Analyzing small data sets using Bayesian estimation: the case of posttraumatic stress symptoms following mechanical ventilation in burn survivors

Abstract

BackgroundThe analysis of small data sets in longitudinal studies can lead to power issues and often suffers from biased parameter values. These issues can be solved by using Bayesian estimation in conjunction with informative prior distributions. By means of a simulation study and an empirical example concerning posttraumatic stress symptoms (PTSS) following mechanical ventilation in burn survivors, we demonstrate the advantages and potential pitfalls of using Bayesian estimation.MethodsFirst, we show how to specify prior distributions and by means of a sensitivity analysis we demonstrate how to check the exact influence of the prior (mis-) specification. Thereafter, we show by means of a simulation the situations in which the Bayesian approach outperforms the default, maximum likelihood and approach. Finally, we re-analyze empirical data on burn survivors which provided preliminary evidence of an aversive influence of a period of mechanical ventilation on the course of PTSS following burns.ResultsNot suprisingly, maximum likelihood estimation showed insufficient coverage as well as power with very small samples. Only when Bayesian analysis, in conjunction with informative priors, was used power increased to acceptable levels. As expected, we showed that the smaller the sample size the more the results rely on the prior specification.ConclusionWe show that two issues often encountered during analysis of small samples, power and biased parameters, can be solved by including prior information into Bayesian analysis. We argue that the use of informative priors should always be reported together with a sensitivity analysis.

On Using Bayesian Methods to Address Small Sample Problems

“…In the last decade or so, Bayesian methods have become vastly more popular in nearly all scientific fields (van de Schoot, 2016). In fact, based on a comprehensive review of Bayesian studies over the last 15 years, van de Schoot (2016) noted that the number of empirical papers in psychology using Bayesian methods increased nearly fivefold between 2010 and 2015.…”

Bayesian PTSD-Trajectory Analysis with Informed Priors Based on a Systematic Literature Search and Expert Elicitation

“…obtained through the Bayesian approach using "accurate" priors (Depaoli, 2013); an incorrect choice of prior might bias the results dramatically (e.g., Hox, van de Schoot, & Matthijsse, 2012;Van de Schoot et al, 2015). However, we can mitigate this issue by increasing the uncertainty in the prior (through the variance hyperparameter) to mimic a weakly informed prior (Kohli et al, 2015).…”

Systematic search of Bayesian statistics in the field of psychotraumatology

“…Van De Schoot, Broere, Perryck, Zondervan-Zwijnenburg, and Van Loey (2015) showed in a simulation study, and with an actual application to a limited data set of burn survivors, that Bayes outperformed the default estimation method for structural equation models. When using maximum likelihood estimation, there appear to be power issues for small samples and therefore it becomes difficult to find meaningful results.…”