Imputation of missing values is superior to complete case analysis and the missing-indicator method in multivariable diagnostic research: a clinical example

BACKGROUND AND OBJECTIVES: To illustrate the effects of different methods for handling missing data--complete case analysis, missing-indicator method, single imputation of unconditional and conditional mean, and multiple imputation (MI)--in the context of multivariable diagnostic research aiming to identify potential predictors (test results) that independently contribute to the prediction of disease presence or absence. METHODS: We used data from 398 subjects from a prospective study on the diagnosis of pulmonary embolism. Various diagnostic predictors or tests had (varying percentages of) missing values. Per method of handling these missing values, we fitted a diagnostic prediction model using multivariable logistic regression analysis. RESULTS: The receiver operating characteristic curve area for all diagnostic models was above 0.75. The predictors in the final models based on the complete case analysis, and after using the missing-indicator method, were very different compared to the other models. The models based on MI did not differ much from the models derived after using single conditional and unconditional mean imputation. CONCLUSION: In multivariable diagnostic research complete case analysis and the use of the missing-indicator method should be avoided, even when data are missing completely at random. MI methods are known to be superior to single imputation methods. For our example study, the single imputation methods performed equally well, but this was most likely because of the low overall number of missing values.     

Multiple bias analysis using logistic regression: an example from the National Birth Defects Prevention Study

Purpose

Exposure misclassification, selection bias, and confounding are important biases in epidemiologic studies, yet only confounding is routinely addressed quantitatively. We describe how to combine two previously described methods and adjust for multiple biases using logistic regression.

Nonparametric multiple imputation for receiver operating characteristics analysis when some biomarker values are missing at random

The receiver operating characteristics (ROC) curve is a widely used tool for evaluating discriminative and diagnostic power of a biomarker. When the biomarker value is missing for some observations, the ROC analysis based solely on complete cases loses efficiency because of the reduced sample size, and more importantly, it is subject to potential bias. In this paper, we investigate nonparametric multiple imputation methods for ROC analysis when some biomarker values are missing at random and there are auxiliary variables that are fully observed and predictive of biomarker values and/or missingness of biomarker values. Although a direct application of standard nonparametric imputation is robust to model misspecification, its finite sample performance suffers from curse of dimensionality as the number of auxiliary variables increases. To address this problem, we propose new nonparametric imputation methods, which achieve dimension reduction through the use of one or two working models, namely, models for prediction and propensity scores. The proposed imputation methods provide a platform for a full range of ROC analysis and hence are more flexible than existing methods that primarily focus on estimating the area under the ROC curve. We conduct simulation studies to evaluate the finite sample performance of the proposed methods and find that the proposed methods are robust to various types of model misidentification and outperform the standard nonparametric approach even when the number of auxiliary variables is moderate. We further illustrate the proposed methods by using an observational study of maternal depression during pregnancy.     

复检核酸阳性的新型冠状病毒感染者分布及传染性特征分析

  目的  回顾性分析福建省2021年3月 — 2022年2月新冠病毒Delta变异株感染与复阳者的流行病学特征。  方法   通过中国疾病预防控制信息系统中的传染病报告卡收集福建省2020年10月1日 — 2022年9月30日的新冠病毒感染者信息,通过突发公共卫生事件管理信息系统中的流行病学调查报告获取本土暴发疫情中的个案传播关系。运用描述流行病学的方法分析Delta变异株感染者的三间分布特征和潜伏期,运用R软件的“R0”、“EpiEstim”包拟合暴发疫情中感染者的代间隔（SI）并估算实时再生数（Rt）;分析复阳的发生率及其核酸检测情况,运用logistic回归分析复阳发生的影响因素。  结果   新冠病毒Delta变异株在福建省的流行时间大致为2021年3月 — 2022年2月,呈持续散在输入和本土局部暴发态势。输入性感染者以海员及长途驾驶员（28.99%）、学生（15.94%）以及商业服务人员（14.49%）为主,由厦门入境的感染者最多,主要来自东南亚和日本、美国、英国等地;本土疫情主要发生在莆田和厦门的学校和工厂,传播速度快,实时再生数（Rt）的最大值达7.35,代间隔（SI）服从Gamma分布,均值和标准差分别为2.28和2.06,中位潜伏期为6.50 d。复阳发生率为37.98%,本土感染者发生复阳的风险是输入性感染者的2.68倍（95%CI = 1.45～4.95）,病程为15～30 d的感染者发生复阳的风险是病程为45 d以上感染者的4.12倍（95%CI：1.18～14.34）。  结论   新冠病毒Delta变异株在福建省的流行时间大致为2021年3月 — 2022年2月,呈持续散在输入和本土局部暴发态势,输入性疫情防控压力较大,但暴发疫情得到迅速而有效的控制;Delta变异株感染者复阳发生率为37.98%,病程可能是复阳的影响因素。     

Extending the critical aspects of the water access indicator using East Africa as an example

The United Nations has declared 2005–2015 the Fresh Water Decade in which more people than ever before will gain access to water. Despite acknowledging that water quantity is important to health, so far only water quality is used in monitoring the Millennium Development Goals. This study examines the changes in national access figures when both water quality and quantity are taken into account to determine access. Using East Africa as an example shows that the number of people with access to water for the region decreased by 9% (7% urban and 10% rural). The largest difference in access is observed in Eritrea 25% (11% urban and 36% rural). Reduction is higher in rural areas. However, significant reduction in access is also observed in urban Ethiopia (14%). In conclusion, the indicators for access to water would be better articulated by adding water quantity to the indicator which currently only includes water quality, while the Demographic Health Survey and Multiple Indicator Cluster Survey routinely collects information on both aspects.     

Bias and efficiency of multiple imputation compared with complete‐case analysis for missing covariate values

When missing data occur in one or more covariates in a regression model, multiple imputation (MI) is widely advocated as an improvement over complete‐case analysis (CC). We use theoretical arguments and simulation studies to compare these methods with MI implemented under a missing at random assumption. When data are missing completely at random, both methods have negligible bias, and MI is more efficient than CC across a wide range of scenarios. For other missing data mechanisms, bias arises in one or both methods. In our simulation setting, CC is biased towards the null when data are missing at random. However, when missingness is independent of the outcome given the covariates, CC has negligible bias and MI is biased away from the null. With more general missing data mechanisms, bias tends to be smaller for MI than for CC. Since MI is not always better than CC for missing covariate problems, the choice of method should take into account what is known about the missing data mechanism in a particular substantive application. Importantly, the choice of method should not be based on comparison of standard errors. We propose new ways to understand empirical differences between MI and CC, which may provide insights into the appropriateness of the assumptions underlying each method, and we propose a new index for assessing the likely gain in precision from MI: the fraction of incomplete cases among the observed values of a covariate (FICO). Copyright © 2010 John Wiley & Sons, Ltd.     

Correcting for bias when estimating the cost of hospital-acquired infection: an analysis of lower respiratory tract infections in non-surgical patients

Hospital acquired infections (HAI) are costly but many are avoidable. Evaluating prevention programmes requires data on their costs and benefits. Estimating the actual costs of HAI (a measure of the cost savings due to prevention) is difficult as HAI changes cost by extending patient length of stay, yet, length of stay is a major risk factor for HAI. This endogeneity bias can confound attempts to measure accurately the cost of HAI. We propose a two-stage instrumental variables estimation strategy that explicitly controls for the endogeneity between risk of HAI and length of stay. We find that a 10% reduction in ex ante risk of HAI results in an expected savings of pound 693 ($ US 984).     

Cost-utility analysis when not everyone wants the treatment: modeling split-choice bias.

Not all clinically eligible patients will necessarily accept a new treatment. Cost-utility analysis recognizes this by multiplying the mean incremental expected utility (EU) by the participation rate to obtain the utility gain per head. However, the mean EU gain over all patients in a defined clinical category is traditionally used as a proxy for the mean EU gain over the subpopulation of acceptors. Even for clinically identical patients, this may lead to a biased assessment of total benefit because a patient motivated to accept the new treatment is likely to value its effects more favorably than a patient who declines. An analysis that ignores this tendency will be biased toward an underestimate of true benefits of a health technology (HT). The extent of this bias is described within a quality-adjusted life year-based utility model for a population of clinically indistinguishable patients who differ with respect to the values that they place on the possible health outcomes of an HT. The size of the bias is sensitive to the proportion of patients who accept the treatment, under both deterministic and probabilistic models of individual decision making. In all cases in which decision making is correlated with personal utility gain, the bias rises steeply as the proportion of acceptors declines.     

A novel polylocus method for linkage analysis using the lod-score or affected sib-pair method

A novel approach to combining data from multiple linked loci is proposed that can provide substantial increases in power over normal two-point linkage analysis or sib-pair analysis, with a substantial saving in computing time over traditional multipoint methods. © 1993 Wiley-Liss, Inc.     

Comparison of methods of handling missing data in individual patient data meta-analyses: an empirical example on antibiotics in children with acute otitis media

What is the influence of various methods of handling missing data (complete case analyses, single imputation within and over trials, and multiple imputations within and over trials) on the subgroup effects of individual patient data meta-analyses? An empirical data set was used to compare these five methods regarding the subgroup results. Logistic regression analyses were used to determine interaction effects (regression coefficients, standard errors, and p values) between subgrouping variables and treatment. Stratified analyses were performed to determine the effects in subgroups (rate ratios, rate differences, and their 95% confidence intervals). Imputation over trials resulted in different regression coefficients and standard errors of the interaction term as compared with imputation within trials and complete case analyses. Significant interaction effects were found for complete case analyses and imputation within trials, whereas imputation over trials often showed no significant interaction effect. Imputation of missing data over trials might lead to bias, because association of covariates might differ across the included studies. Therefore, despite the gain in statistical power, imputation over trials is not recommended. In the authors' empirical example, imputation within trials appears to be the most appropriate approach of handling missing data in individual patient data meta-analyses.     

To treat or not to treat: evidence for "treatment bias" when consumers evaluate physicians

Previous research has generally ignored whether consumers exhibit a "treatment bias" and have more favorable opinions of physicians who provide more treatment even if the benefits of more treatment are equivocal. This research experimentally manipulates three variables, (1) treatment choice (more treatment versus less treatment), (2) interpersonal treatment (patient involvement with treatment decisions), and (3) health outcomes, and examines their influence on respondent's inferences about the physician's ability, concern for patient welfare, quality of care, and accountability for patient death. Results clearly showed evidence of a treatment bias. Consumers made more favorable inferences about the physician in the more treatment condition even though both physicians acknowledged that the less treatment option was recommended for the patient. Results also showed that consumers' inferences about the physician were more favorable in the better health outcomes condition. There was no influence of patient involvement on consumers' inferences about the physician.     

Advocating for clients: successful case management when clients retain an attorney

Have you ever been driving comfortably along a highway and suddenly noticed, looming in the mirror, a very large truck coming up the road? The sight can be startling. Although you do not need to panic or pull off at the next exit, a bit of increased alertness, a review of defensive driving basics, and preparation for possible turbulence is more than appropriate.     

Heavy equipment maintenance exposure assessment: using a time-activity model to estimate surrogate values for replacement of missing data

This study on four pieces of heavy construction equipment was conducted to determine the concentration of airborne asbestos fibers during in-frame maintenance and repair activities, which included aggressive techniques that resulted in visible dust from work involving friction products and gaskets. Despite execution of a carefully planned sampling strategy, approximately 10% (47) of the samples collected could not be analyzed due to overloading or filter damage. To include the overloaded samples in the data analysis, surrogate values were estimated following a time-activity model. Twelve long-term personal samples, 2 short-term, 30-min personal samples, and 31 long-term area samples were modeled. Personal and area time-weighted average (TWA) data were analyzed both with and without the estimated surrogate values and compared. A total of 444 samples were collected over 9 days. Four experienced heavy equipment mechanics removed and replaced friction products and gaskets. Samples were analyzed using NIOSH Method 7400 Phase Contrast Microscopy followed by NIOSH Method 7402 Transmission Electron Microscopy. Sample data information including the surrogate values for the full-shift, TWA personal sample results ranged from 0.002 to 0.064 asbestos f/cc. Personal, short-term, 30-min sample results, including the two surrogate values, ranged from 0.038 to 0.561 asbestos f/cc. Full-shift TWA area samples, including the 31 surrogate values, ranged from 0.005 to 0.039 asbestos f/cc. Area air sample results at the end of the project were similar to levels measured before the start of the project. No fiber concentration buildup within the work area was indicated over the 9-day study. All full-shift personal and area TWA sample results were below 0.1 f/cc, and short-term 30-min personal samples were below 1.0 f/cc. Statistical results of the sample data with and without the surrogate values were consistent. Use of the time-activity model reduced the uncertainty associated with this data analysis and provided a consistent logical process for estimating surrogate values to replace missing data.     

A new method to address verification bias in studies of clinical screening tests: cervical cancer screening assays as an example

ObjectivesStudies to evaluate clinical screening tests often face the problem that the “gold standard” diagnostic approach is costly and/or invasive. It is therefore common to verify only a subset of negative screening tests using the gold standard method. However, undersampling the screen negatives can lead to substantial overestimation of the sensitivity and underestimation of the specificity of the diagnostic test. Our objective was to develop a simple and accurate statistical method to address this “verification bias.”Study Design and SettingWe developed a weighted generalized estimating equation approach to estimate, in a single model, the accuracy (eg, sensitivity/specificity) of multiple assays and simultaneously compare results between assays while addressing verification bias. This approach can be implemented using standard statistical software. Simulations were conducted to assess the proposed method. An example is provided using a cervical cancer screening trial that compared the accuracy of human papillomavirus and Pap tests, with histologic data as the gold standard.ResultsThe proposed approach performed well in estimating and comparing the accuracy of multiple assays in the presence of verification bias.ConclusionThe proposed approach is an easy to apply and accurate method for addressing verification bias in studies of multiple screening methods.     

Hospital efficiency under prospective reimbursement schemes: an empirical assessment for the case of Germany

The introduction of prospective hospital reimbursement based on diagnosis-related groups (DRG) has been a conspicuous attempt to decelerate the steady increase of hospital expenditures in the German health sector. In this work, the effect of the financial reform on hospital efficiency is subjected to empirical testing by means of two complementary testing approaches. On the one hand, we apply a two-stage procedure based on non-parametric efficiency measurement. On the other hand, a stochastic frontier model is employed that allows a one-step estimation of both production frontier parameters and inefficiency effects. To identify efficiency gains as a consequence of changes in the hospital incentive structure, we account for technological progress, spatial dependence and hospital heterogeneity. The results of both approaches do not reveal any increase in overall efficiency after the DRG reform. In contrast, a significant decline in overall hospital efficiency over time is observed.