Adjustment for Missingness Using Auxiliary Information in Semiparametric Regression

Summary .  In this article, we study the estimation of mean response and regression coefficient in semiparametric regression problems when response variable is subject to nonrandom missingness. When the missingness is independent of the response conditional on high-dimensional auxiliary information, the parametric approach may misspecify the relationship between covariates and response while the nonparametric approach is infeasible because of the curse of dimensionality. To overcome this, we study a model-based approach to condense the auxiliary information and estimate the parameters of interest nonparametrically on the condensed covariate space. Our estimators possess the double robustness property, i.e., they are consistent whenever the model for the response given auxiliary covariates or the model for the missingness given auxiliary covariate is correct. We conduct a number of simulations to compare the numerical performance between our estimators and other existing estimators in the current missing data literature, including the propensity score approach and the inverse probability weighted estimating equation. A set of real data is used to illustrate our approach.     

Regression Analysis with a Misclassified Covariate from a Current Status Observation Scheme

Summary Naive use of misclassified covariates leads to inconsistent estimators of covariate effects in regression models. A variety of methods have been proposed to address this problem including likelihood, pseudo‐likelihood, estimating equation methods, and Bayesian methods, with all of these methods typically requiring either internal or external validation samples or replication studies. We consider a problem arising from a series of orthopedic studies in which interest lies in examining the effect of a short‐term serological response and other covariates on the risk of developing a longer term thrombotic condition called deep vein thrombosis. The serological response is an indicator of whether the patient developed antibodies following exposure to an antithrombotic drug, but the seroconversion status of patients is only available at the time of a blood sample taken upon the discharge from hospital. The seroconversion time is therefore subject to a current status observation scheme, or Case I interval censoring, and subjects tested before seroconversion are misclassified as nonseroconverters. We develop a likelihood‐based approach for fitting regression models that accounts for misclassification of the seroconversion status due to early testing using parametric and nonparametric estimates of the seroconversion time distribution. The method is shown to reduce the bias resulting from naive analyses in simulation studies and an application to the data from the orthopedic studies provides further illustration.     

Valid Adjustment of Randomized Comparisons for Binary Covariates

In randomized trials, the treatment influences not only endpoints but also other variables measured after randomization which, when used as covariates to adjust for the observed imbalance, become pseudo‐covariates. There is a logical circularity in adjusting for a pseudo‐covariate because the variability in the endpoint that is attributed not to the treatment but rather to the pseudo‐covariate may actually represent an effect of the treatment modulated by the pseudo‐covariate. This potential bias is well known, but we offer new insight into how it can lead to reversals in the direction of the apparent treatment effect by way of stage migration. We then discuss a related problem that is not generally appreciated, specifically how the absence of allocation concealment can lead to this reversal of the direction of the apparent treatment effect even when adjustment is for a true covariate measured prior to randomization. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于协同克里格的橡胶园土壤速效钾空间变异性

选取有效变量的协同克里格方法能够提高县域尺度橡胶园土壤速效钾的空间预测精度,对橡胶树精准施肥管理具有重要意义。本研究以海南省白沙县橡胶园0～20 cm耕层土壤为对象,采用地统计学分析土壤速效钾的空间变异特征,运用相关分析筛选显著的特征变量,并比较不同变量的协同克里格(COK)空间插值精度。结果表明: 研究区土壤速效钾平均含量为44.65 g·kg^-1,总体处于缺乏状态;变异系数为52.6%,属中等变异强度;块金效应为12.5%,存在较强的空间自相关。有机质、高程与土壤速效钾含量关系密切,均呈极显著相关;有机质(COK₁)、高程(COK₂)、有机质+高程(COK₃)3种协变量的COK空间插值预测精度均高于普通克里格法(OK),交叉验证模型拟合精度为COK₁>COK₃> COK₂>OK;拟合精度与协变量选取的数量不呈正比,选取相关性更高的协变量更有利于反映区域土壤属性的空间异质性。研究区土壤速效钾含量具有西北部较高、中偏东部地区较低的分布特点。研究结果为今后开展橡胶园土壤钾素管理提供了理论依据。     

A note on the bias due to omitted confounders

In observational studies some confounders may be unknown andtherefore omitted from the analysis while others are adjustedfor. Approximations to the functions defining the relationshipbetween the parameters in the full and reduced models are proposedleading to asymptotic bias estimates. Numerical calculationsfor logistic and Poisson regression models show good agreementbetween asymptotic and simulation bias. A data set containingthe relationship between low birth weight and smoking (Hosmer& Lemeshow, 1989) is used as an illustration.     

Analysis of a molecular genetic neuro-oncology study with partially biased selection

Oligodendrogliomas are a common variant of malignant brain tumors, and are unique for their relative sensitivity to chemotherapy and better prognosis. For these reasons, the identification of an objective oligodendroglial marker has been a long sought-after goal in the field of neuro-oncology. To this end, 75 patients who received chemotherapy at the London Regional Cancer Centre between 1984 and 1999 were studied (Ino et al., Clinical Cancer Research, 7, 839-845, 2001). Of these 75 patients, 50 were initially treated with chemotherapy (the current practice) and comprise a population-based sample. The remaining 25 patients were initially treated with radiation and were included in the study only because their tumor recurred, at which time they received chemotherapy. Because this group of 25 patients included neither those radiation patients whose tumors never recurred nor those radiation patients whose tumors recurred but were not treated with chemotherapy, issues of selection bias were of concern. For this reason, the initial analysis of these data included only the 50 population-based patients. This was unsatisfying given the rarity of this disease and of genetic information on this disease and led us to question whether we could undertake an analysis that includes all of the patients. Here we examine approaches for utilizing the entire study population, as well as the assumptions required for doing so. We illustrate that there are both costs and benefits to using the 25 selected patients.     

A comparison of machine learning algorithms and covariate balance measures for propensity score matching and weighting

Propensity score matching (PSM) and propensity score weighting (PSW) are popular tools to estimate causal effects in observational studies. We address two open issues: how to estimate propensity scores and assess covariate balance. Using simulations, we compare the performance of PSM and PSW based on logistic regression and machine learning algorithms (CART; Bagging; Boosting; Random Forest; Neural Networks; naive Bayes). Additionally, we consider several measures of covariate balance (Absolute Standardized Average Mean (ASAM) with and without interactions; measures based on the quantile‐quantile plots; ratio between variances of propensity scores; area under the curve (AUC)) and assess their ability in predicting the bias of PSM and PSW estimators. We also investigate the importance of tuning of machine learning parameters in the context of propensity score methods. Two simulation designs are employed. In the first, the generating processes are inspired to birth register data used to assess the effect of labor induction on the occurrence of caesarean section. The second exploits more general generating mechanisms. Overall, among the different techniques, random forests performed the best, especially in PSW. Logistic regression and neural networks also showed an excellent performance similar to that of random forests. As for covariate balance, the simplest and commonly used metric, the ASAM, showed a strong correlation with the bias of causal effects estimators. Our findings suggest that researchers should aim at obtaining an ASAM lower than 10% for as many variables as possible. In the empirical study we found that labor induction had a small and not statistically significant impact on caesarean section.     

Small Sample Properties of the Likelihood Estimator in Proportional Hazard Regression Models with Omitted Variables

The paper deals with the effects of incorrectly omitted regressor variables in a parametric proportional hazard regression model. By studying conditions for equality between the estimators of correct and incorrect models it is demonstrated analytically that such cases are not to be expected in practise. A small sample Monte Carlo experiment indicates severe negative effects on the retained parameters both in terms of bias and mean square error.