## 1 Introduction  
Laser toning with a low-fluence 1064 nm Q-switched neodymium-doped yttrium aluminum garnet (Nd-YAG) laser can be used for removal of pigmented skin patches and rejuvenation of skin [1; 2]. Laser toning involves multiple passes of a low-fluence Q-switched Nd-YAG laser used for treatment of facial hyperpigmentation and skin rejuvenation. However, the side effects of rebound post-inflammatory hyperpigmentation (PIH) are common after laser toning treatment. PIH is an acquired hyperpigmentation at the sites of previous skin inflammation, injuries, irritants, or allergic dermatitis, and cosmetic procedures such as chemical peeling and laser treatment.  
[PERSON] et al. pointed out that immediate endpoints of laser (IEL) is an indicator of laser tissue response and PIH is caused by inflammation [3; 4]. [PERSON] et al. reported that the increase in epidermal pigmentation after laser irradiation is related to the increased expression of certain inflammatory cytokines, suggesting that they may be the cause of PIH induction [5]. [PERSON] et al. found that the strength of PIH is determined by inherent skin color, inflammatory conditions, and melanocyte stability [6]. However, the authors used a different method than previous authors.  
Such complications not only reduce the quality of life but also decrease patient compliance, and efforts should therefore be directed toward their prevention. The main risk factors related to these complications are likely to include several clinical factors. The risk of treatment complications should be analyzed by multivariate regression including several predictor variables. Identifying the main potential risk factors for complications is important for improving the decision-making process.  
The development of an optimal multivariate logistic regression model requires determination of the optimal number of predictive factors that should be included. Therefore, a predictive model must be developed to analyze the possible risk factors of complications.  
[PERSON] et al. [7; 8; 9] introduced the (east absolute shrinkage and selection operator (LASSO) algorithm for multivariate regression modeling. In addition to its simple use, LASSO has a number of advantages including: (1) variable selection, (2) coefficient shrinkage, (3) consideration of multicollinearity, and (4) low mean squared error (MSE) values [7; 8; 9].  
In this study, regularization and shrinkage techniques were used for LASSO factor selection, which limit the weight of regression to limit the complexity of the model and overcome overfitting problems. Different \(\lambda\) values (tuning parameter) have different shrinkage effects, so we used cross-validation to verify the model's execution results at different \(\lambda\) values. In our previous studies, we successfully used the LASSO-based normal tissue complication probability (NTCP) model to predict the incidence of xerostomia among head-and-neck squamous cell carcinoma (HNSCC) and nasopharyngeal carcinoma (NPC) patients treated with intensity-modulated radiotherapy (IMRT) [10] and other NPC patients treated with helical tomotherapy (HT) [11].  
To the best of our knowledge, no previous reports have been published of risk assessment tools for identifying risk factors of PIH after laser toning or non-ablative skin rejuvenation using the LASSO-based algorithm. LASSO was used to determine the important risk factors for complications. Statistical methods were used to evaluate the pros and cons of the model. We built a LASSO-based multivariate logistic regression model to predict the incidence of PIH complications associated with Nd-YAG laser toning in Asian patients. This study is unique and innovative.