Introduction
Oral mucositis (OM) is the predominant normal tissue complication when treating oral cavity cancers. About 30–60% of the patients receiving concomitant chemoradiation therapy often turn up with mouth sores and ulcers. It results in interruption of therapy leading to poor prognosis. Many types of analgesics, cryotherapy and other supportive care medications could help the patients to some extent. Reference Kanuga1,Reference Zheng, Cotrim and Sunshine2 But many patients deter treatment due to the worsening of their mouth ulcers. Patients are advised to maintain good oral hygiene, not to use tobacco and to have good nutritional diet. With the increase in radiation dose, the incidence of OM tends to increase resulting in a linear response relationship. Dose–response analysis was carried out on a large cohort of patients for the correlation of dose metrics with the mucosal toxicity grades Reference Siegel, Miller, Fuchs and Jemal3–Reference Murphy, Beaumont and Isitt6 in European countries like UK and Italy. But the patients’ demographics defer for the Indian sub-continent. Hence, an independent dose–response modelling must be done for the clinics practicing radiation therapy. The mucosal surface contour (MSC) refers to the physical appearance and texture of the mucous membrane lining the oral cavity. OM is a common side effect of radiation therapy and chemotherapy in cancer patients. It often leads to inflammation of the mucosa, resulting in redness and swelling. Mucosal surface may appear engorged and exhibit an irregular contour due to inflammatory response. As mucositis progresses, it can cause erosions and ulcerations on the mucosal surface. These areas may appear as irregular depressions with varying sizes and shapes, contributing to an uneven contour. In some cases, the mucosal surface may develop white patches or pseudo membranes, which can alter the surface texture and contour. In response to mucositis, the mucosal tissue may thicken, which can lead to changes in the contour. This thickening is a protective response to the damage but can result in an irregular surface. Mucositis can lead to dryness in the mouth, affecting the moisture and appearance of the mucosal surface. MSC in OM can be visually assessed by healthcare professionals during clinical examinations. It may also be documented through imaging techniques, such as endoscopy, which provides a detailed view of the mucosal changes. Monitoring and managing the MSC is important in cancer care to assess the severity of mucositis, guide treatment decisions and provide appropriate interventions to alleviate symptoms and promote healing. Additionally, oral hygiene and care are crucial to maintain the health of mucosal surfaces during cancer therapy.
Choosing simultaneous multiple linear equation (SMLE) for modelling OM can be worth an attempt in certain situations for several reasons. It provides a straightforward and transparent modelling approach. It is easy to understand, interpret and implement, which can be advantageous, especially in clinical settings where complex models may not be feasible. Such a simple modelling method allows us to identify significant variables and their individual contributions to mucositis risk. This can provide valuable insights into the factors that play a role in mucositis development. These equations enable the quantification of the strength and direction of relationships between patient-specific variables (e.g., tobacco use (Tb), oral hygiene (OHy) and nutritional status (Ns) and mucositis incidence. This information can guide clinicians and researchers.
By using multiple linear equations, one can develop a risk assessment model that estimates the probability of mucositis for individual patients based on their unique characteristics. It can help guide treatment planning and patient counselling. It can account for interactions between variables. This interaction is important because variables like Tb, OHy and Ns may not act in isolation and could have combined effects. It can serve as a preliminary analysis to assess the feasibility of modelling mucositis based on patient-specific information. If the linear model demonstrates significant associations, it may justify further exploration with more complex models. In some clinical or research settings, complex models may be impractical due to resource constraints, such as limited access to specialized software or technical expertise. Multiple linear equations can be a more accessible option. Major aims of this research are to develop an institution-based mathematical model using a readily available online statistical tool called multiple linear regression calculator and to know the clinical importance of delineating a pseudo-organ at risk, MSC.
Materials and Methods
This study was reviewed and approved by Institutional Ethical Committee of the hospital Ref No: 1577/P&D-1/TNGMSSH/20a23/BMS/010. It is divided into two phases, Viz.,
Phase 1: 60 oral cavity patients who were on concomitant chemoradiation therapy from March 2023 to May 2023—enrolled for retrospective analysis and dose–response modelling. The patients were equally divided into three sets (T1, T2 and T3) for contouring by three expert Radiation Oncologists. Thus, the resulting clinical outcome in terms of OM incidence was assumed to be independent of each other to account for inter variation of delineation methods by the experts using standard guidelines. Reference Ueno, Sato and Igarashi7–Reference Otter, Schick and Gulliford11
Phase 2: 20 oral cavity patients were enrolled in second phase for prospective analysis and outcome comparison. They were scheduled to start their treatment in June 2023.
In Phase 1, CT images of the enrolled patients were delineated with MSC in Eclipse treatment planning system (Siemens Healthineers Inc., v.10·6. MSC is a pseudo-Organ At Risk defined and proposed by Jean et al. in 2015). Reference Dean, Welsh, Gulliford, Harrington and Nutting12 Totally, 25 patients were planned with intensity-modulated radiation therapy (IMRT) with 7 equally spaced beam angles, and 35 patients were planned with volumetric-modulated arc therapy (VMAT) with 2 full arcs. Treatment was planned for an initial phase of 60 Gy in 30 fractions, which was later boosted to 3 more fractions after a careful clinical examination for the patient’s tolerance. Dose–volume parameters such as Dmean, V30Gy and V50Gy for MSC and Dmean, and Dmax for PTV60 were extracted from the dose–volume histograms. Patients were examined weekly for OM incidence. Mucositis grading was done using CTCAE v5·0 that occur during the entire course of the treatment. Maximum score and time of incidence were noted for each patient. Tobacco use (Tb) was numerically scored using 5A’s model that is based on the patient’s wellbeing in terms of assessing, advising, agreeing, assisting and arranging follow-up related to quitting smoking. Oral hygiene index (OHy) is based on the debris and tartar on the teeth. Nutritional status (Ns) score was done using body mass index (BMI) measurement. The tobacco use in patients is scored as 1, poor oral hygiene as 1 and low BMI as 1. Using an online tool (multiple linear regression calculator), the response variable (y) and predictor variables (x1–x6) are given as input. 13 Values of the response variable y vary according to a normal distribution with standard deviation σ for any values of the explanatory variables x1, x2 and xk. The quantity σ is an unknown parameter. Repeated values of y are independent of one another. The relationship between the mean response of y (denoted as my) and explanatory variables x1, x2 and xk was assumed to be linear and is given by μy = β0 + β1x1 + ⋯ + βkxk where each βi is an unknown parameter. Response variable = OM grades, denoted as OM x1 = Dmean, x2 = V30, x3 = V50, x4 = tobacco use, denoted as Tb, x5 = oral hygiene, denoted as OHy, x6 = nutritional status as Ns. The resulting equation was substituted with the following values, to get optimal values of V30, V50 and Dmean by keeping Dmean and Dmax of PTV60 as constant (100% and 107%) A 20% reduction in OM was intended without compromising the planning target volume constraints (for tumor control). Hence, in Phase 2, the equations 1, 2 and 3 are substituted with the values OM1 = OM2 = OM3 = 0·2. Values of Dmean, V50 and V30 were deduced as follows, by keeping the Tb = 0, OHy = 0 and Ns = 0 (whereas, these entities are assigned to zero for no tobacco use, good oral hygiene and a good nutrition). By solving the above three simultaneous linear algebraic equations, values for Dmean, V50 and V30 were obtained as follows; Dmean = 30·3Gy, V50Gy = 34·1% and V30Gy = 8·38%.
In the Phase 2, 20 oral cavity patients, who are non-tobacco users, with good oral and nutritional status were prospectively enrolled and CT simulation was done. The images were delineated with MSC as an organ at risk. Treatment planning was done by using the above values for dose contains in the optimization process of IMRT/VMAT. Dose constraints for MSC are set as Dmean = 30·3Gy and V50 = 34·1% intuitively to achieve the optimal Dmean and Dmax values of PTV60. Weekly assessment is recorded using CTCAEv.5·0. Phase 1 outcome results and Phase 2 results were compared statistically using Sample t-test method.
Results
Table 1 illustrates the response (OM) and predictor parameters (Dmean, V30Gy, V50Gy, Tb, OHy and Ns) of Set1 (T1), Set2 (T2) and Set3 (T3) of Phase 1 Study. T1, T2 and T3 were the first trials of 20 patients each for generating three corresponding multiple linear regression models (Equation 1, 2 and 3). The models were named OM1_MSC, OM2_MSC and OM3_MSC for the data points from each set T1, T2 and T3, respectively.
Table 1. Descriptive statistics of response (OM) and predictor parameters of T1, T2 and T3 (Phase 1 study)
T1-OM1_MSC model (linear regression mathematical equation), T2-OM2_MSC model (linear regression mathematical equation), T3-OM3_MSC model (linear regression mathematical equation). Mean-average of values. STD, standard deviation; Vol(cc), volume in cc; Dmean, mean dose; V30, volume of MSC receiving 30Gy dose; V50, volume of MSC receiving 50Gy dose; PTV, planning target volume; Dmax, maximum dose; Tb, tobacco use numerical score; OHy, oral hygiene numerical score; Ns, nutritional status numerical score.
Using a multiple regression analysis calculator, three mathematical equations (Models) for the data sets were derived for MSC as follows (1), (2) 1nd (3).
$$\matrix{ {{\rm{OM}}1 = 0.122 + 0.002 \cdot {\rm{Dmean}} + 0.002 \cdot {\rm{V}}30 - 0.001 \cdot {\rm{V}}50} \hfill \cr {\quad \quad \quad \quad + 0.587 \cdot {\rm{Tb}} + 0.015 \cdot {\rm{OHy}} + 0.116 \cdot {\rm{Ns}}} \hfill \cr } $$
$$\matrix{ {{\rm{OM}}2 = 0.646 - 0.006 \cdot {\rm{Dmean}} + 0.003 \cdot {\rm{V}}30 + 0.007 \cdot {\rm{V}}50} \hfill \cr {\quad \quad \quad \quad - 0.264 \cdot {\rm{Tb}} - 0.129 \cdot {\rm{OHy}} + 0.118 \cdot {\rm{Ns}}} \hfill \cr } $$
$$\matrix{ {{\rm{OM}}3 = 0.004 + 0.007 \cdot {\rm{Dmean}} + 0.006 \cdot {\rm{V}}30 - 0.001 \cdot {\rm{V}}50} \hfill \cr {\quad \quad \quad \quad - 0.223 \cdot {\rm{Tb}} - 0.09 \cdot {\rm{OHy}} + 0.443 \cdot {\rm{Ns}}} \hfill \cr } $$
Derived models were three SMLE equations. Linearity of response (OM) with absorbed radiation dose using the models OM1_MSC, OM2_MSC and OM3_MSC for sets T1, T2 and T3 is compared in Figure 1.
Figure 1. Normal Probability Plots Comparison of Three Independent Mathematical Models (T1, T2 and T3).
Variance table (ANOVA Table) OM incidence and its predictors is given in Table 2. The r2 values for the three models such as T1, T2 and T3 were 0·9, 0·137 and 0·494, respectively. r2_Adj values were 0·858, −0·262 and 0·261. And, F_Statistic results for the 3 sets of mathematical models were 21·194, 0·343 and 2·117 with corresponding p_values of 0, 0·902 and 0·2117, respectively. Regression coefficients deduced from the three models were 0·202, 0·027 and 0·093 with residual errors of 0·01, 0·08 and 0·044, respectively.
Table 2. Variance table analysis of three mathematical models (T1, T2 and T3)
OM1_MSC, Oral Mucositis Response Model for Set1 group of patients; OM2_MSC, Oral Mucositis Response Model for Set2 group of patients; OM3_MSC, Oral Mucositis Response Model for Set3 group of patients; r2, r2_Adj (Adjusted r2), F_Statistic, p_vaIue, Regression, Res_Error-ANOVA variance table parameters of deduced models.
Two-sample t-test statistical correlation for Phases 1 and 2 (retrospective and prospective analysis) is given in Table 3. For Phase 1, the mean test score was 0·76, and standard deviation was 0·25. For Phase 2, mean test score was 0·37, and standard deviation was 0·13. The significance level (α = 0·05) has resulted in a p_value of 0·034.
Table 3. OM results of Phase 1 and Phase 2 studies with statistical correlation
Pt. No, patient number; OM, oral mucositis; STD, standard deviation.
Discussion
In multiple linear regression analysis, residual plots are essential for assessing the adequacy of the model and identifying potential issues. Residuals are the differences between the observed and predicted values, and residual plots help us understand patterns and variability in these differences. In a normal Q-Q plot: An ideal normal distribution line indicates the points on the plot are expected to fall approximately along a straight line if the residuals (or a variable’s distribution) are normally distributed. If the points closely follow a straight line, it suggests that the residuals are approximately normally distributed. If the points deviate from the straight line, especially in an S-shaped curve, it indicates non-normality. If the curve slopes upward, it suggests heavier tails than a normal distribution, if it slopes downward, it suggests lighter tails. Points at the ends of the Q-Q plot represent extreme values. Deviation from the line at the tails may indicate outliers. A comparison of normal probability plot of residuals for the three independent models is shown in Figure 1. A normal probability plot (also known as a Q-Q plot or quantile-quantile plot) of residuals in the context of a multiple linear regression model is a graphical tool used to assess whether the residuals follow a normal distribution. This plot compares quantiles of observed residuals to quantiles of a theoretical normal distribution. Comparing Q-Q plots of residuals is significant for validating assumptions, making informed model choices, identifying potential issues, and ensuring the robustness and reliability of the regression models. It is a part of the broader process of model evaluation and selection in statistical analysis.
From Figure 1, it is interesting note that the deviation from normality is very less for three datasets. It indicates that mucositis incidence in our study was less nonlinear. As per our observations, they were not typical S-shaped curves as assumed in the literature of radiation biology, and they had only 3 outliers with each dataset. The residual standard error (RSE) is a measure of the variability of the residuals in a regression analysis. Residuals are the differences between the observed values and the values predicted by the regression model. The variance table (Table 2), often known as the analysis of variance (ANOVA) table, breaks down the total variability in the dependent variable into different components, including variability explained by the regression model.
While multiple linear regression models are interpretable and make fewer assumptions compared to complex machine learning models, assessing model assumptions, and using appropriate performance metrics is still important. We have assessed our three mathematical models with the following six statistical metrics:
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(1) r2
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(2) r2_adj
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(3) F_statistic
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(4) p_value
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(5) Regression Coefficient and
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(6) Res_Error.
R-squared (r2) in multiple linear regression analysis is a statistical measure that represents proportion of variance in dependent variable that is explained by independent variables included in the model. It is a measure of the goodness of fit of the regression model. The calculated value of 0·901 from OM1_MSC (T1) model indicates a better fit among the three mathematical models.
r2_ Adjusted is a valuable metric in multiple linear regression for assessing the goodness of fit while considering the number of predictors. It strikes a balance between explaining variance and avoiding overfitting, providing a more realistic measure of the model’s effectiveness in predicting the dependent variable. r2_ Adj result of OM1_MSC model (T1) was 0·857 (higher among the three).
A high F-statistic suggests that the model is providing a better fit to data than a model with no predictors. The null hypothesis associated with the F-test is that all the regression coefficients are equal to zero (i.e., the model has no predictive power). If the p-value associated with the F-statistic is below a chosen significance level (e.g., 0·05), the null hypothesis is rejected, indicating that at least one predictor is significant in explaining the variability in the dependent variable. In summary, the F-statistic is a crucial tool for assessing overall significance of a regression model. It helps determine whether the inclusion of independent variables improves model’s explanatory power compared with a model with no predictors.
A regression coefficient in a variance table typically refers to variance associated with regression model. RSE is a measure of the variability of residuals in a regression analysis. Residuals are the differences between observed values and values predicted by regression model. It is a method to quantify the spread of these residuals, providing an estimate of how well the model fits the data. It was observed from the results that OM1_MSC had the highest value of F_Statistic with a significant p_value (21·194, 0), regression coefficient and Res_Error values (0·202 and 0·01) of OM1_MSC suggested its goodness of fit and higher predictive power among the three mathematical models. The two-sample t test analysis between the Phase 1 and Phase 2 clinical outcomes showed a strong statistical correlation with p value of 0·034 (confidence interval 95%). Thus, it disapproves null hypothesis and substantiate the alternative hypothesis that there is an impact of newly added dose constraint for MSC in the optimization of treatment planning. Results indicated that OMs were reduced in the Phase 2 investigation. Thus, it was obvious that derived values of dose–volume parameters were helpful in reducing OM is when the patients were maintaining good oral hygiene, without tobacco use and with better nutrition. Results of OM incidence in two patient groups substantiate the conclusion of a previous study done by Khattar et al. Reference Khattar, Kumar and Navitha14 Delineation of MSC impacts the reduction of OM incidence. A primer for data modelling was proposed by Vitali et al. in 2020. Reference Moiseenko, Marks and Grimm15 It gives the guidelines for lung toxicity modelling. Most NTCP models assume the sigmoidal-shaped function of dose–response data. Normal tissue complication probability (NTCP) models, including those for OM, can be valuable tools for predicting and assessing the risk of complications in radiation therapy. However, there are some challenges and limitations that may make their practical implementation in radiation therapy clinics less straightforward.
NTCP models can be complex and require a good understanding of radiobiology, mathematics, and statistics. Implementing these models requires expertise and training, which may not always be available in every clinical setting. Reliable and comprehensive data on patients’ characteristics, radiation dose distribution and clinical outcomes are essential for NTCP modelling. Collecting and managing this data can be resource-intensive and may not be feasible for all clinics. Before implementing NTCP models in a clinical setting, they should be rigorously validated using data from the specific patient population and treatment techniques used at the clinic. This validation process can be time consuming and may require a significant amount of data. Utilizing NTCP models often involves specialized software or tools for calculations and predictions. Access to installation and training on these tools can be a barrier for some clinics. NTCP models may not fully capture individual variation in patient response. Patients can differ significantly in their susceptibility to complications, and personalized approaches may be needed. Patient-specific parameters such as tobacco use, oral hygiene and nutritional status cannot be incorporated in such models. Implementing NTCP models may require changes to the clinical workflow to incorporate additional calculations and considerations. This can be challenging for clinics that already have established procedures. NTCP modelling often requires collaboration between radiation oncologists, medical physicists and radiobiologists. Ensuring effective collaboration can be a challenge. Many NTCP models are research based and may not have received regulatory approval for clinical use. This can create barriers to their implementation in some healthcare systems.
Smaller or under-resourced clinics may have limitations in terms of personnel, budget and technology, making the implementation of advanced models more challenging. OM incidence tends to be nonlinear at higher doses (i.e., >2Gy/fraction). But with a lower fraction size, response modelling with multiple linear regression analysis still holds the following merits. They are as follows, SMLE is simple and transparent. The process of variables identification is easier. The quantification of patient-specific information in the equations (tobacco use, oral hygiene and nutritional status) can guide the clinical researchers in setting a protocol for evidence-based medicine. Other overweighing merits of choosing SMLE are the risk assessment for treatment planning and patient counselling, preliminary feasibility analysis and the resource considerations where limited access is available to model dose response for OM incidence. In many cases, a high-end computing platform is required to study the data for response modelling. When we have a system of linear equations with a same number of equations as unknown variables (i.e., a square system) and equations are linearly independent, a typical unique solution can be obtained. This is in contrast to individual linear equations where multiple solutions may exist. Simultaneous equations are used to model situations where multiple conditions or constraints must be satisfied concurrently. These equations can provide a consistent solution that meets all the requirements, which is often essential in various real-world applications. By solving multiple equations simultaneously, computational effort and time required to find solutions compared to solving each equation independently can be reduced significantly. Simultaneous equations allow you to capture interconnected relationships between variables. This is valuable in fields such as physics, engineering, economics and other sciences where multiple factors influence an outcome. Simultaneous equations are frequently used in optimization problems, helping find values of variables that maximize or minimize an objective function while satisfying certain constraints. It predicts a continuous outcome. It measures severity of radiation-induced mucositis (RIM) on a scale (e.g., grade score). Each predictor variable has a straight-up effect on the severity of RIM. Coefficients associated with each variable indicate their individual contribution to RIM severity. It is not suitable for binary outcomes (e.g., presence/absence of RIM), and it is sensitive to outliers and complex interactions between variables.
In 2020, Li et al. have published a predictive model for OM incidence in nasopharyngeal carcinoma therapy using logistic regression method. Reference Li, Li and Jin16 They have designed two risk score models, one for oral cavity contour (OCC) and another one for MSC. MSC-based predictive model has a higher performance compared with that of OCC in their study. It predicts a binary outcome: Classifies patients as either having RIM or not (e.g., >Grade 2 vs. ≤Grade 2). It estimates the probability of developing RIM based on predictor variables. It handles non-linear relationships and outliers better than SMLE. It has limitations: Interpretability can be challenging, especially with complex models. A linear regression model can be more prone to overfitting with small datasets compared with SMLE.
A machine learning approach was performed for predicting the OM incidence and integrates baseline CT radiomic features with dosimetric and clinical features by Agheli et al. Reference Agheli, Siavashpour, Reiazi, Azghandi, Cheraghi and Paydar17 But machine learning requires more expertise from data scientists working with RT department that is farfetched for a lower- and middle-income country. There are few reviews analysing predictive models for RIM in addition to the original research works on models developed based on machine learning, deep learning and linear regression methods.
In our study, the prospectively enrolled patients were non-tobacco users with good oral hygiene and nutritional statuses. This is to simplify the derived mathematical model to study its feasibility of usage in the clinics for a smaller group of patients with ideal values of Tb, OHy and Ns. While multiple linear regression models are often straightforward and interpretable and can have good predictive power, practice of model validation, including cross-validation, is still valuable. If the research aim is more focused on understanding relationships between variables and making inferences about the population, a separate testing set might be less critical. However, model validation, which can involve techniques like cross-validation or bootstrapping, is still beneficial to assess the model’s performance. Our study’s objective was inferential modelling of data sets to know the impact of each predictor parameters Dmean, V30Gy, V50Gy, Tb, OHy and Ns for OM incidence based on ANOVA variance table assessment. Hence, we did not include the cross-validation of resulting models to assess their individual predictive powers.
Conclusions
In this study, feasibility of using multiple linear regression analysis to model OM incidence in radiation therapy clinics was explored. Derived dose–volume constraints for MSC could be used in IMRT/VMAT optimisation to reduce its incidence. Patient treatment could be individualised by incorporating dose–volume parameters, nutritional status, tobacco use and oral hygiene status in the treatment planning procedure.
Competing interests
None.
Open access
