A Comparative Analysis of Predictive Approaches for COVID-19 Recovery Rates: Evaluating Regional Variations and Uncertainty

3.2. Data Collection

The study used the publicly available COVID-19 Time Series Data dataset compiled by Niket Chauhan and distributed through Kaggle. The source dataset contains daily observations of confirmed cases, recovered cases, and deaths across countries and subnational geographic units. The downloaded dataset contained 156,292 observations and eight variables covering 22 January–15 November 2020. It represented 226 Country/Region labels and 973 distinct country–province/state geographic series across 299 observation dates.

To maintain consistency with the period displayed in the ARIMA, LSTM, and model-performance figures, the empirical analysis was restricted to 22 January–31 October 2020. This selected period contained 145,063 raw records, 225 Country/Region labels, 959 country–province/state series, and 284 observation dates. Records were subsequently aggregated by ObservationDate and Country/Region, producing 46,075 country–date observations.

The recovery rate was calculated as Eq. (1):

(1)

where represents the Country/Region unit and represents the observation date. Forty-eight aggregated observations with zero confirmed cases were removed to avoid division by zero. Seven observations produced recovery-rate values above one because the reported number of recovered cases exceeded the reported confirmed count. These reporting anomalies were also excluded. The final modelling dataset therefore contained 46,020 country–date observations.

Although the dataset provides broad international coverage, it is based on publicly reported administrative data. Differences in testing practices, case definitions, recovery definitions, reporting delays, retrospective revisions, and regional surveillance capacity may affect comparability. Healthcare infrastructure, population density, government interventions, vaccination, testing intensity, and socioeconomic conditions were not included in the empirical models. These factors are discussed only as omitted contextual variables and as priorities for future model development (Table 1).

Table 1. Dataset characteristics and analytical sample.

3.3. Low-Information Forecasting as a Stress Test

During the early stages of a public-health emergency, detailed healthcare, demographic, policy, and socioeconomic information may be incomplete or unavailable. The present study therefore deliberately restricted the feature space of the tabular models to Region_ID. This design was treated as a low-information stress test rather than as a representation of all determinants of COVID-19 recovery.

The restricted design makes it possible to examine how different predictive paradigms behave when contextual covariates are absent. Strong predictive performance under these conditions may reflect the model’s ability to reproduce patterns associated with coded regional membership. However, it may also indicate dependence on non-causal identifiers or memorisation of region-specific averages. Conversely, weaker performance may reflect conservative behaviour when the available predictor contains limited substantive information.

The findings should therefore be interpreted as evidence of model behaviour under information scarcity rather than as evidence that Region_ID causes differences in recovery rates. None of the models can identify the effects of healthcare capacity, population density, government policy, vaccination, demographic structure, or socioeconomic conditions because those variables were not included in the empirical feature set.

3.4. Data Pre-Processing

The data were cleaned, aggregated, and divided into chronological training and test sets using the following procedure.

3.4.1. Date Standardisation: Observation Date was converted to a consistent date format. The empirical period was restricted to 22 January–31 October 2020.

3.4.2. Missing Administrative Labels: Missing Province/State values were labelled “No province/state.” These values represented absent administrative subdivisions and were not imputed as epidemiological measurements.

3.4.3. Aggregation: Confirmed, Recovered, and Deaths were summed for each combination of ObservationDate and Country/Region. This produced one observation for each country or territorial unit on each date.

3.4.4. Recovery-Rate Calculation: Recovery rate was calculated as the number of recovered cases divided by the number of confirmed cases. Forty-eight observations with confirmed equal to zero were removed. Seven observations with recovery-rate values above one were excluded as reporting anomalies. Following these procedures, the final dataset contained 46,020 observations.

3.4.5. Regional Identifier: A unique Region_ID was assigned to each Country/Region unit. Region_ID was used as the sole input variable for Linear Regression, Random Forest, and Bayesian Linear Regression. It is a coded categorical identifier and should not be interpreted as a continuous, causal, demographic, or healthcare-related measurement.

3.4.6. Temporal Ordering: Observations were arranged chronologically. The earliest 227 dates, covering 22 January–4 September 2020, formed the training period and contained 35,167 observations. The most recent 57 dates, covering 5 September–31 October 2020, formed the test period and contained 10,853 observations.

3.4.7. Time-Series Construction: Chronologically ordered recovery-rate observations were used to construct the ARIMA and LSTM inputs. The same recovery-rate definition and empirical end date were maintained throughout the time-series analysis.

3.5. Mathematical Framework

The study evaluates three predictive models, i.e., Linear Regression (LR), Random Forest (RF) and Bayesian Linear Regression (BLR). Each of the models provides an alternative method of prediction of the Recovery Rate, and they are more sophisticated and possess a greater level of uncertainty estimation.

3.5.1. Linear Regression (LR)

Linear regression is a simple yet useful statistical tool, which estimates the dependence between a dependent variable (Recovery Rate) and an independent one (Region_ID). The model assumes such relationship is linear and it is described through the following equation Eq. (2):

(2)

where:

is the Recovery Rate (dependent variable),

is the Region_ID (independent variable),

is the intercept,

is the coefficient for the independent variable, and;

is the error term, which accounts for the random deviations not explained by the model.

This model relies on the Linear Regression with the assumption that the line between recovery rate and the region identifier is linear. It is simple, yet it can be helpful in modelling the linear trends of data, but it might not be in a position to reflect the complexity of COVID-19 recovery.

3.5.2. Random Forest (RF)

Random Forest was used to predict recovery rates from Region_ID, which was the only predictor supplied to the model. The model was configured with 100 trees, a maximum tree depth of 10, a minimum split size of two observations, and a random state of 42. Its tree-based structure enabled nonlinear partitions of the coded regional identifier without imposing the linearity assumption used by Linear Regression. However, the model did not include healthcare capacity, population density, government interventions, vaccination, testing, demographic characteristics, or socioeconomic indicators. Its predictions should therefore be interpreted as nonlinear associations with coded regional membership rather than as interactions among substantive regional determinants. The rule of decision of each tree is as follows Eq. (3):

(3)

where:

is the prediction made by the model for input ,

is the prediction of the tree ,

is the total number of trees in the forest.

Random Forest models are highly versatile and can learn nonlinear relationships in the data as compared to Linear Regression. Random Forest was our choice in this study to predict Recovery Rates using Region_ID and other possible features, as a benefit over linear assumptions and because it can handle complex feature interactions.

3.5.3. Bayesian Linear Regression (BLR)

Bayesian Linear Regression extends conventional linear regression by assigning prior distributions to model parameters and updating those distributions through observed data. The model provides posterior distributions and credible intervals rather than only point estimates. In the present study, the model used Region_ID as its sole predictor. Its uncertainty estimates therefore represent uncertainty associated with the restricted linear specification and should not be interpreted as uncertainty about omitted healthcare, demographic, policy, or socioeconomic determinants. Although Bayesian Linear Regression produced higher prediction errors than the other models, it offered an explicit probabilistic representation of parameter and predictive uncertainty. Likelihood function in Bayesian Linear Regression is as follows Eq. (4):

(4)

where:

is the posterior distribution of the parameters given the data;

is the likelihood of observing the data given the model parameters;

is the prior distribution, representing our initial beliefs about the parameters before observing the data;

represents the parameters, where:

is the mean recovery rate,

as the standard deviation (uncertainty in recovery rates),

as a region-specific offset.

Bayesian Linear Regression benefits include quantifying uncertainty and providing not only a point estimate of the recovery rate but also confidence intervals that indicate how confident the model is in its predictions. This is especially helpful in situations where uncertainty must be reported alongside forecasts, e.g., in public health decision-making.

Bayesian Linear Regression (BLR) is a continuation of the classical linear regression that introduces uncertainty into the model by using prior distributions. The latter model was selected due to its capability to measure the uncertainty of predictions, which is especially useful when it comes to modelling pandemic recovery. In this research, there was an informative choice of the recovery rates based on the accessible healthcare information that enabled further robust interpretation of the model outputs. Despite the strengths in uncertainty estimation, the BLR’s performance was not optimal compared to Random Forest. This is explained by the model’s linearity and sensitivity to prior selection; hence, it could not capture the non-linear relationships observed in the data. Subsidiary studies should consider applying more complex Bayesian models and additional datasets to obtain better priors.

3.5.4. ARIMA (Autoregressive Integrated Moving Average)

The ADF and KPSS statistics cannot be obtained from a web description of the dataset because they depend on the exact series supplied to ARIMA. To make the analysis reproducible, define the ARIMA series explicitly as the global daily recovery rate Eq. (5):

(5)

The ADF test uses a null hypothesis of a unit root, while the KPSS test uses a null hypothesis of level or trend stationarity. The level-series results therefore indicate non-stationarity, whereas the first-differenced results support stationarity and justify (Table 2).

Table 2. Verified results based on the daily series from 22 January to 31 October 2020.

Before ARIMA estimation, the stationarity of the global daily recovery-rate series was examined using the Augmented Dickey–Fuller and Kwiatkowski–Phillips–Schmidt–Shin tests. For the level series, the ADF statistic was −1.836 with p = 0.363, indicating that the unit-root null hypothesis could not be rejected. The KPSS statistic was 2.209 with p < 0.010, rejecting the null hypothesis of level stationarity. Both tests therefore indicated that the recovery-rate series was non-stationary in levels. Following first differencing, the ADF statistic was −4.805 with p < 0.001, while the KPSS statistic was 0.104 with p > 0.100. These results indicated that the first-differenced series was stationary and supported an integration order of . The ARIMA (2, 1, 2) specification was subsequently selected according to Akaike Information Criterion minimisation.

ARIMA is a forecasting statistical time-series model. It embodies the connection of an observation to multiple lagged observations (autoregressive), the variations between observations to render the data stationary (integration) and the lagged forecast errors (moving average). ARIMA is denoted by three parameters:

p: Number of lag observations that the model uses (autoregressive part).

d: Differentiating the raw observations (to render the data stationary) a number of times.

q: Size of the moving average window (moving average part).

The ARIMA model was used to represent autoregressive dependence, non-stationary trend through differencing, and lagged forecast errors. Because ARIMA (2, 1, 2) is a non-seasonal specification, the model should not be described as explicitly capturing seasonal effects.

The general form of the ARIMA model is given as Eq. (6):

(6)

Where:

is the observed value at time ,

are the coefficients for the autoregressive part,

are the coefficients for the moving average part,

is the error term (white noise or residual).

ARIMA model is especially beneficial to be used in modeling time-series data that have a seasonal trend and auto-correlated values.

3.5.5. LSTM (Long Short-Term Memory)

LSTM is a Recurrent Neural Network (RNN) that is used to model time-series data with long-range dependencies. The LSTM model consisted of two LSTM layers with 64 and 32 neurons respectively, followed by a dense output layer. The model was trained using the Adam optimiser with a learning rate of 0.001, batch size of 32, and 50 training epochs. A dropout rate of 0.2 was applied to reduce overfitting and Mean Squared Error (MSE) was used as the loss function. The LSTM models can recall information over long durations as opposed to traditional RNNs, and hence are applicable in predicting sequential data, including COVID-19 recoveries.

An LSTM consists of three main components:

Cell state: It carries information through the sequence, helping to preserve long-term dependencies.

Forget gate: Determines which information should be discarded from the cell state.

Input gate: Decides which new information should be stored in the cell state.

Output gate: Determines which part of the cell state should be output at the current time step.

The LSTM update equations are:

Forget Gate: Eq. (7):

(7)

Where:

is the forget gate output,

is the weight matrix for the forget gate;

is the previous hidden state,

is the input at time ,

is the bias term,

is the sigmoid activation function.

Input Gate: Eq. (8):

(8)

Where:

is the input gate output,

is the weight matrix for the input gate,

is the bias term.

Candidate Cell State: Eq. (9):

(9)

Where:

is the candidate cell state,

is the weight matrix for the candidate cell state.

Update the Cell State: Eq. (10):

(10)

Where:

is the cell state at time ,

is the previous cell state.

Output Gate: Eq. (11):

(11)

Where:

is the output gate,

is the weight matrix for the output gate.

Hidden State Update: Eq. (12):

(12)

Where:

is the hidden state at time ,

is the updated cell state.

3.6. Model Training and Evaluation

LSTM is a Recurrent Neural Network (RNN) that is used to model time-series data with long-range dependencies. The LSTM models can recall information over long durations as opposed to traditional RNNs, and hence are applicable in predicting sequential data, including COVID-19 recoveries. No feature-selection procedure was applied because Region_ID was the only predictor used by the tabular models. Consequently, any Random Forest importance value assigned to Region_ID does not demonstrate that geography is a substantive determinant of recovery. It is a structural consequence of supplying only one input variable. Random Forest nevertheless produced lower tabular prediction errors than Linear Regression and Bayesian Linear Regression, indicating that nonlinear partitions of coded regional membership reproduced the observed recovery-rate patterns more effectively than the corresponding linear specifications.

3.6.1. Root Mean Squared Error (RMSE)

RMSE is a common measure to evaluate the quality of regressions models. It is employed to approximate the average magnitude of the residuals (errors); the smaller the RMSE, the greater the performance of the model. The formula for RMSE is Eq. (13):

(13)

where:

is the true recovery rate for the -th observation,

is the predicted recovery rate for the -th observation,

is the total number of observations.

RMSE additionally displays the mean value of the observed and projected values and the weight of larger errors is represented by the squared term.

3.6.2. Mean Absolute Error (MAE)

Another typical measure is MAE, which is used to determine the average difference between the observed and predicted values in absolute terms. It is also not so prone to large errors as compared to RMSE but it still provides a useful estimate of the overall predictive accuracy. The formula for MAE is Eq. (14):

(14)

where:

is the absolute error for the -th observation.

Linear Regression, Random Forest and Bayesian Linear Regression predictive performance were compared concerning how each of them is able to explain the complexity of regional recovery rates and the uncertainties that are present in the process, based on RMSE and MAE.

Model performance was evaluated using Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) to measure predictive accuracy across all approaches. The dataset was assessed using a chronological train–test split to preserve temporal ordering and avoid data leakage. The results indicate that the Random Forest model achieved lower prediction error compared to Linear Regression and Bayesian Linear Regression, demonstrating stronger performance under constrained feature conditions.

Furthermore, to determine the most significant predictors of the recovery rate variance, the feature selection was applied. The non-linear and complex nature of the relationships demanded by the random Forest also made it the most suitable model to this task, and the performance of linear regression was adversely affected by the assumption of linearity. Bayesian Linear Regression is useful in estimating uncertainty, but it is not as accurate as it is suggested.

3.7. Experimental Setup

The empirical analysis used 46,020 cleaned country–date observations covering 225 Country/Region units from 22 January–31 October 2020. Linear Regression, Random Forest, and Bayesian Linear Regression used Region_ID as their sole input variable. ARIMA and LSTM used chronologically ordered recovery-rate observations.

The dataset was divided using a chronological 80:20 split based on unique observation dates rather than a random row-level split. The training period consisted of 227 dates from 22 January–4 September 2020 and contained 35,167 observations. The test period consisted of 57 dates from 5 September–31 October 2020 and contained 10,853 observations. This approach maintained temporal ordering and prevented later dates from being used to train forecasts for earlier periods.

No random k-fold cross-validation was applied because such validation would disrupt the temporal structure of the observations. Model performance was evaluated using RMSE and MAE on the held-out test period. Before ARIMA estimation, ADF and KPSS tests were used to verify stationarity and the need for first differencing.

Future research should incorporate healthcare infrastructure, population density, government interventions, testing intensity, vaccination, demographic structure, and socioeconomic indicators. It should also employ rolling-origin evaluation, out-of-region validation, repeated LSTM training runs, calibrated uncertainty intervals, and sensitivity analyses. ARIMA and LSTM should not be listed as future modelling approaches because both were already implemented in the present study.

4. RESULTS

4.1. Model Comparison

The evaluated models produced different levels of predictive error. LSTM achieved the lowest overall error, with an RMSE of 0.292 and an MAE of 0.239. Random Forest ranked second, with an RMSE of 0.2977 and an MAE of 0.2463. ARIMA produced an RMSE of 0.318 and an MAE of 0.271, indicating moderate performance in representing temporal recovery-rate patterns. Linear Regression recorded an RMSE of 0.3350 and an MAE of 0.2962. Bayesian Linear Regression produced the highest point-prediction error, with an RMSE of 0.4344 and an MAE of 0.3639, although its Bayesian structure enabled explicit probabilistic representation of uncertainty.

Based on the values reported in Table 3, the correct performance ranking was LSTM, Random Forest, ARIMA, Linear Regression, and Bayesian Linear Regression. LSTM was therefore the most accurate model according to both RMSE and MAE. Random Forest should be described as the best-performing tabular model rather than the best-performing model overall. Bayesian Linear Regression’s principal contribution lies in its explicit uncertainty representation rather than superior point-prediction accuracy.

Table 3. Model comparison.

Fig. (2) compares the Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) of five models namely: Linear Regression, Bayesian Linear Regression, Random Forest, ARIMA, and LSTM. The best predictive performance is the random forest as compared to the other two models as far as RMSE and MAE are concerned. The next one to compete is LSTM with a good performance, and Linear Regression and Bayesian Linear Regression have more errors. Random Forest, as it is observed in the chart, would be more effective to capture the underlying trends in the recovery rate data in the various regions.

5. DISCUSSION

5.1. Model Comparison and Results

The findings demonstrate that the evaluated models differed in predictive accuracy, temporal representation, interpretability, and uncertainty treatment. According to the reported RMSE and MAE values, LSTM achieved the strongest point-prediction performance, followed closely by Random Forest. ARIMA produced moderate prediction errors, while Linear Regression and Bayesian Linear Regression were less accurate. The relatively small difference between LSTM and Random Forest suggests that both temporal sequence learning and nonlinear partitioning provided advantages over the linear specifications [30, 34].

LSTM’s stronger performance indicates that historical temporal dependencies contained useful predictive information that was not available to the tabular models through Region_ID alone. Its RMSE of 0.292 and MAE of 0.239 were the lowest among the evaluated approaches. However, LSTM remains less transparent than Linear Regression and Bayesian Linear Regression, and its predictions may be sensitive to sequence length, input scaling, hyperparameter selection, random initialisation, and changes in the temporal data-generating process [27].

Random Forest was the strongest tabular model, with an RMSE of 0.2977 and an MAE of 0.2463. Its performance indicates that a nonlinear mapping of Region_ID reproduced the observed recovery-rate patterns more effectively than Linear Regression or Bayesian Linear Regression. Nevertheless, this result does not demonstrate nonlinear interactions among healthcare capacity, government intervention, population density, demographic structure, or socioeconomic conditions because none of these variables was included. The model learned only from coded regional membership and should not be interpreted causally [22, 29].

Linear Regression provided a simple and interpretable baseline but generated higher errors than LSTM, Random Forest, and ARIMA. Its nearly constant predictions indicate that a single linear relationship between numerical Region_ID values and recovery rates was insufficient to represent the observed variation. This result reflects the restricted information content and artificial numerical ordering of Region_ID rather than evidence that regional recovery processes are inherently linear [30].

Bayesian Linear Regression produced the highest RMSE and MAE. Its principal advantage was its ability to represent parameter and predictive uncertainty through prior distributions and posterior inference. However, wider credible intervals do not automatically demonstrate well-calibrated uncertainty. Interval coverage, average interval width, and posterior predictive calibration would need to be evaluated before the Bayesian estimates could be described as more reliable. The model’s weaker point-prediction performance is consistent with the limitations of imposing a linear structure on a relationship represented only by Region_ID [26, 34].

ARIMA outperformed Linear Regression and Bayesian Linear Regression but did not outperform LSTM or Random Forest. The ADF and KPSS results showed that the level recovery-rate series was non-stationary and became stationary following first differencing, supporting the use of d = 1. ARIMA therefore provided a transparent statistical representation of autoregressive dependence and lagged forecast error. However, the non-seasonal ARIMA (2,1,2) specification should not be described as explicitly capturing seasonality.

Overall, no single model dominated every evaluation dimension. LSTM achieved the strongest point-prediction accuracy, Random Forest was the strongest tabular model, ARIMA provided a comparatively transparent temporal benchmark, and Bayesian Linear Regression offered explicit probabilistic uncertainty estimates. Model selection should therefore reflect the intended analytical purpose and the relative importance of accuracy, temporal learning, interpretability, and uncertainty representation.

Table 4 taxonomy underscores the fact that the predictive models do not only vary in accuracy but also in the nature of the epistemic and interpretive risks they present when used in policy-based forecasting.

Table 4. Taxonomy of predictive models based on epistemic and policy-relevant properties.