Fast and Accurate Binary Response Mixed Model Analysis Via Expectation Propagation.

Expectation propagation is a general prescription for approximation of integrals in statistical inference problems. Its literature is mainly concerned with Bayesian inference scenarios. However, expectation propagation can also be used to approximate integrals arising in frequentist statistical inference. We focus on likelihood-based inference for binary response mixed models and show that fast and accurate quadrature-free inference can be realized for the probit link case with multivariate random effects and higher levels of nesting. The approach is supported by asymptotic calculations in which expectation propagation is seen to provide consistent estimation of the exact likelihood surface. Numerical studies reveal the availability of fast, highly accurate and scalable methodology for binary mixed model analysis. Supplementary materials for this article are available online.

Roy's largest root test under rank-one alternatives.

Roy's largest root is a common test statistic in multivariate analysis, statistical signal processing and allied fields. Despite its ubiquity, provision of accurate and tractable approximations to its distribution under the alternative has been a longstanding open problem. Assuming Gaussian observations and a rank-one alternative, or concentrated noncentrality, we derive simple yet accurate approximations for the most common low-dimensional settings. These include signal detection in noise, multiple response regression, multivariate analysis of variance and canonical correlation analysis. A small-noise perturbation approach, perhaps underused in statistics, leads to simple combinations of standard univariate distributions, such as central and noncentral [Formula: see text] and [Formula: see text]. Our results allow approximate power and sample size calculations for Roy's test for rank-one effects, which is precisely where it is most powerful.

Prostate cancer is highly predictable: a prognostic equation based on all morphological variables in radical prostatectomy specimens.

PURPOSE: We determine whether biochemical prostate specific antigen (PSA) failure can be accurately predicted from preoperative serum PSA combined with 6 morphological variables from radical retropubic prostatectomy specimens in men with peripheral zone cancers. The unexpected limitation imposed by preoperative serum PSA on biochemical failure led us to compare peripheral zone to transition zone cancers. MATERIALS AND METHODS: A total of 326 peripheral zone and 46 transition zone cancers treated only with radical retropubic prostatectomy were followed for a minimum of 3 years (mean and median greater than 5). All prostates were sectioned at 3 mm. intervals and morphological variables were quantitated using the Stanford technique. Biochemical failure was defined as serum PSA 0.07 ng./ml. or greater and increasing. Multivariate logistic regression was used to identify variables with the most independent influence on biochemical failure and derive a clinical equation to predict failure in peripheral zone cancers. The validity of the predictive equation was assessed by out of sample validation and cross validation techniques. The 46 transition zone cancers were compared to the 326 peripheral zone cancers by Student's t and Wilcoxon tests. RESULTS: Of the peripheral zone failures 60% occurred in the first year after radical retropubic prostatectomy and 95% had occurred by the end of year 4. The highest preoperative serum PSA was 23 ng./ml. among the 181 men biochemically free of disease. Only 15.8% of 57 men with PSA greater than 15 ng./ml. were biochemically disease-free. For the 48 transition zone cancers cure rates were independent of serum PSA with 6 men having PSA greater than 50 ng./ml. Biochemical disease-free status was noted in 80% of transition zone compared to 56% of peripheral zone cancers (p = 0.0009). The most important variables predicting biochemical disease-free status for peripheral zone cancers were percent Gleason grade 4/5, cancer volume, serum PSA and prostate weight. Foci of vascular invasion, intraductal cancer and lymph nodes were less significant variables, and capsular penetration, positive surgical margins and seminal vesical invasion were insignificant. The multivariate logistic equation for predicting failure in peripheral zone cancers was highly accurate and requires only 2 to 3 minutes with a simple calculator. CONCLUSIONS: Failure of radical retropubic prostatectomy to cure peripheral zone prostate cancer is highly predictable based on 6 morphological variables from the prostatectomy specimen and serum PSA. The level of serum PSA profoundly limits biochemical cure rates in peripheral zone cancers. Transition zone cancers have a high cure rate, despite high serum PSA and adverse morphological variables. Men with serum PSA greater than 15 and perhaps even greater than 10 ng./ml. have such a low cure rate for peripheral zone cancer that re-biopsy attempts appear indicated to prove a transition zone location or else therapy other than radical retropubic prostatectomy should be sought. Pathologists should indicate whether the primary (largest) cancer is in the peripheral or transition zone to prevent overoptimistic reports of cure with radical prostatectomy procedures, as 85% of all tumors are in the peripheral zone.

Biological determinants of cancer progression in men with prostate cancer.

CONTEXT: The recent increase in ability to diagnose prostatic adenocarcinoma has created a dilemma for treatment decisions. OBJECTIVE: To determine whether prostate cancer progression is associated with a modified version of the Gleason grading system together with selected morphologic and clinical variables. DESIGN: Retrospective analysis of a cohort of patients with peripheral zone prostate cancers who underwent surgery between August 1983 and July 1992. SETTING: University hospital. PATIENTS: Radical prostatectomy specimens from 379 men treated only by surgical excision were prospectively studied for 8 morphologic variables using previously standardized techniques. Variables were percentage of each cancer occupied by Gleason grade 4/5 (% Gleason grade 4/5, the Stanford modified Gleason scale), cancer volume, vascular invasion, lymph node involvement, seminal vesicle invasion, capsular penetration, positive surgical margin, prostate weight, and preoperative prostate-specific antigen (PSA) level. MAIN OUTCOME MEASURE: Biochemical progression of prostate cancer as indicated by serum PSA level of 0.07 ng/mL and increasing. RESULTS: Cancer grade expressed as % Gleason grade 4/5 and cancer volume were highly predictive of disease progression. In a Cox proportional hazards model that included % Gleason grade 4/5, the traditional Gleason score was not an independent predictor of treatment failure. Positive lymph node findings and intraprostatic vascular invasion were the only other variables that remained significant at the .01 level. CONCLUSION: The % Gleason grade 4/5, cancer volume, positive lymph node findings, and intraprostatic vascular invasion were independently associated with prostate cancer progression, defined by an increasing PSA level. Techniques to accurately measure cancer volume and % Gleason grade 4/5 are needed to better predict which patient will experience cancer progression. The commonly accepted predictors of progression-capsular penetration and positive surgical margins-were not independently predictive of failure after radical prostatectomy.

Detection of colonic polyps in a phantom model: implications for virtual colonoscopy data acquisition.

PURPOSE: Virtual colonoscopy is a new method of colon examination in which computer-aided 3D visualization of spiral CT simulates fiberoptic colonoscopy. We used a colon phantom containing various-sized spheres to determine the influence of CT acquisition parameters on lesion detectability and sizing. METHOD: Spherical plastic beads with diameters of 2.5, 4, 6, 8 and 10 mm were randomly attached to the inner wall of segments of plastic tubing. Groups of three sealed tubes were scanned at 3/1, 3/2, 5/1 collimation (mm)/pitch settings in orientations perpendicular and parallel to the scanner gantry. For each acquisition, image sets were reconstructed at intervals from 0.5 to 5.0 mm. Two blinded reviewers assessed transverse cross-sections of the phantoms for bead detection, using source CT images for images for acquisitions obtained with the tubes oriented perpendicular to the gantry and using orthogonal reformatted images for scans oriented parallel to the gantry. RESULTS: Detection of beads of > or = 4 mm was 100% for both tube orientations and for all collimator/pitch settings and reconstruction intervals. For the 2.5 mm beads, detection decreased to 78-94% for 5 mm collimation/pitch 2 scans when the phantom sections were oriented parallel to the gantry (p = 0.01). Apparent elongation of beads in the slice direction occurred as the collimation and pitch increased. The majority of the elongation (approximately 75%) was attributable to changing the collimator from 3 to 5 mm, with the remainder of the elongation due to doubling the pitch from 1 to 2. CONCLUSION: CT scanning at 5 mm collimation and up to pitch 2 is adequate for detection of high contrast lesions as small as 4 mm in this model. However, lesion size and geometry are less accurately depicted than at narrower collimation and lower pitch settings.

Long-term cost-effectiveness of alternative management strategies for patients with life-threatening ventricular arrhythmias. Electrophysiologic Study versus Electrocardiographic Monitoring (ESVEM) Investigators.

BACKGROUND: Serial antiarrhythmic drug testing guided by Holter monitoring and electrophysiologic study had similar clinical outcomes in the Electrophysiologic Study versus Electrocardiographic Monitoring (ESVEM) trial, while patients treated with sotalol had improved outcomes. The purpose of this study was to compare long-term cost-effectiveness of these management alternatives. METHODS: Patients in the ESVEM trial were linked to computerized files of either the Health Care Finance Administration or the Department of Veterans Affairs. Total hospital costs and survival time over five year follow-up were measured using actuarial methods, and cost-effectiveness was calculated. RESULTS: Patients randomized to therapy guided by electrophysiologic study had more hospital admissions, higher costs, and a cost-effectiveness ratio of $162,500 per life year added compared with therapy guided by Holter monitoring. Patients randomized to sotalol had fewer hospitalizations, lower costs, and better survival than patients randomized to other drugs, and sotalol was a dominant strategy in the cost-effectiveness analysis. Patients for whom an effective drug was found had fewer hospital admissions, lower costs, and longer survival. These findings were robust in sensitivity analyses and in bootstrap replications. CONCLUSIONS: Serial drug testing guided by electrophysiologic study had an unfavorable cost-effectiveness ratio relative to Holter monitoring, while sotalol was cost-effective relative to other antiarrhythmic drugs.

Serum prostate-specific antigen and the biologic progression of prostate cancer.

OBJECTIVES: We have previously shown that serum prostate-specific antigen (PSA) is proportional to prostate cancer volume and that progression of prostate cancer is proportional to volume, but other investigators have not found serum PSA to be as useful in predicting pathologic stage at the time of radical prostatectomy. Because our series is the only study to examine prospectively all radical specimens at 3-mm intervals, we have examined the relationship between serum PSA and the morphologic indicators of cancer progression in our first 350 radical prostatectomies. METHODS: Preoperative serum PSA level was tabulated in 350 consecutive patients with prostate adenocarcinoma and compared with morphologic variables in the radical prostatectomy specimen. Morphologic variables included cancer volume, histologic grade, capsular penetration, seminal vesicle invasion, and lymph node metastasis. RESULTS: Serum PSA showed strong correlation with all morphologic variables, which were highly intercorrelated. Serum PSA level was strongly correlated with cancer volume, histologic grade, and frequency of regional spread to lymph nodes. Close intercorrelations found between all variables were translated into a scale relating each level of serum PSA elevation to stage of disease in morphologic terms. Using this scale, serum PSA level can contribute to patient evaluation and treatment decisions in men with prostate cancer. CONCLUSIONS: Serum PSA is primarily determined by prostate cancer volume and secondarily by the percentage of high-grade cancer (Gleason grades 4 and 5) in the prostate. Because of this basic relationship, serum levels of PSA provide a clinically useful estimate of morphologic findings in the prostate. Serial PSA determinations should reflect the growth of the cancer as well as the gradual evolution of more malignant cells with the passage of time. The use of a serum PSA-based rating scale can contribute to patient evaluation and treatment decisions in men with prostate cancer.

The influence of volumetric tumor doubling time, DNA ploidy, and histologic grade on the survival of patients with intracranial astrocytomas.

PURPOSE: To improve the prediction of individual survival in patients with intracranial astrocytomas through the analysis of volumetric tumor doubling time (VDt) and DNA ploidy. METHODS: A pilot study was retrospectively conducted on a group of 25 patients with intracranial astrocytomas in whom recurrent and/or progressive disease was observed on serial contrast-enhanced CT or MR examinations. VDt was computed using two or more data points from a semilogarithmic plot of tumor volume versus time. Size-adjusted survival was calculated using a method based on VDt and initial tumor volume to decrease the lead time bias attributable to differing tumor sizes at presentation. RESULTS: Slower VDt was associated with significantly longer survival and size-adjusted survival as determined by a univariate Cox proportional hazard analysis. Aneuploidy was a significant indicator of poor survival. Aneuploid and multiclonal astrocytomas had poor size-adjusted survivals compared with diploid astrocytomas. Grade IV astrocytomas had significantly poorer survival and size-adjusted survival compared with lower grades (I to III), which individually were not significantly correlated. However, grade IV histology was not a significant independent predictor of size-adjusted survival in a multivariate Cox model, whereas VDt and DNA ploidy remained significant. VDt also had a significant direct linear correlation to survival and size-adjusted survival. CONCLUSIONS: VDt and DNA ploidy were more sensitive than histologic grading as indicators of individual survival. Initial tumor size needs to be considered when staging and assessing survival in patients with intracranial astrocytomas.

Prediction of prostate cancer volume using prostate-specific antigen levels, transrectal ultrasound, and systematic sextant biopsies.

OBJECTIVES: Prostate-specific antigen (PSA) levels, transrectal ultrasound, and systematic sextant biopsies have each shown limited ability to predict prostate cancer volume. In combination, these studies may allow more accurate estimation of volume and prognosis. METHODS: One hundred twenty-four patients were evaluated prior to radical prostatectomy. Interactive stepwise multiple regression and separate logistic regression analysis were performed for prediction of prostate cancer volume and volume range. RESULTS: The cancer volumes calculated correlated with the volumes in the radical prostatectomy specimens with R2 of 0.76. Cancers were predicted to be in the volume range associated with poor prognosis (more than 12 cc) or clinically insignificant cancer (less than 1.0 cc) with bias corrected error rates of 5.3% and 10%, respectively. CONCLUSIONS: The formula for prediction of cancer volume correlates well with actual cancer volume in 92 patients but is not adequate to predict volume for an individual patient. The formulas for prediction of volume range show promising predictive ability and may be useful if the extent of disease is unclear.

The anatomy of the posterior communicating artery as a risk factor for ischemic cerebral infarction.

BACKGROUND: After the occlusion of an internal carotid artery the principal source of collateral flow is through the arteries of the circle of Willis, but the size and patency of these arteries are quite variable. Study of the anatomy of the collateral pathways in patients with internal-carotid-artery occlusion with or without infarction in the watershed area of the deep white matter may identify patterns that afford protection from ischemic infarction. METHODS: Using conventional magnetic resonance imaging and three-dimensional phase-contrast magnetic resonance angiography, we evaluated 29 consecutive patients (32 hemispheres at risk) with angiographically proved occlusion of the internal carotid artery. Four collateral pathways to the occluded vessel were evaluated: the proximal segment of the anterior cerebral artery, the posterior communicating artery, the ophthalmic artery, and leptomeningeal collateral vessels from the posterior cerebral artery. RESULTS: Only features of the ipsilateral posterior communicating artery were related to the risk of watershed infarction. The presence of posterior communicating arteries measuring at least 1 mm in diameter was associated with the absence of watershed infarction (13 hemispheres, no infarcts; P < 0.001). Conversely, there were 4 watershed infarcts in the 6 hemispheres with posterior communicating arteries measuring less than 1 mm in diameter and 10 infarcts in the 13 hemispheres with no detectable flow in the ipsilateral posterior communicating artery. CONCLUSIONS: A small (< 1 mm in diameter) or absent ipsilateral posterior communicating artery is a risk factor for ischemic cerebral infarction in patients with internal-carotid-artery occlusion.

Effects of intensive multiple risk factor reduction on coronary atherosclerosis and clinical cardiac events in men and women with coronary artery disease. The Stanford Coronary Risk Intervention Project (SCRIP).

BACKGROUND: Recent clinical trials have shown that modification of plasma lipoprotein concentrations can favorably alter progression of coronary atherosclerosis, but no data exist on the effects of a comprehensive program of risk reduction involving both changes in lifestyle and medications. This study tested the hypothesis that intensive multiple risk factor reduction over 4 years would significantly reduce the rate of progression of atherosclerosis in the coronary arteries of men and women compared with subjects randomly assigned to the usual care of their physician. METHODS AND RESULTS: Three hundred men (n = 259) and women (n = 41) (mean age, 56 +/- 7.4 years) with angiographically defined coronary atherosclerosis were randomly assigned to usual care (n = 155) or multifactor risk reduction (n = 145). Patients assigned to risk reduction were provided individualized programs involving a low-fat and -cholesterol diet, exercise, weight loss, smoking cessation, and medications to favorably alter lipoprotein profiles. Computer-assisted quantitative coronary arteriography was performed at baseline and after 4 years. The main angiographic outcome was the rate of change in the minimal diameter of diseased segments. All subjects underwent medical and risk factor evaluations at baseline and yearly for 4 years, and reasons for all hospitalizations and deaths were documented. Of the 300 subjects randomized, 274 (91.3%) completed a follow-up arteriogram, and 246 (82%) had comparative measurements of segments with visible disease at baseline and follow-up. Intensive risk reduction resulted in highly significant improvements in various risk factors, including low-density lipoprotein cholesterol and apolipoprotein B (both, 22%), high-density lipoprotein cholesterol (+12%), plasma triglycerides (-20%), body weight (-4%), exercise capacity (+20%), and intake of dietary fat (-24%) and cholesterol (-40%) compared with relatively small changes in the usual-care group. No change was observed in lipoprotein(a) in either group. The risk-reduction group showed a rate of narrowing of diseased coronary artery segments that was 47% less than that for subjects in the usual-care group (change in minimal diameter, -0.024 +/- 0.066 mm/y versus -0.045 +/- 0.073 mm/y; P < .02, two-tailed). Three deaths occurred in each group. There were 25 hospitalizations in the risk-reduction group initiated by clinical cardiac events compared with 44 in the usual-care group (rate ratio, 0.61; P = .05; 95% confidence interval, 0.4 to 0.9). CONCLUSIONS: Intensive multifactor risk reduction conducted over 4 years favorably altered the rate of luminal narrowing in coronary arteries of men and women with coronary artery disease and decreased hospitalizations for clinical cardiac events.

Radiation-induced damage, repair and exchange formation in different chromosomes of human fibroblasts determined by fluorescence in situ hybridization.

We have used fluorescence in situ hybridization with whole-chromosome probes for human chromosomes 1, 4, 8 and 13 to investigate the extent to which the induction of damage and its repair after exposure to ionizing radiation is distributed randomly among these chromosomes. All the studies were performed with AG1522 human fibroblasts irradiated with 6 Gy and maintained in a nondividing state for at least 6 h after irradiation except for the measurements of initial damage. The extent of initial damage was determined by fusion of the cells immediately after irradiation with metaphase HeLa cells to obtain premature chromosome condensation (PCC). Breaks and exchanges were also scored by PCC 24 h after irradiation and in metaphase spreads at the first division after irradiation. The data obtained were consistent with random breakage and repair in these chromosomes. Comparing PCC 24 h after irradiation with first metaphase, there was a deficit in aberrations at metaphase, particularly in unrejoined breaks, implying loss or slowing of cells containing aberrations prior to the first division. An analysis of dicentrics and translocations in chromosome 4 at first and in subsequent divisions showed that there was an equal number of dicentrics and translocations at first metaphase with loss of dicentrics, but no loss of translocations in subsequent divisions. These data are supportive of the hypothesis tht the total number of chromosome aberrations in cells can be estimated from a single chromosome pair.

Does the maximum entropy method improve sensitivity?

Maximum entropy reconstruction has been used in several fields to produce visually striking reconstructions of positive objects (images, densities, spectra) from noisy, indirect measurements. In magnetic resonance spectroscopy, this technique is notable for its apparent noise suppression and its avoidance of the artifacts that affect discrete Fourier transform spectra of short (zero-extended) data records. In the general case where the length of the reconstructed spectrum exceeds that of the data record or where a convolution kernel is incorporated in the reconstruction, no known analytical solution to the reconstruction problem exists. Consequently, knowledge of the properties of maximum entropy reconstruction has been mainly anecdotal, based on a small selection of published reconstructions. However, in the limiting case where the lengths of the reconstructed spectrum and the data record are the same and a convolution kernel is not applied, the problem can be solved analytically. The solution has a simple structure that helps explain several commonly observed features of maximum entropy reconstructions--for example, the biases in the recovered intensities and the fact that noise near the baseline is more successfully suppressed than is noise superimposed on broad features in the spectrum. The solution also shows that the noise suppression offered by maximum entropy reconstruction could (in this special case) be equally well obtained by a "cosmetic" device: simply displaying the conventional Fourier transform reconstruction using a certain nonlinear plotting scale for the vertical (y) coordinate.

Prostate specific antigen in the diagnosis and treatment of adenocarcinoma of the prostate. II. Radical prostatectomy treated patients.

Serum prostate specific antigen was determined (Yang polyclonal radioimmunoassay) in 102 men before hospitalization for radical prostatectomy. Prostate specimens were subjected to detailed histological and morphometric analysis. Levels of prostate specific antigen were significantly different between patients with and without a Gleason score of 7 or greater (p less than 0.001), capsular penetration greater than 1 cm. in linear extent (p less than 0.001), seminal vesicle invasion (p less than 0.001) and pelvic lymph node metastasis (p less than 0.005). Prostate specific antigen was strongly correlated with volume of prostate cancer (r equals 0.70). Bivariate and multivariate analyses indicate that cancer volume is the primary determinant of serum prostate specific antigen levels. Prostate specific antigen was elevated 3.5 ng. per ml. for every cc of cancer, a level at least 10 times that observed for benign prostatic hyperplasia. Prostate specific antigen is useful as a preoperative marker because no patient with lymph node metastasis had serum levels of less than 10 ng. per ml. (4 times the upper limit of normal range). Of the patients with greater than 50 ng. per ml. two-thirds had microscopic lymph node metastasis and 90 per cent had seminal vesicle invasion. Serum prostatic acid phosphatase levels showed a significantly weaker correlation with cancer volume (r equals 0.51) and every other pathological parameter. Of the patients 73 per cent had serum prostatic acid phosphatase levels in the normal range (0 to 2.1 ng. per ml.), including 7 per cent who had pelvic lymph node metastasis. Postoperative prostate specific antigen values were available in 97 of 102 patients, with a mean and maximum followup of 12 and 38 months. No patient with pelvic lymph node metastasis achieved an undetectable prostate specific antigen level without adjunctive therapy (hormonal or radiation). No difference in preoperative or postoperative prostate specific antigen levels, cancer volume, seminal vesicle invasion or incidence of pelvic lymph node metastasis was seen between patients with no capsular penetration and those with minimal capsular penetration (1 cm. or less total linear extent of full thickness penetration), providing the first quantitative evidence that small amounts of capsular penetration may not be of biological or prognostic significance.