Exploring the role of country social and medical characteristics in patient level mortality in COVID-19 pandemic using Unsupervised Learning

3.1Data preparation

We used data from “COVID-19 Data Repository by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University” for the total number of Cases, Deaths and Recovered.

For “Smoking” we got the data from “Wikipedia: List of countries by cigarette consumption per capita” [19].

The medical and the socio-economic Data came from WHO [20]. These data were age-standardized per 100.000 population by cause.

For the proposed analysis we processed data for 101 countries including the following twenty-two (22) features of each country:

Indicative features of the Countries can be found in the graphs below.

Figure 1.

Descriptive Statistics based on WHO data.

Figure 1.

continued

China, India, Indonesia and Japan have a big proportion of older people.

Figure 2.

Based on data from WHO.

The study is using the “Total death toll” as the depended variable. We normalized the “Total Death toll” number by dividing it with the population of the country. We used the logarithm of this value, because after the former division the resulting value was extremely small.

After this, we transformed the “Total Death toll” values into 3 separate classes “Low”, “Middle” and “High”. Each row was associated with one class according to Log Normalized value of “Total Death toll”. Thus, the initial regression problem turned into a new classification problem.

Our purpose was to find a model that fits the data with high accuracy so that, we know it is a good model although accuracy was not our primary goal. After this we will be able to take the feature importance.

The dataset was highly imbalanced as can be seen in the following chart.

Figure 3.

Histogram of Countries according to the death toll paid.

The challenge of working with imbalanced datasets is that most machine learning techniques will ignore, and in turn have poor performance on, the minority class. Here we have 2 minority classes which are the “Low” (the number of countries low number of deaths) and the “High” (the number of countries high number of deaths).

Our approach to addressing imbalanced datasets was to oversample the minority class. The simplest approach involves duplicating examples in the minority class, although these examples do not add any new information to the model. Instead, new examples can be synthesized from the existing examples. This is a type of data augmentation for the minority class and is referred to as the Synthetic Minority Oversampling Technique or SMOTE for short [21].

3.2 Extreme gradient boosting approach

XGBoost stands for “Extreme Gradient Boosting”, where the term “Gradient Boosting” originates from the paper Greedy Function Approximation: A Gradient Boosting Machine, by Friedman. [22]

Figure 4.

ROC curves of the XGBoost model application. The 3 curves represent the 3 iterations of the cross-validation technique.

The XGBoost [23] library implements the gradient boosting decision tree algorithm.

This algorithm goes by lots of different names such as gradient boosting, multiple additive regression trees, stochastic gradient boosting or gradient boosting machines.

Boosting is an ensemble technique where new models are added to correct the errors made by existing models. Models are added sequentially until no further improvements can be made. A popular example is the AdaBoost algorithm that weights data points that are hard to predict.

Gradient boosting is an approach where new models are created that predict the residuals or errors of prior models and then added together to make the final prediction. It is called gradient boosting because it uses a gradient descent algorithm to minimize the loss when adding new models.

This approach supports both regression and classification predictive modeling problems.

3.3Model estimation

We divided the full dataset into train dataset and test dataset. We trained several algorithm on the train dataset and then tested their performance on the test dataset. The first effort was to use Logistic Regression. Due to low accuracy (9%), we rejected it. The Tree Classifier was the second model we tried. It was rejected also due to instability to results. Then we turned to Random Forest ensemble model with 100 estimators. We used max depth equal to 15 and max features equal to 5 to prevent overfitting. This model gave accurate results of 98% and above. The Cross-Validation accuracy gave 84%.

Lastly, we tried the XGBoost. An algorithm which gave the best estimation. The accuracy was approximately 96%.

From qualitative point of view, we tested the model on the test dataset (Fig. 4). We used cross validation in ROC study as well.

Due to limited number of data (only 101 countries after removal of all null values) the ranking of the importance of each feature was difficult to be stabilized. That resulted in position changing in the sorted importance table.

So, we decided to run the model many times (1000), take the mean position of each feature importance and sort the table according to this value.

The results are as follows.

The values below the “Mean Pos” column is the mean position a feature takes in a table sorted by importance. The “Std” column is the Standard Deviation in the position.

So, we can see that “Asthma” is in the 1st position and has 0.29 standard deviation. This means that “Asthma” is the most important feature and regardless how many times we run the model it keeps this position.

On the other hand, the feature “Life Expectancy from birth for both sexes” can be moved two positions up or down.

This way we can be more objective in determining each feature’s importance. Additionally, we can reach to other conclusions as well. In features “Population rate under 15 Years Old”, “Rate of deaths due to Tuberculosis”, “Rate of deaths due to HIV”, “Rate of deaths due to lower respiratory infections” and “Rate of deaths due to congenital heart defects”, we can see that the variation in importance position is high. It is probably because there is significant difference between African countries and other countries in the number of death toll due to these causes.

In the table below we can see the differences between our results and literature results as they have been mentioned in literature part.

Many differences are due to different diseases and factors we study. Despite these differences we can see that Diabetes, Respiratory problems and heart diseases are common in our research and the general literature research. However, in our study we research on wide scale dataset for 101 countries strengthening the assurance and the accuracy of the results.

4.1Data preparation

Our analysis was based on a publicly available dataset [24] from the “Open Data General Directorate of Epidemiology of Mexico” for November 2020. The dataset contains the patient’s medical features, along with their social characteristics.

Medical features are:

Social features are:

The starting point of the analysis was the data cleansing process. The “Not specified” in several fields had numerous appearances in the dataset. This fact led to the exclusion of several features, and a significant number of records was discarded from the initial dataset.

The “Nationality” and “Immigrant” features were discarded since they were irrelevant to our purpose. In addition, the “Intubation” feature was dropped because after a careful examination of the data, we saw that no death occurred when this feature had the value “No”.

The next stage in the process was feature engineering. We subtracted the date of hospitalization from the date of symptoms to create intervals for every five days, to create a factor that represents the days interval after the first symptom’s appearance. Intervals were created for the age feature as well to transform the number to factor. So, the problem we deal with, is the identification of main factors that contribute the most in the mortality of COVID-19 disease by exploiting the dataset that was descripted above.

4.2Descriptive statistics

The above features can be seen in the following diagrams using descriptive statistics. This way is easier to get a full image of the dataset.

Table 4

Descriptive statistics from Mexico Patients dataset

4.3Algorithmic approach

Our effort is to address the identification of main factors that contribute the most in the mortality of COVID-19 disease in the country of Mexico with unsupervised learning as a use case for our multi-level analysis.

In this case, we have a set of N observations (x1, x2, …, xN) of a random p-vector X having joint density Pr(X). The goal is to infer the properties of this probability density directly without the help of a supervisor providing correct answers or degree-of-error for each observation.

As [25] mention, it is always difficult to validate the inferences drawn from the output of most unsupervised learning algorithms opposite to supervised learning where one can always measure the error and subsequently the accuracy of the method.

Association rule analysis is a tool for mining commercial databases. One can use it to find values of the variables X=(X1,X2,…,Xp) that appear most frequently in the database. It usually is applied to binary-valued data Xj∈{0,1}, which becomes the “market basket” analysis. In “market basket”, the observations are sales transactions, like those at the store’s checkout counter. The items sold in the store are the variables of the model. Each variable Xj in each observation i, is a binary variable; xi⁢j= 1 if the j-th item is included in the transaction, whereas xi⁢j= 0 if it was not purchased. The variables that frequently have joint values of 1 represent items that are frequently bought together.

Association rules show potential relationships between data items with a probability, within large data sets. Association rule mining can help in discovering sales correlations in transactional data and this is its primary use. It uses machine learning models to analyze data for patterns in a database. It can identify frequent if-then associations, which represent the association rules.

Figure 5.

Most frequent diseases and features like sex, days passed from symptom manifestation to hospitalization, age group.

An association rule consists of two parts: an antecedent (which is the “if”) and a consequent (which is the “then”). An item found within the data is an antecedent. This in combination with an item found is a consequent.

Association rules use itemsets for their calculation. Itemsets consist of two or more items. If one used all the possible itemsets to create rules, the rules would be so many that they would be useless. Association rules are created from rules well-represented in data.

There are two indicators about the strength of an association rule and they are the support and the confidence which are two parameters we will describe below in Analysis section.

There is also a third parameter which measures the correlation between data points and it is calculated as the ration of confidence to support.

4.4Analysis

We applied Association Rules in our analysis. Although it is primarily used in Commercial Product Promotion, we attempted using it in finding the most usual comorbidities and infer how they are contributing to mortality. Our original thought was that if we associate the human body with a market basket, we can map all diseases to items in the basket. We assume that the death of the human body is just another item in the basket. A transaction, in our case, is a set of comorbidities.

Suppose the Apriori algorithm results in association rules with death on the right-hand side of the equation. In that case, we can find the most frequent associations (comorbidities) that included death as a result.

The Apriori algorithm, as we saw above, returns three main results as components. These are:

Support refers to the default popularity of an item and can be calculated by finding the number of transactions containing a particular item divided by the total number of transactions.

Confidence refers to the likelihood that an item B co-exists if item A exists.

Lift (A → B) refers to the increase in the ratio of getting B when you already have item A.

The Confidence saws which of the comorbidities set is more frequent with patients of type Death.

Through Lift we can infer how much the mortality increases regarding the comorbidities of a patient.

Figure 6.

Grouped matrix visualization.

In the diagram below, one can observe the most frequent comorbidities along with two other factors (Age interval and Days before hospitalization) in the full dataset. We should keep in mind that this diagram was created from the original dataset before applying the Apriori algorithm. This means that it comprises people who survived as well.

It is obvious that Pneumonia is the more frequent disease, followed by Hypertension Diabetes and Obesity.

Most of the people who died were men, although they were hospitalized almost immediately (days [0,5]) after the COVID-19 symptoms manifested, the age group was [40,60], and most of them were monitored by Mexico’s System USMER.

On the other hand, we can observe that there many variables with a low frequency like all of the day intervals above 15 days, other diseases under the variable Other, Asthma, Immunosuppression, CRD, Smoking, CKF, Heart diseases, and Age between 80–100 and 0–20. These low frequent factors do not necessarily mean that they are not responsible for the death of patients. They indeed affect results like unknown factors. It is just that these diseases exist in limited number in our sample.

4.5Analytic results

The results of our analysis following the proposed algorithmic approach were as below.

The above matrix can be read as follows; The column “lhs” represents the cluster with the comorbidities that result into “rhs” value (the death of the individual).

From the above matrix, one can see that the combination of Pneumonia, Diabetes, Heart Diseases, and CKF, even though the patients were under the supervision of VRDM, and they were hospitalized immediately, has the most contribution to a Death result. This means that someone with all these diseases has a probability of 2,886% bigger than someone else to die. Also, this combination was found at a rate of 80% in patients who died. According to the above translation, one can infer for the rest of the cases.

To visualize the grouped matrix, we use a balloon plot with antecedent groups as columns and consequents as rows (see Fig. 6). Since there is only one consequent (death = Yes) there is only one row. The color of the balloons represents the aggregated interest measure in the group with this consequent and the size of the balloon shows the aggregated support. The aggregation function is the median value in the group. The number of antecedents and the most important (frequent) items in the group are displayed as the labels for the columns. Furthermore, the columns and rows in the plot are reordered such that the aggregated interest measure is decreasing from left to right, placing the most interesting group in the left side.