We thank Dr. Erfan Ayubi1 for his interest in our article,2 in which we described a new prediction equation for maximal heart rate children and adolescents.
Dr. Ayubi states that accurate predictions cannot be guaranteed by cross-sectional study. It is very important to distinguish between prognostic models, in which cohort studies are the most appropriate, and diagnostic models, such as our study, where predictive patient characteristics are identified from existing current parameters. Diagnostic models are usually based on cross-sectional study design.3 The main idea behind the concept of cross-validation is that using the residuals from the model is not enough, because using the same data might lead to overestimation of the model performance. In our study, cross-validation was less relevant because the prediction ability of the model was already low using the original dataset. As presented in the statistical analysis section in our article, the use of additional methods such as the concordance correlation coefficient or intraclass correlation coefficient was deemed unnecessary given the low Pearson correlation coefficients. This also relates to the point of the reliability and calibration of a prediction model by Pearson correlation.
Dr. Ayubi also criticizes the use of a stepwise technique for the multivariable linear regression. In prediction models, we aim to explain the dependent variable in the simplest way while removing redundant predictors. Variable selection methods such as stepwise are intended to select the best subset of predictors. We wish to emphasize that the variables inserted into the regression were selected both by the initial univariate analyses (with resting heart rate, fitness level and body fat percent emerging as significant contributors), and by previous knowledge from previous studies (age, sex, body mass index), as Dr. Ayubi suggested.
In summary, we strongly believe that the application of the statistical methods in our study allowed a comprehensive search for predictors of maximal heart rate in exercising children and adolescents.