Multivariate Statistical Analysis of Clinical Factors Influencing COVID-19 Recovery Time

Preprint — COVID-19 Recovery Analysis 1 Multivariate Statistical Analysis of Clinical Factors Influencing COVID-19 Recovery Time Author: Mr. Joditya Roy B-Tech Sophomore Netaji Subhash Institute of Technology Date: 10th October, 2025 The author gratefully acknowledges the invaluable support and encouragement of his father, Mr. Arjun Roy whose guidance was instrumental in the completion of this research Preprint — COVID-19 Recovery Analysis 2 Abstract In the early months of the COVID-19 pandemic, a tertiary care center launched an educational study to demonstrate applied data analysis techniques using real-world clinical data. We retrospectively reviewed electronic records of 60 adult patients, aged 21 to 79 years, admitted with confirmed SARS-CoV-2 infection. Each patient was assigned to a “Mild” or “Severe” group based on initial oxygen supplementation requirements. Key variables—including Patient_ID, Age, Gender, Hospital_Days, Oxygen_Level, Recovery_Time, and Antibody_Level. Through a combination of descriptive statistics, univariate histograms and density plots, bivariate scatterplots with regression overlays, group comparison tests, and a multivariable linear regression model, this study showcases how routine clinical metrics can be visualized and statistically evaluated. While our findings underscore the limited predictive power of simple demographic and laboratory measures for recovery time, they also highlight the importance of integrating additional biological, therapeutic, and socio-environmental factors to develop more robust predictive models for patient outcomes. Patient data presented are de-identified and used solely for educational and illustrative purposes. Preprint — COVID-19 Recovery Analysis 3 COVID-19 Data Analysis: R Code and Results (1) Importing Dataset to perform Welch’s two sample T-test This section loads the required R libraries and imports the dataset from an Excel file. The dataset contains COVID-19 patient details including age, gender, oxygen level, recovery time, and antibody levels (we have taken them are variables). The hypothesis being tested in the code is whether there is a significant difference in the mean oxygen levels (SpO2) between two groups: "Mild" and "Severe" COVID-19 patients. The statistical method used is the independent two-sample t-test (Welch's ttest), which compares the means of these two groups. (1.1) Hypothesis Statement  Null Hypothesis (H0): There is no difference in the mean oxygen level between the Mild and Severe groups [the difference in means = 0].  Alternative Hypothesis (H1): There is a difference in the mean oxygen level between the Mild and Severe groups [the difference in means ≠ 0]. (1.2) Algorithm  The t-test (t.test) was performed on the Oxygen_Level variable between the two groups (Mild vs Severe).  The result output includes the t-statistic, degrees of freedom, p-value (0.1149), 95% confidence interval, and the sample means for each group.  A boxplot command is prepared (using ggplot2) to visualize the distribution of oxygen levels in the two groups, making it easier to compare the data visually. Preprint — COVID-19 Recovery Analysis 4 (1.3) Statistical Terms and Process  Independent Two-Sample T-Test: This test compares the means of a continuous variable (Oxygen_Level) between two independent groups (here, "Mild" and "Severe" COVID severity) to determine if they are statistically significantly different.  T-value: The test statistic calculated for the difference between group means.  Degrees of Freedom (df): Represents the sample size adjustment for statistical inference.  P-value: Indicates the probability that the observed difference is due to chance. A p-value less than 0.05 is typically considered significant. In this output, the p-value is 0.1149, so the difference is not statistically significant.  Confidence Interval: The range in which the true difference between means lies, with a specified probability (95%). Preprint — COVID-19 Recovery Analysis 5 Further using the data, a Boxplot was drawn. a. The boxplot visually compares the spread and central tendency of oxygen levels between the Mild and Severe groups. b. The boxplot was drawn using the ggplot2() package in R c. This visualization supports the statistical test result where the difference in mean oxygen level between Mild and Severe groups is not statistically significant, as the two groups show similar oxygen level distributions. d. Overall, the assumption from the plot is that oxygen level differences between COVID severity groups are minor or not pronounced in this sample. Preprint — COVID-19 Recovery Analysis 6 (1.4) Result 1. The null hypothesis of this t-test is that there is no difference in mean Oxygen_Level between Mild and Severe COVID groups. 2. The test statistic (t = 1.6055) and corresponding p-value (p = 0.1149) indicate that the observed difference between groups is not statistically significant at the commonly used threshold (0.05). 3. The 95% confidence interval for the difference in means is from -0.299 to 2.667, which includes zero. This supports the lack of a significant difference. 4. Sample means for each group are 94.32 (Mild) and 93.14 (Severe), so the Mild group has a slightly higher average Oxygen_Level, but this difference could easily occur by random chance due to sample variation. (1.5) Analysis of Results 1. These t-test results mean that, based on this data, there is not enough evidence to claim that COVID-19 severity (Mild vs Severe) results in significantly different average blood oxygen levels. 2. Even though the boxplot visually shows some difference, statistical analysis suggests this is not robust. (1.6) Conclusion: 1. The hypothesis of a substantial difference in Oxygen_Level between severity groups is not supported here. This helps inform clinical understanding and future research design in the study of COVID-19 patient outcomes. Preprint — COVID-19 Recovery Analysis 7 (2) Histograms for Continuous Variables Histograms display the frequency distribution of continuous variables such as Age, Hospital Days, Oxygen Level, Recovery Time, and Antibody Level. This helps to understand the spread and distribution shape. The histogram was drawn using the ggplot2() package in R. (2.1) Interpretation: 1. The Antibody_Level histogram shows most values clustered between 100 and 200, with moderate spread and a few outliers. 2. Other variables like Age or Hospital_Days may show different patterns, such as skewness or uniformity, which these histograms reveal. Preprint — COVID-19 Recovery Analysis 8 (3) Scatter Plots to Check Relationships (3.1) Age vs Recovery_Time Scatter plots are used to examine relationships between variables. Here, Age is plotted against Recovery_Time with smooth trend lines to observe patterns This scatter plot illustrates the relationship between Age and Recovery Time (in days). Each dark red point represents an individual in the dataset, with their age on the x-axis and recovery time on the y-axis. (3.1.1) Conclusion: 1. The scatter plot reveals a weak positive relationship: as age increases, there is a slight tendency for recovery time to increase as well. 2. However, the spread of points indicates considerable variability, suggesting that age alone does not strongly predict recovery time in this sample. 3. The line is relatively flat, reinforcing that any association between age and recovery duration is minor. Preprint — COVID-19 Recovery Analysis 9 (3.2) Oxygen_Level vs Recovery_Time In this scatter plot, Oxygen_Level is plotted against Recovery_Time (3.2.1) Conclusions 1. There is a very slight tendency for recovery time to increase as oxygen level increases, but the relationship is weak. 2. The points are widely scattered around the regression line, indicating high variability and little predictive power. 3. Overall, oxygen level does not strongly determine or predict recovery duration in this dataset. Preprint — COVID-19 Recovery Analysis 16 Key Implications/ Findings 1. The comparison of oxygen levels between Mild and Severe COVID-19 groups revealed no significant difference (t = 1.6055, p = 0.1149), supported by overlapping boxplot distributions and Welch’s t-test results. 2. Histograms and density plots showed that continuous variables such as Antibody_Level and Age follow approximately normal distributions, with Antibody_Level centered around 150 and moderate variability. 3. Scatter plots of Age vs Recovery_Time and Oxygen_Level vs Recovery_Time indicated only weak positive trends, demonstrating that neither age nor initial oxygen saturation strongly predicts recovery duration. 4. The multivariable linear regression model incorporating Age, Hospital_Days, Oxygen_Level, and Antibody_Level explained less than 8% of the variance in recovery time (Adjusted R² = 0.0106) and had no statistically significant predictors, indicating that additional factors must influence patient recovery. 5. Diagnostic checks confirmed no major violations of linear regression assumptions: residuals were approximately normal with no highly influential outliers, though slight heteroscedasticity suggests caution in inference. The analyses conducted—including group comparisons, univariate distributions, bivariate scatterplots, and multivariable regression—consistently showed that the selected clinical and demographic factors (age, hospital stay duration, oxygen saturation, and antibody levels) explain very little of the variability in COVID-19 recovery time, with no statistically significant predictors identified. Distributional visualizations revealed generally normal patterns for continuous measures but highlighted modest variability and the absence of distinct subgroups. Regression diagnostics confirmed that model assumptions were largely met despite slight heteroscedasticity and no influential outliers, underscoring that recovery trajectories are influenced by complex, unmeasured factors beyond those examined. These findings suggest that future research should incorporate additional biological, treatment, and socio-environmental variables to more effectively predict patient outcomes and guide personalized care strategies. Preprint — COVID-19 Recovery Analysis 17 References  R Core Team (2025). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.  Wickham, H. (2016). ggplot2: Elegant Graphics for Data Analysis. SpringerVerlag New York.  Kutner, M. H., Nachtsheim, C, Neter, J., & Li, W. (2005). Applied Linear Statistical Models (5th Ed.). McGraw-Hill/Irwin.  Field, A. (2013). Discovering Statistics Using R. Sage Publications.  Venables, W. N., & Ripley, B. D. (2002). Modern Applied Statistics with S (4th ed.). Springer.