What the calculator does, why it works, and what it means for your animals.
Using what you already know to reduce what you need next.
Every new animal study requires a concurrent control group — animals that receive no treatment, providing a baseline. But your lab has run similar experiments before. Those past control groups contain valuable information.
Borrowing means channeling that historical information into your new study design, allowing you to reduce the number of concurrent control animals. But you cannot simply dump old data into a new analysis — that would be naive pooling, and it inflates your false positive rate. Instead, the data passes through a statistical filter that accounts for how consistent your past results actually were.
The filter is the Effective Sample Size (ESS). Out of your 89 historical animals, the filter lets through only as many as the consistency of your data warrants. If your lab has been rock-solid, most get through. If results have been variable, very few survive the filter.
Why you can never use all your historical animals at face value.
The key variable is τ (tau) — the between-study standard deviation. Think of it as laboratory noise between experiments. Even a well-run lab has some noise: different days, slight protocol variations, seasonal effects. The more noise, the less your historical data is worth.
The curve drops steeply. Even moderate heterogeneity (τ ≈ 5) slashes the effective sample size dramatically. This is not a flaw — it is honesty. The formula refuses to let you borrow more than the data deserve.
The direct 3R impact of laboratory consistency.
The discount translates directly into animal numbers. The better your lab's consistency (lower τ), the more concurrent control animals you can save. Here are three realistic scenarios — all assuming 89 historical animals, a classical control group of 37, and a within-study SD of 15:
Each dot represents one animal. Filled dots are animals you still need in the new study. Outline dots are animals saved — experiments that don't need to happen. The 3R principle made concrete.
An extra margin of safety, because the future may surprise you.
Even after the discount, we add one more safeguard. The robust borrowing method mixes 80% of the historical information with 20% of a completely uninformative "know-nothing" prior. This protects against the possibility that your next experiment is unexpectedly different from the past.
Think of it as wearing a seatbelt even when you are a good driver. The 20% vague component costs you a small amount of borrowing power but protects against model misspecification. This is the default recommended by Schmidli et al. (2014).
Five steps from historical data to ethics application.
This tool is Step 1. The study analysis is Step 2.
The calculator tells you how many concurrent controls to use. But when the study is done and you analyse the results, you need to formally incorporate the historical data into the analysis — otherwise your reduced control group will be underpowered for a standard test.
If you are a biologist or veterinarian: involve your statistician before the study starts — not after. They will need to perform the MAP prior analysis at study completion.
Naive pooling looks simpler but breaks your statistics.
Some researchers are tempted to simply merge historical and concurrent controls into one big group — "we have 89 historical animals, why not just use them?" This is called naive pooling, and it ignores the between-study variance. The result: your confidence intervals become falsely narrow, and your false positive rate inflates beyond the nominal 5%.
At τ = 5, naive pooling inflates your false positive rate to roughly 20% — meaning one in five experiments would appear significant by chance alone. The borrowing framework avoids this entirely by honestly accounting for the between-study variance.