Covariates for inclusion in the propensity score model is an important issue. The performances of the estimator are improved in the estimation of the average treatment effect by including covariates related to outcome in the propensity score model. However, discussions on the covariates that should be included in the propensity score model when estimating quantile treatment effects are limited. This study examines the performances of the estimators of quantile treatment effects depending on the covariates included in the propensity score model through numerical experiments. Under several scenarios, we evaluate the performances (standard deviation, relative bias, relative RMSE) of the estimation methods by specifying the covariates related to outcome. The results confirm that the methodology for the selection of covariates performs better in a heterogeneous error variance of the outcome regression model. Furthermore, we confirm covariates that affect the variance and not the value, perform better when included in the propensity score model.

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  This study developed a method for evaluating stimuli using a Q-learning model. We demonstrate that stimuli for more elaborate Q-learning models can be selected using a two-step procedure that extends Fujita, Okada, and Katahira (2022b) model. In the two-step procedure, the goodness of fit of the stimuli was evaluated based on Fisher information and Markov chain Monte Carlo (MCMC) estimation. The evaluation with Fisher information narrows down the better candidates for the stimuli (first step). Furthermore, stimuli regarded as desirable in the first step are evaluated more precisely in the second step. From Fisher information-based and MCMC-based simulations, the superiority of specific stimuli in the Fisher information-based simulation aligns with that of the MCMC-based simulation. The Fisher information can precisely predict the order of the estimation precision of the stimuli, validating the two-step procedure. Moreover, there is a superior stimulus design regardless of the model for the inverse temperature parameter. Nonetheless, no such stimulus design exists for the learning rate parameters. In actual experiments, it is preferable to consider the model, research method, and purpose (e.g., parameters that researchers should focus on) and optimally select stimuli using a two-step procedure.

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  In this study, we analyzed the impact of promotional events on the sales of an e-commerce website (i.e. Rakuten Ichiba) using data provided by Rakuten Group. Our approach involved formulating a state-space model to classify the sales data based on product genres, distinguishing between sales affected by promotions and sales unaffected by promotions. Subsequently, we performed an in-depth analysis utilizing the results derived from the state-space model. The results demonstrated a significant coefficient of determination for the total sales, indicating that our model exhibits a strong explanatory capability. Furthermore, we observed similarity between the promotions uplift effect on sales and the actual sales, suggesting that the implementation of promotional events has a significant impact on the company's revenue. Our work provides valuable insights for companies seeking to optimize their promotional strategies.

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  Meta-analysis is a method for appropriately integrating and summarizing some study results and is widely accepted as strong evidence. Recently, network meta-analysis (NMA), which compares multiple treatments, has become popular. Although there is a number of literature that discusses how to use software to implement NMA and how to demonstrate hypotheses in the NMA, most of them are for binary outcome with odds ratios, and are explained with a single basic model. In this paper, we summarized how to implement NMA for survival outcome and discuss how to apply each of two different basic models. NMAs were performed using four different R packages, and the performance of each model was evaluated via simulation studies, including the use of an applied method, called shared parameter model.

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