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Novel Screening Methods for Binary Outcomes with Rare Events

This paper introduces and validates two novel screening methods, Rare-Screening and Firth-ttScreening, designed to improve the detection of CpG sites associated with rare binary events in high-dimensional epigenome-wide association studies, demonstrating superior sensitivity compared to traditional FDR and Bonferroni approaches.

Original authors: Mohammad Nahian Ferdous Abrar, Hongmei Zhang, Meredith Ray, Yuanjin Liu, Hasan Arshad, Yu Jiang

Published 2026-10-09

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CC BY 4.0

Original authors: Mohammad Nahian Ferdous Abrar, Hongmei Zhang, Meredith Ray, Yuanjin Liu, Hasan Arshad, Yu Jiang

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the vast landscape of human biology, scientists are increasingly turning their attention to the chemical switches that sit atop our DNA. These switches, known as methylation marks, act like volume knobs for our genes, turning them up or down without changing the genetic code itself. When researchers study these marks across the entire genome, they are looking for patterns that might explain why some people develop certain diseases while others do not. This field, called epigenetics, often involves sifting through hundreds of thousands of these chemical marks simultaneously. The challenge arises when the disease being studied is rare. If a researcher is looking for a link between a specific chemical mark and a disease that affects only a tiny fraction of people, the usual statistical tools often stumble. They struggle to find a signal in the noise because there are so few examples of the disease to learn from, leading to unstable results and missed connections.

A team of researchers at the University of Memphis and Maryville University has developed a new way to navigate this difficult terrain. They focused on a specific problem: how to efficiently screen for important biological markers when the event of interest, such as a specific disease or developmental milestone, happens in fewer than five percent of the people being studied. In these scenarios, standard methods often fail to detect true associations or produce unreliable data. To solve this, the researchers proposed two new techniques, which they named Rare-Screening and Firth-ttScreening. These methods are designed to act as a filter, sifting through the massive amount of data to keep the most promising candidates while discarding the unimportant ones, all while accounting for the scarcity of the disease cases.

The researchers tested their new methods using computer simulations that mimicked real-world biological data. They created scenarios with different numbers of people and different levels of rarity for the event, ranging from one percent to five percent. They then compared their new approaches against established statistical techniques that are commonly used to handle large datasets. The results showed that the traditional methods, which rely on strict rules to control for false alarms, often missed the true signals when the event was very rare. In contrast, the new Rare-Screening and Firth-ttScreening methods were much better at finding the true connections. In simulations where the event rate was as low as one percent, the new methods successfully identified the relevant markers far more often than the standard approaches, while still keeping the number of false alarms extremely low.

One of the key strengths of these new tools is their ability to handle the mathematical instability that occurs when there are very few cases. Traditional methods often break down or produce erratic results when the group of people with the disease is too small to provide a stable average. The new methods use clever statistical adjustments to stabilize these estimates, allowing them to work effectively even when the data is sparse. For instance, one of the new approaches uses a technique that borrows information from all the chemical marks being studied to stabilize the measurements for each individual mark. Another approach uses a specialized type of calculation that prevents the results from becoming infinite or undefined when the data is unbalanced. By repeating the analysis many times with slightly different versions of the data, the researchers ensured that only the most consistent and reliable markers were kept.

To see if these methods worked in the real world, the team applied them to a study of children born on the Isle of Wight in the United Kingdom. The researchers were interested in finding chemical marks present at birth that might be linked to early onset of menstruation, a developmental event that occurred in only about four percent of the girls in the study. This is a classic example of a rare event in a large dataset. Using their new methods, the team identified hundreds of potential markers associated with early menstruation. When they looked at the markers that both new methods agreed upon, they found a set of three hundred sixteen candidates. Further analysis of these candidates revealed connections to specific biological pathways, including those involved in cell membranes and energy production in cells. This real-world application demonstrated that the new tools could successfully find meaningful biological signals in a dataset where standard methods would likely have struggled or failed.

The researchers emphasize that these new methods are designed as a first step, a way to narrow down a massive list of possibilities to a manageable size for further study. They are not intended to provide the final proof of a disease link, but rather to generate a high-quality list of candidates for scientists to investigate more deeply. The team has made their new functions available to other researchers through a widely used software package, ensuring that the scientific community can apply these improved screening techniques to their own studies of rare diseases and complex traits. By making it easier to find true signals in sparse data, these tools offer a more reliable path forward for understanding the biological roots of rare conditions.

Technical Summary: Novel Screening Methods for Binary Outcomes with Rare Events

Problem Statement
Epigenome-wide association studies (EWAS) face a critical challenge when analyzing high-dimensional DNA methylation data (hundreds of thousands of CpG sites) against binary outcomes that occur rarely (event rates < 5%). In such scenarios, conventional association testing, including single-CpG logistic regression, often fails due to unstable regression coefficients, inflated standard errors, convergence issues, and separation problems. Furthermore, standard multiple testing correction methods, such as Bonferroni and False Discovery Rate (FDR) controls (e.g., Benjamini–Hochberg), are often overly conservative in rare-event settings. They tend to discard true associations because the effective number of cases is too small to generate strong signals, leading to a significant loss of power. While existing screening tools like ttScreening are effective for moderate event rates, they struggle when the case group is too small to provide stable estimates during training-testing splits.

Methodology
To address these limitations, the authors propose two novel screening frameworks designed specifically for high-dimensional data with rare binary outcomes: Rare-Screening and Firth-ttScreening. Both methods aim to reduce the search space of CpG sites to a manageable set of candidates for downstream analysis, prioritizing sensitivity over strict false discovery rate control at the screening stage.

Rare-Screening:
- Formulation: This method treats DNA methylation levels as a continuous response and the rare-event status as the primary predictor (a differential methylation approach).
- Mechanism: It employs linear modeling using the limma framework in R. Specifically, it uses lmFit followed by empirical Bayes moderation (eBayes). This moderation stabilizes CpG-specific variance estimates by borrowing information across sites, which is crucial when event counts are low.
- Resampling: The method utilizes repeated resampling with replacement (bootstrapping) at a 1:1 ratio of cases to controls. For each iteration, CpG sites are evaluated for significance (p < 0.05). A site is retained if it passes the significance threshold in a specific proportion of iterations (the cutoff value).
Firth-ttScreening:
- Formulation: This method adapts the original ttScreening framework but integrates Firth's bias-reduced logistic regression to handle separation and small-sample bias.
- Mechanism: It utilizes a training-testing split (2/3 training, 1/3 testing). Within each split, logistic regression with Firth's penalty correction is applied to all predictors. The penalty term, derived from the Fisher information matrix, prevents infinite estimates and reduces bias in the presence of rare events.
- Validation: A predictor is marked as a "pass" only if it is statistically significant in both the training and testing sets. This process is repeated over multiple iterations, and predictors are retained if they achieve a "pass" in a prespecified number of iterations.

Key Contributions

Novel Algorithms: The introduction of two distinct screening strategies tailored for the specific statistical pathologies of rare events (separation, instability, and low power).
Integration into Software: The implementation of these methods into the ttScreening R package, making them accessible via the Comprehensive R Archive Network (CRAN).
Optimization of Parameters: The study systematically evaluates cutoff thresholds for resampling iterations to find the optimal trade-off between sensitivity and specificity for different sample sizes.

Results
The authors evaluated the proposed methods through extensive simulations across varying sample sizes ( $n$ ), numbers of predictors ( $p$ ), and event rates (1% and 5%).

Simulation Performance:
- Sensitivity: Both Rare-Screening and Firth-ttScreening consistently outperformed standard FDR and Bonferroni approaches in rare-event settings. For a 1% event rate with $n=1000$ (10 events), Firth-ttScreening (cutoff 30) achieved the highest sensitivity (0.770–0.784), compared to 0.050–0.202 for FDR and Bonferroni.
- Specificity: All methods maintained high specificity (close to or above 99%), indicating that the increased sensitivity did not come at the cost of a high false-positive rate.
- Parameter Sensitivity: For Rare-Screening, a cutoff of 70% was found to provide a favorable balance across sample sizes. For Firth-ttScreening, a lower cutoff (30%) was optimal for smaller samples ( $n=500$ ), while a cutoff of 50% was preferred for larger samples ( $n \ge 750$ ).
- Scalability: Performance remained stable as the number of predictors increased to 50,000, demonstrating robustness in ultra-high-dimensional designs.
Case Study (Isle of Wight Cohort):
- The methods were applied to an EWAS of DNA methylation at birth associated with early onset of menarche (defined as <11 years), a rare event occurring in 4.1% of the 319 participants.
- Rare-Screening (cutoff 70) identified 1,031 CpG sites, while Firth-ttScreening (cutoff 50) identified 353 sites.
- The intersection of these methods yielded 316 common CpG sites. Gene Ontology analysis on these sites highlighted biological pathways related to the omegasome membrane and mitochondrial proton-transporting ATP synthase complex, though these did not survive strict FDR correction in the final analysis, reinforcing the role of these methods as candidate generators rather than definitive discovery tools.

Significance and Claims
The paper claims that Rare-Screening and Firth-ttScreening provide practical, efficient first-stage screening strategies for high-dimensional studies with rare binary outcomes. The primary significance lies in their ability to retain a higher proportion of truly associated markers (higher sensitivity) compared to conventional multiple-testing corrections, which often fail in sparse data environments.

The authors explicitly position these methods as screening tools rather than final inferential procedures. The goal is to generate a candidate set of CpG sites for downstream validation, biological pathway analysis, or formal multiple-testing correction, rather than to provide definitive discoveries with guaranteed FDR control. Additionally, the study highlights a computational advantage: Rare-Screening is significantly faster (approx. 1 minute vs. 15 minutes for 10,000 predictors) than Firth-ttScreening, offering a scalable option for large-scale EWAS. The authors note that while the methods are effective for main effects, they do not currently account for predictor interactions, suggesting this as a direction for future methodological extension.

Technical Summary: Novel Screening Methods for Binary Outcomes with Rare Events

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