Patricia Grambsch

• PhD
• University of Minnesota

This is a book for statistical practitioners, particularly those who design and analyze studies for survival and event history data. Its goal is to extend the toolkit beyond the basic triad provided by most statistical packages: the Kaplan-Meier estimator, log-rank test, and Cox regression model. Building on recent developments motivated by countin...

Although highly active antiretroviral therapy (HAART) has improved HIV survival, some patients receiving therapy are still dying. This analysis was conducted to identify factors associated with increased risk of post-HAART mortality. We evaluated baseline (prior to HAART initiation) clinical, demographic and laboratory factors (including CD4+ count...

Selective congruence, namely a pairing of various biospheric cycles of certain frequencies with different environmental ones and further selectivity of phase behavior at the given frequency characterize an ultradian to infradian, prominently circadian transdisciplinary spectrum. Diseases documented among others to be influenced by the cosmos range...

Among HIV-infected persons initiating highly active antiretroviral therapy (HAART), early CD4+ lymphocyte count increases are well described. However, whether CD4+ levels continue to increase or plateau after 4-6 years is controversial. To address this question and identify other determinants of CD4+ response, we analyzed data for 1,846 persons fro...

Originally a remembrance of an elderly physiologist, this paper illustrates the need for a standardizedspecification of certain experimental or survey conditions beyond those usually necessarily disclosed inconventional publications, namely calendar-dates, clock-times and geographic locations, to allow referenceto helio-ionosphero-geomagnetics alon...

The self-reported number of children was compared for men and women from the National Epidemiologic Survey of Alcoholism and Related Conditions Survey (NESARC). Subjects with a diagnosis of major depressive disorder or bipolar disorder were compared to those without an axis I disorder. The effect of age, gender, marriage and diagnostic status on nu...

This paper considers model ling data arising in post-treatment preventive care settings, where cancer patients who have undergone disease-directed treatment discontinue seeking preventive care services. Clinicians and public health researchers are interested in explaining such behavioural patterns by modelling the time-to-receiving care while accou...

Prostate cancer is the most frequently diagnosed cancer in men. Whereas chronic calorie restriction (CCR) delays prostate tumorigenesis in some rodent models, the impact of intermittent caloric restriction (ICR) has not been determined. Here, transgenic adenocarcinoma of the mouse prostate (TRAMP) mice were used to compare how ICR and CCR affected...

The relationship between state Murder rates and the liberalization of conditions under which a citizen can obtain a permit to carry a concealed weapon (shall-issue laws) is controversial and important for policy. Many analyses have been done during the last decade, but regression to the mean has been ignored with the exception of two papers which c...

Many clinical trials have multiple outcomes. Formal interim monitoring guidelines that take account of multiple outcomes can be useful to Data Monitoring Committees (DMC). Previous research has focused on marginal criteria that control the overall type I error for bivariate endpoints corresponding to efficacy and safety. Usually, an 'or' decision r...

Background Most methods of sample size calculations for survival trials adjust the estimated outcome event rates for noncompliance based on the assumption that non-compliance is independent of the risk of the outcome event although there has been published evidence that noncompliers are often at a higher risk than compliers. More recent work has st...

Tree mortality has traditionally been assessed in forest inventories through summaries of mortality by location, species, and causal agents. Although these methods have historically constituted the majority of tree mortality summarizations, they have had limited use in assessing mortality trends and dynamics. This study proposed a novel method of a...

Survival analysis methodologies provide novel approaches for forest mortality analysis that may aid in detecting, monitoring, and mitigating of large-scale forest health issues. This study examined survivor analysis for evaluating a regional forest health issue – Missouri oak decline. With a statewide Missouri forest inventory, log-rank tests of th...

Objective To examine regional differences in the Controlled ONset Verapamil INvestigation of Cardiovascular Endpoints (CONVINCE) trial. Design Double-blind, randomized, international clinical trial. Setting Six hundred and sixty-one clinical centers in 15 countries. Patients Hypertensive volunteers (n = 16 602) with ≥1 additional cardiovascular...

Group sequential tests are widely used for interim analyses in randomized clinical trials. These tests have been extended to bivariate outcomes, but calculation of boundary values is computationally intensive. In this paper, we compare 3 algorithms: (1) quasi-Monte Carlo; (2) Schervish's MULNOR; and (3) a bivariate version of Armitage's recursive f...

A method is proposed for the estimation of drug or toxicity potencies using in vitro data. A typical experiment in cancer research is presented where cells from a tumor-derived cell line were deposited as fixed volumes in 12-well cell culture plates. After waiting for 72 hours (for further growth), the wells were exposed to different concentrations...

A method is proposed for the evaluation of in vitro experiments for combination chemotherapy, a new and growing area of cancer research. We first describe and review a popular graphical device called an isobologram. We then propose a statistical framework, a simple experimental design, and a statistical test for use with this widely accepted method...

Two independent groups recently published data comparing pulsatile luteinizing hormone (LH) release between depressed and control women. Despite similar populations and LH sampling frequency, they reached different conclusions: Meller et al. [Am. J. Psych. 154 (1997) 1454] found disruption of normal LH pulsatility in depressed women, whereas Young...

Control of blood pressure (BP) to lower than 140/90 mm Hg occurs in 6-34% of hypertensive patients in population-based surveys, but in more than 60% in several clinical trials. To determine the predictors of controlled BP, we examined data from the Controlled ONset Verapamil INvestigation of Cardiovascular Endpoints (CONVINCE) Trial, in which incre...

In hypertension trials comparing new and standard (S) regimens, the latter is often fixed by design for all patients. In the Controlled ONset Verapamil INvestigation of Cardiovascular Endpoints (CONVINCE) trial, the physician pre-selected the S treatment for each patient, either atenolol (A) or hydrochlorothiazide (H). Patients were then randomized...

The benefits of an initial beta-blocker for hypertension in individuals over age 60 are controversial. In the Controlled ONset Verapamil INvestigation of Cardiovascular Endpoints (CONVINCE) trial, 16,476 hypertensive patients were randomized to verapamil or the physician's choice of atenolol or hydrochlorothiazide (HCTZ), and followed for 3 years....

Myocardial infarction, sudden cardiac death and stroke all occur more commonly in the morning (6 AM to noon). Diabetic hypertensives have a 2-4 fold higher absolute risk for cardiovascular events, compared to non-diabetics, but often have blunted or reversed circadian variations in pulse rate, blood pressure, and plasma cortisol levels. To compare...

Objetivo Determinar si una nueva forma de verapamilo de liberación retardada (COER) es igual de eficaz que el atenolol y la hidroclorotiazida en la prevención de la enfermedad cardiovascular Diseño Ensayo clínico, aleatorio y doble ciego Emplazamiento El estudio se llevó a cabo en 661 centros de 15 países. El período de inclusión fue entre septie...

First vaccines are traditionally licensed after showing favourable results from phase III efficacy trials. Subsequent competing vaccines, however, have been licensed primarily on the basis of immunogenicity data rather than clinical efficacy. Focusing on pneumococcal vaccines where optical densities are measured and serum antibody concentrations ar...

To evaluate sampling strategies used to estimate survival after uveal malignant melanoma that exclude some patients who would be censored from the analysis. Simulation was performed on a population-based data set of 133 patients who had an eye enucleated because of uveal melanoma. One thousand bootstrap samples of 80 patients were drawn, without re...

The Controlled ONset Verapamil INvestigation of Cardiovascular Endpoints (CONVINCE) Trial randomized 16,602 hypertensive volunteers from 15 countries to initial antihypertensive therapy with either Controlled-Onset, Extended Release (COER)-verapamil or “Standard of Care” (SOC), a physician-directed choice of atenolol or hydrochlorothiazide (HCTZ)....

Context. Hypertensive patients are often given a calcium antagonist to reduce cardio-vascular disease risk, but the benefit compared with other drug classes is controversial. Objective. To determine whether initial therapy with controlled-onset extended- release (COER) verapamil is equivalent to a physician’s choice of atenolol or hydrochlorothiazi...

Abstract Interest m,the use of random,effects in the survrval analysis settmg,has been mcreasmg,How- ever, the computational complexity of such fradty models has hmrted then general use. Whrle fittmg frarlty models has traditronally been,standard algorithms for fittmg Cox semr- parametrrc,and,parametrrc,regression models,can be readily extended,to...

Pulse detection algorithms and spectral analysis are the two most common methods for analysing pulsatile hormone data. We compared a popular high quality pulse detection algorithm (CLUSTER) to spectral analysis on a data set comparing luteinizing hormone data in depressed and control women. For these data, periodogram analysis methods, in particula...

Although high vegetable intakes have been associated with a lower risk of colorectal cancer, this relation is less well established for the precursor lesions, adenomatous polyps. With a case-control design involving adenomatous polyp cases (n = 564), colonoscopy-negative controls who were polyp free at colonoscopy (n = 682), and community controls...

Although a potential relationship between depression and infertility has been described throughout history, only recently has this topic been subjected to systematic investigation, and the literature is often confusing. The present study uses well-established structured psychiatric interviews--Structured Clinical Interview for DSM-III-R (SCID), Bec...

In order to examine HPG axis regulation in women with major depression, luteinizing hormone (LH) pulsativity was studied in 26 depressed and 24 normal women. Blood was sampled every 10 min for an 8-h period during the first week of their menstrual cycle. LH pulsatile release was analyzed using the computerized cluster analysis algorithm of Veldhuis...

The Treatment of Mild Hypertension Trial was a randomized, double-blind clinical trial conducted from 1986 to 1992 comparing the efficacy of six antihypertensive treatment regimens in 902 participants with stage I hypertension. To satisfy a secondary objective of the study, follow-up information on mortality and cardiovascular morbidity was collect...

—Blood pressure (BP) control rates around the world are suboptimal. Part 2 of the National Health and Nutrition Educational Survey (NHANES) III indicates that only 27.4% of hypertensive Americans aged 18 to 74 years have a BP of <140/90 mm Hg. We wanted to assess BP control during the first 2 years and to describe the baseline characteristics of pa...

Blood pressure (BP) control rates around the world are suboptimal. Part 2 of the National Health and Nutrition Educational Survey (NHANES) III indicates that only 27.4% of hypertensive Americans aged 18 to 74 years have a BP of <140/90 mm Hg. We wanted to assess BP control during the first 2 years and to describe the baseline characteristics of pat...

To test the effect of daily supplemental calcium on serum total and high-density lipoprotein cholesterol (HDL-C) levels and blood pressure in adults. Randomized, double-blind, placebo-controlled clinical trial; adjunct study to a trial of calcium and colon cell proliferation in patients with sporadic adenoma. Outpatient clinic. A total of 193 men a...

Introduction.- Estimating the Survival and Hazard Functions.- The Cox Model.- Residuals.- Functional Form.- Testing Proportional Hazards.- Influence.- Multiple Events per Subject.- Frailty Models.- Expected Survival.

A key assumption of the Cox model is proportional hazards.

There is increasing interest, and need, to apply survival analysis to data sets with multiple events per subject. This includes both the cases of multiple events of the same type, and events of different types. Examples of the former would be recurrent infections in AIDS patients or multiple infarcts in a coronary study. Examples of the latter are...

In the last several years there has been significant and active research concerning the addition of random effects to survival models. In this setting, a random effect is a continuous variable that describes excess risk or frailty for distinct categories, such as individuals or families. The idea is that individuals have different frailties, and th...

The calculation of an expected survival (based on some reference population) for a cohort of patients under study has a long history. These methods are most familiar when the reference population is census based, for example, the overall survival experience of the United States population by age and sex. Recently, these ideas have been rediscovered...

This chapter gives an introduction to the simplest concept: estimating the survival curve when there are no covariates. Although simple, it forms a platform for understanding the more complex material that follows. We do it twice, once informally (although making use of counting process ideas) in Section 1, and then a second time with the connectio...

The Cox proportional hazards model [36] has become by a wide margin the most used procedure for modeling the relationship of covariates to a survival or other censored outcome.

In the Cox model, we assume that the hazard function satisfies $${\lambda _i}(t) = {\lambda _0}(t)\exp ({X_i}\beta ),$$ that is, a proportional hazards structure with a loglinear model for the covariates. For a continuous variable, age, for instance, this implicitly assumes the ratio of risks between a 45- and a 50-year-old is the same as that betw...

There are four major residuals of interest in the Cox model: the martingale, deviance, score, and Schoenfeld residuals, along with two others, the dfbeta and scaled Schoenfeld residuals, that are derived from these. This chapter gives an overview of the definitions and mathematical underpinnings of the residuals; later chapters take up their uses o...

Our third important use for residuals is to assess influence, the impact of each point on the fit of a model.

Since its introduction, the proportional hazards model proposed by Cox [36] has become the workhorse of regression analysis for censored data. In the last several years, the theoretical basis for the model has been solidified by connecting it to the study of counting processes and martingale theory, as discussed in the books of Fleming and Harringt...

Arylamine N-acetyltransferase 2 (NAT2) is involved in both the detoxification and bioactivation of carcinogenic arylamines and other mutagens. This enzyme is polymorphic, and the fast and slow phenotypes are thought to be risk factors for colon and bladder cancer, respectively. Here, we report on a case-control study of adenomatous and hyperplastic...

The Controlled ONset Verapamil INvestigation of Cardiovascular Endpoints (CONVINCE) Trial is a randomized, prospective, double-blind, parallel-group, two-arm, actively controlled, multicenter, international 5-year clinical trial involving 15,000 patients. CONVINCE will compare the incidence of fatal or nonfatal myocardial infarction (MI), fatal or...

Colorectal epithelial cell proliferative kinetics are altered in patients at increased risk for colon cancer: proliferation rates [labeling index (LI)] are higher and there is a shift of the proliferative zone from one confined to the lower 60% of the colonic crypt to one that includes the entire crypt (higher phi(h)). To assess factors associated...

The methodological issues for measuring colorectal epithelial cell proliferation, an intermediate end point for studies of colon neoplasia, in epidemiological studies are deceptively numerous and complex, with few methodological data available. Accordingly, during our experience with measuring colorectal epithelial cell proliferation from nearly 50...

Evidence of a role for steroid hormones and reproduction in colon neoplasia remains tantalizing but unclear. Hormone replacement therapy (HRT) has been reported in a number of recent studies to be associated with a reduced risk of colon cancer. A case-control study was undertaken to establish whether HRT is associated with lower risk of adenomatous...

We show how plots based on the residuals from a proportional hazards model may be used to reveal the correct functional form for covariates in the model. A smoothed plot of the martingale residues was suggested for this purpose by Therneau, Grambsch, and Fleming (1990, Biometrika 77, 147-160); however, its consistency required that the covariates b...

The kinetics of colorectal epithelial cell proliferation is altered in patients at increased risk for colon cancer. Calcium administration ameliorates such proliferative changes in rodents. Findings in preliminary clinical trials have suggested similar effects in humans. A randomized, double-blind, placebo-controlled, clinical trial was designed to...

This article presents exploratory data analytic methodology for visualizing and summarizing data that can be represented as individual-specific curves. We propose a simplified form of functional data analysis. A nonparametric scatterplot smooth is applied to each individual's data, followed by a principal components analysis of the smoothed data. W...

SUMMARY Nonproportional hazards can often be expressed by extending the Cox model to include time varying coefficients; e.g., for a single covariate, the hazard function for subject i is modelled as exp {β(t)Zi(t)}. A common example is a treatment effect that decreases with time. We show that the function βi(t) can be directly visualized by smoothi...

A common clinical study design follows patients over time, recording end-point events as they occur for each individual. In a cancer clinical trial with death as the endpoint, there can be at most one event per patient. In other cases, multiple events are possible — for example, studies of recurrent infections in bone marrow transplantation recipie...

Measurements of proliferative activity in colonic epithelial cells are being used as surrogate endpoints in clinical trials for colon cancer prevention. Proliferative index data exemplify an important type of clinical trial endpoint. The outcome variable is a proportion in which the denominator is an ancillary statistic and in which measurement err...

The progression of primary biliary cirrhosis was studied in 312 patients who were seen at the Mayo Clinic between January 1974 and May 1984. Follow-up was extended to April 30, 1988, by which time 140 of the patients had died and 29 had undergone orthotopic liver transplantation. These patients generated 1,945 patient visits that enabled us to stud...

SUMMARY The classical statistical test for assessing the difference between the two scale parameters in paired data due to Pitman (1939) and Morgan (1939) is not robust. This paper explores robust alternatives to Pitman's test, using the framework of the one-sample t-test. The asymptotic behaviour of the tests under the null hypothesis is examined....

Several models of a population survival curve composed of two piecewise exponential distributions are developed. In one formulation the hazard rate changes at a point that is an unobservable random variable that varies between individuals. The population hazard function may decrease with age even when all individuals' hazards are increasing. In a s...

An application of the method of rank correlation is proposed for testing independence between a censored survival time and an ordinal covariate. The test statistic counts the number of concordances minus the number of discordances at each time with event(s) and adds across times; it is expressible as a score statistic within the proportional hazard...

Colonic epithelial cell proliferation is increased in patients at high risk for colon cancer. Calcium administration has ameliorated the proliferative changes in rodents, and findings in small, uncontrolled clinical trials have suggested similar effects in humans. This preliminary, double-blind, randomized clinical trial was designed 1) to investig...

The natural history of primary sclerosing cholangitis was studied in 426 patients from five medical centers. The median follow-up time was 3.0 years (range, 0.01-16.6 years); 100 patients had died by the time of last follow-up. Survival analysis (Cox proportional-hazards regression) was used to identify the variables most useful in predicting survi...

An alternative way to implement the Akaike Information Criterion (AIC) is proposed for the evaluation of staging systems for colorectal cancer.

A normative sample of 880 children was contrasted with a sample of 276 sexually abused children on the Child Sexual Behavior Inventory (CSBI), a 35-item behavior checklist assessing sexual behavior in children 2–12 yrs old. The CSBI total score differed significantly between the 2 groups after controlling for age, sex, maternal education, and famil...

We studied cholangiograms in 129 patients with primary sclerosing cholangitis (PSC) to determine if there was a correlation between any of the findings and the prognosis of the disease. The grade, length, and extent of strictures, the degree of bile duct dilatation, and the distribution of lesions were evaluated. Survival curves were generated to t...

Peyronie's disease was diagnosed in 101 male residents of Rochester, Minnesota between 1950 and 1984. Mean patient age at diagnosis was 53 years. The average age-adjusted annual incidence rate of 25.7 and a prevalence rate of 388.6 per 100,000 male population were noted. The steady increase in incidence with time may reflect an increasing tendency...

A large-scale, community-based survey was done to assess the frequency of a wide variety of sexual behaviors in normal preadolescent children and to measure the relationship of these behaviors to age, gender, and socioeconomic and family variables. A sample of 880 2- through 12-year-old children screened to exclude those with a history of sexual ab...

A large-scale, community-based survey was done to assess the frequency of a wide variety of sexual behaviors in normal preadolescent children and to measure the relationship of these behaviors to age, gender, and socioeconomic and family variables. A sample of 880 2-through 12-year-old children screened to exclude those with a history of sexual abu...

We studied the relationship between selected variables of hepatic and pulmonary function in 47 patients with primary biliary cirrhosis, who were participating in a prospective study to assess sequential pulmonary function at yearly intervals. An additional 20 patients with primary biliary cirrhosis, who were liver transplant candidates awaiting tra...

Non-linear relationships between two variables are often detected as a result of a preliminary statistical test for linearity. Common approaches to dealing with non-linearity are to (a) make a linearizing transformation in the independent variable or (b) fit a relationship that is non-linear in the independent variable, such as including a quadrati...

A retrospective cohort study of 1597 low-risk pregnancies assessed the effects of obstetrical intervention using logistic regression. Both maternal and neonatal morbidity were low (15.2 percent and 3.8 percent, respectively). Epidural analgesia, oxytocin, or both, were associated with worse maternal outcome, and neonatal outcome was worse when oxyt...

Data from 73 asymptomatic patients with primary biliary cirrhosis were analyzed to determine clinical course and long-term survival. Of these, 44 entered a D-penicillamine treatment trial; 29 qualified but chose not to participate. Median follow-up was 7.6 yr (range, 2.8-12.2 yr). Liver biopsy at the initial visit showed advanced disease (fibrosis,...

Previous studies have described significant elevations in the concentrations of secretory immunoglobulin A (sIgA) in bronchial washings obtained from cancerous lungs. To date, there have been no prospective investigations examining the predictive value of sIgA measurements in clinically relevant settings. Our goal was to determine if measurement of...

Graphical methods based on the analysis of residuals are considered for the setting of the highly-used D. R. Cox [J. R. Stat. Soc., Ser. B 34, 187-220 (1972; Zbl 0243.62041)] regression model and for the P. K. Andersen and R. D. Gill [Ann. Stat. 10, 1100-1120 (1982; Zbl 0526.62026)] generalization of that model. We start with a class of martingale-...

Future demand for services or goods is usually forecasted by fitting ARIMA models and using the optimal rules based on the squared error criterion. When analyzing a large number of time series describing Special Services in the telephone business, we found that a model with independent increments with stable distributions was more suitable and led...

The generalizability of the Mayo model for predicting survival in individual primary biliary cirrhosis patients without liver transplantation was tested and confirmed. The model was applied to a data base of patients from the New England Medical Center Hospitals (n = 141) and the Scott and White Clinic (n = 35) and found to predict their survival a...

The natural history of primary sclerosing cholangitis was assessed in 174 patients; 37 were asymptomatic and 137 had symptoms related to underlying liver disease. At the time of diagnosis, the mean age was 39.9 years, 66% of the primary sclerosing cholangitis patients were male and 71% had associated inflammatory bowel disease, most commonly chroni...

The 136 patients who underwent total laryngectomy as the primary treatment for squamous cell carcinoma of the glottis at the Mayo Clinic in 1970 through 1981 were followed by retrospective record review for at least 4 years or until death, local recurrence, neck recurrence, or delayed neck metastasis. Cancer recurred or progressed in a previously u...

The ideal mathematical model for predicting survival for individual patients with primary biliary cirrhosis should be based on a small number of inexpensive, noninvasive measurements that are universally available. Such a model would be useful in medical management by aiding in the selection of patients for and timing of orthotopic liver transplant...

Liver transplantation is considered lifesaving for selected patients with end-stage primary biliary cirrhosis (PBC). A mathematical model to predict survival in the patient with PBC who has not undergone transplantation would be valuable for improving selection of patients for and timing of transplantation and for providing control information for...

In sequential estimation, the investigator obtains data sequentially, collecting observations until his estimator for parameters of interest is sufficiently precise. This note examines sequential estimation in the context of asymptotic likelihood inference in which sampling continues until the smallest eigenvalue of the estimated Fisher information...

No controlled trials have been performed to assess the efficacy of liver transplantation. Because of the marked improvement in survival after liver transplantation since 1981, random assignment of patients to a control group not undergoing transplantation is considered clinically inappropriate. To assess the efficacy of liver transplantation in pat...

We reviewed the records of 83 patients who underwent 100 orthotopic liver transplantations in order to determine the following: (1) the methods to predict blood usage, (2) the consequences of an ABO-incompatible transplant, (3) the benefit of providing cytomegalovirus (CMV)-negative blood products to CMV-negative patients receiving a liver from a C...

We studied the serum levels of soluble interleukin-2 receptors (SIL-2R) in liver allograft recipients: a control group without rejection or CMV disease, a group with only rejection episodes, and a group with only cytomegalovirus disease. Rejection was diagnosed by the presence of compatible laboratory and histologic abnormalities and absence of oth...

A retrospective cohort study of 863 pregnancies cared for by family physicians at three sites--rural-rural (RR), rural-urban (RU), and urban-urban (UU)--was designed to test the hypothesis that ready on-site access to perinatal subspecialists would improve pregnancy outcome. No differences in delivery type, length of gestation, birth weight, or nur...

The clinicopathologic features and natural history of primary sclerosing cholangitis were reviewed in 53 patients followed at the Yale Liver Center during the past 30 yr. At presentation, the mean age of patients was 46 yr, and the male to female ratio was 1.4:1. Biliary sclerosis was limited to the intrahepatic ductal system in 21% of the patients...

Primary biliary cirrhosis is a chronic, progressive, cholestatic liver disease thought to be related to abnormalities in immune regulation. The disease is associated with granulomatous bile duct destruction, cholestasis, hepatic copper overloading and the development of hepatic fibrosis or cirrhosis or both. There have been numerous therapeutic tri...

In order to identify depressed patients with hypothalamic-pituitary-adrenal (HPA) axis abnormalities who have a normal response to the dexamethasone suppression test (DST), the authors administered a series of neuroendocrine tests including insulin-induced hypoglycemia, arginine vasopressin challenge, and a DST. Using standard sensitivity measures,...

Among the first 52 recipients of primary liver allografts with follow-up of 2 weeks or greater, 6 patients had biopsy-confirmed vanishing bile duct syndrome (VBDS) and required retransplantation. Five of these six patients had positive lymphocyte crossmatches. Of the 46 remaining liver transplant recipients, 11 had positive crossmatches. Thus, the...