Diagnostic plots to reveal functional form for covariates in multiplicative intensity models

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 be independent. They also noted that the plot could be biased for large covariate effects. We introduce two refinements which overcome these difficulties. The first is based on a ratio of scatter plot smooths, where the numerator is the smooth of the observed count plotted against the covariate, and the denominator is a smooth of the expected count. This is related to the Arjas goodness-of-fit plot (1988, Journal of the American Statistical Association 83, 204-212). The second technique smooths the martingale residuals divided by the expected count, using expected count as a weight. This latter approach is related to a GLM partial residual plot, as well as to the iterative methods of Hastie and Tibshirani (1990, Biometrics 46, 1005-1016) and Gentleman and Crowley (1991, Biometrics 47, 1283-1296). Applications to survival data sets are given.

Primary biliary cirrhosis: prediction of short-term survival based on repeated patient visits

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 study the change in the prognostic variables of primary biliary cirrhosis (age, bilirubin value, albumin value, prothrombin time and edema) from the time of referral. Also, using this database and the Cox proportional-hazards regression model, we developed an updated model for primary biliary cirrhosis that can be used to predict short-term survival at any time in the course of the disease. This model uses the values of the prognostic variables measured at the latest patient visit. Comparison of predicted survival from the update model and the natural history model of primary biliary cirrhosis showed that the updated model was superior to the original model for predicting short-term survival. This finding applied to both the Mayo Clinic patients and an independent set of 83 Dutch patients. The Mayo updated model is recommended for improving the accuracy of predictions of survival during the 2 yr after a patient visit.

Piecewise exponential survival curves with smooth transitions

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 second formulation, the population hazard function is modeled directly. Several models are fit to the survival history of a cohort of 5751 highly inbred male Drosophila melanogaster and the British coal mining disaster data.

Association between survival time and ordinal covariates

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 hazards framework. The proposed test includes, as a special case, a generalization of Jonckheere's test against ordered alternatives and as applied to the analysis of categorical data, it can be seen as a generalization of the Mantel-Haenszel procedure.

Primary sclerosing cholangitis: refinement and validation of survival models

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 survival of patients with primary sclerosing cholangitis. Serum bilirubin concentration, histological stage on liver biopsy, age, and the presence of splenomegaly were independent predictors of a high risk of dying. A mathematical model to predict survival of patients with primary sclerosing cholangitis (based on referral values of those predictors) was statistically validated using two methods. Confidence intervals for predicting patient-specific survival probabilities are also presented. This model to predict survival could be used to stratify participants in therapeutic trials, counsel patients and their families, decide on candidacy for and timing of liver transplantation, and provide mathematical controls for evaluating the efficacy of therapies for primary sclerosing cholangitis, including transplantation.

Primary sclerosing cholangitis: value of cholangiography in determining the prognosis

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 test the association of these radiologic signs with subsequent survival. High-grade intrahepatic duct strictures (greater than 75% narrowing) were associated with a 19% decrease in 3-year survival (p = .05) compared with lower-grade strictures. Diffuse intrahepatic strictures (involving greater than 25% of the ducts) were associated with a 16% decrease in 3-year survival (p = .012) compared with localized strictures. Statistically insignificant (p greater than .05) but measurable decreases in survival were observed with high-grade extrahepatic duct strictures, diffuse involvement of the extrahepatic ducts, long confluent strictures anywhere in the biliary tree, and marked dilatation of the intrahepatic ducts. In general, intrahepatic duct disease was found to have greater prognostic significance than extrahepatic duct disease. High-grade strictures and diffuse strictures of the intrahepatic ducts were found to be indicators of a poor prognosis in PSC and were more predictive of a poor prognosis than was extrahepatic duct disease.

Primary biliary cirrhosis: relation between hepatic function and pulmonary function in patients who never smoked

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 transplantation, were studied. None of the 67 patients ever smoked cigarettes. Severity of primary biliary cirrhosis was characterized by histological stage and the Mayo risk score derived from a Cox regression model that used the following variables: serum bilirubin and serum albumin levels, age, prothrombin time and clinical severity of edema. Pulmonary function assessment included key variables describing expiratory airflow (forced expiratory volume in 1 sec divided by forced vital capacity) and efficiency of gas exchange (steady-state diffusing capacity for carbon monoxide). We found a significant relationship between histological stage of primary biliary cirrhosis and steady-state diffusing capacity (p = 0.02) and between the Mayo risk score for disease severity and steady-state diffusing capacity (p = 0.03). Progressive deterioration of steady-state diffusing capacity was associated with increasing severity of primary biliary cirrhosis. No relationship existed between pulmonary function and the presence of sicca complex or Sjögren's syndrome or the clinical manifestations of portal hypertension (e.g., esophageal varices, ascites and splenomegaly). No significant relationship existed between expiratory airflow and severity of primary biliary cirrhosis. We conclude that in patients with primary biliary cirrhosis who have never smoked, a statistically significant relationship exists between the severity of the liver disease and the efficiency of gas exchange measured by steady-state diffusing capacity.(ABSTRACT TRUNCATED AT 250 WORDS)

The effects of transformations and preliminary tests for non-linearity in regression

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 quadratic term. With either approach, the resulting test for association between the two variables can have an inflated type I error. We consider testing the significance of the quadratic term in a quadratic model as a preliminary test for non-linearity. Using simulation experiments and asymptotic arguments, we quantify the type I error inflation and suggest simple modifications of standard practice to protect the size of the type I error. In the case of quadratic regression, the type I error will be increased by roughly 50 per cent. The simple strategy of appropriately correcting the alpha-level is shown to have minimal loss of power if the relationship is truly linear. In the case of a linearizing transformation, the impact on the type I error will depend on the values of the independent variable and on the set of potential linearizing transformations considered. Simulation results suggest that a procedure which adjusts the test statistic according to the results of the preliminary test may offer adequate protection.

Intrapartum intervention and delivery outcome in low-risk pregnancy

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 oxytocin was used. However, epidural analgesia seemed to provide a protective neonatal effect when oxytocin was used during labor. Both elective and medically necessary use of these interventions were associated with increased morbidity. If obstetrical interventions, particularly oxytocin and epidural analgesia, are applied in low-risk pregnancies, labors must be monitored carefully and the risk-benefit ratios judged advantageous.

Diminished survival in asymptomatic primary biliary cirrhosis. A prospective study

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, cirrhosis) in 61% of the patients. During prospective clinical follow-up, which was available for 37 of the 44 study patients, one or more symptoms of liver disease developed in 33 (89%); esophageal varices were found in 15 (41%), and histologic progression to cirrhosis was found in 20 (67%) of the 30 precirrhotic patients. Significant (p less than 0.01) biochemical progression was reflected by a decrease in mean serum albumin concentrations and an increase in mean serum bilirubin levels in 32 patients followed for 4-6 yr. Survival data were available for all 73 patients; 17 died (11 secondary to liver failure), and 1 underwent liver transplantation. These patients had a 4-fold increase in mortality rate (p less than 0.001) compared with the U.S. population matched for age, race, and sex.

A prospective pilot study evaluating the effectiveness of secretory IgA measurements in bronchoalveolar lavage to detect non-small cell lung cancer

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 sIgA in bronchoalveolar lavage (BAL) at the time of bronchoscopic evaluation of potentially malignant lung nodules might prospectively predict the presence of cancer. We observed no significant increase in the sIgA obtained from eight BALs obtained from cancerous lungs as compared with BALs taken from these same patients' contralateral cancer-free lungs. We also saw no significant difference in BAL (sIgA) obtained from patients eventually found to have cancer (N = 8) as compared with those found to have noncancer diagnoses (N = 6). In light of these findings, we think it unlikely that measurement of sIgA will be clinically useful in the diagnosis of pulmonary malignant neoplasms.

Extramural cross-validation of the Mayo primary biliary cirrhosis survival model establishes its generalizability

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 accurately. It was also shown to be accurate for Mayo primary biliary cirrhosis patients with very advanced disease (n = 30), those with less than a 33% chance of surviving 12 months. The analyses confirmed that the addition of histologic stage did not significantly improve the predictive power of the model (p greater than 0.10). We suggest that the Mayo model is a practical tool for clinical management and decision making.

Primary sclerosing cholangitis: natural history, prognostic factors and survival analysis

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 chronic ulcerative colitis. Long-term follow-up (mean: 6.0 years; range: 2.7 to 15.5 years) was available in all patients. During follow-up, 59 (34%) of the patients died: 55 in the symptomatic group and four in the asymptomatic group. Median survival from the time of diagnosis of primary sclerosing cholangitis at the Mayo Clinic was 11.9 years. Survival in the asymptomatic group was significantly decreased compared with that in a control population matched for age, race and sex. Multivariate analysis (Cox proportional hazards regression modeling) revealed that age, serum bilirubin concentration, blood hemoglobin concentration, presence or absence of inflammatory bowel disease and histologic stage on liver biopsy were independent predictors of high risk of dying. The development of a multivariate statistical survival model is a major step in identifying individual primary sclerosing cholangitis patients at low, moderate and high risk of dying. Such models will be useful for stratifying patients in therapeutic trials, in patient counseling and in patient selection and timing of liver transplantation.

Patterns of failure after total laryngectomy for glottic carcinoma

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 untreated area in 35 patients; for the 29 affected above the clavicles, the median time to manifestation was 9.9 months. A Cox model with four risk factors (P less than 0.05) was found to predict failure above the clavicles: lymph node metastasis in the laryngectomy specimen (Delphian, pretracheal, tracheoesophageal, parathyroid), primary tumor more than 1.5 cm in greatest diameter, subglottic extension, and lymph node metastasis in the neck dissection specimen. A simple risk score computed from the Cox model shows that the more factors present, the higher the risk of disease progression or recurrence.

Prognosis in primary biliary cirrhosis: model for decision making

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 transplantation. This paper describes the development, testing and use of a mathematical model for predicting survival. The Cox regression method and comprehensive data from 312 Mayo Clinic patients with primary biliary cirrhosis were used to derive a model based on patient's age, total serum bilirubin and serum albumin concentrations, prothrombin time and severity of edema. When cross-validated on an independent set of 106 Mayo Clinic primary biliary cirrhosis patients, the model predicted survival accurately. Our model was found to be comparable in quality to two other primary biliary cirrhosis survival models reported in the literature and to have the advantage of not requiring liver biopsy.

Efficacy of liver transplantation in patients with primary biliary cirrhosis

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 patients with primary biliary cirrhosis, we compared survival in 161 patients with this diagnosis who had undergone a liver transplantation with survival in patients with the same diagnosis who had been treated conservatively. The comparison was performed with use of a recently developed statistical technique, the Mayo model. All patients had undergone liver transplantation between March 1980 and June 1987 and were followed for a median of 25 months. Three months after liver transplantation, the Kaplan-Meier survival probabilities in the recipients were substantially higher than the Mayo-model "simulated-control" survival probabilities (P less than 0.001). At two years, the Kaplan-Meier survival probability was 0.74, whereas the mean Mayo-model survival probability was 0.31. The patients who were at low risk according to the Mayo model had the best probability of survival after liver transplantation; however, patients at all risk levels who had undergone liver transplantation had higher probabilities of survival that those who had not. We conclude that liver transplantation is an efficacious treatment in patients with advanced primary biliary cirrhosis.

Application of the Mayo primary biliary cirrhosis survival model to Mayo liver transplant patients

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 assessment of the efficacy of transplantation. The Cox regression method and data from 312 Mayo Clinic patients with PBC were used to develop a model based on age, total serum bilirubin, serum albumin, prothrombin time, and severity of edema. When cross-validated on an independent set of 106 Mayo patients, the model accurately predicted their survival. It was similar to two other published survival models in terms of risk measurement but had the advantage of not necessitating liver biopsy. The model was used to assess the efficacy of liver transplantation by comparing the Kaplan-Meier survival of 32 Mayo patients after transplantation with the average model prediction of survival without transplantation. Beyond 3 months after transplantation, Kaplan-Meier survival probabilities were significantly greater than control survival predicted by the model (P less than 0.001). Examples of using the model for aiding in selection of patients for and timing of transplantation are provided.

Intraoperative blood loss and patient and graft survival in orthotopic liver transplantation: their relationship to clinical and laboratory data

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 CMV-negative donor, (4) the association of donor anti-hepatitis B core antigens and subsequent hepatitis B, and (5) the prognostic consequences of rouleaux observed in pretransplant blood compatibility testing. Patient diagnosis, the presence of ascites, a preoperative prothrombin time greater than 15 seconds, and a multifactorial "risk category" were all predictive of intraoperative blood loss. A history of previous gastrointestinal bleeding or an operation that involved the right upper abdominal quadrant was not predictive of intraoperative blood loss. Although CMV infection is common after liver transplantation, the prophylactic use of CMV antibody-negative blood products in CMV-negative recipients receiving a liver from a CMV-negative donor in our series was not associated with postoperative CMV infection. The transplantation of a liver positive for anti-hepatitis B core antigen was associated with subsequent hepatitis B surface antigen seroconversion in two of four cases. Transplantation of an ABO-incompatible liver and the presence of rouleaux observed in pretransplant blood compatibility testing were both associated with a significantly higher mortality. A careful review of laboratory data and medical records of patients undergoing liver transplantation should enhance the ability to modify the approach to the allocation of limited blood resources and the care and management of these patients.

Soluble interleukin-2 receptor level as an indicator of liver allograft rejection

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 other causes of graft dysfunction. CMV disease was diagnosed by isolation of CMV in blood or liver specimen cultures or identification of cytomegalic inclusions in the liver biopsy specimen. Of 82 consecutive recipients treated with cyclosporine and prednisone, 12 were in the control group, 20 in the rejection group, and 5 in the CMV disease group. The remaining 45 had other or multiple complications. In the control group the SIL-2R levels (determined by an ELISA) decreased by a mean of 4% per day after transplantation; in the rejection group the levels increased by a mean of 17% per day in the 10 days prior to the diagnosis of rejection; in the CMV disease group the levels tended to increase prior to the diagnosis of CMV disease. The rejection group had significantly higher SIL-2R levels than the control group at comparable times. Thus, SIL-2R levels were significantly increased at the time of allograft rejection compared with levels in a control group, and recipients with CMV disease had increased levels of SIL-2R but they were not as high as in recipients with rejection episodes.

Influence of site of obstetric care and delivery on pregnancy management and outcome

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 nursery care were found. An Apgar score of less than 7 at 1 minute or less than 8 at 5 minutes was 2.17 and 2.31 times more likely at RU and 2.48 and 2.60 times more likely at UU, respectively, than at RR. The overall Cesarean section rate was 9.6 percent, forceps rate was 7.2 percent, and nonroutine nursery care rate was 7.9 percent. Neonatal and perinatal mortality rates were 3.5 and 4.6 per 1,000 live births. There is no evidence that on-site perinatal subspecialists improve perinatal outcome when care is provided by board-certified family physicians. Small obstetric centers provide quality perinatal care with outcome dependent on physician's skill rather than on technology.

Clinical and statistical analyses of new and evolving therapies for primary biliary cirrhosis

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 trials evaluating immunosuppressive, antifibrotic and cupruretic agents. Prednisolone, D-penicillamine, azathioprine, colchicine and chlorambucil have been evaluated in controlled clinical trials, and biochemical improvement of liver function has been noted with all of the agents, except D-penicillamine. Improved survival has also been reported in patients treated long-term with azathioprine and colchicine. However, none of the therapeutic agents has been demonstrated to halt histologic progression of the disease or to induce a complete clinical, biochemical and histologic remission as has been reported in patients with autoimmune chronic active hepatitis treated with corticosteroids. Many of the trials did not use a double-blind design, failed to use the "intent to treat" rule or failed to define an objective time to analyze results. Many of the studies involved small numbers of patients with short-term follow-up and thus potentially were inadequate to appreciate drug effects that might be of clinical benefit. Currently, there is no totally effective therapy for primary biliary cirrhosis. We believe that well-designed clinical trials can provide important information to better understand this disease until a totally effective therapy is available. New clinical trials should use well-established methodologic guidelines in study design and well-accepted statistical standards in the analysis and interpretation of results.

Influence of positive lymphocyte crossmatch and HLA mismatching on vanishing bile duct syndrome in human liver allografts

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 incidence of VBDS was 5/16 in recipients with a positive crossmatch and 1/36 in recipients with a negative crossmatch. The positive-crossmatch group was significantly more likely to develop VBDS than the negative-crossmatch group (P less than 0.004, log rank test). Additional HLA studies comparing degree of donor-recipient mismatch at the various HLA loci showed no significant difference between the groups for class I disparity. However, class II mismatch was of borderline significance (P less than 0.056). When evaluated individually, the DQ mismatch (P less than 0.04) appeared to be more important than the DR mismatch (P = NS). Our data suggest that a positive lymphocyte crossmatch and a class II mismatch, in particular HLA DQ disparity, may play an important role in the pathogenesis of VBDS.