一種適用於群組檢測資料之潛在個體陽性率時空建模方法

Abstract

在蚊媒傳染病監測中，群組檢測（pooled testing）雖然能有效降低檢測成本，但是由於觀測結果僅反映 pool 是否陽性，如果忽略 pool size 與資料聚合機制，將難以正確推論個體感染風險。本文以西尼羅病毒（West Nile Virus, WNV）蚊蟲監測資料為例，在 pooled Bernoulli 機制下，採用一個以概似為基礎的方法來估計潛在個體陽性率，並檢視其時間與空間變化。研究中建構 pooled logistic regression model，將年份與季節納入時間固定效應，並以低秩空間基底函數近似空間效應，再整合為時空模型。參數估計用最大概似法配合數值最佳化進行，並以概似比檢定、空間效應檢定與交叉驗證評估模型表現。實證結果顯示，WNV 感染風險具有明顯的年際差異與季節性變化，並且在控制時間效應後仍存在空間異質性。雖然本文採用的方法相較於完整的貝氏空間群組檢測模型更為簡化，但本文並不主張取代該類方法；其主要優點在於提供一個可解釋、以概似為基礎，且適合反覆重新配適以進行概似比檢定、bootstrap 推論與位置分組交叉驗證的分析框架。因此，本文所採用的建模方式可作為 pooled testing 監測資料的一種實用且可重複的分析工具。

In mosquito-borne disease surveillance, pooled testing can substantially reduce laboratory costs, but the observed outcome only indicates whether a pool is positive. As a result, standard individual-level binary models are not directly applicable, and ignoring pool size and the aggregation mechanism may lead to distorted inference on the underlying individual infection risk. Using West Nile Virus (WNV) mosquito surveillance data, this thesis adopts a likelihood-based approach under the pooled Bernoulli mechanism to estimate the latent individual positivity rate and to examine its temporal and spatial variation. A pooled logistic regression model is constructed by incorporating year and season as fixed temporal effects and approximating spatial effects through low-rank spatial basis functions, which are then integrated into a spatio-temporal model. Parameters are estimated by maximum likelihood with numerical optimization, and model performance is evaluated using likelihood ratio tests, spatial effect tests, and cross-validation. The empirical results indicate clear interannual differences and seasonal variation in WNV infection risk, and spatial heterogeneity remains after adjusting for temporal effects. Although the proposed approach is simpler than fully Bayesian spatial group-testing models, it is not presented as a replacement for those methods. Its main advantage is that it provides an interpretable likelihood-based framework that can be refit repeatedly for likelihood-ratio testing, bootstrap inference, and location-blocked cross-validation while preserving the pooled Bernoulli structure of the data. Overall, the proposed model provides a practical and reproducible analytical tool for pooled testing surveillance data.