基於非參數稀釋效應模型之群體檢測迴歸

Abstract

群體檢測在大規模傳染病篩檢中被廣泛應用，能有效降低檢測成本並提升篩檢效率。然而，在實務操作中，由於樣本混合所造成的稀釋效應，可能降低檢測靈敏度，進而導致偽陰性結果的增加，影響推論的準確性與可靠性。傳統方法多假設檢測靈敏度與群體大小無關，此假設在許多實際情境下並不合理。 為了解決上述問題，本文考慮群體檢測迴歸模型，並引入一個具單調性約束之非參數子模型，以彈性刻劃稀釋效應對群體檢測機率的影響，避免因錯誤的參數模型假設而導致模型錯配。在此架構下，我們進一步建立一套基於概似比檢定的統計推論方法，用以檢驗稀釋效應是否存在。 透過模擬研究，我們系統性地比較非參數方法與多種常見參數模型在不同稀釋結構與樣本設定下的表現。結果顯示，所提出之非參數方法在多數情境下具有穩健性，並能有效捕捉不同型態之稀釋效應。

Group testing has been widely used for large-scale infectious disease screening due to its efficiency in reducing testing costs. However, in practical applications, the dilution effect caused by sample pooling may reduce assay sensitivity, leading to an increased probability of false negatives and potentially biased inference. Many existing methods assume that sensitivity is constant and independent of pool size, an assumption that is often unrealistic in practice. To address this issue, we consider a group testing regression framework and introduce a nonparametric submodel with monotonicity constraints to flexibly characterize the relationship between the number of infected individuals in a pool and the pooled testing probability. This approach avoids potential model misspecification arising from restrictive parametric assumptions. Within this framework, we further develop a likelihood ratio test to assess the presence of dilution effects. Simulation studies are conducted to compare the proposed nonparametric method with several commonly used parametric models, including logistic, probit, and complementary log-log models, under various dilution structures and experimental settings. The results indicate that the proposed approach is robust across a range of scenarios and effectively captures different patterns of dilution effects.