考慮母體異質性之下合成外部綜合資訊的比例風險模式的半參數估計

Abstract

隨著大型資料庫的建立，愈來愈多可信的摘要統計量得以取得，因此，納入這些外部輔助資訊以提升內部小樣本個別資料下統計分析的有效性的研究也日漸受到重視。本研究假設在Cox比例風險模式下，考慮收集了更為全面之個別層級共變數資訊的右設限存活資料作為內部資料，而外部輔助資訊則包含了外部少數共變數之摘要統計量，以及考慮這些共變數下外部縮減Cox模式的迴歸係數。當這些外部共變數的分布不同於內部資料中對應之共變數的分布時，本研究提出一個新的估計方法，考慮以密度比模式來處理內外部共變數分布異質性之下，合成外部資訊與內部個別資料資訊以改善內部迴歸係數估計的有效性。在容許共變數分布異質性下，本研究應用廣義動差法來合成內部個別資訊與外部綜合資訊，提出內部Cox模式係數與密度比模式係數的估計方法。在允許外部縮減Cox模式和密度比模式中估計迴歸係數的不確定性存在下，推導所提出估計量的大樣本性質。根據大樣本性質可知所提出估計量比僅使用內部個別資料的估計量更有效。本研究之數值模擬結果指出，本研究提出的估計量能在不同情境下提升有效性，且當內外部共變數分布至少期望值存在異質性時，還能夠進一步改善準確度。

As large-scale databases continue to expand, a wide variety of reliable summary statistics are increasingly prevalent and readily available from public domains. Therefore, how to synthesize such external auxiliary information from public domains to improve efficiency in the analysis of the internal data from a relatively small-scale study has become an important research issue. In this study, we consider the right censored survival data with more thorough patient-level covariate information as the internal data under Cox proportional hazards model. The external auxiliary information includes the summary statistics of the external reduced covariates and regression coefficients from a reduced Cox model with the external covariates. When the distributions of the external covariates may be different from those of the corresponding internal covariates, we present a novel approach to improve the efficiency in estimating the regression coefficients by integrating the external information into the internal individual-level data. A density ratio model is considered for addressing the heterogeneity in distributions of the internal and external covariates. For the development of estimating of the regression coefficients in Cox model and those in density ratio model for covariates, the generalized method of moments is adopted to incorporate information from internal individual-level data and external aggregate data to allow the heterogeneity of covariate distributions. The large-sample property of the proposed estimator is established by considering the uncertainty for estimated regression coefficients in reduced model from external source and those in density ratio model. Moreover, the proposed estimator is more efficient than the estimator only using internal individual-level data. The simulation results indicate that the proposed estimators gain efficiency under various scenarios. In particular, when the internal and external distributions of covariates have at least different means, the accuracy of the proposed estimators are also improved.