2.1 Big data analytics and healthcare

Data collected and stored digitally is growing rapidly. Data storage and analysis are in high demand due to the internet and the digital economy’s rapid growth. Thus, data management and analysis are improving to help firms turn this massive supply of data into information and knowledge that helps them succeed [43–45]. Big data comes from massive datasets that typical database management solutions cannot handle. The majority of software and storage systems cannot quickly store, manage, and process massive data [46]. Organizations and health institutions keep and collect more data than ever since businesses and lives depend on it [1]. Accessing petabytes and zettabytes of data is essential. It shows how to avoid losing important data, ergo big data analytics in healthcare. Big data analytics finds invisible patterns and connections in data that current approaches cannot manage [30,45]. Health institutions are slow to adopt and study big data analytics, despite its value [47,48]. Data analytics can process and analyze patient data to improve diagnosis and treatment outcomes, relieving the overburdened healthcare system [49–51]. Data on new studies, emergencies, and disease outbreaks shows evolving trends. As electronic medical record systems progress, healthcare systems and personnel improve their ability to document patient experience and visit details [52]. Monitoring public health involves data analysis. This option is meaningless without connecting, trending, and patterning data. Outside of data analysis, healthcare record standards and the human condition may affect patients’ symptoms and indications [53]. Costs, chronic sickness, and aging are forcing healthcare industry changes. Healthcare data analytics may treat old health conditions, and episodic approaches are unhelpful [54,55]. Healthcare payers and providers use data and analytics to improve service and lower costs [56]. Health researchers need useful and intelligent tools to aid in their work [57,58]. Systemic quality and cost improvements in health reforms require data analytics. Due to the widespread use of electronic medical records and health outcome data, academics can study health analytic methods to find and evaluate effective interventions and anticipate patient health outcomes and costs [46].

2.2 Tableau as a data visualization tool

Tableau provides data insights through dynamic, interactive reporting and visualization [59]. Tableau exposes latent correlations within datasets. Graphs are employed to underscore relationship principles and facilitate code-free data exploration. Tableau efficiently extracts meaningful insights from data [60]. We used double exponential smoothing for our predictions in this investigation. Analytics software streamlines the procedure, provides visual feedback, and responds to complex questions. This makes data more important [61]. Tableau Desktop supports Amazon Redshift, MySQL, Oracle, Google Analytics, Microsoft SQL, OLAP databases [62]. Tableau supports hundreds of texts, PDF, Excel, geographic, statistical, and database data connections. Tableau supports numerous data types, making it convenient. Tableau’s data-modified images let customers quickly spot visual trends [63,64]. In cancer research, RNNs and LSTMs operate as powerful microscopes, peering into intricate datasets to reveal previously unknown associations between risk factors [65]. Such models are masters of analysis, but Tableau provides the magnifying glass by simplifying their complex outputs into comprehensible visuals. Bridge the gap between AI and human comprehension with Tableau [66], which cleans and prepares data for the models before showing their predictions [67]. Together, they bring researchers a clearer view of cancer risk, which in turn leads to more effective preventative efforts and better dissemination of these vital results [68].

2.3 Common data interpolation methods

Linear spline interpolation provides straight lines between data points in table gaps, usually astronomical data. It is criticized for its rapid trend change from one segment to the next, which does not occur naturally [69]. However, it is a good way to generate accurate lookup tables with quick look-ups for smooth functions without many table entries [70]. This method is a valuable tool used across fields to approximate values between known data points. Linear interpolation, which assumes a straight line between two neighboring points, is common [71]. Interpolating curves with polynomials and data points. Spline interpolation fits a polynomial while segmenting the dataset for smoother results. The nearest neighbor interpolation replaces missing or interpolated data points with their closest known values [72]. Inverse distance weighting uses the weighted average of neighboring sites to compute interpolated values, unlike kriging interpolation, which accounts for spatial correlations in geostatistical data [73]. The linear spline is mathematically; P_i(x) = a_ix+b_i with two parameters a_i and b_i can only satisfy the following two equations required S(x) to be continuous:

Linear spline: P_i(x) = a_ix+b_i with two parameters a_i and b_i can only satisfy the following two equations required S(x) to be continuous: (Eq 1) or, equivalently, P_i(x) has to pass the two endpoints (x_i−1,y_i−1) and (x_i,y_i) (Eq 2)

Solving either of the two problems above, we get: which is represented in the form of P_i = a_ix+b_i the first expression, or a linear interpolation of the two endpoints y_i−1 = f(x_i−1) and y_i = f(x_i) in the second expression. As P_i(x_i) = P_i+1(x_i) = y_i, the linear spline S(x) is continuous at x_i. But as in general (Eq 3) S(x) is not smooth, i.e., k = 0.

Quadratic spline: with three parameters a_i, b_i and c_i can satisfy the following three equations required for S(x) to be smooth (k = 1) as well as continuous: (Eq 4)

To obtain the three parameters a_i, b_i and c_i in Q_i(x), we consider Q′_i(x) = 2a_ix+b_i, which, as a linear function, can be linearly fit by the two end points f′(x_i−1) = D_i−1 and f′(x_i) = D_i: (Eq 5)

Integrating, we get As Q_i(x_i) = y_i, we have, and then solving this for c_i and substituting it back into the expression of Q_i(x), we get, as Q_i(x_i−1) = y_i−1 we have (Eq 6)

Given f′(x₀) = D₀, we can get iteratively all subsequent D₁,…,D_n, and thereby Q_i(x) Alternatively, given f′(x_n) = D_n, we can also get iteratively all previous D_n−1,⋯,D₀. It is obvious that with only three free parameters, the quadratic polynomials cannot satisfy both boundary conditions and . The third area cubic splines excel in is smooth interpolation modeling. Cubic spline interpolation uses a continuous formula to compute the first and second derivatives inside intervals and at interpolating nodes. A smoother interpolating function will result. First derivative continuity implies graph y = Z(x) will not have sharp corners. The continuity of the second derivative means that the radius of the curve is defined at each point. Given the n data points (x₁, y₁),…,(x_n, y_n) where x₁ are distinct and in increasing order. A cubic spline Z(x) through the data points (x₁, y₁),…,(x_n, y_n) is a set of cubic polynomials: Given the n data points (x₁, y₁),…,(x_n, y_n) where x₁ are distinct and in increasing order. A cubic spline Z(x) through the data points (x₁, y₁),…,(x_n, y_n) is a set of cubic polynomials: (Eq 7) (Eq 8) (Eq 9) With the following conditions (known as properties) (Eq 10)

This property guarantees that the spline S(x) interpolates the data points.

(Eq 11)

Z′(x) is continuous on the interval [x₁, x_n]; this property forces the slopes of the neighboring parts to agree when they meet.

(Eq 12)

Z′′(x) is continuous on the interval [x₁, x_n], which also forces the neighboring spline to have the same curvature, to guarantee smoothness.

2.4 Artificial neural networks ANN

Imitate cognitive and theoretical knowledge of how the human brain learns, including neural interconnections in the network. ANN is a fully linked multi-neuron network having an input layer that communicates with the following layer [74–76]. Artificial Neural Networks (ANN) try to mimic the human brain. Humans may be slower and less precise than neural networks [77]. An artificial neural network (ANN) is a fully linked multi-neural network that consists of an input layer, a layer that communicates with the layer below it (hidden layers), a layer that processes additional weighted connections and links to the output layer, and finally, an output layer of nodes that provide a variable for output [78,79]. Neural network nodes output real numbers from inputs. Nodes’ outputs are calculated by applying a function (ψ) to the previous layer nodes’ outputs [80]. Before that, the input layer output (o(0)) equals the input. We calculate the output layer output by computing layer outputs sequentially. This is an inferential procedure. Neural networks are structured according to the number of layers and the functions that govern the outputs of each layer. (Eq 13) Where o^{k) = the output vector representing the outputs of nodes in the layer l^k, = the general output of the node l^k, = function to determine the outputs of nodes and x_n ≕ nth input data. In order for two consecutive layers to be fully connected, all nodes in the previous layer must be connected to the next. Fully linked neural network topology is shown in Fig 1.

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Fig 1. The graph representation of a fully connected neural network.

https://doi.org/10.1371/journal.pone.0317148.g001

Neural network predictions are closer to actual standards since the model may be changed iteratively to reduce inaccuracies. Handwriting recognition, medicine, forecasting, and many other fields use ANNs because they outperform conventional technologies [81,82]. Convolutional neural networks (CNNs) are derived from visual cortical neurobiology. It interprets visuals as RGB layers of color and perceives them as three-dimensional entities. It then applies filters on convolutions of inputs in order to extract useful features [83]. In recent times, CNN’s achievements in computer vision tasks including as object identification, real-time face recognition, and image categorization and recognition have garnered significant attention [20]. Recurrent Neural Networks (RNN) are feed-forward networks with feedback edges that provide context [84]. ANNs’ hidden layers have duplicate cells whose states are modified by past and current feedback input. The ANN’s t-1 decisions affect its t-time judgment [50,85]. Cell-internal connection differences determine network design capability. Backpropagate over time with RNN memory, which stores all concealed states. Our networks learned short-range dependencies but not intermediate-range ones. Other scientists have addressed this restriction by allowing RNN to acquire mid-term dependencies Recurrent neural networks may feature a bidirectional, gated, or long-short-term memory architecture (LSTM). The challenge arises when the RNN must store in memory long-term dependencies. Long short-term memory networks solved this problem (LSTM) [86]. The LSTM uses truncation to efficiently flow a range of constant faults in special unit internal states.

2.5 Deep learning approach

Deep learning algorithms have outperformed computer vision in recent years, but their time series models are still shallow. Data scientists in most sectors utilize autoregressive models instead of deep learning. Common reasons for using these methods include interpretability, constrained data, convenience of use, and training cost [87]. It typically improves both performance (compared to other vanilla LSTMs/RNNs) and interpretability [88]. Their speed surpasses that of RNN/LSTM in a few of cases [89]. In addition, attention networks include categorical inference in deep neural networks [90]. These brain networks control consciousness, sensory orientation, and competing reactions. Many sequence transduction models use complex recurrent or convolutional neural networks in an encoder-decoder arrangement, but they only work locally and lack global information [91]. This constraint prompted attention networks to record long-range interactions. Attention networks are popular due to their parallel computation and relationship modeling adaptability. A simple residual network model that replaced all spatial convolutions with self-attention showed attention networks’ impact. This fully self-attentional model surpassed the baseline with less categorization parameters [92]. Additionally, subsequent tests on attention in general deep neural networks show continuous progress in categorization and detection with varied models. This influenced this study’s use of attention networks [93].

2.6 RNN & LSTM

Recurrent Neural Networks (RNNs) and Long Short-Term Memory (LSTM) models exhibit remarkable capabilities in processing sequential data and uncover complex relationships that are concealed within time series. Long-sufficiency-term (LSTM) models, classified as a subtype of RNNs, exhibit exceptional efficacy in managing data dependencies that endure for an extended duration. Furthermore, the greatest distinction between RNN and other networks is that it shows the relationship between current and historical information, although gradient dispersion limits its ability to learn relevant content quickly. LSTM (Long short-term memory) was introduced in 1997 to address the vanishing gradient issue [94]. Unlike the standard RNN, the LSTM has the same repeated modules, but its underlying structure is three "Gates" instead of a single neural network layer, making it better for processing and predicting critical events with lengthy intervals and delays in time series [95]. RNNs are crucial to deep learning algorithms that operate on time-series data. Remembering historical data allows these neural networks to predict current events. [96]. Due to fading and expanding gradients, conventional RNNs struggle to manage long-term dependencies in extended time series. After developing the LSTM network, critical state information was extracted from historical time-series data [97]. This event reinforces the link between past and future data. LSTM has been effective in welding quality monitoring and penetration prediction [98].

Another major perk is the TSA-LSTM model’s ability to process massive amounts of time-series data quickly without sacrificing forecast accuracy [99]. Cancer researchers and practitioners can benefit greatly from its sophisticated design and capacity to simulate intricate temporal patterns, which enhances their predicting abilities and allows them to deliver superior patient treatment [100]. However, unlike RNN, LSTM allows just one memory superposition formula. Show two network diagrams. Data analysis and modeling are done using the LSTM neural network for long-term time series data [101]. Long Short-Term Memory RNNs are efficient in deep learning. LSTM temporal model emphasizes keyhole progression during welding. The LSTM network learns temporal feature information from image sequences, demonstrating keyhole dynamics [102]. LSTMs use memory cells instead of artificial neurons in the hidden layer, unlike feedforward neural networks [103–105]. Also, systems can rapidly correlate memories and input remotely with memory cells to understand and predict data structure over time. Internal indirect state units are LSTM long-term or short-term memory. A gate to the conventional recurrent cell improves retention for “long-term dependencies” in the LSTM cell. Researchers used this to produce LSTM topologies with and without forget gates [106,107]. In the LSTM network, indirect state units function as either short-term or long-term memory. Unit status regulates the generation of an LSTM network. This is not only the last entry; it is a fundamental quality when a network forecast must be influenced by input history. It processes video, audio, and image data [108].

In the end, the TSA-LSTM is an advanced deep-learning architecture used in predictive analytics to predict cancer incidence rates. This approach exploits LSTM networks’ ability to capture long-term associations in sequential data. The model utilizes LSTM networks, known for their proficiency in processing sequential data such as cancer development, enabling the model to grasp the evolving characteristics of the disease. Furthermore, the two-stage architecture has the potential to learn intricate correlations among various elements in the data. The initial phase extracts fundamental patterns, which are then utilized in the subsequent phase for prediction or classification purposes. At various levels of prediction, attention processes focus on key traits [109,110]. This study used TSLM to predict cancer, which has two stages: Feature extraction first. Use LSTM layers to uncover temporal correlations and sequential patterns from cancer incidence data [111]. After two steps, the model accurately forecasts cancer incidence rates by capturing their complex dynamics. Previous research and articles on TSA-LSTM models for cancer incidence prediction may inform technical implementation [112,113]. The following section describes this model’s cancer prediction benefits. We provide historical cancer incidence data, which contains demographics, environmental variables, cancer diagnosis rate time series, and other essential information, unlike other studies. Normalize, fix missing values, and create LSTM-friendly data windows [114]. The TSA-LSTM model captures sequential data long-term dependencies with several LSTM cell layers. LSTM prediction uses attention to highlight relevant traits. Identify and refine important qualities for successful forecasting in two steps. Compare predicted values against real-world findings to assess the model’s accuracy [115]. Assess model estimates using epidemiology, historical patterns, and cancer risk indicators. Attention processes and LSTM networks in a dual-stage framework assess cancer incidence and capture its complex temporal patterns in TSA-LSTM [116]. Through enhanced deep learning, researchers and data scientists can improve cancer risk assessment, resource distribution, and public health policy [117]. This section has comprehensively examined the emergence of big data analytics within enterprises, as well as its application in the healthcare industry [118]. This article examines cancer analytics data visualization. The varied statistical models, deep learning models, and architectures used to anticipate data throughout time are also examined, along with the obstacles that spurred our research.

3.1 Data source and experimental manipulation

The dataset came from the Centers for Disease Control and prevention (CDC) and the American Cancer Society (S1 Appendix). The data includes cancer incidence rates, risk factors such as tobacco smoking, alcohol consumption, physical inactivity, obesity/excess body weight, and cancers caused by these risk factors. Our 1990–2021 data spans 32 years. Moreover, the study sets itself apart by developing a methodology to forecast the occurrence of cancer by the year 2025. The deployment of a novel two-stage attention model is used to forecast the rate of growth in cancer incidence, with 2017 serving as the reference year. It has been established that the prevalence of cancer is projected to increase by 9 percent by December 2020 and 12 percent by December 2021. There is an expected increase of 14 percent and 16 percent in newly diagnosed cancer cases by the end of 2022 and 2023, respectively. Furthermore, it is estimated that the number of cancer cases will rise by 19 percent and 21 percent in the years 2024 and 2025, respectively. The expected increase in cancer rates can be ascribed, partially, to a rise in detrimental lifestyle choices, such as the consumption of alcohol and tobacco, lack of physical activity, and a subpar diet. These factors contribute to the high occurrence of obesity in the United States. The accuracy and generalizability of a methodology are significantly influenced by the quality and completeness of the training data, in the case of data dependence. Inconsistencies, anomalies, and missing data points can all hinder a model’s ability to discover accurate patterns. During the feature selection phase for the TSA-LSTM model, the most pertinent variables or characteristics that are probable to exert a substantial influence on the prediction of cancer incidence and mortality rates are identified. By eliminating extraneous complexity and noise and concentrating on the most informative data points, this procedure is vital for optimizing the model’s performance. Furthermore, the complexity of the model. While simpler models may offer greater interpretability, they may fail to encompass the complete intricacy of the data. Extremely complex models, on the other hand, are susceptible to overfitting and have difficulty generalizing to unobserved data. Moreover, with regard to generalizability, it is frequently constructed and evaluated on particular datasets. The TSA-LSTM model selects features by extracting relevant variables from big datasets and using domain expertise to find those most likely to be associated with cancer outcomes. Environmental factors (pollution, carcinogen exposure), genetic markers, lifestyle factors (smoking, nutrition), demographic data (age, gender, ethnicity), and prior cancer incidence rates are commonly considered for feature selection [31,119]. It also protects Americans from international and domestic health, safety, and security risks with special reaction teams to fight diseases [120,121]. It oversees public health trend research.

The American Cancer Society’s mission is to save and celebrate lives and fight for a world without cancer. The organization estimates the present cancer burden by projecting the number of new cancer cases and deaths expected each year as cancer incidence and mortality data are three to four years behind [122,123]. Researching and pursuing public health trends is its responsibility. The American Cancer Society is a nonprofit organization dedicated to eliminating cancer and promoting a future without it. Additionally, they save and celebrate lives. Since cancer incidence and mortality data are three to four years behind the current year, the organization estimates the current cancer burden by projecting future cancer cases and deaths. The TSA-LSTM model consistently shows better predictive performance metrics, such as accuracy, precision, recall, and F1 score, compared to traditional models like logistic regression, decision trees, random forests, and simpler LSTM architectures. The TSA-LSTM model excels in cancer prediction tasks by effectively capturing long-range dependencies and temporal linkages, leading to superior accuracy and reliability compared to other models. Accurate cancer incidence and mortality rate estimates are crucial for healthcare planning and patient outcomes due to the significant impact of early diagnosis and exact forecasting [124,125]. In this regard, we wish to illustrate the correlation between cancer incidence and risk factors including obesity, smoking, drinking, and inactivity. In order to achieve our visualization objective, four preprocessing procedures are necessary. First, we verify each lifestyle choice and its annual cancer incidence in Excel for missing data. In R, we use mean imputation to fill missing values. Missing values are imputed with the sample mean. Third, we delete duplicate observations using Excel. Fourth, we classify lifestyle choices by age, sex, or type of cancer. Finally, for correlation analysis, we use R to sum the average classification data.

The study aims to create a more accurate forecasting algorithm. Our initial cancer data comprises just 32 yearly entries (February 1990 to March 2021), which is not enough to improve model training and prediction. To improve outcomes, the study interpolates data into numerous points. Use interpolation to discover the optimum data enhancement method. Interpolation is estimating an unknown quantity between two known variables or inferring missing information from one. Building a function that intersects a discrete set of known data points is the core of this strategy. When missing data is available and cycles are long, this technique works [126,127]. A variable’s predictive strength, relevance to the result, and multicollinearity concerns usually determine its inclusion. When variables are highly correlated with the target variable and can illuminate patterns, they are more likely to be included in the model. Superfluous variables that don’t affect predictions or add noise may be deleted to simplify the model. Through domain knowledge-based pruning, correlation analysis, feature importance ranking, and mutual information analysis, TSA-LSTM model feature selection variables can be identified. The feature selection method is critical for ensuring that the TSA-LSTM model can accurately capture the complex correlations in cancer data and to optimize its performance. Constantly, it is assumed that the performance of the model will effectively extrapolate to unobserved data that possesses comparable attributes. Nevertheless, such an outcome cannot always be ensured, particularly in cases where the unobserved data diverges substantially from the training data. The model’s ability to generate more reliable estimates of cancer incidence and mortality rates is due to its rigorous selection process that eliminates extraneous or redundant components.

A frequent interpolation method is spline. Spline interpolation uses a piecewise polynomial as the interpolant. Many prefer spline interpolation over polynomial interpolation because the inaccuracy can be minimized even with low-degree polynomials. Spline interpolation eliminates Runge’s phenomenon, which causes oscillation between locations when using high-degree polynomials [28,123,128]. As in 2.4, spline interpolation can be linear, quadratic, or cubic. We purposely construct missing values in 32 data points to decide the study’s interpolation strategy (Linear, Quadratic, or Cubic). We keep only certain years’ data (1990, 1994, 1997, 2001, 2004, 2007, 2010, 2012,2014,2017,2019 and 2021). We now utilize each interpolation method to predict and fill in missing data for other years (1991, 1992, 1993, 1995, 1996, 1998, 1999, 2000, 2002, 2003, 2005, 2006, 2008, 2009, 2011 2013,2015,2017,2019, and 2021) Interpolation, which anticipates missing figures more accurately, is our choice. Each method’s missing value-filling results are in (S2 Appendix) The table shows that all three models predicted but did not match. Therefore, we augmented our data using the cubic spline technique which upgraded and increased the data into hundreds of entries [41,113]. This folded the data from yearly to monthly entries, using some for-model testing and the rest for training. Adding synthetic data points to our data would improve model training for accurate deployment. The data is augmented using the cubic spline. Focusing on our raw data (from 1990–2021), we have 32 data points for the cubic spine for 420 data points.

3.2 Variable construction and correlation design

Tableau will be used to highlight the association between lifestyle and cancer incidence. Our dependent variable new cases, fatalities, and cancers are linked to lifestyle choices. Smoking, alcohol, nutrition, inactivity/lack of exercise, and bad nutrition cause obesity. In this study, cancer data shows a dependent variable, where the total number of new cancer incidences per year. Tobacco smoking, alcohol consumption, physical inactivity, and obesity show the independent variables.

3.3 Tableau data visualization

Effectively using people and data is as important as the method. Data must be reviewed, cleaned, processed, and modeled to find usable information, draw conclusions, and aid decision-making [31,129].Tableau is a powerful intelligence platform that uses analytics to harness data. It streamlines data viewing, processing, and comprehension. New data modeling tools in Tableau make sophisticated data analysis easier without database knowledge. We can seamlessly mix data utilizing table relationships to maintain the data model adaptable for analysis [130,131]. We describe forecasting, analysis modeling, statistical measures, and smoothing coefficients dataset processing. For comprehension, Tableau visualizes data. Launch. Tableau’s launch page links to databases, text files, and other data. Tableau analysis and source access begin. Once connected and imported, Tableau instantly displays all associated data sets on the data source display page. Without unnecessary data, the data translator cleans and visualizes loaded data on this page. Create Tableau visualizations and spreadsheets using all loaded data. Create dashboard and story visualizations by dragging and dropping measures and dimensions in Tableau’s spreadsheet. Enhancing perspectives Dashboards should make sense from data visualization. Dashboards with many stories allow users to make crucial decisions. In Tableau dashboards, data can be dragged and dropped into stories. [31,125,127]. In the results and analysis, many visualizations are discussed. LSTMs are neural network architectures, not models, therefore they can be changed for specific operations. A rudimentary LSTM model may perform poorly due to weak operations. The basic LSTM model presented to handle gradient issues (Exploring Gradient Problems and Vanishing Gradient Problems) contained simply an input and output gate and maintained the RNN’s cell state [113]. Besides gradient difficulties, the RNN had input and output weight conflicts that the simple LSTM solved. Though better than the RNN, this technique does not fully solve its problems [113,132]. A forget gate reduced the number of sequences truncated in the original LSTM Model by deleting valuable material from the hidden state and forgetting unneeded ones. Forget-gate biases impact LSTM performance. Many academics have presented Vanilla, Stacked, CNN, Bidirectional, and other LSTM designs. Evolutionary approaches were preferred over gradient descent by Shalev-Shwartz, Shamir, and Shammah (2017). Attention emphasizes certain data [23,133]. Studies have shown that attention networks are needed to exhibit data parts. This study proposes a two-stage attention model to improve the LSTM model’s attentiveness and prediction accuracy [28,123]. Our work visualizes lifestyle patterns and specific malignancies and estimates future cancer incidences using raw data cleanup and sample enlargement. Interpretive research and an innovative way to examine complicated lifestyle datasets with Tableau dashboard visual analytics were also discussed. The chapter explained our data preparation materials and new model design. This part also checks our data interpolation strategy for optimal results.

4.1 Double exponential smoothing data analysis modeling and forecasting

Here, we examine and describe the data analytic modeling used to anticipate cancer data using Tableau’s double exponential smoothing approach. Alpha and beta values of 0.5 produced the lowest error margin in LSTM-based data processing and analysis models. In testing, these coefficients were employed. Table 1 shows forecast alternatives based on actual yearly time series entries from 1990 to 2021 and measured by age-standardized measure per 100,000.

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Table 1. Summary of forecast options and model used in DES.

https://doi.org/10.1371/journal.pone.0317148.t001

The forecast is extended to three years without seasonal pattern, although the model seeks a recurrent seasonal pattern in every period [134]. The forecast model shows multiplicative levels, trends, and no seasonality. Root mean squared error (RMSE), Akaike information criterion (AIC), mean absolute scaled error (MASE), mean absolute percentage error (MAPE), and mean absolute error (MAE) are used to ensure forecast quality in DES [135,136]. Each quality indicator provides statistical model quality data. Level, trend, and seasonal smoothing coefficients are alpha, beta, and gamma. Level and trend smoothing coefficients alpha and beta are 0.50 and gamma is 0.00 for the forecast. Forecasts are more naïve because to smoothing coefficients in our investigation. In this study when assessing the effectiveness of a prediction technique, it is essential to consider more than just one measurement. Two important approaches, Root Mean Squared Error (RMSE) and R-squared (R²), provide essential information’s primarily measures the size of mistakes, giving the average proximity between predictions and actual values (lower RMSE indicates better accuracy). The coefficient of determination, R², quantifies the degree to which the model’s predictions align with the general pattern observed in the data (a greater R² indicates a stronger fit). By utilizing both measurements, one can acquire a fuller comprehension of the model’s performance—its average accuracy and its ability to effectively capture the overall patterns. Furthermore, the use of boxplots to visualize the distribution of errors is quite useful. Boxplots can expose outliers or biases in the predictions, offering a more comprehensive examination beyond the average error measured by RMSE. Overall, the performance of a prediction approach can be thoroughly assessed by using a combination of RMSE, R² (Coefficient of Determination), and boxplots.

4.2 TSA-LSTM model design using LSTM

The paper’s model is based on time series lifestyle and cancer incidence data from the Centers for Disease Control and Prevention and the American Cancer Association from 1990–2021. Thus, it is better for LSTM network applications since it solves the complexity and timeliness issues produced by the three gates. First and foremost, the TSA-LSTM model attention mechanism prioritizes the input characteristics, specifically their significance, to guarantee that the model encoder converges to specific characteristics of the input sequence when predicting the specific characteristics of the output sequence. This enhances the model’s natural learning trend and prediction quality. The quality of predictions is enhanced by selecting network features and maintaining model performance in real-time. Our model employs a Long Short-Term Memory (LSTM) Recurrent Neural Network that is capable of training long-term dependencies. LSTMs avoid long-term reliance, making long-term recall possible [23,113]. We exploited attention mechanisms and their strong operations to retain major cancer trend features for a decent forecasting model for active cancer research. The network uses attention processes to focus on one part of a complex input until classification. To simplify difficult tasks, process smaller regions sequentially. Like the human mind breaks down a new difficulty into smaller tasks and addresses them separately [41,127]. Input attention, temporal attention, and repetition help our model outperform baseline models in studies. Based on the model idea, we propose the Two-Stage Attention LSTM (TSA-LSTM) model for cancer data prediction in this research [137]. Sensitivity analysis helps users understand the model’s sensitivity to a wide range of scenarios and potential sources of uncertainty. This improves user decision-making. These goals are achieved by perturbing input features and analyzing the results. Healthcare practitioners can develop trust in the model and understand its restrictions by providing model-specific documentation on its structure, training methods, input characteristics, and output assessments. These techniques increase the TSA-LSTM model’s interpretability, making it accessible to healthcare practitioners without machine learning experience [23,35].

The following sections of this section provide a detailed explanation of the model’s components and provide essential insights into its testing configuration. In this work, we suggest a time series model for the accurate evaluation and long-term prediction of cancer incidences. Given n and τ as input sequence and window size length respectively; the yearly incidence movement is denoted . Then, the moving sequence of length τ is denoted an, d a vector of n moving input sequence at time t as . Again, given the previous values of the target sequence as (y₁,y₂,y₃,…,y_τ−1) and y_t∈ℝ, and the current and past values of the n moving sequence as (x₁,x₂,x₃,…,x_τ);x_t∈ℝⁿ, non-linear autoregressive exogenous models aim to optimize nonlinear mappings to the current value of a target sequence y_τ using with F(•) as the non-linear mapping function to determine via optimization. In the suggested model, we used LSTM units as encoding units [127,138]. We chose an LSTM encoding unit because its cell states sustain states across time, avoiding vanishing gradients and improving long-term information retention in our time series model. Formally, taking each time t, an input vector x_t, a memory state vector c_t, and h_t as the output of c_t, then the LSTM units can be formulated as: where, W and U are the weight matrices. b is a bias vector. i_t, f_t, o_t are the input, forget, and output gating units and σ is our activation function for the gating units. For our time series prediction at the time t, given the input sequence X = (x₁,x₂,x₃,…,x_τ)|x_t∈ℝⁿ, we apply our LSTM encoder to learn the mapping optimum mapping from x_t to h_t using h_t = f₁(h_t−1,x_t) h_t∈ℝ^s, where h_t is the hidden state of the encoder at the time t f₁ is our LSTM non-linear activation function s is the size of the hidden state h_t.

The existing models are compared in (Fig 2) based on their average accuracy ratings in testing and forecasting the cancer data. We trained and evaluated each model ten times in the same environment. Each model overwrote the training losses of the previously implemented models. The initial testing of the Gated Recurrent Unit model yielded an average accuracy of 94.27% for 128 units. The first tested network, the GRU network, showed a clear intent with an accuracy of 93.158. The second indicator is the BIGRU network (92.099), which displays 94.14%. Three, the LSTM network (94.101) exhibits a 79.23% percentage. Following this, the BILSTM network (91.686) exhibits a 54.87% increase. Fifth, the GRU seq-2 network (78.132) displays a 93.78% accuracy. The sixth network, the BIGRU seq-2 network (51.555), displays a 93.43%. Seventh, the LSTM seq-2 network (92.212) exhibits a 93.38% rating. Eighth, the BILSTM seq-2 network (91.799) boasts a 95.98% efficiency. On the ninth position, the LSTM seq-2-seq network with input intention (95.959) exhibits an accuracy of 87.98%. The LSTM network with two stages of attention (97.763) demonstrates a 98.87% accuracy the tenth time. Finally, the testing set executes the proposed TSA-LSTM model. Each model overwrote the training losses of the previously implemented models. Results indicate an average accuracy of 87.96%.

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Fig 2. TSA-LSTM design.

https://doi.org/10.1371/journal.pone.0317148.g002

4.3 Two stage attention mechanism

Our LSTM encoder reads and encodes input sequences into fixed-length vectors for two-stage attention. Sequences encoded as fixed-length vectors prohibit models from memorizing longer ones (Eqs 14–18). We augment our model’s encoding unit to boost prediction accuracy. The model’s LSTM encoder’s convergence on input and output sequence features is examined first. Learning improved model prediction. We construct a second attention mechanism, temporal attention, to choose critical network attributes at all times while decoding to preserve model performance as sequence length rises [125,139]. Real-time model performance picks network features and improves prediction. Assuming a-th moving sequence input, , we create an input attention mechanism with a multilayer perceptron by applying the LSTM cell state c_t−1 and the previous hidden state h_t−1 in the equation: (Eq 14) Where

• is the attention weight that holds the relevance of the a-th input feature at time t.
• , W_e∈ℝ^τ×2s, U_e∈ℝ^τ×τ are learnable parameters.

Lastly, we sum all the attention weights to 1 by applying a soft auction to . In combining the attention mechanism with the LSTM encoder, a resulting sequence, , the hidden state of the encoder is updated as and thus, allows the LSTM encoding unit of the model can selectively focus on unique characteristics of the input sequence. We construct an LSTM decoding unit that uses the model’s internal representation to predict output . We construct an LSTM decoding unit that uses the model’s internal representation to predict output a. In order to maintain the performance of the model through the entire network with as the sequence length increases, we construct a temporal attention mechanism that chooses vital features of the network at all times while decoding. Given that at time t, the attention weight of an encoder’s hidden state is computed as: (Eq 15) with (Eq 16) where

1. ■ d_t−1∈ℝ^p is the hidden state of a previous decoder.
2. ■ is the cell state of the LSTM unit.
3. ■ are learnable parameters.

Similar to the encoding unit’s input attention mechanism, the temporal attention mechanism holds the relevant features, but this time, of the i-th encoder hidden state for prediction using attention weight at the decoding level [140]. Considering the encoder’s hidden state h_i is mapped to the input’s temporal component, the attention mechanism evaluates the context vector c_t (unique at each time) as the weighted sum of all the hidden states {h₁,h₂,h₃,…,h_τ} of the encoding units: (Eq 17)

Hence, the combination of the target sequence and context vectors arrives at: (Eq 18) where and maps [y_t−1;c_t−1] to the decoder’s size. is then used to update the decoder’s hidden state at time t. We created and implemented nine neural baseline models to compare our model to others using neural networks. Our hierarchical neural model has customizable window and encoder/decoder hidden state sizes. We chose the two-stage attention encoder-decoder model since it obtained the best results among state-of-the-art models. The TSA-LSTM model pseudocode is in S3 Appendix. The analysis and correlational data have been refined with the inclusion of six subfactors. Priority is given to the following associations: alcohol use and cancer, tobacco use and cancer, obesity and cancer, physical inactivity and cancer, and cancer itself. The sixth proportion of malignancies in the United States that are ascribed to risk factors exhibits temporal patterns of incidence. Female breast cancer is one of the most common alcohol-related cancers in the US, with 138.3 per 100,000 cases [41,141]. Women who drink excessively are at risk of breast cancer. Alcohol intake is also linked to 65.8 colon and rectum cancers, 21.7 lip cancers, 8.1 liver cancers, 5.8 esophageal cancers, and 3.3 larynx cancers per 100,000 persons This visual uses a horizontal polygon map to quickly visualize data patterns. Second, (Fig 3) depicts how tobacco smoking promotes cancer. Tracheal, lung, bronchus, colon rectal, and urinary bladder cancers are the most common tobacco-related malignancies. Smoking causes 58.80 cases of tracheal, lung, and bronchus cancer per 100,000 persons, making it the most common cancer caused by smoking. Tobacco smoking causes 49.70 colon and rectal cancers, 30.10 urinary bladder cancers, and 36.60 kidney/renal pelvis cancers. Additionally, tobacco smoking causes 14.20 cases of acute myeloid leukemia per 100,000 people. Additionally, the cancer is the most terrifying outcome of smoking, which casts a dark cloud over people’s health. And smoke increases the chance for a terrifying array of malignancies due to its over 7,000 compounds, including 70 proven carcinogens, which rampage through the body [142]. There is extensive harm, including but not limited to lung cancer (the leading cause of cancer-related deaths, accounting for 80% of all cases) and malignancies of the esophagus, larynx, lip, mouth, pharynx, bladder, and kidneys [143].

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Fig 3. Cancers attributable to tobacco smoking.

https://doi.org/10.1371/journal.pone.0317148.g003

Third, the bubble chart in (Fig 3) illustrates that obesity is a major cause of cancer. Breast cancer after menopause is the most common cancer-related obesity, followed by colon, rectum, uterine, thyroid, pancreatic, ovary, and kidney malignancies. Obesity is linked to 439 postmenopausal female breast cancer, 43.9 colon/rectum cancer, 46.7 corpus/uterine cancer, and 31.4 thyroid cancers per 100,000 cases. Due to obesity, 21.2 new pancreatic, 31.2 ovarian, and 40.9 kidney malignancies are diagnosed. Obesity is linked to liver, gallbladder, esophageal, and meninges cancers [123,144]. The smoke can reach every part of the body, including the digestive tract. It can alter the balance of good bacteria in the gut, which can lead to colon cancer, as well as other malignancies in the liver and stomach. Smoking raises the risk of Acute Myeloid Leukemia, while the link is less clear [145]. Cancer risk drops considerably after the body’s extraordinary healing mechanisms take effect. When people stop smoking, they reclaim agency, enhance air quality, and dramatically reduce their cancer risk. Color and size of circles demonstrate how fat impacts cancer [146]. Attribution increases with circle size. The bubble chart is visually appealing and makes it easier to identify categories and compare obesity attribution data by bubble size. The aspect of interpretability holds significant importance, particularly within healthcare environments where the outcomes of patient outcomes can be profoundly impacted by decisions predicated on predictive models [18,127]. The TSA-LSTM model is difficult, however healthcare professionals without machine learning model knowledge can apply many approaches to simplify its conclusions. Essentiality of the feature Visualisations or quick summaries of the model’s essential characteristics may help healthcare providers[20]. During the process of prediction, the visualization of the attention mechanism that is utilized by the TSA-LSTM model might provide information regarding which particular segments of the input data are given priority by the model. In the process of making judgments, this can be of assistance to users in understanding the manner in which the model assigns weights to different time steps or qualities [22]. Explaining forecasts may help healthcare providers understand the model’s logic for predicting a patient or case.

Fourth, physical inactivity and cancer show (Fig 4) that physical inactivity is the leading cause of US female breast, colon, and corpus/uterine cancers. Physical inactivity causes 438.2 postmenopausal female breast cancers per 100,000 persons. Physical inactivity also causes 38.6 colon, rectum, and 35.7 corpus/uterine cancers in men and women. If female youngsters exercise more, the worrying number of female breast cancers may decrease [147]. It is possible that the present graph, which attempts to demonstrate a correlation between obesity and cancer incidence, is deceiving. It probably shows the total number of cancer cases, but it doesn’t show how much of an increase in risk there is because of fat [148]. This is due to the fact that, similar to breast cancer, a high total incidence does not always indicate that a large percentage of those instances are attributed to obesity. The ideal representation would center on the percentage of cancer cases linked to obesity for each kind in order to offer a more accurate picture. Alternatives include stacked bars, proportionate bars, and heatmaps. A heatmap would use color intensity to show attributable risk, proportionate bars to show obesity’s percentage of cases, and stacked bars to divide the total incidence into obesity, other risk factors, and unknown causes. Consider age and sex for a clearer image[149]. Menopause may affect breast cancer obesity risk factors. The graphic should be accompanied by the number of obesity-related cancer cases for clarity. Focusing on these regions helps researchers understand obesity’s particular impact in cancer risk.

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Fig 4. Cancer-related obesity in the USA.

https://doi.org/10.1371/journal.pone.0317148.g004

Fig 5 bar chart simplifies comparing malignancies caused by physical inactivity and speeds up decision-making. Fifth, US cancer incidence statistics from 1990 to 2021 reveal that cancer incidence for all ages is rising, indicating a bigger number of cancers. New cancer cases soared to approximately 23 million. Cancer rates worsened and increased with time [150]. The line chart in this study simplifies these perspectives and trends. Sixth, Fig 6’s bar chart reveals that health risk factors directly cause all cervical cancers and 4.4% of prostate cancers and deaths. Risk factors cause 84.1 percent of tracheal, bronchus, and lung cancer, 71.8 percent of laryngeal cancer, 78.94 percent of lip and oral cavity, 69.8 percent of esophageal, and 64 percent of nasopharynx cancer cases and deaths. Health risk factors did not affect brain and nervous system cancer, pulmonary sarcoidosis, lymphatic filariasis, malignant skin melanoma, non-melanoma skin cancer, or testicular cancer. Health risk factors are linked to > 50% of 7 of 26 cancer types. Health risks cause 43.2% of colon and rectum cancers, 41.5 percent of liver cancer, 36.5 percent of uterine cancer, 42.3 percent of kidney cancer, 52 percent of bladder cancer, 27.5 percent of pancreatic cancer, 34.9% of breast cancer, 21.78% of stomach cancer, and 35% of gallbladder and biliary tract cancers. The bar’s height and color indicate how much health risk factors contribute to cancer incidence and death. Risk factors cause 7.9% of thyroid cancer and 7.8% of Non-Lymphoma Hodgkin’s incidence and mortality. The existing graph appears to have an issue with the presentation of the cervical cancer risk variables. The shade and bar height provide the wrong idea, even though they are meant to indicate the risk associated with obesity. The Centers for Disease Control and Prevention (CDC) reports that the Human Papillomavirus (HPV) is the causative agent of cervical cancer in around 90% of cases [151]. However, being overweight is not a primary cause. It isn’t the main cause of the condition, but it could weaken the immune system and impact HPV progression in some circumstances. The existing layout of the graph, which uses color shading and bar height to portray the same data, incorrectly suggests that obesity significantly increases the risk of cervical cancer [152,153].This might be because of an error in the data mapping process or because the graph is lacking a data point that would indicate the risk of HPV infection. Having two separate data points for cervical cancer would be excellent for a clearer picture[154]. A large value, maybe the entire height of the bar or a dark shade, would indicate a high risk of HPV infection, whereas a little value, maybe a minimal height of the bar or a light shade, would indicate a low risk of obesity. It is essential to have labels that clearly explain the meaning of the colors and heights in order to prevent any misunderstandings. These changes will make the graph a better tool for learning about the real cervical cancer risk factors[155].

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Fig 5. Share of cancer deaths by type attributable to risk factors in the USA.

https://doi.org/10.1371/journal.pone.0317148.g005

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Fig 6. Forecasted results.

https://doi.org/10.1371/journal.pone.0317148.g006

4.4 Forecasting results

All models were trained and tested 10 times in the same environment. We test on a GPU cluster of eight NVIDIA 1080Ti 32GB in simultaneously. Mini batching (128-person) was employed during training. A joint Stochastic Gradient Descent and Adam optimizer with 0.001 learning rate were used. We use 1000 training epochs and an early stopping strategy to cease when training losses do not decrease after 20 epochs. Our goal function was Mean Squared Error. Dropping 20% on all layers of each model we tested prevents overfitting. LSTM models are susceptible to overfitting, particularly when data is sparse. This can happen when the model grasps patterns that are unique to the training data but do not apply effectively to new data. Fig 6 presents the experimental results from the testing of cancer data on the Double Exponential Smoothing method. It is observed that the Double Exponential Smoothing model diverges as the years increase, even after testing data points of two years, unlike the neural networks models which undulate evenly and smoothly along the timeline [127,144,156]. This could be due to the absence of seasonality in the Double Exponential Smoothing, whereas the neural networks approach and factor the seasonality. After the model testing, it is realized that the Double Exponential Smoothing has an average accuracy of 88.50% in the prediction of cancer data.

This implies that the Double Exponential Smoothing method may help in short-term predictions (1–6 months), however, this method is comparatively low/weak in accuracy and not good for a long-term cancer projection for effective policy formulation. To test our model’s network, we first conduct experiments on nine existing prediction state-of-the-art model networks, including: A Gated Recurrent Unit (GRU), A Bidirectional Gated Recurrent Unit (BiGRU), A Sequence-to-Sequence Gated Recurrent Unit (Seq-2-Seq GRU), A Bidirectional Sequence-to-Sequence Gated Recurrent Unit (Seq-2-Seq BiGRU), A Long short-term memory (LSTM), A Bidirectional Long short-term memory (BiLSTM), A Sequence-to-Sequence Long short-term memory (Seq-2-Seq LSTM), A Sequence-to-Sequence Bidirectional Long short-term memory (Seq-2-Seq BiLSTM), A Sequence-to-Sequence Long short-term memory with Input Attention (Seq-2-Seq LSTM + Input Attention). The average cancer data testing and predicting accuracy scores of existing models are compared [150,156]. The models underwent 10 rounds of training and evaluation in a consistent context. Each subsequent model replaced the training loss of the previous models. The initial testing findings of the Gated Recurrent Unit (GRU) model, as demonstrated in Fig 6, indicate an accuracy of 98.26%. Subsequently, the performance of the Bidirectional Gated Recurrent Unit model, consisting of 128 units, was evaluated, yielding an average accuracy of 97.1 percent. After the completion of the third round of testing, the Gated Recurrent Unit Sequence to Sequence network consisting of 128 units demonstrated an accuracy of 88.23%. The Bidirectional Sequence-to-Sequence Gated Recurrent Unit that was displayed was subjected to four tests. The Long short-term memory model, which incorporated post-training data training, had an average accuracy of 95.34 percent, whereas this model achieved 64.36 percent. Subsequently, the performance of the Bidirectional Long short-term memory Network, consisting of 128 units, was evaluated and yielded an average accuracy of 94.31 percent. Sequence-to-Sequence Long short-term memory, Bidirectional Long short-term memory, and long short-term memory with Input Attention were directly tested and achieved average accuracies of 89.21, 94.30, and 86.86. Finally, the set of testing is implemented on our proposed TSA-LSTM model. Just like the other State of the Art models, we trained ours and evaluated it ten times in the same environment. Each model overwrote the training loss of the previously implemented models. The result shows an average accuracy of 98.23%.

4.5 Quantitative analysis of models

Using real forecasts is crucial for accuracy evaluation. Thus, residual size does not predict genuine forecast errors. Only by testing a model on new data not utilized when fitting it can forecast accuracy be verified. Data is usually split into training and test data when picking models, with the former used to estimate forecasting technique parameters and the latter to assess accuracy. Since the test data is not used to forecast, it should give a good indicator of how well the model will forecast fresh data. In this study, training lasted from February 1990 to March 2021 and testing was from We also increased the test size to the maximum prediction horizon. We presume that a model that matches the training data well will not forecast well when creating our new model [157]. A model with enough parameters produces a perfect match every time. Overfitting a model is as harmful as not finding a pattern in data. Some publications call the test set the “hold-out set” since these data are “held out” of fitting data. This study uses “training data” and “test data” instead of “in-sample data” and “out-of-sample data” as references do.

We defined forecast error as the difference between an actual value and its forecast in this investigation. Thus, an error is the unpredictable component of an observation, not a mistake. Write it as: (Eq 19) Where the training data is given by {y₁,…,y_T} and the test data is given by {y_T+1, y_T+2,_⋯}.

Forecast errors differ from residuals in two ways. Remainders are calculated on the training set and forecast mistakes on the test set. Second, residuals use one-step forecasts whereas forecast errors use multi-step forecasts. We use scaled-dependent errors to quantify forecast accuracy. This study’s forecast mistakes are on the same scale as the data hence the models’ accuracy metrics are scaled-dependent as the cancer data is in numerous time series with the same units (date and cancer incidence). Different forecasting models are compared by their error and accuracy rates. Forecasting models vary in accuracy. Table 2 compares double exponential smoothing, deep learning techniques, and our model. As mentioned earlier, accuracy is a key indicator of predictive algorithm success [158].

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Table 2. Summary of quantitative comparison of models.

https://doi.org/10.1371/journal.pone.0317148.t002

Our algorithm has the maximum accuracy of 98.96 percent and the lowest error rate of 3.24 percent. Double exponential smoothing predicts cancer incidence 9th among deep learning methods. We employed one double exponential smoothing approach, but the alpha-beta values with the fewest mistakes were used during implementation. Thus, the amount of double exponential methods utilized will not affect performance but may decrease it. Again, deep learning systems outperform double exponential smoothing in cancer data prediction accuracy. Comparatively, our model is the most accurate. Our algorithm uses two-stage attention. Attention models might provide interpretability while keeping deep learning’s flexibility and versatility. Comprehending the prediction process of the model might be challenging because of the intricate structure of LSTMs. In cancer research, the inability to grasp the model’s reasoning can be a drawback for creating novel therapy approaches. We initially use an input attention technique to adaptively extract important driving series at each time step by referencing the encoder’s hidden state. We pick relevant encoder hidden states across all time steps in the second stage using temporal attention. Our model can predict and interpret well with this dual-stage attention method [123,159,160]. Time series prediction and feature learning in computer vision tasks are possible with our model. This implies that our model forecasts cancer data better than others. Our algorithm may have a low margin error since the model’s attentions provide interpretability and flexibility.

4.6 Qualitative algorithm description

This section describes each algorithm based on three essential time series observations on our predicting outcomes. 1). predict smoothness 2) movement distance and orientation; 3) training average time. These observations may help explain algorithm behavior on cancer data. We discuss the neural network and DES algorithm training procedures to elucidate the observations. The first section gives four rudimentary forecasts and the second four refined ones. Primitive forecasts are training’s first projections without error margin. Refined forecasts are error margin-influenced. Both crude and sophisticated forecasts improve accuracy. The last two training instances just increased the error margin [161,162]. The two training instances and error margin are meant to help refined forecast training instances match the genuine trend [163]. The predicting results are supported by the error margin and two training instances using three fundamental time series data. The training procedures are exclusive to DES. However, as DES is not a neural network, the training instance only constituted a piece of the process. We assessed the effectiveness of each method in improving forecast accuracy by applying filtering techniques. Smoothing helps to clarify the trends in forecasting [35,164] Smoothing describes time series trend components. Smoothing can be linear, undulating, or non-undulating [165]. The optimal neural network algorithm increases undulating trends and minimizes non-undulating.

According to Table 3, the best neural network has a whole undulating pattern for forecast results and full distances between forecast results and true trends. Such a neural network needs to be trained for over 1700 seconds. Several experiments led to this conclusion. We trained our data with basic LSTM and GRU. We found that the simple LSTM model outperforms the GRU. This supports our decision to build on the basic LSTM with an attention network [166]. We fed the basic LSTM algorithm a one-stage attention network to improve performance. Our next hypothesis is that a two-stage attention network as an input to the basic LSTM would improve performance. We found that the two-stage attention network improves cancer data performance but requires many hours of training.

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Table 3. Observations that influence the accuracy of the algorithm.

https://doi.org/10.1371/journal.pone.0317148.t003

4.7 Prediction of cancer incidences using the TSA-LSTM model

Fig 6 shows our unique TSA-LSTM model’s experimental cancer incidence forecasts. Predictions for new cancer cases are until 2025. The new cancer incidence estimates are increasing linearly, indicating high cancer rates until 2025. Our actual numbers ending 2021 suggest cancer cases may rise 9% by December 2020 and 18% by December 2021. Additionally, 2022 and 2023 are predicted to see 18% and 21% more cancer cases. Cancer incidences are expected to grow by 20% and 22% in 2024 and 2025 [167,168]. The forecasts are reasonable and incremental, with close prediction intervals reflecting previous data fluctuation. Table 4 summarizes the total projected cancer incidence in December each year. Additionally, it has been determined that the eating of particular foods is likely to elevate the risk of developing cancer. For example, consuming meals that induce hyperglycemia has been associated with an elevated risk of developing colorectal, stomach, and breast malignancies [31,62]. High-temperature cooking techniques, including grilling, frying, and barbecuing, can generate heterocyclic amines (HA), which have been linked to the development of cancer and various other ailments [62]. A high dairy intake is associated with an increased risk of getting prostate cancer. According to [169] an increased consumption of whole milk significantly heightens the likelihood of illness progression and mortality. Furthermore, it is widely acknowledged that physical inactivity is the leading cause of breast, colon, and corpus/uterine malignancies among women in the United States. Our projection shows rising US cancer rates by 2025. As shown in sections 4–20, lifestyle decisions and other risk factors contribute to the rising cancer rate [170]. Lifestyle choices including alcohol, smoke, inactivity, and poor diet have boosted obesity in the US, and this trend is expected to continue. Previous studies have connected poor lifestyle choices to cancer. The International Agency for Research on Cancer showed increased colon, breast, and endometrial cancer risk. Smoking causes breast and lung cancer, research shows [24,25,171].

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Table 4. Summary of predicted cancer incidence rate.

https://doi.org/10.1371/journal.pone.0317148.t004

Our results reveal that the Double Exponential Smoothing model diverges on cancer data over time. but bad for long-term forecasting. One of our 11 study algorithms. Comparatively, our model has a maximum accuracy of 98.96 percent. LSTM model sequenced by our technique used a two-stage attention sequence. We forecast US cancer incidence growth using our two-stage attention model with 2021 as our baseline (Table 4). Furthermore, our research findings suggest that the Double Exponential Smoothing model exhibits a divergence from the observed outcomes over time. This result is attributable to the Double Exponential Smoothing model’s absence of seasonal variation. This indicates that while the Double Exponential Smoothing method may be advantageous for short-term forecasts (1–6 months), it is not considered suitable for long-term forecasting. One of eleven algorithms that were implemented in our research. In comparison to alternative models, our proposed model exhibits the maximum magnitude of accuracy at 97.76 percent. The attention sequence to sequence LSTM (TSA-LSTM) model was utilized by our method in two stages. The rate of growth in cancer incidence in the United States is predicted using our two-stage attention model, with 2017 serving as the baseline year. By December of 2020, 2021, 2022, 2023, 2024, and 2025, the incidence of cancer is projected to grow by 9 percent, 12 percent, 14 percent, 16 percent, 19 percent, and 21 percent, respectively.