Vital signs and pertinent data taken from the MIMIC-IV database were used in our investigation [31,32]. We received permission to extract data from the MIMIC-IV for research purposes (Certification Number: 50640755) and completed the web-based training course offered by the National Institutes of Health to ensure the safety of human study participants before gaining access to the database. High-quality data from 2008 to 2019 is included in the publicly accessible MIMIC-IV database, which was created by the review boards of Beth Israel Deaconess Medical Center and Massachusetts Institute of Technology (MIT), both located in Cambridge, Massachusetts. MIMIC-IV contains extensive patient data, including demographics, hospitalization records, diagnoses made under the International Classification of Diseases, Ninth Revision (ICD-9), laboratory tests, prescription drugs, procedures, fluid balance, discharge summaries, bedside vital sign measurements, treatment notes, radiology reports, and survival data. The MIMIC-IV database consists of numerous linked tables that use standardized ICD-9 numbers to describe the data of each ICU patient.

Data preprocessing in this study entails some procedures and techniques meant to handle missing or insufficient data, as depicted in Fig. 1. The primary procedures for Preprocessing data for imputation usually entail: Missing Data Detecting: Identifying that attributes or variables within the dataset contain missing values. To approximate missing values, one can do the following: remove rows or columns containing missing values; replace missing values with the mean of the available values within the corresponding attribute; create predictive models to estimate missing values based on relationships with other variables, and utilize statistical distributions to create random values that roughly match the distribution of the available data. Use a large query based on a specific value from the chart events table of the MIMIC-IV database in the itemid column to obtain the vital signs dataset of ICU patients.

The total raw data from the ICU patient vital signs dataset is 7.786.008 with missing data (Table 2), has a unique id or stay_id for each patient from 38675535 to 37145532, and the duration of each patient’s stay in the ICU from 2182-01-25 07:00:00+00:00 to 2146-04-27 09:33:00+00:00.

Our proposed model analyzes eight vital sign features: heart rate, systolic blood pressure, diastolic blood pressure, mean blood pressure, respiratory rate, body temperature, oxygen saturation, and glucose level. We used an inner join to get a more extensive dataset. Consequently, our final dataset contained 119,948 unique ICU patients (vital signs) as a result (Table 3). This entire dataset includes the min and max data of vital signs recorded during a patient’s ICU stay.

Standardization, after imputation of the missing data the dataset was normalized using the Min-Max Scaler [33,34], this procedure is vital to guarantee uniformity or standardization among the features. The following Eq. (1) illustrates the data normalization: (1)xnorm=xinp−xminxmax−xminwhere xnorm denotes the normalized data; xinp denotes the input value; xmin denotes the minimum value of the feature; and xmin denotes the maximum value of the feature.

We have a dataset structured as m×n matrix, where n stands for features and m for cases. The training data (Xrawt∈Rm×n) and the testing data (Xrawt′∈Rm′×n) are two halves of the original data set. We intentionally manufactured the missing data in (Xrawt∈Rm×n) and (Xmisst′∈Rm′×n), where duplicate data was initially provided with these missing values (Fig. 2). This was done following the division of data to produce training and test sets. New versions of the training and testing data (Xmisst∈Rm×n) and (Xmisst′∈Rm′×n), respectively, are obtained when the missingness value is created. To add missing values to the clean test data during the testing phase, (Xmisst′∈Rm′×n), we repeat the same training process, resulting in the corrupted test data (Xmisst′∈Rm′×n). Subsequently, after training the DRes-CNN (refer to Algorithm 1), we assess its performance on (Xmisst′∈Rm′×n) to impute the missing data, as depicted in Fig. 1. Similarly, after the completion of the imputation process in our scenario, artificial data emerges wherein all values have been altered due to the convolution operation. Therefore, as shown in Fig. 1, we use masking on the newly created data matrix to recover the imputed values.

The proposed method utilizes a specific type of neural network architecture known as Convolutional Neural Networks (CNN). Our network architecture, which is a dense convolutional neural network with residual connections (DRes-CNN), is depicted in Fig. 2. This DRes-CNN network structure resembles the original CNN architecture for image super-resolution [20], but is modified to fit tabular or time-series data in capturing complex patterns and relationships within structured data [18]. This architecture is made to maximize the information flow between network levels using a straightforward connecting scheme. All other levels are directly connected. Every layer passes its feature map to all the following levels and receives extra input from all prior layers to preserve the feed-forward character of the system. Dense networks are one type of CNN that connects each layer layer in a feed-forward way. These dense networks increase feature propagation, stimulate feature reuse, and solve the vanishing-gradient problem in contrast to typical convolutional networks, where each layer is merely connected to the next layer.

The convolutional layers in our proposed DRes-CNN architecture are specifically designed to detect dependencies between features in the EHR dataset, both temporally and contextually. By employing dense and residual connections, the model enhances feature propagation, reuses information from earlier layers, and improves the learning process for long-range feature dependencies. Dense and residual connections function differently. While feature maps in residual connections are combined by summation before being transmitted to a specific layer, feature maps in dense connections are merged based on all prior feature maps. The benefit of having both kinds of connections is that, in a dense connection, all of the features from the prior convolution block may be used, whereas, in a residual connection, we are limited to using one historical feature map.

As can be seen in Fig. 2, the suggested DRes-CNN architecture consists of two residual connections and ten convolutional layers with progressively more filters. The residual connection in Fig. 2 is the solid line that carries the input layer to the summing operator. In ideal circumstances, a deep neural network with more layers can outperform shallower networks and drastically minimize error rates. To outperform a straightforward deep neural network, we incorporate residual blocks.

The architecture in our model has 64 filters with multiple kernel sizes of 3 × 3, followed by the LeakyReLU activation function. After multiple convolution layers, there is residual linking which is done by adding the output of the first layer to the output of the last layer before the next convolution layer. This architectural design helps in learning more detailed features and retains the original information of the input. This study, provided detailed descriptions of our architecture, specifying that it consists of ten convolutional layers with both dense and 2 residual connections. We explained the advantages of using both connection types, as dense connections facilitate the utilization of features from previous convolutional blocks, while residual connections enhance the flow of information by summing the outputs of earlier layers with later ones. We also justified the choice of architecture by noting that deeper networks tend to outperform shallower counterparts, especially when incorporating residual blocks that minimize error rates. The total parameters in the model amount to 8.545, which also includes the weights and biases in each convolution layer. To offer transparency, we included Table 3, which outlines the architecture modification information, detailing output shapes and the number of parameters for each layer. The architecture in our model has modification information shown in Table 4.

Residual connections are introduced after Conv 5 and Conv 10, which are created by adding a convolutional layer’s output to a preceding layer’s output before the layer’s activation function is sent through (Table 3). A situation with randomly generated missing data in the input data matrix and the same whole data matrix produced at the output is shown in Fig. 3. Assume that we have a kernel with dimensions M × N (where M represents the number of rows and N denotes the number of columns), and there’s a missing value for a unit Oij within the feature map. An input-weighted total within a given patch size M×N is computed to find the value of Oij. These kernel weights are adjustable parameters that are learned by utilizing the linear characteristics present in the given data. Once optimized during the training phase, these weights can then be employed for imputing missing data during the testing phase. Eq. (3) illustrates the process by which a filter convolves over the data and imputes the missing data Oij.

(3)Oij=f(∑m∑nIi+m,j+nKm,n+b)where Km,n is the weight (kernel) at position (m,n) used for convolution. b representing the bias term. f represents a residual function. This process involves the summation of the dot product of each position in the input data between the input and the kernel weights, which is then added with a bias. The mathematical function for LeakyReLU as shown in Eq. (4). (4)f(x)={xjikax≥0∝xjikax<0where ∝ is a small positive value Thus, when x is less than 0, the output is ∝x, while when x is greater than or equal to 0, the output is x. LeakyReLU is chosen as the activation function due to its effectiveness and widespread use in practical applications. Additionally, LeakyReLU can help neural networks learn patterns and relationships between features in the dataset. Usually in ReLU, negative input values become zero, while positive values do not change. However, in LeakyReLU, when the input is negative, it does not become zero but is scaled by a small positive value Eq. (4). This can help overcome the “dead neuron” problem that can occur in ReLU, where the neuron saturates at negative values and does not update its weights during training. After several layers of convolution, there is a residual linking which is done by adding the output of the first layer to the output of the last layer before the next convolution layer. The imputation of a randomly missing value in a data sample that goes through a trained model is further demonstrated in Fig. 3. Once the model undergoes training, it gains the capability to impute missing values through the learned kernels.

The evaluation process entails using the available data to train the network to predict missing data, with the model being adaptable for tabular or time series data. Important features are preserved across levels by using jump connections. Several hyperparameters, such as the Adam optimizer, 200 epochs, batch sizes of 16 and 32, and a learning rate of 0.001, are used to maximize the model’s performance. The model’s activation function is linear, and the loss function is a mean squared error. By partitioning the dataset into multiple subsets, we were able to validate the model’s performance across different data segments, thereby enhancing the generalizability of the results. Additionally, a learning rate schedule based on exponential decay is employed to enhance the training. Algorithm 2 presents the pseudocode for the DRes-CNN algorithm.

During training, the learning rate of the model can be adjusted to facilitate a more efficient convergence to the optimal solution. Combining optimization methods with hyperparameters improves the performance of the DRes-CNN algorithm. The Intel^® CoreTM i9-9920X CPU running at 3.50 GHz, 490,191 MB of RAM, and GeForce 2080 RTX Ti from NVIDIA Corporation GV102 (rev a1) were the characteristics of the personal computer (PC) used to train the network. Pytorch 1.7.1 package together with Python were used to create the network.

Model evaluation in filling data with DRes-CNN involves evaluating how the trained deep learning model is used to predict missing values in the dataset. Model performance evaluation uses the root mean squared error (RMSE) metric to assess the average error produced by the model [9]. The smaller the value of mean absolute error (MAE) and RMSE, the better the performance of our imputation method. MAE and RMSE are used as model evaluation metrics [9] and are described in Eqs. (5) and (6). (5)MAE=1n∑j=1n|(yact−ypred)^|

(6)RMSE=1n∑j=1n(yact−ypred)^2where yact is the actual value, ypred^ is the predicted values by the regression model, and n number of observations/rows [9].

This section presents the study results of our suggested approach and evaluates the significant improvement in handling missing data performance compared to other methods. We use the MIMIC-IV dataset described in Section 3.2. At first, data cleaning for missing data are randomly added, replacing the missing values with zero. Next, our proposed DRes-CNN approach is used to impute those missing values, and other imputation techniques, such as U-Net and LL-CNN, are selected for comparison purposes. Moreover, the robustness of the DRes-CNN approach is tested with various missing ratios (10%, 20%, 30%, 40%, 50%, 60%, and 70%) on the MIMIC-IV dataset. We also evaluated the imputation performance of DRes-CNN by using three supervised learning algorithms to train classifiers on the imputed data. Experiments were conducted three times with random data partitioning (90% for training and 10% for testing), and the average classification accuracy along with the standard deviation was calculated as the final performance score. Initially, 10% of attribute values from all clean data were artificially removed to generate a dataset with missing values.

This section provides a thorough examination of comparing the proposed technique with alternative imputation methods. Table 4 illustrates the assessment outcomes (RMSE) acquired through various approaches when dealing with randomly generated missing values, alongside other advanced imputation methods like U-Net, LL-CNN, and DRes-CNN. Experimental results were obtained through various missing ratios (i.e., 10%–70%). It can be seen in Table 5 that the a substantial difference in performance between the proposed method and the others. Notably, regardless of the missing ratio, the RMSE results remain relatively stable, indicating that the proposed approach maintains its efficacy even when the level of missing data increases. Fig. 3, a graphical depiction of Table 5, makes this distinction easy to see. The best value for each dataset is displayed in a column of Table 4 in bold type. Particularly, the superiority of the DRes-CNN method is underscored, showcasing its adeptness in accurately imputing missing values within vital signs data, even under high missing data scenarios. Our results demonstrated that the Dres-CNN model consistently outperformed the other models, particularly when handling higher ratios of missing data. This performance can be attributed to key architectural enhancements, such as the use of skip and residual connections, which allow the model to retain both high-level and low-level features across layers. This retention is critical for capturing complex spatial relationships and non-linear dependencies, which are essential for accurate imputation.

The experimental findings showcased that the several models, trained used batch size of 16, 64 segments, a 20% missing ratio, and undergoing 200 epochs, attained an impressive on the MIMIC-IV dataset (as depicted in Table 6). Through scrutinizing the model’s efficacy across varied segment sizes and missing rates, we discern its capability to address an array of data patterns and handle missing data occurrences that mirror real-world scenarios, wherein data may manifest varying levels of incompleteness.

From the data presented in Tables 5 and 6, it’s evident that DRes-CNN surpasses both U-Net and LL-CNN in performance. The model’s ability to generate low RMSE suggests that the imputed data closely aligns with the true values missing from the dataset. A primary factor contributing to DRes-CNN superiority in data imputation is its tailored design for data processing tasks, where missing or corrupted data is common. Also, we conduct a comparison of each attribute from U-Net, LL-CNN, and DRes-CNN (Table 7).

Table 6 presents a comparison of the RMSE values of three different models: U-Net, LL-CNN, and DRes-CNN, in predicting various vital signs attributes. The analysis results show that DRes-CNN consistently has a lower RMSE compared to U-Net and LL-CNN for each attribute. This indicates that DRes-CNN tends to perform better in predicting vital signs values. However, there were variations in model performance between attributes, where some attributes had smaller RMSE than others, such as “spo2” which had relatively low RMSE for all models. The lower the RMSE value, the closer the model prediction is to the true value, so models with lower RMSE tend to have more accurate predictions. A direct comparison between the models can provide insight Into the relative merits of each in predicting certain attributes, although overall DRes-CNN dominates. The best model to use for the vital sign prediction challenge can be chosen with the help of this analysis, as well as highlighting areas where improvements or adjustments may be needed.

The Ablation Study

In this study, we conducted an ablation study to evaluate the performance of our proposed Dres-CNN model for handling missing data in structured datasets. The study focused on assessing the impact of different hyperparameters, and missing data ratios. We tested the model with varying missing data percentages (10% to 70%) and systematically tuned hyperparameters such as segment size (8, 16, 32, 64), batch size (16, 32), and learning rate (0.001), as well as the optimizer (Adam) and the number of epochs (200). to determine their influence on imputation accuracy. A comprehensive experiment and a detailed comparison of the results are provided in the subsequent section with an in-depth analysis shown in Fig. 4.

The performance of each model was assessed using the parameter RMSE. Our results demonstrate that the Dres-CNN model outperforms traditional methods, such as LL-CNN and U-Net, especially when dealing with higher missing data ratios. First, we evaluated the effect of different missing ratios, ranging from 10% to 70%. The results showed that the model performed best at lower missing ratios (around 10%), with performance gradually decreasing as the missing ratio increased. This indicates that the model is more efficient at handling datasets with fewer missing entries. Next, we examined segment sizes (8, 16, 32, 64) and found that larger segment sizes (32 and 64) provided better accuracy, as they allowed the model to capture a broader context, though they required more computational resources. We also set the number of training epochs to 200, which appeared to strike a balance between sufficient training time and avoiding overfitting. In terms of batch size, we tested sizes 16 and 32, with the larger batch size proving to be more effective due to its more stable gradient updates during training. The Adam optimizer was chosen for its adaptive learning rate, which allowed the model to converge efficiently. Finally, we found that a learning rate of 0.001 provided the best balance between speed and accuracy, ensuring the model did not converge too quickly or slowly.

Our proposed DRes-CNN approach shows superior performance compared to other state-of-the-art imputation methods, such as U-Net and LL-CNN. Our proposed validation technique involves splitting the data into 90% for training and validation and 10% for testing. This split allows the model to train on a significant portion of the data while using the separate test set to rigorously evaluate the model’s performance on unseen data. Performance evaluation based on the RMSE value shows that the DRes-CNN architecture is more effective in learning features and estimating missing values accurately, even with a significant amount of missing data. Fig. 3, a graphical depiction of Table 4, makes this distinction easy to see. The best value for each dataset is displayed in a column of Table 4 in bold type. As a result, the DRes-CNN architecture produces lower RMSE values compared to the U-Net and LL-CNN architectures. The experimental results also show that in most cases, the DRes-CNN approach outperforms other methods in various data imputations. Although the imputation of missing data with LL-CNN architecture gives better results on the original (clean) version compared to U-Net architecture, DRes-CNN architecture shows better performance on the MIMIC-IV dataset. The superior performance of these imputation methods is most likely due to the suitability of the particular learning algorithm to the data used. Residual connections facilitate deeper network training and utilize convolutional layers with the LeakyReLU activation function to extract features from the input data.

The architecture of DRes-CNN incorporates specialized features like convolutional layers with LeakyReLU activation functions to extract features from input data and have residual connections to facilitate the training of deeper networks. These characteristics render it well-equipped to handle missing or corrupted data within datasets. The ability of DRes-CNN to handle temporal and spatial dependencies within data is very useful in situations when missing data appears sequentially, like in time series data. By leveraging convolutional and pooling layers, DRes-CNN effectively captures these dependencies, enhancing predictive accuracy and enabling more effective imputation of missing data values.

Additionally, DRes-CNN considers spatial relationships among features by reorganizing data or applying convolution operations with larger windows to capture broader contexts, facilitating better data imputation. Non-linear information is utilized through non-linear activation functions and optimized training methods, allowing the network to adjust its weights and biases according to the complex data structure. Through optimized training and testing phases, the network is trained on incomplete data to optimize imputation performance and then tested on incomplete data to evaluate its ability to accurately impute missing values.

To see the robustness of the DRes-CNN model, we use box plots to illustrate the impact of handling data. Box plots show the median value, interquartile range, and outliers, giving a clear view of the distribution of the data. Initially, the box plot depicts the data distribution before imputation (Fig. 5a), followed by a representation of the post-imputation process (Fig. 5b to d). The noticeable trend is that the proposed imputation method consistently handles missing data with values to the data mean. Comparing the box plots of the imputed data with the raw data shows a narrower interquartile range and a reduction in data dissemination (Fig. 5d). These observations suggest that the imputation method, rooted in DRes-CNN, effectively minimizes data variability without introducing bias, confirming its suitability for the task at hand.

To Validate the robustness of our proposed data imputation model, we conducted a comparative analysis against recent studies that use the existing architecture of the CNN method. However, the use of DRes-CNN architecture for data imputation is still not common. We also use some non-health datasets to test the robustness of our architecture (Table 8). To the best of our knowledge, we are the pioneer in applying the DRes-CNN architecture for data imputation in medical records or other datasets. Our simple DRes-CNN model shows outstanding performance, as evidenced by Table 7, in terms of RMSE beyond previous studies. In the research conducted by Yoon et al. [35], the imputation method used was multi-directional recurrent neural network (M-RNN), which was evaluated on the MIMIC-III database. The evaluation results showed that M-RNN had an RMSE of 0.0295, indicating a fairly good level of imputation accuracy in the context of such medical data.

When it comes to imputing missing data across different datasets, the DRes-CNNs model performs exceptionally well, beating other current techniques such as M-RNN and U-Net50. The DRes-CNNs continue to demonstrate greater accuracy in other databases, including Beijing Multi-Site Air Quality, MIMIC III, and IV, where this trend is also evident. The DRes-CNNs routinely yield the lowest errors even among the suite of suggested models, which includes U-Net and LL-CNN, demonstrating its efficacy in managing challenging data imputation jobs. The DRes-CNNs model’s precision and resilience are highlighted by this comparative analysis, which makes it a highly useful tool for situations where exact imputation is crucial.

Despite the proposed DRes-CNN has a good performance. However, to capture the non-linear correlations in the data, for example, the DRes-CNN technique employs learnable weights that are updated iteratively. However, if there are no geographical links in the data, the learning process can proceed incorrectly and produce poor imputation. As is common with most healthcare datasets, our datasets comprised both numerical and categorical factors. It’s important to keep in mind, though, that the results of our method could not be the same for data that just includes categorical variables. Imputation may be difficult with this kind of data since there may not be many learnable inter-variable correlations. But solving this problem was outside the purview of our work.