Design and cost optimization for hierarchical data

type="main"> In this paper, we consider balanced hierarchical data designs for both one-sample and two-sample (two-treatment) location problems. The variances of the relevant estimates and the powers of the tests strongly depend on the data structure through the variance components at each hierarchical level. Also, the costs of a design may depend on the number of units at different hierarchy levels, and these costs may be different for the two treatments. Finally, the number of units at different levels may be restricted by several constraints. Knowledge of the variance components, the costs at each level, and the constraints allow us to find the optimal design. Solving such problems often requires advanced optimization tools and techniques, which we briefly explain in the paper. We develop new analytical tools for sample size calculations and cost optimization and apply our method to a data set on Baltic herring.

[1]  Nikolaos V. Sahinidis,et al.  Exact Algorithms for Global Optimization of Mixed-Integer Nonlinear Programs , 2002 .

[2]  Mika Rahikainen,et al.  Evaluation and management of the Finnish herring fishery , 2005 .

[3]  Mika Rahikainen,et al.  A linear mixed model with temporal covariance structures in modelling catch per unit effort of Baltic herring , 2008 .

[4]  R. Stephenson,et al.  Consequences of growth variation in northern Baltic herring for assessment and management , 2004 .

[5]  Joakim Westerlund,et al.  Some transformation techniques with applications in global optimization , 2009, J. Glob. Optim..

[6]  Martijn P. F. Berger,et al.  Design Issues for Experiments in Multilevel Populations , 2000 .

[7]  Wim Van Den Noortgate,et al.  ML-DEs: A program for designing efficient multilevel studies , 2008, Behavior research methods.

[8]  Weng Kee Wong,et al.  Sample size formulae for trials comparing group and individual treatments in a multilevel model , 2008, Statistics in medicine.

[9]  Tapio Westerlund,et al.  Convex underestimation strategies for signomial functions , 2009, Optim. Methods Softw..

[10]  Spyros Konstantopoulos,et al.  Incorporating Cost in Power Analysis for Three-Level Cluster-Randomized Designs , 2009, Evaluation review.

[11]  Stephen P. Boyd,et al.  A tutorial on geometric programming , 2007, Optimization and Engineering.

[12]  Todd C. Headrick,et al.  ON OPTIMIZING MULTI‐LEVEL DESIGNS: POWER UNDER BUDGET CONSTRAINTS , 2005 .

[13]  William J. Browne,et al.  A guide to sample size calculations for random effect models via simulation and the MLPowSim Software Package , 2009 .

[14]  Moonseong Heo,et al.  Statistical Power and Sample Size Requirements for Three Level Hierarchical Cluster Randomized Trials , 2008, Biometrics.

[15]  Hannu Oja,et al.  Power, sample size and sampling costs for clustered data , 2011 .

[16]  S. Raudenbush.  Statistical analysis and optimal design for cluster randomized trials , 1997 .

[17]  David B. Allison,et al.  Power and money: Designing statistically powerful studies while minimizing financial costs. , 1997 .

[18]  X. Liu,et al.  Statistical Power and Optimum Sample Allocation Ratio for Treatment and Control Having Unequal Costs per Unit of Randomization , 2003 .

[19]  S. Raudenbush,et al.  Statistical power and optimal design for multisite randomized trials. , 2000, Psychological methods.