Minimum Distance Matched Sampling With Fine Balance in an Observational Study of Treatment for Ovarian Cancer

Abstract

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 × 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.KEY WORDS: Assignment algorithm; Matched sampling; Observational study; Optimal matching; Propensity score. EXACT BALANCE WITHOUT EXACT MATCHINGIn an observational study of treatment effects, matched sampling is often used to select subjects for study who, before to treatment, appeared similar with respect to observed covariates. As one example, the Surgical Outcomes Study (Silber et al. 2001(Silber et al. , 2005 examined the effects of preoperative antibiotics on mortality after surgery in the Pennsylvania Medicare population by matching deaths to survivors using many covariates available from Medicare. For 681 matched pairs, paper hospital charts were located throughout Pennsylvania and individually abstracted to determine, among other things, preoperative antibiotics use. Although performing chart abstraction is too expensive for the entire Medicare population, it is essential if information not recorded by Medicare is to be used, and it is practical for a matched sample.Traditionally, matched samples have been constructed either by finding close matches on one or two key covariates, by finding close matches on the propensity score to stochastically balance large numbers of covariates, or by doing both at once. For a few key covariates, the Mahalanobis distance is often used (Rubin 1980). The propensity score is the conditio...

A Matched Observational Study

“…A matched comparison has been presented as it might be, and was, presented in a scientific journal [8], with little reference to the procedures used to construct the matched sample [6]. Matching procedures are the focus of Part II.…”

“…Jeffrey Silber, Dan Polsky, Richard Ross, Orit Even-Shoshan, Sandy Schwartz, Katrina Armstrong, Tom Randall, and I [6,8] asked how the intensity of chemotherapy for ovarian cancer affected patient outcomes. We thought that greater intensity might prolong survival, perhaps at the cost of increased toxicity.…”

“…In fact, although this is not visible in Table 7.1, the joint behavior of the three time intervals and the SEER site is exactly balanced; for instance, the number of GO patients in 1991-1992 from Iowa equals the number of matched MO patients in 1991-1992 from Iowa. The balance on SEER site and year of diagnosis was obtained using "fine balance" [5,6], a technique discussed in Chapter 10. The large imbalances before matching in surgeon type, year of diagnosis, and SEER site, and the much smaller imbalances before matching in clinical stage, grade and comorbid conditions are somewhat encouraging.…”

Impact of online channel use on customer revenues and costs to serve: Considering product portfolios and self-selection

“…Its limitation is that when there are many characteristics that could drive self-selection effects, it becomes infeasible to match customers directly. The Mahalanobis distance can map multiple characteristics into a single measure that expresses the gap between any two customers (Rosenbaum, Ross, & Silber, 2007). However, this approach requires customer characteristics measured on metric scales.…”

A Greedy Algorithm for Representative Sampling:repsampleinStata

“…Subjects are matched across groups on their propensity scores, the conditional probabilities of assignment given a group of observed covariates (Rosenbaum and Rubin 1983). More recently, a 'fine balance' method was proposed, which attempts to provide identical marginal distributions of the covariates of interest within each group, without a one-to-one matching of subjects (Rosenbaum, Ross, and Silber 2007). An alternative to propensity score matching is coarsened exact matching, under which the covariates of interest are reduced (or 'coarsened') into acceptable categories (bins) that define a range of strata.…”