## 1 Introduction  
Speech is an essential means of communication in everyday life, and speech disorders can have a negative impact on an individual's vocal health and social participation [1, 2, 3, 4, 5, 6, 7]. Individuals with speech disorders aim to improve their vocal function through speech therapy [8, 9]. However, not all patients show the same results from speech therapy. This suggests that personal characteristics and prognostic factors can influence the effectiveness of speech therapy [10, 11]. Examining the relationship between the factors and the effectiveness of speech therapy is a crucial step in developing and implementing personalized treatment strategies for individuals with speech disorders [12]. By conducting a comprehensive analysis of prognostic factors, we can identify which patients are likely to derive the greatest benefit from speech therapy. Furthermore, the development of personalized treatment approaches by considering prognostic factors is an important strategy to enhance the effectiveness of speech therapy and improve patients' vocal function and quality of life. Past studies have explored the association between the prognostic factors of individuals with speech disorders and the outcomes of speech therapy. [PERSON] et al. conducted a partial correlation analysis to explore the connection between initial phonatory characteristics and fluctuations in clinical scores. The XGBoost models demonstrated an ability to forecast alterations in clinical scores with an error margin ranging from 11% to 26%. This research proposed a potential method for forecasting the advancement of [PERSON]'s disease (PD) through the acoustic examination of speech patterns [13]. [PERSON] et al. examined the extent of the relationship between aerodynamic assessments, acoustic measurements, and auditory-perceptual factors. They observed a robust correlation between local jitter and shimmer and parameters G, R, B, and S, all with a significance level of \(p<0.001\). This investigation found noteworthy associations between these vocal evaluations, highlighting the potential of combined analyses using a multi-parametric approach to provide a comprehensive and unbiased assessment of pathological voice conditions in their early stages [14]. [PERSON] et al. studied the predictive factors for the efficacy of voice therapy for pediatric vocal fold nodules. They found that good prognostic factors for voice therapy in vocal fold nodules were gender and older age. However, acoustic and perceptual measures of the voice before treatment could not predict the effectiveness of voice therapy [15]. In the most recent notable paper, the authors focused on forecasting vocal recovery three months after thyroid surgery using deep neural networks applied to spectrograms. The approach involved utilizing a pretrained model, based on the GRBAS framework, and training it on preoperative and two-week-postoperative voice spectrograms using the EfficientNet architecture combined with long short-term memory (LSTM) in order to predict vocal outcomes at the three-month mark. The results of the correlation analysis for the predicted grade, breathiness, and asthenia scores were 0.741, 0.766, and 0.433, respectively. This research showed the potential for predicting vocal recuperation three months post-surgery via spectrogram analysis [16]. [PERSON] et al. conducted a study to identify clinical parameters that are sensitive to functional voice disorders using boosted decision stumps. Their findings indicated that a smaller subset of parameters (specifically, 4 out of 13) was effective in distinguishing between three groups: one healthy group and two groups with voice disorders [17]. However, these studies have been limited in terms of considering the association between prognostic factors and the outcomes of speech therapy. Some studies have focused only on one prognostic factor or used subjective evaluation tools to assess the effectiveness of speech therapy [14; 15].