle, separated by a two day wash out period. To account for any overall time period effects, some animals receive the vehicle first and some receive the 5-HT_{4} treatment first; this is represented on the diagram with an allocation node which splits the animals into two groups, depending on which treatment they will receive first. This design allows a smaller sample size to be used as the effect of the 5HT_{4} agonist is only tested against the within-animal variability and hence the sensitivity of the test will not be affected by the variability between animals.

Because animals receive distinct treatments on each test period, the experimental unit is an animal for a period of time and each animal is associated with two experimental units.

Group sizes are calculated based on the planned analysis method, to ensure that the experiment yields enough power to detect a biologically relevant difference between the groups if there is one. In this case, even though there are three factors in the analysis, two of the factors are blocking factors and the experiment only needs to be sensitive enough to detect differences between the two treatments: 5HT_{4} agonists or vehicle, with each animal used as its own control. Therefore a power calculation for an unpaired t-test can be used, as long as a within-animal estimate of the variability is used in the power analysis.

For this design it is best to have some preliminary data collected under identical conditions to the planned experiment to estimate the within-animal variability. Using InVivoStat, a one-way ANOVA analysis with two blocking factors is performed on the preliminary data to obtain an estimate of the within-animal variability; note that by fitting the blocking factor ‘animal’ in the 3-way ANOVA, all of the between-animal variability is accounted for by this factor and hence the variability estimated in the ANOVA table is the within-animal variability. In this example, the variance (mean square of the residuals) is 2. The standard deviation is calculated as the square root of the variance: √2=1.4

The sample size can be calculated in InVivoStat, using the power analysis module. It can also be calculated using the power calculation tab for unpaired t-test in the EDA web app with the following input parameters:

- Effect size (m
_{1}– m_{2}): 2 - (within-animal) Variability (SD): 1.41
- Significance level: 0.05
- Power: 0.9
- One or two-sided test: 2

The N per group calculated is 12, which corresponds to the number of experimental units required for each treatment group. So if each animal receives all treatments, then it corresponds to the total number of animals in the experiment. Thus the experiment contains 24 experimental units in total, 12 per treatment group. Twelve animals in total are enough to detect a minimum difference of two incorrect responses with 90% power.

Several potential sources of variability have been identified in this experiment: the sequence of treatments (whether animals receive the 5HT_{4} agonist or its vehicle first), the animals themselves (between-animal variability) and the test period (first or second); these are indicated on the diagram as nuisance variables.

The potential variability induced by the treatment sequence is mitigated by randomising the rats in a balanced way to one of the two treatment sequences; animals allocated to group 1 will receive the 5HT_{4} agonist during the first test period and vehicle during the second test period whereas animals allocated to group 2 will receive vehicle first and then the 5HT_{4} agonist. The randomised allocation of animals into groups 1 and 2 is done using the spreadsheet generated within the EDA.

During the training phase, all animals receive the same treatment: Behavioural training to respond to a visual stimulus using the five-choice serial reaction time task. Then, during each test period, the process is the same: rats receive an injection of the 5HT_{4} agonist or vehicle, then each animal is shown 100 visual stimuli in 100 trials and, amongst the total number of incorrect trials is recorded for each animal. On the diagram, after the measurement all animals are subjected to at the end of the first test period, groups 1 and 2 are reformed to indicate explicitly the treatment each group of animals receives during the second test period.

There is only one variable of interest in this experiment: the treatment, determining whether the 5HT_{4} agonist has an effect on the number of incorrect trials, is the only objective in this study.

The nuisance variables ’animal’ and ‘test period’ are included as blocking factors in the analysis so that the variability induced by the animals and the test period is accounted for; this reduces the overall variability and increase the precision of the result. If the data fits parametric assumptions, it can be analysed with a one-way ANOVA with two blocking factors (this can also be called a three-way ANOVA without interaction).

Note that the nuisance variable ‘treatment sequence’ does not need to be included in the analysis, because the categories of this variable correspond to the combination of the levels of the variables ‘treatment’ and ‘test period’, in other words, if you know what treatment an animal will receive and during which test period, you can identify whether the animal belongs to group 1 or group 2 and hence in what sequence the animal will receive the treatments. This is reflected on the diagram.

### Keywords

Crossover | Blocking factor | Order of treatments | Test period

### References

This experiment is loosely based on example 3.16 (Bate and Clark, 2014).

Bate, ST and Clark, RA (2014). *The Design and Statistical Analysis of Animal Experiments*. Cambridge University Press.

*Behav Brain Res* 195(1):180-6. doi: 10.1016/j.bbr.2008.08.007