{"id":2167,"date":"2021-11-29T04:40:09","date_gmt":"2021-11-29T04:40:09","guid":{"rendered":"http:\/\/optimumsportsperformance.com\/blog\/?p=2167"},"modified":"2022-11-08T03:38:34","modified_gmt":"2022-11-08T03:38:34","slug":"bayesian-updating-of-reference-ranges-for-serial-measurements","status":"publish","type":"post","link":"https:\/\/optimumsportsperformance.com\/blog\/bayesian-updating-of-reference-ranges-for-serial-measurements\/","title":{"rendered":"Bayesian Updating of Reference Ranges for Serial Measurements"},"content":{"rendered":"

Introduction<\/u><\/strong><\/p>\n

The collection of serial measurements on athletes across a season (or multiple seasons) is one of the more common types of data being generated in the applied sport science environment. The question that coaches and practitioners often have is, \u201cIs this player outside of their \u2018normal range\u2019?\u201d<\/em><\/p>\n

The best approach for establishing a reference range of \u2018normal\u2019 values is a frequently discussed topic in sport science. One common strategy is to use z-scores and represent the reference range as 1 standard deviation above or below the mean (Figure A<\/strong>) or plot the raw values and set the reference range 1 standard deviation above or below the raw mean (Figure B<\/strong>), for practitioners who might have a difficult time understanding standardized scores. Of course, the mean and standard deviation will now be related to all prior values. As such, if the athletes go through a training phase with substantially higher values than other phases (e.g., training camp) it could skew your reference ranges. To alleviate this issue, some choose to use a rolling mean and standard deviation, to represent the normal range of values relative to more recent training sessions (Figure C<\/strong>).<\/p>\n

\"\"<\/a><\/p>\n

A problem with the approaches above is that they require a number of training sessions to allow a mean and standard deviation to be determined for the individual athlete. One solution to this issue is to base our initial normal reference ranges off of prior knowledge that we have from collecting data on players in previous seasons (or prior knowledge from research papers, if we don\u2019t have data of our own yet). This type of Bayesian updating approach has been applied in WADA\u2019s drug testing practices1<\/sup>. More recently, Hecksteden<\/a> <\/strong><\/span>et al., used this approach to evaluate the CK levels of team-sport athletes in both fatigued and non-fatigued states2<\/sup>.<\/p>\n

The mathematics of the approach was presented in the paper but might look intimidating to those not used to looking at mathematical equations in this manner. \"\"<\/a>\"\"<\/a><\/p>\n

The author\u2019s provided a nice excel sheet where you can input your own data and get the updated reference ranges. However, the sheet is a protected sheet, which doesn’t afford the opportunity of seeing how the underlying equations work and you can’t alter the sheet to make appropriate for your data (for example, the data in the sheet log transforms the raw data automatically). Thus, I\u2019ve decided to code the analysis out, both in excel and R, to help practitioners looking to adopt this approach.<\/p>\n

Setting Priors<\/u><\/strong><\/p>\n

To apply this type of analysis, we need to first establish some prior values for three parameters: Prior Mean (mu), Prior Standard Deviation (tau), and a Prior Repeated-Measures Standard Deviation (sigmaRM). These values represent our current knowledge of the variable we are measuring before<\/em> seeing any new data. As new data is collected, we can update these priors to get an individual (posterior) estimate for the athlete. I\u2019ll use the priors set by Hecksteden and colleagues for CK levels of Male athletes:<\/p>\n