Characteristics associated with differences in survival among black and white women with breast cancer

IMPORTANCE

Difference in breast cancer survival by race is a recognized problem among Medicare beneficiaries.

OBJECTIVE

To determine if racial disparity in breast cancer survival is primarily attributable to differences in presentation characteristics at diagnosis or subsequent treatment.

DESIGN, SETTING, AND PATIENTS

Comparison of 7375 black women 65 years and older diagnosed between 1991 to 2005 and 3 sets of 7375 matched white control patients selected from 99,898 white potential controls, using data for 16 US Surveillance, Epidemiology and End Results (SEER) sites in the SEER-Medicare database. All patients received follow-up through December 31, 2009, and the black case patients were matched to 3 white control populations on demographics (age, year of diagnosis, and SEER site), presentation (demographics variables plus patient comorbid conditions and tumor characteristics such as stage, size, grade, and estrogen receptor status), and treatment (presentation variables plus details of surgery, radiation therapy, and chemotherapy).

MAIN OUTCOMES AND MEASURES

5-Year survival.

RESULTS

The absolute difference in 5-year survival (blacks, 55.9%; whites, 68.8%) was 12.9% (95% CI, 11.5%-14.5%; P < .001) in the demographics match. This difference remained unchanged between 1991 and 2005. After matching on presentation characteristics, the absolute difference in 5-year survival was 4.4% (95% CI, 2.8%-5.8%; P < .001) and was 3.6% (95% CI, 2.3%-4.9%; P < .001) lower for blacks than for whites matched also on treatment. In the presentation match, fewer blacks received treatment (87.4% vs 91.8%; P < .001), time from diagnosis to treatment was longer (29.2 vs 22.8 days; P < .001), use of anthracyclines and taxols was lower (3.7% vs 5.0%; P < .001), and breast-conserving surgery without other treatment was more frequent (8.2% vs 7.3%; P = .04). Nevertheless, differences in survival associated with treatment differences accounted for only 0.81% of the 12.9% survival difference.

CONCLUSIONS AND RELEVANCE

In the SEER-Medicare database, differences in breast cancer survival between black and white women did not substantially change among women diagnosed between 1991 and 2005. These differences in survival appear primarily related to presentation characteristics at diagnosis rather than treatment differences.

Impact of multiple matched controls on design sensitivity in observational studies

In an observational study, one treated subject may be matched for observed covariates to either one or several untreated controls. The common motivation for using several controls rather than one is to increase the power of a test of no effect under the doubtful assumption that matching for observed covariates suffices to remove bias from nonrandom treatment assignment. Does the choice between one or several matched controls affect the sensitivity of conclusions to violations of this doubtful assumption? With continuous responses, it is known that reducing the heterogeneity of matched pair differences reduces sensitivity to unmeasured biases, but increasing the sample size has a highly circumscribed effect on sensitivity to bias. Is the use of several controls rather than one analogous to a reduction in heterogeneity or to an increase in sample size? The issue is examined for Huber's m-statistics, including the t-test, the examination having three components: an example, asymptotic calculations using design sensitivity, and a simulation. Use of multiple controls with continuous responses yields a nontrivial reduction in sensitivity to unmeasured biases. An example looks at lead and cadmium in the blood of smokers from the 2008 National Health and Nutrition Examination Survey. A by-product of the discussion is a new result giving the design sensitivity for the permutation distribution of m-statistics.

Racial disparities in breast cancer survival

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Background: Reducing racial disparities in breast cancer survival has been a federal priority since the early 1990’s. We present a new method to assess disparities using sequential multivariate matching. We ask if racial disparities have increased or decreased over time and if so, what were potential reasons for such changes. Methods: We studied all women over 65 years of age in the Medicare fee for service system diagnosed with breast cancer between 1991 and 2005 who were treated in one of 12 SEER sites (the sites in SEER since 1991). There were 5,251 black patients (74% early stage (I-III), 9% late stage (IV) and 17% missing stage) and 72,695 white patients (81% early stage, 5% late stage and 14% missing stage). All black cases represented the focal group for all matches. Using multivariate matching and the propensity score, white controls were matched to blacks in steps: (1) White controls matched to black cases on age and year of diagnosis; (2) Age, year of diagnosis, and stage; (3): Age, year, stage, estrogen receptor status, grade, and 30 comorbidities. We then compare 5-year survival in the Pre and Post-Taxane periods (1991-1998, 1999-2005). Results: When whites were matched to blacks on age and diagnosis year, 5-year Kaplan-Meier survival was 69.2% vs. 56.7%, P < 0.0001. Matching additionally on stage, differences = 64.1% vs. 56.7%, P < 0.0001; Matching further on tumor characteristics and 30 comorbidities, the disparity reduced to 61.6% vs. 56.7%, P < 0.0001. Comparing trends over time, white-black differences in survival matched for age and year were 67.6% vs. 55.2% (P < 0.0001) in the pre-Taxane era (difference = 12.4%) and 71.2% vs. 58.7% (P < 0.0001) in the post Taxane era (difference = 12.5%); age and year matched paired racial differences were not different across eras (P = 0.389). Conclusions: While there may have been some improvements in overall survival, racial disparities in breast cancer survival have not improved, despite important policy initiatives and treatment advances. Adjusting for presentation at diagnosis does reduce differences in survival, but even these differences remain large and significant, suggesting that differences in both presentation and treatment given presentation are contributing to this disparity.

Contrasting Evidence Within and Between Institutions That Provide Treatment in an Observational Study of Alternate Forms of Anesthesia

In a randomized trial, subjects are assigned to treatment or control by the flip of a fair coin. In many nonrandomized or observational studies, subjects find their way to treatment or control in two steps, either or both of which may lead to biased comparisons. By a vague process perhaps affected by proximity or sociodemographic issues, subjects find their way to institutions that provide treatment. Once at such an institution, a second process, perhaps thoughtful and deliberate, assigns individuals to treatment or control. In the current paper, the institutions are hospitals, and the treatment under study is the use of general anesthesia alone versus some use of regional anesthesia during surgery. For a specific operation, the use of regional anesthesia may be typical in one hospital and atypical in another. A new matched design is proposed for studies of this sort, one that creates two types of nonoverlapping matched pairs. Using a new extension of optimal matching with fine balance, pairs of the first type exactly balance treatment assignment across institutions, so each institution appears in the treated group with the same frequency that it appears in the control group; hence, differences between institutions that affect everyone in the same way cannot bias this comparison. Pairs of the second type compare institutions that assign most subjects to treatment and other institutions that assign most subjects to control, so each institution is represented in the treated group if it typically assigns subjects to treatment or alternatively in the control group if it typically assigns subjects to control, and no institution appears in both groups. By and large, in the second type of matched pair, subjects became treated subjects or controls by choosing an institution, not by a thoughtful and deliberate process of selecting subjects for treatment within institutions. The design provides two evidence factors, that is, two tests of the null hypothesis of no treatment effect that are independent when the null hypothesis is true, where each factor is largely unaffected by certain unmeasured biases that could readily invalidate the other factor. The two factors permit separate and combined sensitivity analyses, where the magnitude of bias affecting the two factors may differ. The case of knee surgery in the study of regional versus general anesthesia is considered in detail.

Inference with interference between units in an fMRI experiment of motor inhibition

An experimental unit is an opportunity to randomly apply or withhold a treatment. There is interference between units if the application of the treatment to one unit may also affect other units. In cognitive neuroscience, a common form of experiment presents a sequence of stimuli or requests for cognitive activity at random to each experimental subject and measures biological aspects of brain activity that follow these requests. Each subject is then many experimental units, and interference between units within an experimental subject is likely, in part because the stimuli follow one another quickly and in part because human subjects learn or become experienced or primed or bored as the experiment proceeds. We use a recent fMRI experiment concerned with the inhibition of motor activity to illustrate and further develop recently proposed methodology for inference in the presence of interference. A simulation evaluates the power of competing procedures.

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

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 read-mission 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 × 15 × 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 × 5 = 235 category variable representing the interaction of the 47 hospitals and the five surgical procedure groups. The method is easily implemented in R.

Optimal matching with minimal deviation from fine balance in a study of obesity and surgical outcomes

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.

A new u-statistic with superior design sensitivity in matched observational studies

In an observational or nonrandomized study of treatment effects, a sensitivity analysis indicates the magnitude of bias from unmeasured covariates that would need to be present to alter the conclusions of a naïve analysis that presumes adjustments for observed covariates suffice to remove all bias. The power of sensitivity analysis is the probability that it will reject a false hypothesis about treatment effects allowing for a departure from random assignment of a specified magnitude; in particular, if this specified magnitude is "no departure" then this is the same as the power of a randomization test in a randomized experiment. A new family of u-statistics is proposed that includes Wilcoxon's signed rank statistic but also includes other statistics with substantially higher power when a sensitivity analysis is performed in an observational study. Wilcoxon's statistic has high power to detect small effects in large randomized experiments-that is, it often has good Pitman efficiency-but small effects are invariably sensitive to small unobserved biases. Members of this family of u-statistics that emphasize medium to large effects can have substantially higher power in a sensitivity analysis. For example, in one situation with 250 pair differences that are Normal with expectation 1/2 and variance 1, the power of a sensitivity analysis that uses Wilcoxon's statistic is 0.08 while the power of another member of the family of u-statistics is 0.66. The topic is examined by performing a sensitivity analysis in three observational studies, using an asymptotic measure called the design sensitivity, and by simulating power in finite samples. The three examples are drawn from epidemiology, clinical medicine, and genetic toxicology.

The Hospital Compare mortality model and the volume-outcome relationship

OBJECTIVE

We ask whether Medicare's Hospital Compare random effects model correctly assesses acute myocardial infarction (AMI) hospital mortality rates when there is a volume-outcome relationship.

DATA SOURCES/STUDY SETTING

Medicare claims on 208,157 AMI patients admitted in 3,629 acute care hospitals throughout the United States.

STUDY DESIGN

We compared average-adjusted mortality using logistic regression with average adjusted mortality based on the Hospital Compare random effects model. We then fit random effects models with the same patient variables as in Medicare's Hospital Compare mortality model but also included terms for hospital Medicare AMI volume and another model that additionally included other hospital characteristics.

PRINCIPAL FINDINGS

Hospital Compare's average adjusted mortality significantly underestimates average observed death rates in small volume hospitals. Placing hospital volume in the Hospital Compare model significantly improved predictions.

CONCLUSIONS

The Hospital Compare random effects model underestimates the typically poorer performance of low-volume hospitals. Placing hospital volume in the Hospital Compare model, and possibly other important hospital characteristics, appears indicated when using a random effects model to predict outcomes. Care must be taken to insure the proper method of reporting such models, especially if hospital characteristics are included in the random effects model.