For dichotomous or ordinal dependent variables, logistic regression models as one of the generalized linear models have been intensively applied in several fields. We proposed a more powerful performance of logistic regression model analysis when a modified extreme ranked set sampling (modified ERSS) is used and further improved the performance when a modified double extreme ranked set sampling (modified DERSS) is used. We assume that ranking could be performed based on an available and easy-to-rank auxiliary variable, which is associated with the response variable. Theoretically and by simulations, we showed the superiority of the performance of the logistic regression analysis when ERSS and DERSS are used compared with using the simple random sample. We illustrated the procedures developed using real data from the 2011/12 National Survey of Children’s Health.