Optimal Experimental Designs for Repeated Measurements

Repeated measurements designs allocate treatments to experimental units over successive time periods, enabling estimation of both direct and residual treatment effects. Optimality in this context seeks configurations that minimise estimator variance, control carryover bias and make efficient use of limited subjects or resources. Classical criteria such as A-, D- and E-optimality guide selection of sequences and sample sizes to balance precision and robustness. Circular arrangements and block structures often address symmetry and neighbour influences, while computational algorithms facilitate construction of designs under complex dependency models. Applications span clinical crossover trials, pharmacokinetic studies, agricultural field trials and behavioural experiments, where temporal correlation and treatment interactions pose unique challenges. Recent advances focus on flexible generation of minimal balanced or strongly balanced sequences, removal of circularity constraints, and algorithmic routines that ensure high efficiency under interference and carryover scenarios.

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Optimal Experimental Designs for Repeated Measurements publication trend

The graph below shows the total number of articles in optimal experimental designs for repeated measurements across all publications each year (not limited to Nature Index journals).

Technical terms

Repeated measurements design: An experimental layout in which each unit receives multiple treatments over time periods.

Carryover effect: Influence of a treatment applied in a previous period on current responses, potentially biasing direct-effect estimates.

Circular design: A sequence arrangement in which the first and last periods are treated as adjacent to control period-end carryover symmetrically.

Optimality criterion: A statistical rule (e.g., A, D or E) used to evaluate and compare designs based on variance or information measures.

Minimal balanced design: A design using the fewest experimental units that still achieves balance in treatment sequences and carryover control.

Neighbour effect: Bias arising when the response in one unit is influenced by treatments applied to neighbouring units, common in spatial or block experiments.

References

1. A simple method to construct circular repeated measurement design classes and efficiently control carry over effects. Kuwait Journal of Science (2024).
2. Some new constructions of minimal efficient circular nearly strongly balanced neighbor designs. Journal of King Saud University - Science (2023).
3. Algorithm to generate efficient circular designs robust to neighbor effects. Kuwait Journal of Science (2024).