This study adopted a quantitative, comparative, and retrospective research design ([8]). Month-to-month historical utilisation and stock records of renal consumables were analysed over a period of 36 months (January 2023 to December 2025). Graphical analysis was used to describe historical utilisation patterns, after which comparative analysis evaluated the forecasting performance of the SMA method and selected time series forecasting models using the same datasets. This study was retrospective because it relied on historical numerical data and statistical accuracy measures. Comparative because it assessed forecasting methods against each other. This study was conducted at the UTH in Lusaka, Zambia. The institution constituted the study site from which the study population and relevant data on renal consumable demand were obtained.

The study included all critical renal consumable stock keeping units at UTH that had availability of at least 36 consecutive months of historical monthly consumption data. Data completeness of at least 90% corresponding to fewer than 10% missing monthly observations was ascertained. Other considerations included routine and continued use in dialysis service delivery throughout the observation period and classification of clinically critical for dialysis treatment cases based on facility protocols and expert consultation. Monthly consumption was defined as the total quantity of each renal consumable SKU issued for use in dialysis services within a calendar month, as recorded in pharmacy stock issue records, dialysis unit consumption registers, bin cards and electronic logistics management records where available. Consumption values represented quantities physically utilised or issued for patient care during each month. The study took account of external factors such as number of dialysis sessions and patient load as predictors for the dynamic regression model. The use of external factors depended on data availability. During the study period, dialysis sessions were sometimes reduced from three times a week to twice a week because of supply shortages of consumables as evidenced by logistics and clinical records. Including these factors helped improve the forecast accuracy for the dynamic regression model. Months affected by stock-outs or rationed dialysis sessions were not excluded from analysis because they reflected operational realities influencing observed utilisation. However, these periods were identified using logistics and clinical records and interpreted cautiously since observed consumption during stock-outs may underestimate actual clinical demand. Information on reduced dialysis frequency and patient load was incorporated as external covariates in the dynamic regression model where such records were available.

This study excluded all renal consumable SKUs which had more than 10% missing or inconsistent monthly data which would render time-series modelling unreliable. Thus, only SKUs with at least 90% complete monthly observations corresponding to no more than 10% missing values were eligible for inclusion. Other exclusion parameters included discontinued SKU, substituted drugs, major formulation change during the study period without continuous record linkage and items used sporadically or only during emergencies, where consumption patterns could not be meaningfully modelled.

The study utilised a total enumeration sampling approach, incorporating all critical renal consumables identified as essential for dialysis procedures at UTH. Critical in the sense that unavailability of any one of these consumables would result in a missed dialysis session. The critical renal consumables included, bloodlines giving sets for carrying blood from the patient to the dialyser for filtration and back to the patient, dialysers or artificial kidneys for cleaning blood by removal of waste and extra fluid, renal concentrate dialysate blood cleanser, disinfectant equipment sterilization, heparin as an anticoagulant and sodium bicarbonate for blood pH maintenance. This method ensured complete coverage of the critical stock-keeping units based on clinical relevance, consumption volume and data completeness.

A formal sample size calculation time steps were not performed because time-series forecasting models do not depend on hypothesis testing, statistical power, or predefined effect sizes ([17]). Unlike inferential statistical models, forecasting approaches such as simple and weighted moving averages, SARIMA, and dynamic regression are evaluated primarily based on their ability to produce accurate out-of-sample predictions ([17]). The adequacy of the data was ensured by assessing the length of the historical series relative to the model complexity and validating the model performance against out-of-sample (2025) data. Furthermore, this study encompassed all critical renal consumables recorded from 2023 to 2025, providing a comprehensive dataset for predictive analysis.

Data from the UTH Adult Hospital were extracted using a standardised extraction tool imported into Python (SciPy) for analysis. Data analysis was performed using Python (version 3.x) with the following key libraries: pandas for data manipulation and descriptive statistics; NumPy and SciPy for numerical computations, correlation analysis, autocorrelation (ACF) plots, and paired t-tests; Matplotlib and Seaborn for visualisation of trends, scatter plots, and monthly profiles; and stats models for SARIMA model fitting and diagnostics. To understand the data, basic descriptive statistics were computed for each renal consumable, including the mean monthly consumption, standard deviation, minimum and maximum consumption used from 2023 to 2025, and coefficient of variation to compare variability relative to the average.

Pre-model diagnostics were conducted on the time-series data prior to model testing. Stationarity was assessed using the Augmented Dickey-Fuller (ADF) test to determine whether differencing was required. Autocorrelation function (ACF) plots were examined to identify temporal dependencies and inform model order selection for SARIMA and related approaches.

Forecasting was undertaken using a rolling-origin cross-validation approach to assess out-of-sample predictive performance ([5]). This method involves training models on expanding historical windows and generating forecasts for subsequent periods and simulating real-world rolling forecasts ([14]).

Model specification procedures were predefined to improve reproducibility of the forecasting comparison. The SMA model used a three-month moving window, while the weighted moving average (WMA) model applied a three-month weighted window with greater emphasis placed on the most recent observations using weights of 0.5, 0.3 and 0.2. Exponential smoothing was implemented using the Holt-Winters error, trend and seasonality (ETS) framework, with model forms selected automatically based on the lowest Akaike Information Criterion (AIC). Final SARIMA model orders for each SKU were selected after examining stationarity, ACF and partial autocorrelation function (PACF) plots together with AIC and diagnostic residual checks. The dynamic regression model incorporated external covariates including monthly dialysis sessions and patient load where records were available, with lag structures assessed using cross-correlation analysis and model fit statistics.

To determine the most suitable forecasting approach, multiple methods were compared. These included the SMA and the comparator and selected time-series forecasting models exponential smoothing, SARIMA, weighted moving average, and dynamic regression. Forecast accuracy was evaluated using two standard metrics, mean absolute error (MAE) and mean absolute percentage error (MAPE). Mean Absolute Percentage Error (MAPE) was predefined as the primary model-selection metric because it provides a scale-independent measure that allows comparison of forecasting accuracy across different renal consumables with varying utilisation volumes. Mean Absolute Error (MAE) was treated as the secondary metric to provide interpretation of forecasting deviations in original consumption units. These metrics quantify different aspects of error. MAE provides an average absolute deviation in original units, and MAPE offers a scale-independent percentage-based measure ([17]). Lower values indicate better performance in healthcare supply chain contexts ([24]). MAPE values below 20% - 30% are often considered acceptable for stable demand items, while higher thresholds may apply to intermittent or variable demand ([24]; [35]). Comparative statistical tests, specifically paired t-tests, were applied to assess whether the observed differences in predictive performance between SMA and the best advanced model were statistically significant. A 95% confidence interval was used and p-values < 0.05 were considered statistically significant. The followed conventional thresholds in forecasting model comparisons ([24]). This process was rigorously analysed to ensure a transparent evaluation of model performance, which was tailored to the characteristics of the renal consumable time-series data at UTH.

A paired t-test was used to determine whether the reduction in forecasting error achieved by the advanced models was statistically significant. The differences in errors were calculated for each month from January to December. The analysis was performed using Python (SciPy), and the paired t-test was run in Python (SciPy). A significance level of p < 0.05 was used, indicating that the results were considered statistically significant if the p-value was less than 0.05.

Dynamic regression results were analysed and reported alongside SMA, weighted moving average, exponential smoothing and SARIMA models for all SKUs where external covariate data were available. The external variables consistently available for modelling included monthly dialysis session counts and patient load records. Where external variables were incomplete or unavailable for specific SKUs or months, dynamic regression was excluded from comparative interpretation for those instances and this was clearly indicated in the results section.

The selected models, dynamic regression, exponential smoothing, SARIMA and weighted moving average, were chosen because they are widely used in time-series forecasting and capture different demand patterns such as trends and seasonality ([1]; [40]).

Missing data were filled in using linear interpolation. Linear interpolation estimates missing values by drawing a straight line between known points ([27]). This helps keep the data’s trend steady without sudden changes. Linear interpolation was used instead of methods such as seasonal decomposition because it offers a balance of simplicity and transparency for small gaps in demand data which can reasonably be presumed to change gradually over time. Only datasets with no more than 10% missing monthly observations were eligible for interpolation and inclusion in the analysis. The number and proportion of interpolated observations for each SKU were documented and reported in the results section to ensure transparency regarding the extent of missing-data adjustment.

The study adhered to Zambia’s Data Protection Act and Institutional data governance requirements. The Ministry of Health and ZAMMSA are the official data controllers and the University of Zambia kept the data legally as the academic data custodian. Only the main researcher could see the raw data. All data were made anonymous by replacing the facility name with a code to protect privacy. Data were stored safely on secure devices and were not shared openly. Data were kept only as long as needed for the study and then stored safely.

To make sure the results were correct, only reliable and complete records were used. The models were tested using train-test splits and cross-validation to ensure they worked well in different cases ([30]). Consistency was improved by following standard procedures and using trusted software. Additional tests checked if the models were strong across different times and product types.

The researchers first tested their methods with data from a pilot hospital to see if everything worked well. This pilot checked data quality, model setup and accuracy. The pilot needed at least 24 months of good data to ascertain accuracy. The pilot results helped improve the main study’s methods. If some data was poor, replacement with better data in the final study was made.

The study upheld the highest ethical standards in accordance with recognised principles of research ethics, including respect for persons, beneficence, non-maleficence, and justice. Ethical approval was obtained from the University of Zambia Health Sciences Research Ethics Committee (UNZAHSREC) Protocol ID 2023270450 and the Zambia National Health Research Authority (NHRA) Protocol ID NHRA-2735/23/09/2025. We also got clearance UTH management to conduct the study at their institution.

The data used were historical and applied solely for forecasting and public health improvement, and not for personal purposes. Facility stock levels were anonymised and stored securely. No personal identifiers or patient-level information were collected or analysed. This approach ensured that individual privacy and autonomy were fully respected.

Finally, the study upheld scientific integrity by maintaining transparency, objectivity accountability throughout the design, analysis and reporting of the results. All data handling complied with the ethical and legal standards for data protection.

Table 1 presents the descriptive statistics of monthly consumption for the six critical renal consumables. Renal concentrate recorded the highest average consumption (mean = 664.6 units), followed by bloodlines and sodium bicarbonate. Disinfectant exhibited the lowest mean consumption (95.7 units), indicating stable use. Sodium bicarbonate demonstrated the highest relative variability (CV = 47.4%), suggesting substantial fluctuations in monthly demand. Dialysers, bloodlines, renal concentrates, and heparin exhibited moderate variability (CVs ranging from 24.9% to 33.7%). This indicated relative stable demand with occasional fluctuations.

Table 1. Descriptive statistics of renal consumables at UTH-adult hospital from 2023-2024.

Most consumables displayed gradual declining demand trends over the period under observation with varying fluctuations across the SKUs (Figure 1). Bloodlines and renal concentrates showed consistent downward patterns indicating relative demand stability. Dialysers and heparin exhibited moderate demand declines with occasional fluctuations whereas disinfectant exhibited steady demand. Sodium bicarbonate had the most irregular demand pattern. The trends indicated that most consumables had a long-term declining demand and the degree of variability differed across consumables.

Figure 1. Monthly consumption trends for renal consumables with fitted linear trend lines, illustrating long-term usage patterns and demand variability. Bloodlines exhibited p-value < 0.0243, heparin < 0.0045, sodium bicarbonate < 0.0001, disinfectant < 0.0007 whereas dialysers and renal concentrate were not significant.

Several consumables correlated with dialysis session volumes, although the strength of this relationship differed among the SKUs (Figure 2). Dialysers and bloodlines showed a generally positive association with the number of dialysing sessions, with higher consumption often coinciding with periods of increased dialysis activity. Renal concentrate and sodium bicarbonate showed greater fluctuations in relation to dialysis session counts. Consumption of disinfectants remained remarkably stable across the study period, with minimal changes in session volume. The consistency of usage was largely unaffected by short-term fluctuations in operational activity. Heparin showed a moderate correlation with dialysis session volume. However, heparin displayed significant deviations, especially during periods of increased consumption. This did not match with corresponding rise in dialysis sessions.

Figure 2. Faceted dual-axis plots showing monthly consumable usage (left y-axis) and number of dialysis sessions (right y-axis), highlighting varying degrees of association across consumables. Bloodlines exhibited p-value < 0.0243, heparin < 0.0045, sodium bicarbonate < 0.0001, disinfectant < 0.0007 whereas dialysers and renal concentrate were not significant.

The data was analysed using Python to plot a faceted scatter plot graph to compare and assess an observable relationship between renal consumables and the number of dialysis sessions at UTH. Dialysers, bloodlines, renal concentrates, and sodium bicarbonate showed positive associations with dialysis session volume, as indicated by upward-sloping trend lines (Figure 3). Renal concentrates and sodium bicarbonate showed the steepest trends, indicating stronger sensitivity to changes in renal service volume. Disinfectants displayed a flat trend, with usage remaining largely constant across a wide range of session volumes. Heparin showed a weak association with session volume, with a near-horizontal trend and considerable scatter, suggesting that factors, such as dosing practices, play an important role in determining usage.

Figure 3. Faceted scatter plots showing the relationship between monthly consumable usage and the number of dialysis sessions, with fitted linear trend lines.

Python was used across all consumables to assess whether there was an observable trend during the monthly profiles for 2023 and 2024 (Figure 4). Consumables did not exhibit consistent or repeating peaks and troughs in the same calendar months, indicating that consumption patterns of renal consumables at UTH showed no predictable seasonal or cyclical fluctuations within the year.

Figure 4. Faceted monthly consumption patterns by year (2023-2024) for renal consumables, indicating the absence of consistent effects.

For all consumables, the autocorrelation coefficients at a 12-month gap detected yearly irregular patterns in monthly data. At 95% confidence limits no statistical significance was observed (see Figure 5). This indicates an absence of consistent annual seasonal patterns in the demand.

Figure 5. Faceted autocorrelation function (ACF) plots for monthly renal consumable usage during the training period (2023-2024), showing no evidence of seasonal autocorrelation at lag 12.

Renal concentrate had stronger connections with itself at short time. This showed slow changes over time but these connections became weaker at longer gaps and did not follow an irregular demand pattern. Sodium bicarbonate exhibited irregular autocorrelation patterns with alternating signs, indicating high fluctuations rather than structured irregularity. Renal disinfectant showed very little connection with itself over time because demand was very steady and was based on a set routine. Heparin exhibited modest autocorrelation at short time intervals but did not show significant correlations at longer time intervals.

Model performance differed noticeably depending on the type of consumable. This differed performance reflected the variability of the demand at UTH. To evaluate how well each model performed, two standard error metrics were used, the mean absolute error (MAE) and mean absolute percentage error (MAPE). These metrics compare forecasted values with actual consumption for the length of the study period.

Mean Absolute Error (MAE) measures the average size of the errors without considering their direction ([38]). It is calculated as:

where n is the number of observations and | Actual t − Forecast t | is the absolute difference at time t. MAE is easy to interpret and gives a good sense of typical error in the same units as the data.

The mean absolute percentage error (MAPE) expresses errors as a percentage of the actual values, making it easier to compare across consumables with significantly different scales ([20]).

The MAPE is intuitive for communicating performance to non-technical stakeholders, although it can become very large or undefined when the actual consumption is zero. This occurred occasionally for some items, such as sodium bicarbonate ([21]).

All data processing, statistical analysis, and visualisation were performed in Python (version 3.x) within a Jupyter Notebook environment for reproducibility. Key libraries included,

1) Pandas—for data cleaning, descriptive statistics, rolling calculations, and data frame manipulation

2) NumPy—for numerical operations and array-based computations

3) SciPy.Stats—for correlation tests and paired t-tests

4) Matplotlib—for line plots and scatter plots

5) Statsmodels—for Exponential Smoothing, SARIMA, and ACF diagnostics

6) Customfunctions—for SMA, WMA, MAPE and MAE

Table 2 shows the formulas used to acquire the results that are displayed in Table 3.

Table 2. Formulas used in this study.

Table 3. Comparison of forecasting model performance for monthly consumable usage.

In Table 3, for bloodlines, exponential smoothing had the lowest MAPE (25.80%) and dialysers were best forecasted by SMA (22.88). Disinfectant was the easiest to forecast, with nearly every model performing well, but SARIMA yielded the smallest errors (MAPE = 0.60%). This fits very stable usage. Heparin forecasts were strongest with exponential smoothing (MAPE = 14.80%), whereas renal concentrate came out best using weighted moving average (MAPE = 16.59%). Sodium bicarbonate had the highest item error levels across the board, although weighted moving average still yielded the least bad result (MAPE = 35.94%).

FormulaforErrorReduction

Error Reduction % = Baseline Error (SMA) − Time Series Model Error/Baseline Error (SMA) × 100

The results in Table 4 show the error improvement reduction baseline that was achieved by the time-series models.

Table 4. Shows the summary of time-series model error improvement reduction of baseline.

Figure 6 compares actual 2025 consumption with model forecasts for each consumable at the UTH. SMA, WMA, exponential smoothing produced flat forecasts that captured the yearly average level well but missed sharp monthly fluctuations for dialysers, bloodlines, renal concentrate, sodium bicarbonate and heparin. SARIMA exhibited weak trends and did not align well with peaks and troughs reflecting no seasonality. Dynamic regression showed session-linked patterns but deviated when the relationship was weak. Disinfectant showed stable demand. Therefore, all models tracked actual values closely.

Table 5 compared the forecasting accuracy of SMA with the best forecasting model for each consumable using MAPE. The error between months was calculated from January to December, and a paired t-test was calculated in Python (SciPy) at every time step. Difference in error was calculated by subtracting SMA MAPE from advanced model MAPE. Sodium bicarbonate error difference was 72.84%, showing significant improvement. Bloodlines error difference was 10.74%, disinfectant reduced difference was 0.28%, heparin error difference was 2.3%, renal concentrate error difference was 0.14% and dialysers error difference was 0.34%. Heparin, renal concentrate and dialyser error difference was not significant. Advanced models significantly improved the forecasting for sodium bicarbonate, bloodlines and disinfectant. Heparin improvement was marginal, no meaningful improvement for renal concentrate and dialysers were observed.

Figure 6. Observed versus forecasted monthly consumption for renal consumables in 2025, comparing Simple Moving Average (SMA), Weighted Moving Average (WMA), Exponential Smoothing, SARIMA, and Dynamic Regression models across consumable type.

Table 5. Comparison of best-fit models with SMA for each consumable using MAPE.

In Table 6, the error between months was calculated from January to December, and a paired t-test was calculated in Python (SciPy) at every time step. Difference in error was calculated by subtracting SMA MAE from advanced model MAE. Sodium bicarbonate error difference was 96.21, showing significant improvement. Disinfectant reduced difference was 0.26, heparin error difference was 13.85, bloodlines error difference was 17.71, renal concentrate error difference was 1.61 and dialysers error difference was 1.97. The difference in renal concentrate and dialyser error was not significant. Advanced models significantly improved the forecasting for sodium bicarbonate, disinfectant, heparin and bloodlines. No meaningful improvement for renal concentrate and dialysers was observed.

Table 6. Comparison of best-fit models with SMA for each consumable using MAE.

The study was conducted solely at the UTH-Adult Hospital. Therefore, the findings may not fully represent consumption patterns or forecasting performance in other provincial or district facilities. The analysis relied entirely on historical consumption records and did not incorporate external factors, such as supply chain disruptions, budget constraints, procurement delays, or policy changes. These factors influence actual demand and model performance. Potential data quality issues, including manual recording errors, incomplete stock cards, and missing entries, may have affected the results despite efforts to clean and impute data. Finally, the short historical series limited the detection of longer-term trends or structural shifts.

The findings of this study highlight critical policy implications for strengthening forecasting and supply chain management of renal consumables in Zambia (Table 7). Evidence demonstrates that reliance on a single, basic forecasting method such as the simple moving average is insufficient, particularly for commodities with variable demand. Instead, adopting SKU-specific, data-driven time-series models, such as exponential smoothing, SARIMA, and weighted moving averages, can significantly improve forecasting accuracy and reduce stockouts. These improvements are essential for ensuring uninterrupted dialysis services and better patient outcomes.

Table 7. Policy recommendations and implications for strengthening renal consumables forecasting and supply chain management in Zambia.

At the systems level, there is a need to transition toward integrated, digital forecasting platforms that incorporate real-time consumption data and service utilisation indicators, such as dialysis session volumes. Strengthening electronic logistics management systems and improving data quality will enhance decision-making and responsiveness. Capacity building for pharmacists and supply chain personnel is equally important to support the adoption and sustainability of advanced forecasting tools.

Furthermore, policy reforms should institutionalise routine model comparison and evidence-based procurement planning, while promoting differentiated inventory strategies based on demand variability. Scaling these approaches beyond renal care to other chronic disease commodities will strengthen overall health system resilience. Collectively, these measures provide a practical pathway toward more efficient, data-driven supply chains in Zambia.

Future studies should extend the analysis to multiple provinces and facilities to improve generalisability. Comparative assessments between urban and rural dialysis units would provide valuable insights into regional variations. The incorporation of machine learning approaches alongside classical time series models could be explored where data volume permits. Similar forecasting methods should also be applied to other chronic disease commodities, such as antihypertensive drugs, antidiabetic agents, and oncology drugs. This would broaden the evidence base for data-driven supply chain management in Zambia.

Based on these findings, it is recommended that health facilities adopt SKU-specific forecasting models rather than relying on a single method for all consumables, and routinely compare model performance before finalising procurement quantities to ensure optimal accuracy. Renal consumables should be integrated into the national forecasting system to strengthen coordinated planning and supply chain efficiency. In addition, there is a need to build capacity among pharmacists, supply chain personnel, and dialysis unit staff through structured training in basic time-series forecasting and interpretation of model outputs. Finally, improving data quality through routine digital capture of dialysis session volumes and consumable utilisation at the facility level will enhance the accuracy, timeliness, and reliability of forecasting, ultimately supporting uninterrupted dialysis services and better patient outcomes.