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Optimal Matching with Minimal Deviation from Fine Balance in a Study of Obesity and Surgical Outcomes

BIOMETRICS 2012年第2期68卷 628-636页

作者： Yang, Dan Small, Dylan S. Silber, Jeffrey H. Rosenbaum, Paul R. Univ Penn Wharton Sch Dept Stat Philadelphia PA 19104 USA

In multivariate matching, fine balance constrains the marginal distributions of a nominal variable in treated and matched control groups to be identical without constraining who is matched to whom. In this way, a fine balance constraint can balance a nominal variable with many levels while focusing efforts on other more important variables when pairing individuals to minimize the total covariate distance within pairs. Fine balance is not always possible;that is, it is a constraint on an optimization problem, but the constraint is not always feasible. We propose a new algorithm that returns a minimum distance finely balanced match when one is feasible, and otherwise minimizes the total distance among all matched samples that minimize the deviation from fine balance. Perhaps we can come very close to fine balance when fine balance is not attainable;moreover, in any event, because our algorithm is guaranteed to come as close as possible to fine balance, the investigator may perform one match, and on that basis judge whether the best attainable balance is adequate or not. We also show how to incorporate an additional constraint. The algorithm is implemented in two similar ways, first as an optimal assignment problem with an augmented distance matrix, second as a minimum cost flow problem in a network. The case of knee surgery in the Obesity and Surgical Outcomes Study motivated the development of this algorithm and is used as an illustration. In that example, 2 of 47 hospitals had too few nonobese patients to permit fine balance for the nominal variable with 47 levels representing the hospital, but our new algorithm came very close to fine balance. Moreover, in that example, there was a shortage of nonobese diabetic patients, and incorporation of an additional constraint forced the match to include all of these nonobese diabetic patients, thereby coming as close as possible to balance for this important but recalcitrant covariate.

关键词： assignment algorithm Fine balance Matching Network optimization Observational study Optimal matching

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Optimal Matching of an Optimally Chosen Subset in Observational Studies

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2012年第1期21卷 57-71页

作者： Rosenbaum, Paul R. Univ Penn Dept Stat Philadelphia PA 19104 USA

An algorithm is proposed for optimally matching to controls an optimally chosen subset of treated subjects. The algorithm makes three optimal decisions at once: (i) the number of treated subjects to match, (ii) the identity of the treated subjects to match, and (iii) the identity of the controls with whom they are paired. The algorithm finds an optimal assignment for an augmented distance matrix. An example from critical care medicine is considered in detail. An R-workspace is available under "supplemental materials";it can reproduce the matches in the example.

关键词： assignment algorithm Matched sample Network optimization

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Feature point tracking combining the Interacting Multiple Model filter and an efficient assignment algorithm

Feature point tracking combining the Interacting Multiple Mo...

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Conference on Visual Communications and Image Processing 2007

作者： Marimon, David Abdeljaoued, Yousri Palacios, Bruno Ebrahimi, Touradi Swiss Fed Inst Technol EPFL Signal Proc Inst CH-1015 Lausanne Switzerland

ISBN: (纸本)9780819466211

An algorithm for feature point tracking is proposed. The Interacting Multiple Model (IMM) filter is used to estimate the state of a feature point. The problem of data association, i.e. establishing which feature point to use in the state estimator, is solved by an assignment algorithm. A track management method is also developed. In particular a track continuation method and a track quality indicator are presented. The evaluation of the tracking system on real sequences shows that the IMM filter combined with the assignment algorithm outperforms the Kalman filter, used with the Nearest Neighbour (NN) filter, in terms of data association performance and robustness to sudden feature point manoeuvre.

关键词： feature point extraction and tracking Interacting Multiple Model filter assignment algorithm track management

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Matching for Several Sparse Nominal Variables in a Case-Control Study of Readmission Following Surgery

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AMERICAN STATISTICIAN 2011年第4期65卷 229-238页

作者： Zubzarreta, Jose R. Reinke, Caroline E. Kelz, Rachel R. Silber, Jeffrey H. Rosenbaum, Paul R. Univ Penn Wharton Sch Dept Stat Philadelphia PA 19104 USA Univ Penn Sch Med Philadelphia PA 19104 USA

Matching for several nominal covariates with many levels has usually been thought to be difficult because these covariates combine to form an enormous number of interaction categories with few if any people in most such categories. Moreover, because nominal variables are not ordered, there is often no notion of a "close substitute" when an exact match is unavailable. In a case-control study of the risk factors for readmission within 30 days of surgery in the Medicare population, we wished to match for 47 hospitals, 15 surgical procedures grouped or nested within 5 procedure groups, two genders, or 47 x 15 x 2 = 1410 categories. In addition, we wished to match as closely as possible for the continuous variable age (65-80 years). There were 1380 readmitted patients or cases. A fractional factorial experiment may balance main effects and low-order interactions without achieving balance for high-order interactions. In an analogous fashion, we balance certain main effects and low-order interactions among the covariates;moreover, we use as many exactly matched pairs as possible. This is done by creating a match that is exact for several variables, with a close match for age, and both a "near-exact match" and a "finely balanced match" for another nominal variable, in this case a 47 x 5 = 235 category variable representing the interaction of the 47 hospitals and the five surgical procedure groups. The method is easily implemented in R.

关键词： assignment algorithm Caliper match Finely balanced match Near-exact match

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Using biomarkers prospectively in adaptive clinical trials

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Trials 2011年第1期12卷 1-1页

作者： Donald A Berry M.D. Anderson Cancer Center Houston TX USA

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An algorithm for Optimal Tapered Matching, With Application to Disparities in Survival

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2008年第4期17卷 914-924页

作者： Daniel, Shoshana R. Armstrong, Katrina Silber, Jeffrey H. Rosenbaum, Paul R. Univ Penn Wharton Sch Dept Stat Philadelphia PA 19104 USA Covance Periapproval Serv Inc Conshohocken PA 19428 USA Univ Penn Sch Med Philadelphia PA 19104 USA Childrens Hosp Philadelphia Ctr Outcomes Res Philadelphia PA 19104 USA

In a tapered matched comparison, one group of individuals, called the focal group, is compared to two or more nonoverlapping matched comparison groups constructed from One Population in such a way that Successive comparison groups increasingly resemble the local group. An optimally tapered matching solves two problems simultaneously: it optimally divides the single comparison population into nonoverlapping comparison groups and optimally pairs members of the focal group with members of each comparison group. We Show how to use the optimal assignment algorithm in a new way to solve the optimally tapered matching problem, with implementation ill R. This issue often arises in studies of groups defined by race, gender, or other categorizations such that equitable public policy might require all understanding of the mechanisms that produce disparate outcomes, where certain specific mechanisms would be judged illegitimate, necessitating reform. In particular, we use data from Medicare and the SEER Program of the National Cancer Institute as part of all ongoing study of black-white disparities in survival among women with endometrial cancer.

关键词： assignment algorithm Combinatorial optimization Matched sampling

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Minimum distance matched sampling with fine balance in an observational study of treatment for ovarian cancer

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2007年第477期102卷 75-83页

作者： Rosenbaum, Paul R. Ross, Richard N. Silber, Jeffrey H. Univ Penn Wharton Sch Dept Stat Philadelphia PA 19104 USA Childrens Hosp Philadelphia Ctr Outcomes Res Philadelphia PA 19104 USA Univ Penn Sch Med Dept Pediat Philadelphia PA 19104 USA

In observational studies of treatment effects, matched samples have traditionally been constructed using two tools, namely close matches on one or two key covariates and close matches on the propensity score to stochastically balance large numbers of covariates. Here we propose a third tool, fine balance, obtained using the assignment algorithm in a new way. We use all three tools to construct a matched sample for an ongoing study of provider specialty in the treatment of ovarian cancer. Fine balance refers to exact balance of a nominal covariate, often one with many categories, but it does not require individually matched treated and control subjects for this variable. In the example the nominal variable has 72 = 9 x 8 categories formed from 9 possible years of diagnosis and 8 geographic locations or SEER sites. We obtain exact balance on the 72 categories and close individual matches on clinical stage, grade, year of diagnosis, and other variables using a distance, and stochastically balance a total of 61 covariates using a propensity score. Our approach finds an optimal match that minimizes a suitable distance subject to the constraint that fine balance is achieved. This is done by defining a special patterned distance matrix and passing it to a subroutine that solves the optimal assignment problem, which optimally pairs the rows and columns of a matrix using a polynomial time algorithm. In the example we used the function Proc Assign in SAS. A new theorem shows that with our patterned distance matrix, the assignment algorithm returns an optimal, finely balanced matched sample whenever one exists, and otherwise returns an infinite distance, indicating that no such matched sample exists.

关键词： assignment algorithm matched sampling observational study optimal matching propensity score

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A Laser Based Multi-Target Tracking for Mobile Robot

A Laser Based Multi-Target Tracking for Mobile Robot

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9th International Conference on Intelligent Autonomous Systems (IAS-9)

作者： Hashimoto, Masafumi Ogata, Satoshi Oba, Fuminori Murayama, Takeshi Doshisha Univ Fac Engn Dept Informat Syst Design Kyoto 6100321 Japan

ISBN: (纸本)9781586035952

This paper presents a method for tracking multiple moving objects with in-vehicle 2D laser range sensor (LRS) in a cluttered environment, where ambiguous/false measurements appear in the laser image due to observing clutters and windows, etc. Moving objects are detected from the laser image with the LRS via a heuristic rule and an occupancy grid based method. The moving objects are tracked based on Kalman filter and the assignment algorithm. A rule based track management system is embedded into the tracking system in order to improve the tracking performance. The experimental results of two people tracking validate the proposed method.

关键词： Mobile robot Laser range sensor Multi-target tracking Occupancy grid method Kalman filter Data association assignment algorithm

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Dynamic Cramer-Rao bound for target tracking in clutter

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2005年第4期41卷 1154-1167页

作者： Zhang, X Willett, P Bar-Shalom, Y Univ Connecticut Dept Elect & Comp Engn Storrs CT 06269 USA

Recently, there have been several new results for an old topic, the Cramer-Rao lower bound (CRLB). Specifically, it has been shown that for a wide class of parameter estimation problems (e.g. for objects with deterministic dynamics) the matrix CRLB, with both measurement origin uncertainty (i.e., in the presence of false alarms or random clutter) and measurement noise, is simply that without measurement origin uncertainty times a scalar information reduction factor (IRF). Conversely, there has arisen a neat expression for the CRLB for state estimation of a stochastic dynamic nonlinear system (i.e., objects with a stochastic motion);but this is only valid without measurement origin uncertainty. The present paper can be considered a marriage of the two topics: the clever Riccati-like form from the latter is preserved, but it includes the IRF from the former. The effects of plant and observation dynamics on the CRLB are explored. Further, the CRLB is compared via simulation to two common target tracking algorithms, the probabilistic data association filter (PDAF) and the multi-frame (N-D) assignment algorithm.

关键词： .state estimation parameter estimation alarms CRLB measurement noise assignment algorithm Dynamic Cramer-Rao Bound

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Optimal pair matching with two control groups

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2004年第2期13卷 422-434页

作者： Lu, B Rosenbaum, PR Brown Univ Ctr Stat Sci Providence RI 02912 USA Univ Penn Wharton Sch Dept Stat Philadelphia PA 19104 USA

In an effort to detect hidden biases due to failure to control for an unobserved covariate, some observational or nonrandomized studies include two control groups selected to systematically vary the unobserved covariate. Comparisons of the treated group and two control groups must, of course, control for imbalances in observed covariates. Using the three groups, we form pairs optimally matched for observed covariates-that is, we optimally construct from observational data an incomplete block design. The incomplete block design may use all available data, or it may use data selectively to produce a balanced incomplete block design, or it may be the basis for constructing a matched sample when expensive outcome information is to be collected only for sampled individuals. The problem of optimal pair matching with two control groups is shown by a series of transformations to be equivalent to a particular form of optimal nonbipartite matching, a problem for which polynomial time algorithms exist. In our examples, we implement the procedure using a nonbipartite matching algorithm due to Derigs. We illustrate the method with data from an observational study of the employment effects of the minimum wage.

关键词： assignment algorithm balanced incomplete block design bipartite matching multiple control groups nonbipartite matching observational studies

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