Bayesian sample size determination for longitudinal studies with continuous response based on different scientific questions of interest

ABSTRACT Longitudinal study designs are commonly applied in much scientific research, especially in the medical, social, and economic sciences. Longitudinal studies allow researchers to measure changes in each individual’s responses over time and often have higher statistical power than cross-sectional studies. Choosing an appropriate sample size is a crucial step in a successful study. In longitudinal studies, because of the complexity of their design, including the selection of the number of individuals and the number of repeated measurements, sample size determination is less studied. This paper uses a simulation-based method to determine the sample size from a Bayesian perspective. For this purpose, several Bayesian criteria for sample size determination are used, of which the most important one is the Bayesian power criterion. We determine the sample size of a longitudinal study based on the scientific question of interest, by the choice of an appropriate model. Most of the methods of determining sample size are based on the definition of a single hypothesis. In this paper, in addition to using this method, we determine the sample size using multiple hypotheses. Using several examples, the proposed Bayesian methods are illustrated and discussed.

[1]  Pierpaolo Brutti,et al.  Robust Bayesian sample size determination in clinical trials , 2008, Statistics in medicine.

[2]  K. Muller,et al.  Statistical tests with accurate size and power for balanced linear mixed models , 2007, Statistics in medicine.

[3]  S. Zeger,et al.  Longitudinal data analysis using generalized linear models , 1986 .

[4]  James D. Stamey,et al.  Bayesian sample size determination for binary regression with a misclassified covariate and no gold standard , 2012, Comput. Stat. Data Anal..

[5]  Jiayang Sun,et al.  Modern sample size determination for unordered categorical data , 2014 .

[6]  P. Diggle.  Analysis of Longitudinal Data , 1995 .

[7]  D. Bloch,et al.  Sample size requirements and the cost of a randomized clinical trial with repeated measurements. , 1986, Statistics in medicine.

[8]  Sin-Ho Jung,et al.  Sample size estimation for GEE method for comparing slopes in repeated measurements data , 2003, Statistics in medicine.

[9]  Sabine Landau,et al.  Sample size and power calculations for medical studies by simulation when closed form expressions are not available , 2013, Statistical methods in medical research.

[10]  Adam J Branscum,et al.  Bayesian approach to average power calculations for binary regression models with misclassified outcomes , 2009, Statistics in medicine.

[11]  M. Ganjali,et al.  A Transition Model for Ordinal Response Data with Random Dropout: An Application to the Fluvoxamine Data , 2009, Journal of biopharmaceutical statistics.

[12]  Christian P. Robert,et al.  Bayesian Ideas and Data Analysis , 2012 .

[13]  Richard Gerlach,et al.  Bayesian sample size determination for case-control studies with misclassification , 2007, Comput. Stat. Data Anal..

[14]  D. Shalloway.  The Evidentiary Credible Region , 2014 .

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

[16]  Fei Wang,et al.  A simulation-based approach to Bayesian sample size determination for performance under a given model and for separating models , 2002 .

[17]  MICHAEL S. Williams,et al.  Monte Carlo approaches for determining power and sample size in low-prevalence applications. , 2007, Preventive veterinary medicine.

[18]  Sin-Ho Jung,et al.  EFFECT OF DROPOUTS ON SAMPLE SIZE ESTIMATES FOR TEST ON TRENDS ACROSS REPEATED MEASUREMENTS , 2004, Journal of biopharmaceutical statistics.

[19]  N. Turkkan,et al.  Algorithm AS 308: Highest Posterior Density Credible Region and Minimum Area Confidence Region: the Bivariate Case , 1997 .

[20]  Ram C Tiwari,et al.  Bayesian approach to the design and analysis of non‐inferiority trials for anti‐infective products , 2014, Pharmaceutical statistics.

[21]  P. Houck,et al.  Sample size and power calculations based on generalized linear mixed models with correlated binary outcomes , 2008, Comput. Methods Programs Biomed..

[22]  J. Gittins,et al.  A behavioral Bayes method to determine the sample size of a clinical trial considering efficacy and safety , 2009, Statistics in medicine.

[23]  James D. Stamey,et al.  A Bayesian approach to sample size determination for studies designed to evaluate continuous medical tests , 2010, Comput. Stat. Data Anal..

[24]  Yi Guo,et al.  Selecting a sample size for studies with repeated measures , 2013, BMC Medical Research Methodology.

[25]  L. Joseph,et al.  Bayesian sample size determination for estimating binomial parameters from data subject to misclassification , 2000 .

[26]  Scott Tonidandel,et al.  Sample size and power calculations in repeated measurement analysis , 2001, Comput. Methods Programs Biomed..

[27]  D. Hedeker,et al.  Sample Size Estimation for Longitudinal Designs with Attrition: Comparing Time-Related Contrasts Between Two Groups , 1999 .

[28]  Hamid Pezeshk,et al.  Bayesian techniques for sample size determination in clinical trials: a short review , 2003, Statistical methods in medical research.

[29]  W. Cumberland,et al.  Sample size requirement for repeated measurements in continuous data. , 1992, Statistics in medicine.

[30]  L. Joseph,et al.  Bayesian sample size determination for normal means and differences between normal means , 1997 .

[31]  Dean M. Young,et al.  Bayesian sample-size determination for two independent Poisson rates , 2011, Comput. Methods Programs Biomed..

[32]  Nandini Dendukuri,et al.  Bayesian Sample Size Determination for Prevalence and Diagnostic Test Studies in the Absence of a Gold Standard Test , 2004, Biometrics.

[33]  T. Pham-Gia,et al.  Sample Size Determination in Bayesian Analysis , 1992 .

[34]  J D Dawson,et al.  Sample size calculations based on slopes and other summary statistics. , 1998, Biometrics.

[35]  H. I. Patel,et al.  Sample size for comparing linear growth curves. , 1999, Journal of biopharmaceutical statistics.

[36]  O. Kempthorne,et al.  Linear Model Theory , 2007 .

[37]  J. Seaman,et al.  Bayesian Sample Size Determination for a Clinical Trial with Correlated Continuous and Binary Outcomes , 2013, Journal of biopharmaceutical statistics.

[38]  Jaeil Ahn,et al.  Case–Control Studies of Gene–Environment Interaction: Bayesian Design and Analysis , 2010, Biometrics.

[39]  J Rochon,et al.  Application of GEE procedures for sample size calculations in repeated measures experiments. , 1997, Statistics in medicine.

[40]  M. Breth.  Bayesian Confidence Bands for a Distribution Function , 1978 .

[41]  J. Schlesselman,et al.  Planning a longitudinal study. I. Sample size determination. , 1973, Journal of chronic diseases.

[42]  S. Raudenbush,et al.  Effects of study duration, frequency of observation, and sample size on power in studies of group differences in polynomial change. , 2001, Psychological methods.

[43]  J. Schlesselman,et al.  Planning a longitudinal study. II. Frequency of measurement and study duration. , 1973, Journal of chronic diseases.

[44]  Ana Ivelisse Avilés,et al.  Linear Mixed Models for Longitudinal Data , 2001, Technometrics.

[45]  K. Muller,et al.  Power Calculations for General Linear Multivariate Models Including Repeated Measures Applications. , 1992, Journal of the American Statistical Association.

[46]  K Y Liang,et al.  Sample size calculations for studies with correlated observations. , 1997, Biometrics.

[47]  Song Zhang,et al.  Sample Size Calculations for Clustered and Longitudinal Outcomes in Clinical Research , 2014 .

[48]  L. Joseph,et al.  Some comments on Bayesian sample size determination , 1995 .

[49]  Sean L Simpson,et al.  POWERLIB: SAS/IML Software for Computing Power in Multivariate Linear Models. , 2009, Journal of statistical software.

[50]  J. Overall,et al.  Estimating sample sizes for repeated measurement designs. , 1994, Controlled clinical trials.

[51]  M. Ganjali,et al.  A Transition Model for Analysis of Repeated Measure Ordinal Response Data to Identify the Effects of Different Treatments , 2007 .

[52]  G. Molenberghs,et al.  Models for Discrete Longitudinal Data , 2005 .

[53]  Xianggui Qu,et al.  Linear Model Theory: Univariate, Multivariate, and Mixed Models , 2007, Technometrics.

[54]  Nandini Dendukuri,et al.  Bayesian sample size for diagnostic test studies in the absence of a gold standard: Comparing identifiable with non‐identifiable models , 2010, Statistics in medicine.