Reproducibility of strength performance and strength-endurance profiles: A test-retest study

The present study was designed to evaluate the test-retest consistency of repetition maximum tests at standardized relative loads and determine the robustness of strength-endurance profiles across test-retest trials. Twenty-four resistance-trained males and females (age, 27.4 ± 4.0 y; body mass, 77.2 ± 12.6 kg; relative bench press one-repetition maximum [1-RM], 1.19 ± 0.23 kg•kg-1) were assessed for their 1-RM in the free-weight bench press. After 48 to 72 hours, they were tested for the maximum number of achievable repetitions at 90%, 80% and 70% of their 1-RM. A retest was completed for all assessments one week later. Gathered data were used to model the relationship between relative load and repetitions to failure with respect to individual trends using Bayesian multilevel modeling and applying four recently proposed model types. The maximum number of repetitions showed slightly better reliability at lower relative loads (ICC at 70% 1-RM = 0.86, 90% highest density interval: [0.71, 0.93]) compared to higher relative loads (ICC at 90% 1-RM = 0.65 [0.39, 0.83]), whereas the absolute agreement was slightly better at higher loads (SEM at 90% 1-RM = 0.7 repetitions [0.5, 0.9]; SEM at 70% 1-RM = 1.1 repetitions [0.8, 1.4]). The linear regression model and the 2-parameters exponential regression model revealed the most robust parameter estimates across test-retest trials. Results testify to good reproducibility of repetition maximum tests at standardized relative loads obtained over short periods of time. A complementary free-to-use web application was developed to help practitioners calculate strength-endurance profiles and build individual repetition maximum tables based on robust statistical models.

exceptions, priors were based on the results of a preceding pilot study to facilitate chain convergence during sampling. A prior sensitivity analysis was conducted by introducing a set of three competing priors with larger scales, following a similar approach to Deapoli and colleagues [1]. A prior was considered appropriate (i.e. truly weakly informative) when the posterior overlap with the competing priors was at least 90%.
▪ Third, posterior distributions of model parameters were estimated by using the Hamiltonian Monte Carlo (HMC) algorithm of the probabilistic programming language Stan [2]. Four chains sampled from random initial values for 4000 iterations, respectively, the first 2000 iterations of each chain being discarded as warm-up.
▪ Fourth, sampling diagnostics (R-hat, number of divergent transitions, effective sample size, and traceplots) were evaluated to ensure chain convergence and reliability of the parameter estimation process. In particular, the following criteria had to be fulfilled to assume reliable posterior estimates: (1) R-hat < 1.05, (2) no divergent transitions, (3) effective sample size > 1000, and (4) visual convergence of all chains. When necessary, sampling specifications (HMC acceptance rate, number of iterations) or model specifications (parameterization) were adapted, as suggested by the software developer.

Priors
A weakly informative zero-centered normal prior was selected for the fixed effect of time (Δt) to represent the uncertainty about whether the test protocol allowed for systematic positive The hierarchical structure for the models using 2 parameters (Lin and Ex2) was modeled as: The hierarchical structure for the models using 3 parameters (Ex3 and Crit) was modeled as: The following equations account for different parameter labels in Crit. Importantly, the two parameters L' and ΔL' were reparameterized to facilitate sampling of the HMC algorithm: The selected boundaries for L' and k were chosen as suggested by Morton and colleagues [5] to achieve the characteristic hyperbolic shape of the function and allow for a y-intercept.
However, we decided not to limit CL to positive values as suggested by the authors. Morton and colleagues reported a concentration of CL estimates at 0 for 12 out of 16 subjects when defining a [0, ∞] boundary [5]. Since this could be interpreted as an improper parameter truncation, we advocate that CL should be free to vary across positive and negative values.

Priors
For change effects, weakly informative zero-centered normal priors were defined to represent the uncertainty about the direction of parameter changes. Weakly informative Half-Cauchy priors were applied for scale parameters (τ and σ). For the group-level parameters at T1, priors were defined by moment-matching the posterior distributions of a pilot study that was conducted on a different sample of eight subjects, in order to facilitate chain convergence during HMC sampling. These subjects were not included in the main analysis because they did not undergo a retest, hence only providing data for T1. Moreover, subjects of the pilot study performed the bench press without using safety pins as delimiter for the eccentric phase of the movement, but instead performed a standard touch-and-go bench press. To reduce the information provided by these "pilot-informed" priors and therefore fulfill the previously described prerequisite for truly weakly informative priors, the scale of the moment-matched posterior distribution of the pilot study was multiplied by the factor 10. A Lewandowski-Kurowicka-Joe (LKJ) prior with a shape parameter of 2 was used for the correlation effect among subject-level parameters and change effects, respectively, to represent a prior believe of the correlation being centered on 0.