Peter A. Lachenbruch

Estimation of Error Rates in Discriminant Analysis

Several methods of estimating error rates in Discriminant Analysis are evaluated by sampling methods. Multivariate normal samples are generated on a computer which have various true probabilities of misclassification for different combinations of sample sizes and different numbers of parameters. The two methods in most common use are found to be significantly poorer than some new methods that are proposed.

Regional differences in brain electrical activity in dementia: use of spectral power and spectral ratio measures ☆

The pathologic changes in dementia of the Alzheimers type (DAT) commonly affect selected brain regions. The cortical areas affected in multi-infarct dementia (MID) are less predictable and may be secondary to subcortical gray or white matter damage that is widespread in MID. We compared several types of quantitative EEG power measures (absolute and relative power, and ratios of power) to determine their regional distribution, and their association with changes in cognitive status and age. We examined 49 subjects with clinically diagnosed mild-to-moderate DAT, 29 with mild-to-moderate MID, and 38 elderly controls (CON). We used discriminant analysis to identify, for each parameter type, the brain region and frequency band where the parameter best distinguished between groups of subjects. The parameters showed regional differences in distinguishing between DAT and MID subjects, and in their association with age and cognitive status. All parameters were useful for detecting differences between normal and demented subjects and correctly identified comparable proportions of subjects as having dementia. Subjects who were abnormal on several parameters were much more likely to have dementia. The additive effects of these parameters in correct classification suggest that they may be monitoring different physiologic processes. Combinations of several types of parameters may be more useful than individual parameters for distinguishing demented from non-demented subjects.

Analysis of data with excess zeros.

This paper is an introduction to a set of papers on two-part models that were presented at the 2000 Joint Statistical Meetings of American Statistical Association, International Biometric Society (ENAR), International Biometric Society (WNAR), Institute of Mathematical Statistics, and Statistical Society of Canada. The second part of the paper summarizes results of a study of the size and power of two-part models. It proposes that two-part models are a useful alternative to the t-test and the Wilcoxon test.

Early Undifferentiated Connective Tissue Disease: III. Outcome and Prognostic Indicators in Early Scleroderma (Systemic Sclerosis)

Scleroderma, or systemic sclerosis, varies widely in its presentation and course. Many patients with scleroderma have a disease course of 10 to 20 years [1-4], but some patients experience a rapidly progressive form of disease characterized by early organ failure and death. Of 91 patients studied retrospectively by Lally and colleagues [3], 16 developed renal or cardiorespiratory failure (or both) an average of 15.8 months after the onset of symptoms; 11 of these 16 patients died. Retrospective assessments are inherently weighted toward the selection of patients with a longer disease duration, and patients experiencing early death or rapidly progressive disease may be under-represented. A few clinical studies and therapeutic trials have targeted patients with a disease duration of less than 5 years [3-5]; however, additional prospective information on the course and prognosis of patients with early scleroderma is needed to make appropriate risk/benefit decisions about potentially toxic therapies. Recently, a prospective study was done in 410 patients with early undifferentiated or early defined connective tissue disease [6]. Selecting 48 patients with early scleroderma from this cohort, we analyzed short-term outcomes and identified some features occurring within the first year of disease that may be useful in distinguishing patients at high risk for an unfavorable outcome. Methods The Cooperative Systematic Studies of the Rheumatic Diseases Program is funded under a National Institute of Arthritis and Musculoskeletal Diseases contract through the Coordinating Center at the University of Utah, Salt Lake City, Utah, and includes 10 centers participating in the study of early undifferentiated connective tissue disease. Outpatients and inpatients seen at participating centers were eligible for the study if they met diagnostic criteria for rheumatoid arthritis, scleroderma, systemic lupus erythematosus, or poly/dermatomyositis [7-10] and had experienced symptoms for less than 1 year. Patients who had features of a connective tissue disease, including Raynaud phenomenon, unexplained polyarthritis, or 3 of 11 findings characteristic of connective tissue disease, but who did not meet established criteria for a specific connective tissue disease were classified as having undifferentiated connective tissue disease. Patients were evaluated at baseline and at follow-up intervals of 1, 3, and 5 years. Details on data collection and on the clinical and laboratory features of the patients with early undifferentiated connective tissue disease have been described previously [6, 11]. Enrollment for the study began in July 1982 and was completed in June 1987. Survival status was confirmed through at least 5 years after symptom onset in all cases except one (patient lost to follow-up after 1.6 years). A diagnosis of scleroderma was made in 52 patients (in 46 within 1 year of symptom onset and in 6 within 4 years of symptom onset). Four of these patients (including 2 of 6 diagnosed after the baseline evaluation) developed overlap syndromes during the 5-year follow-up period and were excluded from the study, leaving 48 patients for analysis. Deaths and causes of death were reported to the Coordinating Center; every possible effort was made to confirm the cause of death through hospital records and autopsy reports from the participating centers. Five patients died at home, on the way to the hospital, or shortly after arrival at the hospital. Sclerodermatous skin findings on physical examination were categorized as follows: sclerodactyly (involvement distal to the metacarpophalangeal joints); acrosclerosis (involvement distal to elbows and knees); or generalized or diffuse scleroderma. A skin score was not determined. Physical findings for each organ system were recorded as a yes or no response to a list of abnormal findings. Twelve cardiorespiratory signs were assessed on the baseline physical examination: These included the presence or absence of rales, wheezes, pleural or pericardial rubs, pleural effusion, systolic or diastolic murmurs, abnormal second heart sounds, cardiomegaly, arrhythmia, dependent edema, and tachycardia (pulse 100 beats/min). All patients had routine hematology and biochemical laboratory tests. Many patients also had a determination of erythrocyte sedimentation rate (Westergren method) (n = 47), pulmonary function tests (n = 43), an electrocardiogram (n = 40), a chest radiograph (n = 40), and the Schirmer test. Serum specimens from all patients were analyzed for serologic markers of rheumatic disease at the Centers for Disease Control [11]. In addition, frozen serum specimens from 45 of the 48 patients with scleroderma were analyzed at Specialty Laboratories, Inc. (Santa Monica, California): Interleukin-2 levels were assessed by enzyme-linked immunosorbent assay (ELISA); soluble interleukin-2 receptor levels by ELISA; and neopterin levels by radioimmunoassay; anti-Scl-70 antibody levels by ELISA; and anticentromere antibody titer by immunofluorescence assay. Lung diffusing capacity was considered to be abnormal if it was less than 70% of the predicted diffusing capacity. Chest radiographs were considered to be abnormal if infiltrates, effusions, pleural thickening, or heart enlargement was present. Electrocardiograms were considered to be abnormal if evidence of arrhythmia, heart block, ventricular enlargement, repolarization abnormalities, significant shift in axis, or infarction was found. For the purposes of our study, nonspecific ST or T-wave abnormalities were not considered to be abnormal. Baseline clinical, laboratory, and other features of patients with early death were compared with those of survivors. Mean values were compared using the Student t-test. Comparisons between dichotomous variables were done using chi-square distribution with Yates correction. Life-table analyses using Kaplan-Meier survival estimation [12] and Mantel-Haenszel statistics [13] were done to predict survival rates for the group of patients with early scleroderma and the various subgroups generated by stratification based on selected variables. Variables were evaluated using univariate Cox proportional-hazards analysis for their ability to predict survival [14]. The variables found to be most significant, as determined by univariate Cox proportional-hazards analysis, and for which less than 10% of data were missing, were then evaluated by multivariate Cox analysis with stepwise regression modeling. We did not apply the Bonferroni correction to our results; however, because of the many variables compared, we defined statistical significance by a probability level of 0.01. Results Forty-eight patients with scleroderma were enrolled in the study. One patient was lost to follow-up 1.6 years after symptom onset, and the data gathered on her were used only in the survival and Cox analyses. During the 5-year follow-up period, 15 of the 47 evaluable patients with early scleroderma died. Kaplan-Meier estimation yielded overall survival rates at 1, 3, and 5 years after symptom onset of 92%, 75%, and 68%, respectively (Figure 1). Five patients died within 1 year of symptom onset. The cohort of patients with scleroderma accounted for 41% of all early deaths recorded for the entire study population of 410 patients. The causes of death are summarized in Table 1. Multiorgan involvement was frequently observed at the time of death, although pulmonary or cardiac system failure (or both) was thought to be the immediate cause of death in 8 of the 15 patients who died. Renal crisis was substantiated or suspected in 4 of the patients who died. The time from symptom onset to death was similar for those dying of renal causes (21 11 months) and those dying of cardiopulmonary causes (25 17 months). Table 1. Suspected Immediate Causes of Death, Average Age at Death, and Survival in Patients with Early Scleroderma* Figure 1. Cumulative survival probabilities: Kaplan-Meier survival curve with Greenwood confidence limits from onset of symptoms for the 48 early scleroderma patients. Clinical Features In Table 2, baseline characteristics of patients who died within 5 years after symptom onset are compared with those of the survivors. Twelve of the 15 (80%) patients who died had at least one abnormal cardiopulmonary sign at baseline compared with 13 of 32 (41%) survivors (P = 0.03). Among individual cardiopulmonary findings, resting heart rate was significantly different between survivors (79 13 beats/min; range, 50 to 110 beats/min) and patients who died (93 12 beats/min; range, 70 to 120 beats/min) (P = 0.001). Baseline blood pressure was similar in the subgroups (survivors: 120 17/76 12 mm Hg; patients who died: 127 27/78 16 mm Hg; P > 0.3), as was the frequency of chest radiographic, pulmonary function, and electrocardiographic abnormalities (P = 0.09). Table 2. Baseline Features of Patients with Early Scleroderma Who Survived and of Those Who Died* Chest pain, dyspnea, orthopnea, dependent edema, cough, and wheezing were common complaints; 57% of the entire group had at least one symptom. Dyspnea was the most common single cardiorespiratory complaint (36%). No significant difference in frequency of cardiopulmonary symptoms was detected between those who died and those who survived. Ninety-two percent of our patients developed skin involvement within 1 year of symptom onset, implying that patients with gradual-onset scleroderma were not included in our study. Four of the 48 patients did not have diagnosable scleroderma at their first visit, but they did develop skin disease within 3 years of follow-up (or within 4 years of disease onset). At entry, two patients had Raynaud phenomenon only and two were diagnosed with undifferentiated connective tissue disease. When baseline variables for these 4 patients with intermediate-onset scleroderma were compared with those of the remaining 44 patients with earlier-onset disease, no significant differences were

Assessing screening tests: extensions of McNemar's test

We address the problem of comparing a new screening test to a currently available screening test in the absence of a gold standard. When both tests are given to each participant in a clinical trial, the usual analytical approach is to apply McNemars test for equality of the off-diagonal probabilities, with rejection of the null hypothesis implying that the tests differ. For assessing equivalence, however, we consider a compound null hypothesis that the new test gives either fewer or more positive results than the standard. If both parts of this hypothesis are rejected, we assert equivalence in the rate of positive responses. We propose an extension of McNemars test for this situation. A companion step is to construct a confidence interval for the ratio of the marginal probabilities and assert equivalence if the interval is sufficiently small. It is also important that the tests agree a large proportion of the time. This can be verified with a complementary two-tailed binomial test. Another situation arises when there is a gold standard for disease diagnosis, and we wish to compare the sensitivity and specificity of two screening tests. We show that a 2 degrees-of-freedom chi-square test based on two McNemar-like tables is an appropriate test.

Biomarkers and Surrogate Endpoints in Renal Transplantation: Present Status and Considerations for Clinical Trial Design

Of major importance in clinical trials is the ability to predict individual patient outcome or endpoints using biomarkers, also known as variables or predictors, in as safe, efficient, and accurate a manner as possible. This review addresses the concepts and possible strategies for use of predictor and surrogate biomarkers in the design of clinical trials in renal transplantation. The statistical concepts apply equally well to other organ grafts.

Genital tract abnormalities and female sexual function impairment in systemic sclerosis.

Abstract OBJECTIVE: Our purpose was to determine the involvement of the female genital tract and its functional consequences on menstrual and sexual aspects in systemic sclerosis. STUDY DESIGN: Sixty women with systemic sclerosis and 23 age- and disease duration-matched women with either rheumatoid arthritis or systemic lupus erythematosus were surveyed with a comprehensive questionnaire addressing problems before and after disease onset. Fourteen systemic sclerosis patients also had gynecologic evaluations. RESULTS: Vaginal dryness (71%), ulcerations (23%), and dyspareunia (56%) were significantly more frequent in patients with systeic sclerosis after disease onset than before and also in comparison with control subjects. Vaginal tightness and constricted introitus were present in 5 of 60 systemic sclerosis patients. More than half of systemic sclerosis patients reported a decrease in the number ( p = 0.04) and intensity ( p = 0.02) of orgasm,, compared to CONCLUSIONS: Although impairment in various indexes of sexual function occurs in a number of autoimmune diseases, decreased orgasmic function appears to be limited to systeic sclerosis. Vaginal involvement and other systemic sclerosis-related systemic symptoms adversely influence sexual relations. Menstrual abnormalities, including early menopause, affect many patients. Genital tract involvement occurs in a substantial proportion. Prospective longitudinal studies are warranted.

Damage Extent and Predictors in Adult and Juvenile Dermatomyositis and Polymyositis as Determined With the Myositis Damage Index

OBJECTIVE We undertook this study to validate the Myositis Damage Index (MDI) in juvenile and adult myositis, to describe the degree and types of damage and to develop predictors of damage. METHODS Retrospective MDI evaluations and prospective assessment of disease activity and illness features were conducted. Patients with juvenile-onset disease (n = 143) were evaluated a median of 18 months after diagnosis; 135 patients were assessed 7-9 months later, and 121 were last assessed a median of 82 months after diagnosis. Ninety-six patients with adult-onset dermatomyositis or polymyositis had a baseline assessment a median of 30 months after diagnosis; 77 patients had a 6-month followup evaluation, and 55 had a final assessment a median of 60 months after diagnosis. RESULTS Damage was present in 79% of juvenile patients and in 97% of adult patients. In juveniles, scarring, contractures, persistent weakness, muscle dysfunction, and calcinosis were most frequent (23-30%) at the last evaluation. In adults, muscle atrophy, muscle dysfunction, and muscle weakness were most frequent (74-84%). MDI severity correlated with physician-assessed global damage, serum creatinine, and muscle atrophy on magnetic resonance imaging, and in juveniles also with functional disability and weakness. MDI damage scores and frequency were highest in patients with a chronic illness course and in adult patients who died. Predictors of damage included functional disability, duration of active disease, disease severity at diagnosis, physician-assessed global disease activity, and illness features, including ulcerations in children and pericarditis in adults. CONCLUSION Damage is common in myositis after a median duration of 5 years in patients with adult-onset disease and 6.8 years in patients with juvenile-onset disease. The MDI has good content, construct, and predictive validity in juvenile and adult myositis.

Fraud in Medical Research: An International Survey of Biostatisticians

Abstract The characteristics of scientific fraud and its impact on medical research are in general not well known. However, the interest in the phenomenon has increased steadily during the last decade. Biostatisticians routinely work closely with physicians and scientists in many branches of medical research and have therefore unique insight into data. In addition, they have methodological competence to detect fraud and could be expected to have a professional interest in valid results. Biostatisticians therefore are likely to provide reliable information on the characteristics of fraud in medical research. The objective of this survey of biostatisticians, who were members of the International Society for Clinical Biostatistics, was to assess the characteristics of fraud in medical research. The survey was performed between April and July 1998. The participation rate was only 37%. We report the results because a majority (51%) of the participants knew about fraudulent projects, and many did not know whether the organization they work for has a formal system for handling suspected fraud or not. Different forms of fraud (e.g., fabrication and falsification of data, deceptive reporting of results, suppression of data, and deceptive design or analysis) had been observed in fairly similar numbers. We conclude that fraud is not a negligible phenomenon in medical research, and that increased awareness of the forms in which it is expressed seems appropriate. Further research, however, is needed to assess the prevalence of different types of fraud, as well as its impact on the validity of results published in the medical literature. Control Clin Trials 2000;21:415–427

Discriminant Analysis When the Initial Samples Are Misclassified

Discriminant functions are based on samples which are assumed to be correctly classified. If some members of the original samples are incorrectly classified the utility of the discriminant function may not be seriously affected.