More Power for Less Money: Statistical, Power, and Cost Analyses That Account for Intracluster Correlation in Experiments with Same-Group Cage Mates
In experiments with cohoused animals, outcome variables can become correlated among cage mates. This is called intracluster correlation. When cage mates are all of the same group, the experiment is similar to a cluster randomized trial in human studies. Intracluster correlation in same-group cage mate experiments is a type of pseudoreplication, and ignoring it in statistical analyses increases false-positive results. Herein, we provide a tutorial on how to account for intracluster correlation in statistical analyses. Specifically, this is done by including cage identifiers as an independent variable in a linear mixed model, a type of ANOVA. Because power analyses must be based on the planned statistical analyses, we also include effect size calculations and sample size calculations (types of power analyses) in the tutorial. Effect size and sample size calculations help assure regulatory committees, such as IACUCs, granting agencies, and journals, that experiments are properly powered. These calculations will show that designing experiments to have more cages and fewer animals per cage is more efficient than fewer cages with more animals per cage. This statistical efficiency, which means more power, can be translated into reduced animal numbers, one of the 3Rs (replace, reduce, refine) of animal research. We then perform cost analyses and show how the costs of more cages with fewer animals overall are often less expensive than the costs of fewer cages with more animals overall. Altogether, accounting for intracluster correlation in the experiment design and analysis of same-group cage mate experiments results in fewer statistical errors, reduced costs, and fewer animals. Finally, analyses are demonstrated using JASP, a free, open-source, user-friendly statistical software, and provide R and SAS code to perform the analyses.
Twenty-four same-sex, unrelated mice of the same age were equally randomized to treatment groups, C, D, and E. The first 4 mice randomized to a group were individually administered the treatment and placed in the same cage; the last 4 randomized to the group were similarly treated and caged. The 6 cages were then randomized on the rack. Col, column.
Data for examples 1 and 2 in the JASP data editor.
From the Estimate marginal means field, we must specify the comparisons of interest, or ‘contrasts.’ Here, we make all pairwise comparisons among treatments C, D, and E in contrasts 1 to 3, then compare the average of treatments D and E to the mean of C in contrast 4.
Cohen’s effect size examples for comparing means (μs) between 2 populations (Cohen’s d) and among ≥2 populations (Cohen’s f). The example outcome is the percentage of splenic CD4 cells, assumed to be normal in distribution with the animals in each population having an SD (σA) of 4.5 percentage points. Cohen’s d is the distance between 2 means divided by σA; d is in σA units. Cohen’s f is the SD of the populations’ means (σμ) divided by σA. In all panels, the f and d values are mathematically equivalent, noting that the number of d values is one fewer than the number of population means being compared. Across all panels, Cohen’s f is constant to illustrate how its interpretation is more complicated than interpreting Cohen’s d values. (A) Hypothesized means for 2 populations. (B) Hypothesized means for 3 populations with the dispersion of the means at its mathematical minimum and (C) at its mathematical maximum for the given Cohen’s f value.28 Note that this explanation assumes that any extra variability (such as variability among cages, σC) has been accounted for in the comparisons. Popn, population.
Twenty-four same-sex, unrelated mice of the same age will be equally randomized to treatment groups, control (C) and experimental (E). (A) The first 2 mice randomized to a group will be individually administered the treatment and placed in the same cage; remaining sets of 2 same-group mice will be similarly treated and caged. (B) The first 4 mice randomized to a group will be individually administered the treatment and placed in the same cage; remaining sets of 4 same-group mice will be similarly treated and caged. For both experiment designs, the cages will then be randomized on the rack. Col, column.
For all panels, power is targeted at 0.80 on a 2-sided test comparing 2 means and conducted at the 0.05 significance level within a LMM (Equation 2). The assumed experiment designs are like those in Figure 4. (A) Effect size, dA, varies by ρ. Two animal-number-equivalent caging schemes are compared. A smaller dA is preferred. (B) Sample size varies by ρ. Sample sizes are counts of cages and animals needed per group to detect a dA = 1.2. Two power-equivalent caging schemes are compared. Smaller counts are preferred. (C) The breakpoint day, DBP, varies by ρ. DBP is for the 2 power-equivalent caging schemes in (B). Experiments ending before DBP are less expensive when cages contain 2 animals; otherwise, caging 4 animals per cage will be less expensive. DBP assumes the cost of a single animal is 25-fold greater than the per diem cost of a single cage; that is, the costs ratio is 25. Although not illustrated, DBP increases as the costs ratio increases. A costs ratio of 25 is quite small for our institution, so we would expect to be DBP farther out in most cases. R code used to produce figure values is in the Supplementary Materials.
Contributor Notes
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