The problem of sample size estimation is important in medical applications, especially in cases of expensive measurements
of immune biomarkers. This paper describes the problem of logistic regression analysis with the sample
size determination algorithms, namely the methods of univariate statistics, logistics regression, cross-validation and
Bayesian inference. The authors, treating the regression model parameters as multivariate variable, propose to estimate
the sample size using the distance between parameter distribution functions on cross-validated data sets.
Herewith, the authors give a new contribution to data mining and statistical learning, supported by applied mathematics.

‎Dynamic panel data models include the important part of medicine‎, ‎social and economic studies‎. ‎Existence of the lagged dependent variable as an explanatory variable is a sensible trait of these models‎. ‎The estimation problem of these models arises from the correlation between the lagged depended variable and the current disturbance‎. ‎Recently‎, ‎quantile regression to analyze dynamic panel data has been taken in to consideration‎. ‎In this paper‎, ‎quantile regression model by adding an adaptive Lasso penalty term to the random effects for dynamic panel data is introduced by assuming correlation between the random effects and initial observations‎. ‎Also‎, ‎this model is illustrated by assuming that the random effects and initial values are independent‎. ‎These two models are analyzed from a Bayesian point of view‎. ‎Since‎, ‎in these models posterior distributions of the parameters are not in explicit form‎, ‎the full conditional posterior distributions of the parameters are calculated and the Gibbs sampling algorithm is used to deduction‎. ‎To compare the performance of the proposed method with the conventional methods‎, ‎a simulation study was conducted and at the end‎, ‎applications to a real data set are illustrated‎.