Some features of this site may not work without it. Attention submitters: Web accessibility policy to take effect October 15, For more information, please see our web accessibility policy and web accessibility help for submitters. No Access Until Collections Cornell Theses and Dissertations. Metadata Show full item record. Author Steingrimsson, Jon. Abstract This dissertation focuses on utilizing information more efficiently in several settings when some observations are right-censored using the semiparametric efficiency theory developed in Robins et al. Chapter 2 focuses on estimation of the regression parameter in the semiparametric accelerated failure time model when the data is collected using a case-cohort design.

The previously proposed methods of estimation use some form of HorvitzThompsons estimators which are known to be inefficient and the main aim of Chapter 2 is to improve efficiency of estimation of the regression parameter for the accelerated failure time model for case-cohort studies. University A to Z Departments.

Article in Annals of the Institute of Statistical Mathematics. Article in Annals of Statistics. Article in Econometrics and Statistics. Article in Journal of Nonparametric Statistics. Article in Journal of Time Series Analysis. Variations on this problem have been considered by a number of authors, including Chatterjee et al.

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We motivate many of these estimators from the point of view of importance sampling and compare estimators and algorithms for bias and efficiency with the profile estimator when the observations and covariates are discrete or continuous. Bin Nan University of Michigan A new look at some efficiency results for semiparametric models with missing data Missing data problems arise very often in practice. Many ad hoc useful tools have been developed in estimating finite dimensional parameters from semiparametric regression models with data missing at random.

In the mean while, efficient estimation has been paid more and more attention, especially after the landmark paper of Robins, Rotnitzky, and Zhao We review several examples on information bound calculations.

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Our main purpose is to show how the general result derived by Robins, Rotnitzky, and Zhao can apply to different models. Anastesia Nwankwo Enugu State University Missing multivariate data in banking computations In processing data emanating from multiple files in financial markets, ranking methods are called into play if set probability indices are to be maintained. Horizontal computations yield many evidences of missing entries from nonresponse and other factors.

James L. Following imputation, analysis results for the imputed datasets can easily be combined to estimate sampling variances that include the effect of imputation. However, situations have been identified where the usual combining rules can overestimate these variances. More recently, variance underestimates have also been shown to occur. A new multiple imputation method based on estimating equations has been developed to address these concerns, although this method requires more information about the imputation model than just the analysis results from each imputed dataset.

Furthermore, the new method only handles i. In this talk, this method is extended to accommodate complex sample designs, and is applied to two complex surveys with substantial amounts of missing data. Results will be compared with those from the traditional multiple imputation variance estimator, and the implications for survey practice will be discussed. Application of a Unified Theory of Parametric, Semi, and Nonparametric Statistics Based On Higher Dimensional Influence Functions to Coarsened at Random Missing Data Models The standard theory of semi-parametric inference provides conditions under which a finite dimensional parameter of interest can be estimated at root-n rates in models with finite or infinite dimensional nuisance parameters.

The theory is based on likelihoods, first order scores, and first order influence functions and is very geometric in character often allowing results to be obtained without detailed probabilistic epsilon and delta calculations. The modern theory of non-parametric inference determines optimal rates of convergence and optimal estimators for parameters whether finite or infinite dimensional that cannot be estimated at rate root-n or better.

This theory is based largely based on merging mini-max theory with measures of the size of the parameter space e. It often makes great demands on the mathematical and probabilistic skills of its practioners. In this talk I extend earlier work by Small and McLeish and Waterman and Lindsay and present a theory based on likelihoods, higher order scores i. The theory is applied to estimation of functionals of the full data distribution in coarsened at random missing data models.

Andrea Rotnitsky Doubly-robust estimation of the area under the operating characteristic curve in the presence of non-ignorable verification bias. The area under the receiver operating characteristic curve AUC is a popular summary measure of the efficacy of a medical diagnostic test to discriminate between healthy and diseased subjects. A frequently encountered problem in studies that evaluate a new diagnostic test is that not all patients undergo disease verification because the verification test is expensive, invasive or both.

Furthermore, the decision to send patients to verification often depends on the new test and on other predictors of true disease status.

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In such case, usual estimators of the AUC based on verified patients only are biased. In this talk we develop estimators of the AUC of markers measured on any scale that adjust for selection to verification that may depend on measured patient covariates and diagnostic test results and additionally adjust for an assumed degree of residual selection bias.

Such estimators can then be used in a sensitivity analysis to examine how the AUC estimates change when different plausible degrees of residual association are assumed. More interestingly, we describe a doubly robust estimator that has the attractive feature of being CAN if either the disease or the selection model but not necessarily both are correct. We illustrate our methods with data from a study run by the Nuclear Imaging Group at Cedars Sinai Medical Center on the efficacy of electron beam computed tomography to detect coronary artery disease.

### Working Papers & Publications

Donald B. Rubin John L. Loeb Professor of Statistics, Department of Statistics. Multiple imputation has become, since its proposal a quarter of a century ago Rubin , a standard tool for dealing with item nonresponse.

## Subject Sylbus: Semiparametric Models -

There is now widely available free and commercial software for both the analysis of multiply-imputed data sets and for their construction. The methods for their analysis are very straightforward and many evaluations of their frequentist properties, both with artificial and real data, have supported the broad validity of multiple imputation in practice, at least relative to competing methods.

The methods for the construction of a multiply-imputed data set, however, either 1 assume theoretically clean situations, such as monotone patterns of missing data or a convenient multivariate distribution, such as the general location model or t-based extensions of it; or 2 use theoretically less well justified, fully conditional "chained equations," which can lead to "incompatible" distributions in theory, which often seem to be harmless in practice.

Thus, there remains the challenge of constructing multiply-imputed data sets in situations where the missing data pattern is not monotone or the distribution of the complete data is complex in the sense of being poorly approximated by standard analytic multivariate distributions. A current example that illustrates current work on this issue involves the multiple imputation of missing immunogenicity and reactogenicity measurements in ongoing randomized trials at the US CDC, which compare different versions of vaccinations for protection against lethal doses of inhalation anthrax.

## Semiparametric Theory And Missing Data

The method used to create the imputations involves capitalizing on approximately monotone patterns of missingness to help implement the chained equation approach, thereby attempting to minimize incompatibility; this method extends the approach in Rubin used to multiply impute the US National Medical Expenditure Survey. In many prospective studies, subjects are evaluated for the occurrence of an absorbing event of interest e.

Since subjects often miss scheduled visits, the underlying visit of first detection may be interval censored, or more generally, coarsened. Interval-censored data are usually analyzed using the non-identifiable coarsening at random CAR assumption. In some settings, the visit compliance and underlying event time processes may be associated, in which case CAR is violated. To examine the sensitivity of inference, we posit a class of models that express deviations from CAR.

These models are indexed by nonidentifiable, interpretable parameters, which describe the relationship between visit compliance and event times.

### ISBN 10: 0387324488

Plausible ranges for these parameters require eliciting information from scientific experts. For each model, we use the EM algorithm to estimate marginal distributions and proportional hazards model regression parameters. The performance of our method is assessed via a simulation study. Alastair Scott University of Auckland Fitting family-specific models to retrospective family data Case-control studies augmented by the values of responses and covariates from family members allow investigators to study the association of the response with genetics and environment by relating differences in the response directly to within-family differences in the covariates.

Most existing approaches to case-control family data parametrize covariate effects in terms of the marginal probability of response, the same effects that one estimates from standard case-control studies.