Analyzing disease data at appropriate geographical scales is crucial for understanding spatial patterns of disease burden and informing relevant public policy[1]. However, limitations in data collection and privacy protection requirements often result in data aggregated at coarser scales and with missing values. Such an issue is particularly prevalent in cancer datasets[2, 3], yet estimates at smaller geographic units are often needed for population-level measurement and analyses. Therefore, developing reliable methods to estimate those suppressed values is valuable for spatial analysis at sharper resolutions[4] and enables precision public health interventions[5].

There have been significant advancements in interpolating missing data[6] and downscaling population [7]over the past decades. However, health (e.g., cancer) data downscaling faces unique challenges[8]. Cancer data suppression is geographically nested, and the level of suppression correlates with geographic precision[9]. While data at higher levels might be reliable, the proportion of suppressed data increases with finer population groupings and geographic scales. Traditional regression methods for handling missing data often fail to satisfy total volume constraints at higher geographic levels[10]. Population downscaling techniques, such as areal interpolation or dasymetric mapping, need to account for the relationship between auxiliary data and cancer data[11]. Incorrect auxiliary data can lead to erroneous results, e.g., overestimated cases in urban areas and underestimated cases in rural areas[12]. Methods based on Monte Carlo (MC) simulations show promise by estimating cancer incidences proportionally to specific population groups[13, 14]. However, more work is needed to account for the nested structure in area units and risk factors associated with demographic structure for further evaluation.

This study employs an innovative multi-constraint Monte Carlo simulation method to estimate suppressed county-level subgroup cancer counts and extend the downscaling from county to ZIP Code Tabulation Areas (ZCTA). Using cancer incidence data from Utah for the period 2016–2020, the proposed approach is rigorously validated and benchmarked against several machine learning models. The National Cancer Institute (NCI) data and Census data were selected to align with the availability of granular ZIP Code-level cancer data from Utah’s SEER cancer registry. Although SEER data are not publicly accessible, their completeness and granularity at the ZIP Code level provide a unique opportunity to evaluate the accuracy and robustness of the Monte Carlo simulation method. This level of validation is particularly critical for estimating suppressed cancer counts in small subgroups, where suppression rules are most frequently applied.

Methods for addressing missing data and population downscaling in health research largely derive from general population science[15]. Wright introduced dasymetric mapping in 1936 to create downscaled density map based on inhabited and uninhabited areas in towns[16]. Subsequent development in this field can be broadly classified into areal interpolation and spatial smoothing, based on whether spatial autocorrelation is considered. Figure 1 illustrates the knowledge tree structure of related methods.

Initially, areal interpolation methods primarily relied on area-weighted calculations within and across administrative boundaries[17]. By incorporating more ancillary data such as cadastral data, land use information, and street data, population-weighted methods have made significant improvements over areal interpolation methods[18–22]. High-quality ancillary data provide proxies for population downscaling based on geographic boundaries or locations, marking a substantial shift towards data-driven and precise mapping techniques[23]. Regression methods have been used to integrate the effects of various geographic and demographic variables[24–26]. The introduction of machine learning and deep learning techniques adds a new dimension to population mapping, enables the incorporation of complex nonlinear relationships, and thereby enhances prediction accuracy[27–29].

Tobler’s Pycnophylactic interpolation method was among the first spatial smoothing methods for considering spatial autocorrelation and meeting the total number of observations [30]. Subsequent developments have shifted away from total volume constraints towards pure spatial smoothing techniques such as centroid kernel density methods, inverse distance weighting (IDW), geostatistics, and kriging[31, 32]. Methods like geographically weighted regression (GWR) and spatial Bayesian models integrate spatial correlation with regression and smoothing concepts, and become an adaptable tool for areal interpolation or spatial smoothing[33–35]. By integrating deep learning and machine learning methods with geographic features, Geospatial AI (GeoAI) represents the forefront in a knowledge tree for spatially varying models on population downscaling[36].

These methods need to be adjusted to account for the specific nature of medical data and enforce total volume constraints[37], when applied to cancer data processing. More recently, areal interpolation has gained more attention than spatial smoothing in health research and been expanded into geo-imputation[38]. Figure 2 illustrates the evolution of the related methods suitable for cancer data imputation.

Areal interpolation method was first introduced to interpolate breast cancer cases from towns to census tracts based on the proportion of females[39]. The methods are termed “geo-imputation” by using population data segmented by sex, age, and race to allocate cancer proportions to smaller spatial unit centroids[40]. Based on comparisons of multiple imputation methods in nested geographic units, population weighting has been validated as more optimal than area weighting[41]. However, a recent study argued that population weighting could underestimate case numbers in rural areas[42]. These discussions highlight the importance of selecting appropriate auxiliary data for downscaling to better align with the target dataset.

Random cancer case simulation was introduced in geo-imputation to conduct uncertainty analysis on distribution statistics, and thus extended fixed proportion allocation to probability distribution[43]. Building on this, the Monte Carlo simulation method was further applied with simple constraints to improve dynamic proportion constraints during the case generation process[14]. Random spatial imputation began with generating random spatial points based on population proportions to enhance data granularity[44]. These methods later incorporated dasymetric mapping techniques by using additional ancillary data such as property locations and daily activity spaces for finer spatial distribution[11, 45]. A combination of random case numbers and random geographic locations was proposed as the Restricted and Controlled Monte Carlo method, which combines the restriction of geographic boundaries and controls of health data prevalence by population[13].

Similar to population downscaling, regression methods and spatial smoothing were also applied on cancer data. For example, some employed both geo-imputation and regression methods to disaggregate or predict cancer cases at different scales[40]. Subsequent regression and prediction methods, ranging from Tobit models to machine learning, were widely applied to various types of data imputation[46–48]. Spatial smoothing methods such as kriging, spatial Bayesian, and spatial panel models were also commonly used[38, 49]. However, these methods cannot ensure total volume consistency.

In general, despite significant advancements in data imputation and population downscaling techniques, several critical gaps remain unaddressed in the context of health data, particularly cancer data. Most existing methods, such as regression-based approaches and machine learning models, struggle to simultaneously satisfy demographic and geographic constraints, often leading to biased estimates. For example, population-weighted methods, while effective in some scenarios, have been shown to underestimate rural case numbers and overestimate urban cases, reducing their robustness across diverse geographic contexts. Furthermore, many spatial smoothing and regression methods fail to ensure total volume consistency, a critical requirement for accurate health data imputation.

The Restricted and Controlled Monte Carlo method generally provides accurate and comprehensive insights for cancer data imputation while preserving total volume at higher geographic scales[50, 51]. However, additional challenges remain in implementing simulations that span nested geographic levels and account for multiple subgroup population controls. This study addresses these challenges by proposing an innovative multi-constraint Monte Carlo simulation method. The method ensures total volume consistency, robust performance across urban and rural contexts, and reliable estimation of suppressed cancer counts at fine geographic levels, thus filling a critical gap in the existing literature. By integrating dynamic demographic constraints and probabilistic case generation, the proposed approach provides actionable insights for precision public health interventions.

This paper aims to interpolate suppressed cancer data and downscale to fine spatial scales to maintain hierarchical total volume consistency and robust performance across rural and urban areas. The innovative multi-constraint Monte Carlo simulation method is effective in estimating suppressed county-level cancer counts and further disaggregating these counts to the ZIP Code Tabulation Area (ZCTA) level. The methodology leverages existing demographic structure as risk factors and reported cancer counts in higher geographic levels or larger demographic groups as constraints and ensures a consistent and accurate imputation of cancer data across different geographic levels. The model comparison shows its advantages over traditional machine learning and regression methods for suppressed cancer data estimation.

The case study in Utah largely validates the effectiveness of the method. Our findings validate the robustness of population-weighted approaches[41], especially for health data as reported in recent literature[56, 57]. By applying Monte Carlo simulations with simple constraints to improve dynamic proportion constraints during the case generation process, our study extends the capabilities of restricted and controlled Monte Carlo methods (RCMC) in the context of cancer data[13]. Our method’s high accuracy across areas of various urbanicities contrasts with the concern of less accuracy for rural cases by population-based interpolation methods[42]. Our results also suggest that geo-imputation methods can achieve high effectiveness even without considering spatial correlation. The method provides a reliable framework for accurately estimating suppressed cancer cases in small population subgroups or geographic areas with small population and demonstrates its ability to manage uncertainty and improve prediction[58, 59]. Among the machine learning models tested, XGB shows the best potential in handling complex spatial data imputation tasks[60], but still underperforms the multi-constraint Monte Carlo simulation method.

The performance decline observed with ancillary data highlights the importance of careful variable selection in health data modeling. Variables that are weakly correlated with cancer incidence or are prone to data quality issues may add complexity without improving model accuracy. This finding aligns with existing studies[3, 29], which emphasize that introducing redundant or noisy variables can negatively impact machine learning models.

Although the introduction of additional socioeconomic variables can alter the estimation performance of various machine learning models, their overall performance remains inferior to the multi-constrained Monte Carlo method. This confirms the applicability and accuracy of the Monte Carlo approach in scenarios with data suppression, particularly in complex contexts involving multidimensional population constraints[50, 51].

While the proposed multi-constraint Monte Carlo method demonstrates strong performance, several limitations should be acknowledged. First, the method’s adaptability to other regions with different population structures, suppression rules, or health data characteristics remains uncertain and requires further validation with diverse datasets. Secondly, the method does not explicitly address spatial autocorrelation, which may impact precision in regions with strong geographic clustering. Incorporating spatial models, such as geographically weighted regression or Bayesian methods, could improve accuracy. Thirdly, the reliance on publicly available data limits the granularity of inputs, and the absence of higher-resolution ancillary data may constrain performance in more complex scenarios. Finally, during the modeling process, the suppression rules (e.g., fewer than 11 cases in the NCI dataset) might be explicitly incorporated as constraints within the Monte Carlo simulation. Specifically, any simulated estimates for suppressed values must adhere to these rules, ensuring that the final output remains within the suppression limits. However, as the dataset contains both suppressed and missing values, our analysis applies overall population and geographic constraints to ensure accuracy.

Future research should explore integrating fixed geo-imputation methods and further refining the simulation process to enhance precision and applicability in other health data. Additionally, more work is needed to develop methods that can closely approximate potential proportions for detailed analysis, particularly in rural and underrepresented areas. Emerging studies suggest that hybrid approaches combining statistical and machine learning methods may offer significant improvements in this area. When ancillary data sources with improved resolution and quality become available, feature selection techniques can be employed to further enhance model performance.

This study demonstrates the effectiveness of the multi-constraint Monte Carlo method in estimating suppressed cancer data and downscaling to fine spatial scales. The proposed method achieves robust performance by maintaining hierarchical consistency and accurately addressing data suppression issues. However, while our results validate the method’s utility in Utah, its generalizability to other regions and health conditions remains an avenue for future exploration.

First, extending the method to other geographic regions or disease types—such as chronic or infectious diseases—would allow for validation under diverse population structures and data suppression rules. Secondly, while this study does not explicitly account for spatial autocorrelation, incorporating spatial statistical techniques, such as geographically weighted regression or spatial Bayesian models, could enhance the accuracy of the estimates by addressing potential geographic clustering of cancer incidence. Thirdly, privacy concerns in health data remain a critical challenge. Future studies could integrate differential privacy or advanced anonymization techniques into the Monte Carlo framework to improve both data security and precision. Fourthly, moving beyond static five-year averages to incorporate dynamic time-series data would enable the capture of temporal trends, providing deeper insights into changing cancer incidence patterns. Finally, integrating Monte Carlo simulations with machine learning models offers significant potential for developing hybrid approaches that leverage the strengths of both paradigms to enhance prediction accuracy and applicability.

By addressing these areas, the proposed method will not only advance the state-of-the-art in suppressed health data imputation but also lay a foundation for broader applications in privacy-preserving public health data analysis. These directions underscore the flexibility and scalability of the Monte Carlo approach, reinforcing its potential for addressing critical challenges in health data analysis across varying contexts and constraints.