Robust Sandwich Variance Estimator Research Articles

Breast cancer: Does where you get treated affect survival?

28 Background: Under the ACA, more women are insured with Medicaid which should improve access to cancer care. However, Disproportionate Share Hospitals (DSH) are due to receive reduced subsidies thereby threatening resource stressed facilities and poorer hospitals are experiencing greater financial penalties due to higher readmission rates. In NYS, 83% of Medicaid breast cancer patients got their cancer surgery at DSH hospitals. As women gain more choice and access, they will require information about hospitals’ quality and outcomes of cancer care. We sought to determine whether there are survival advantages among breast cancer patients treated at hospitals with varying proportions of Medicaid patients. Methods: We used non-obstetric delivery Medicaid discharges from NYS hospitals in 2005-13 to create quintiles of hospitalized patients with Medicaid. Women treated for breast cancer were identified with a diagnostic and procedure code for breast cancer. Based on NYS hospital discharge database linked with vital statistics death records, we calculated hazard ratios using marginal Cox model with a robust sandwich variance estimator controlling for clustering of patients within the hospital, age and comorbidity. Results: Quintiles of Medicaid hospitals ranged from low (0-15%), to low medium (15-22%), medium (22-29%), medium-high (29-50%), to high ( > 50%). 26% of breast cancer patients were treated at the low; 22% at the low medium; 20% at the medium; 21% at the medium-high and 11% at high quintile hospitals. Patients treated in hospitals with > 50% Medicaid patients had a higher long-term mortality (HR = 1.51; 95%CI: 1.19-1.93) compared to those treated at the lowest quintile hospitals. Sensitivity analyses to adjust for stage are underway. Conclusions: While the ACA may improve access to breast cancer treatment, the long term impact on survival remains questionable as women with breast cancer treated at hospitals with high proportions of Medicaid patients may have worse survival. Analyses to control for stage are underway. Pending these results, hospitals with high proportions of Medicaid patients may need to target cancer quality improvement efforts to assure equitable outcomes.

Effect of covariate omission in Weibull accelerated failure time model: a caution.

The accelerated failure time model is presented as an alternative to the proportional hazard model in the analysis of survival data. We investigate the effect of covariates omission in the case of applying a Weibull accelerated failure time model. In an uncensored setting, the asymptotic bias of the treatment effect is theoretically zero when important covariates are omitted; however, the asymptotic variance estimator of the treatment effect could be biased and then the size of the Wald test for the treatment effect is likely to exceed the nominal level. In some cases, the test size could be more than twice the nominal level. In a simulation study, in both censored and uncensored settings, Type I error for the test of the treatment effect was likely inflated when the prognostic covariates are omitted. This work remarks the careless use of the accelerated failure time model. We recommend the use of the robust sandwich variance estimator in order to avoid the inflation of the Type I error in the accelerated failure time model, although the robust variance is not commonly used in the survival data analyses.

A unified model for estimating and testing familial aggregation

Investigations of familial aggregation of disease can provide important clues for genetic mechanisms, and many such studies have been published in the epidemiological literature using various statistical methods. We developed a unified model for familial risk by extending a Cox regression model to enable estimation of the detailed effects of kinship. By appropriate parameterisation of the model, we show how the risks to all specific first-degree kinships can be estimated and formally compared using simple interaction terms and how the model can be extended to accommodate higher-degree relatives. The correlation due to observations from family members and from the potential for repeated observations is accommodated by a robust sandwich variance estimator or a bootstrap estimate. Hazard ratios for different kinships are formally compared using a robust Wald test. We illustrate the method with applications to studies of adult leukemia and non-Hodgkin's lymphoma in the Swedish population and display our results on a pedigree diagram. Our estimates are consistent with published work that used simpler stratified methods, and our model enabled the detection of a number of statistically significant effects of kinship. The recognition of such kindred-specific disease risk could be a first step in the design of more informative genetic biomarker studies.

On the proportional hazards model for occupational and environmental case-control analyses

BackgroundCase-control studies are generally designed to investigate the effect of exposures on the risk of a disease. Detailed information on past exposures is collected at the time of study. However, only the cumulated value of the exposure at the index date is usually used in logistic regression. A weighted Cox (WC) model has been proposed to estimate the effects of time-dependent exposures. The weights depend on the age conditional probabilities to develop the disease in the source population. While the WC model provided more accurate estimates of the effect of time-dependent covariates than standard logistic regression, the robust sandwich variance estimates were lower than the empirical variance, resulting in a low coverage probability of confidence intervals. The objectives of the present study were to investigate through simulations a new variance estimator and to compare the estimates from the WC model and standard logistic regression for estimating the effects of correlated temporal aspects of exposure with detailed information on exposure history.MethodWe proposed a new variance estimator using a superpopulation approach, and compared its accuracy to the robust sandwich variance estimator. The full exposure histories of source populations were generated and case-control studies were simulated within each source population. Different models with selected time-dependent aspects of exposure such as intensity, duration, and time since cessation were considered. The performances of the WC model using the two variance estimators were compared to standard logistic regression. The results of the different models were finally compared for estimating the effects of correlated aspects of occupational exposure to asbestos on the risk of mesothelioma, using population-based case-control data.ResultsThe superpopulation variance estimator provided better estimates than the robust sandwich variance estimator and the WC model provided accurate estimates of the effects of correlated aspects of temporal patterns of exposure.ConclusionThe WC model with the superpopulation variance estimator provides an alternative analytical approach for estimating the effects of time-varying exposures with detailed history exposure information in case-control studies, especially if many subjects have time-varying exposure intensity over lifetime, and if only one control is available for each case.

Survival Models on Unobserved Heterogeneity and their Applications in Analyzing Large-scale Survey Data.

In survival analysis, researchers often encounter multivariate survival time data, in which failure times are correlated even in the presence of model covariates. It is argued that because observations are clustered by unobserved heterogeneity, the application of standard survival models can result in biased parameter estimates and erroneous model-based predictions. In this article, the author describes and compares four methods handling unobserved heterogeneity in survival analysis: the Andersen-Gill approach, the robust sandwich variance estimator, the hazard model with individual frailty, and the retransformation method. An empirical analysis provides strong evidence that in the presence of strong unobserved heterogeneity, the application of a standard survival model can yield equally robust parameter estimates and the likelihood ratio statistic as does a corresponding model adding an additional parameter for random effects. When predicting the survival function, however, a standard model on multivariate survival time data can result in serious prediction bias. The retransformation method is effective to derive an adjustment factor for correctly predicting the survival function.

Variance estimation for clustered recurrent event data with a small number of clusters

Often in biomedical studies, the event of interest is recurrent and within-subject events cannot usually be assumed independent. In semi-parametric estimation of the proportional rates model, a working independence assumption leads to an estimating equation for the regression parameter vector, with within-subject correlation accounted for through a robust (sandwich) variance estimator; these methods have been extended to the case of clustered subjects. We consider variance estimation in the setting where subjects are clustered and the study consists of a small number of moderate-to-large-sized clusters. We demonstrate through simulation that the robust estimator is quite inaccurate in this setting. We propose a corrected version of the robust variance estimator, as well as jackknife and bootstrap estimators. Simulation studies reveal that the corrected variance is considerably more accurate than the robust estimator, and slightly more accurate than the jackknife and bootstrap variance. The proposed methods are used to compare hospitalization rates between Canada and the U.S. in a multi-centre dialysis study.

Assessing Accuracy of Mammography in the Presence of Verification Bias and Intrareader Correlation

The performance of a medical diagnostic test is often evaluated by comparing the outcome of the test to the patient's true disease state. Receiver operating characteristic analysis may then be used to summarize test accuracy. However, such analysis may encounter several complications in actual practice. One complication is verification bias, i.e., gold standard assessment of disease status may only be partially available and the probability of ascertainment of disease may depend on both the test result and characteristics of the subject. A second issue is that tests interpreted by the same rater may not be independent. Using estimating equations, we generalize previous methods that address these problems. We contrast the performance of alternative estimators of accuracy using robust sandwich variance estimators to permit valid asymptotic inference. We suggest that in the context of an observational cohort study where rich covariate information is available, a weighted estimating equations approach may be preferable for its robustness against model misspecification. We apply the methodology to mammography as performed by community radiologists.

Robust variance estimators for fixed-effect estimates with hierarchical-likelihood

In longitudinal studies, robust sandwich variance estimators are often used, and are especially useful when model assumptions are in doubt. However, the usual sandwich estimator does not allow for models with crossed random effects. The hierarchical likelihood extends the idea of the sandwich estimator to models not currently covered. By simulation studies, we show that the new sandwich estimator is robust against heteroscedastic errors and against misspecification of overdispersion in the y v v component.