Probability binning comparison: a metric for quantitating univariate distribution differences

BACKGROUND

Comparing distributions of data is an important goal in many applications. For example, determining whether two samples (e.g., a control and test sample) are statistically significantly different is useful to detect a response, or to provide feedback regarding instrument stability by detecting when collected data varies significantly over time.

METHODS

We apply a variant of the chi-squared statistic to comparing univariate distributions. In this variant, a control distribution is divided such that an equal number of events fall into each of the divisions, or bins. This approach is thereby a mini-max algorithm, in that it minimizes the maximum expected variance for the control distribution. The control-derived bins are then applied to test sample distributions, and a normalized chi-squared value is computed. We term this algorithm Probability Binning.

RESULTS

Using a Monte-Carlo simulation, we determined the distribution of chi-squared values obtained by comparing sets of events derived from the same distribution. Based on this distribution, we derive a conversion of any given chi-squared value into a metric that is analogous to a t-score, i.e., it can be used to estimate the probability that a test distribution is different from a control distribution. We demonstrate that this metric scales with the difference between two distributions, and can be used to rank samples according to similarity to a control. Finally, we demonstrate the applicability of this metric to ranking immunophenotyping distributions to suggest that it indeed can be used to objectively determine the relative distance of distributions compared to a single control.

CONCLUSION

Probability Binning, as shown here, provides a useful metric for determining the probability that two or more flow cytometric data distributions are different. This metric can also be used to rank distributions to identify which are most similar or dissimilar. In addition, the algorithm can be used to quantitate contamination of even highly-overlapping populations. Finally, as demonstrated in an accompanying paper, Probability Binning can be used to gate on events that represent significantly different subsets from a control sample. Published 2001 Wiley-Liss, Inc.

Probability binning comparison: a metric for quantitating multivariate distribution differences

BACKGROUND

While several algorithms for the comparison of univariate distributions arising from flow cytometric analyses have been developed and studied for many years, algorithms for comparing multivariate distributions remain elusive. Such algorithms could be useful for comparing differences between samples based on several independent measurements, rather than differences based on any single measurement. It is conceivable that distributions could be completely distinct in multivariate space, but unresolvable in any combination of univariate histograms. Multivariate comparisons could also be useful for providing feedback about instrument stability, when only subtle changes in measurements are occurring.

METHODS

We apply a variant of Probability Binning, described in the accompanying article, to multidimensional data. In this approach, hyper-rectangles of n dimensions (where n is the number of measurements being compared) comprise the bins used for the chi-squared statistic. These hyper-dimensional bins are constructed such that the control sample has the same number of events in each bin; the bins are then applied to the test samples for chi-squared calculations.

RESULTS

Using a Monte-Carlo simulation, we determined the distribution of chi-squared values obtained by comparing sets of events from the same distribution; this distribution of chi-squared values was identical as for the univariate algorithm. Hence, the same formulae can be used to construct a metric, analogous to a t-score, that estimates the probability with which distributions are distinct. As for univariate comparisons, this metric scales with the difference between two distributions, and can be used to rank samples according to similarity to a control. We apply the algorithm to multivariate immunophenotyping data, and demonstrate that it can be used to discriminate distinct samples and to rank samples according to a biologically-meaningful difference.

CONCLUSION

Probability binning, as shown here, provides a useful metric for determining the probability with which two or more multivariate distributions represent distinct sets of data. The metric can be used to identify the similarity or dissimilarity of samples. Finally, as demonstrated in the accompanying paper, the algorithm can be used to gate on events in one sample that are different from a control sample, even if those events cannot be distinguished on the basis of any combination of univariate or bivariate displays. Published 2001 Wiley-Liss, Inc.

Issues confronting lesbian and gay elders: the challenge for health and human services providers

During the past two decades, the number of people over the age of 65 in the United States has been increasing twice as fast as the rest of the population. Within this diverse group, gerontologists are increasingly aware that there also exists a large population of older lesbian, gay men, and bisexuals. Health professionals must learn to acknowledge and meet the needs of this population. This article assists in addressing the knowledge gap by acquainting the reader with the aging concerns of lesbian and gay men; the impact of homophobia on their health; common heterosexual practices and their impact on care; retirement and leisure issues; the hidden incidence of abuse and neglect; and some suggested strategies that will assist health and human services workers in providing quality care for lesbians and gays as they age.

HPV DNA testing of the residual sample of liquid-based Pap test: utility as a quality assurance monitor

HPV DNA testing of the residual sample volume of liquid-based Pap tests has been recommended as a way to determine the appropriate follow-up for women who have equivocal results in routine clinical screening. A major aspect of quality assurance in the cytopathology laboratory consists of correlation of smear interpretation with biopsy or conization results as mandated by CLIA '88. However, the use of histology as the gold standard suffers from similar problems of subjectivity and sampling as the Pap smear. In this study we explore the potential use of HPV DNA testing of the residual volume from the ThinPrep Pap Test (Cytyc Corporation, Boxborough, Massachusetts) as a substitute gold standard in quality assurance monitoring of a cervical cytology screening program. The residual samples from 397 ThinPrep Pap cases were retrospectively analyzed for high-risk HPV DNA using the Hybrid Capture II technique. Sensitivity (71.8%), specificity (86.5%), predictive value of positive (77.1%) and negative (82.9%) ThinPrep Pap interpretations were calculated on the basis of HPV DNA results for 266 cases classed as either squamous intraepithelial lesion (SIL) or negative. Overall, there was agreement between the two tests in 80.8% of cases (Cohen's kappa =.59). The percentage of HPV DNA-positive cases interpreted as atypical squamous cells of uncertain significance (ASCUS) was 43.7%, and the percentage of negative cases was 17.1%. We believe that this approach is an objective adjunct to the traditional quality assurance protocol, with the added benefit that it includes cases interpreted as negative, as well as abnormal cases that do not come to biopsy.

Timing for repeated treatment of hyperthyroid disease with radioactive iodine after initial treatment failure

PURPOSE

It has been reported that the effect of radioactive iodine (RAI) treatment is complete in 4 to 6 months. This retrospective study evaluated the appropriate time for repeated treatment of hyperthyroid disease with RAI after initial treatment failure.

METHODS

Outcomes of 128 patients treated with RAI for hyperthyroid disease were reviewed retrospectively at 3 and 6 months.

RESULTS

Eighty patients (group A) were treated successfully with a single dose of RAI. Twenty patients (group B) required a second treatment dose. Twenty-eight patients were lost to follow-up. All patients in group A were clinically improved to various degrees at 3 months and continued to improve at 6 months. All eight patients in group B who showed no improvement at 3 months remained the same at 6 months. The difference between the two groups was statistically significant.

CONCLUSION

Patients with hyperthyroid disease who are unimproved at 3 months can be retreated with RAI without further delay.

Carotid endarterectomy without pre-operative angiography

Carotid endarterectomy is being performed with increasing frequency without the benefit of preoperative angiography, based purely on duplex scanning. The available data attest to its safety, with the caveats that the duplex scan is unimpeachable, and that the symptoms and duplex scan findings are consistent. Given the well documented risk of stoke as a consequence of cerebral angiography being at least 1%, the elimination of this risk by the omission of contrast angiography would reduce the neurological morbidity and mortality rate of the diagnosis and treatment of carotid bifurcation disease by approximately 50%. The available data make a compelling case for carotid endarterectomy based on duplex scanning, without preoperative angiography, as the preferred approach to treatment of carotid artery stenosis.

Outcomes of a brief inpatient treatment program for mood and anxiety disorders

Findings are reported from a study on outcomes of a brief psychiatric inpatient treatment program (7-day average) for 67 patients with mood and anxiety disorders. Multiple outcomes measures were completed by patients, family members, and clinicians at admission, discharge, and 3 months after discharge. Findings included significant improvement from admission to discharge, with maintenance of gains 3 months later and few readmissions. Implications for psychiatric nursing practice in today's health care environment are discussed.

Mutation detection in the breast cancer gene BRCA1 using the protein truncation test

About 400 distinct mutations have been defined in the BRCA1 gene, and these are spread fairly evenly through the 5592 bp of coding DNA. This circumstance presents a formidable challenge for mutation screening. Apart from total direct sequencing, the preferred screening method has been single-strand conformation polymorphism (SSCP) gels, with a smaller input from constant denaturant gradient electrophoresis (CDGE), heteroduplex (HD) analysis, and mismatch cleavage. The protein truncation test (PTT) was used early in BRCA1 mutation screening but has not been widely adopted, perhaps because a straightforward analysis of the whole BRCA1 gene requires working with RNA and all its perceived problems. The present work was undertaken to assess the practicality of using the PTT under routine conditions for the screening of long genes such as BRCA1 that are not highly expressed in lymphocytes. We conclude that, provided RNA preparation is carried out effectively and consistently, the PTT approach has significant advantages over other methodologies such as SSCP gels.

Underperforming doctors. Back from the brink

The UK has a poor record on retraining underperforming doctors and rehabilitating sick ones. But that is set to change. Wendy Moore examines new attitudes and plans of action aimed at meeting the demands of the clinical governance revolution.

The role of patch angioplasty in prevention of early recurrent carotid stenosis

The aim of this study was to determine the effect of primary closure versus patch angioplasty on the incidence of early recurrent stenosis after carotid endarterectomy in the hands of a single surgeon, and to analyze the risk factors associated with early recurrent stenosis after carotid endarterectomy. A retrospective review was performed of 178 consecutive patients who underwent 200 carotid endarterectomies-100 done consecutively with primary closure and 100 done consecutively with patch angioplasty. Of these patients, 126 qualified for analysis by having had at least 18 months of follow-up by serial duplex scanning. Of this group, the first 65 patients underwent 75 routine primary closures, while the last 61 underwent 67 routine patch angioplasties. All patients underwent a completion angiogram at the end of the case. Recurrent stenosis was defined as luminal diameter narrowing >60% on duplex scan. A multifactorial analysis was performed to analyze the effect of age, sex, tobacco use, diabetes, hypertension, peripheral vascular disease, coronary artery disease, and contralateral stenosis on recurrent stenosis. The results of this study showed that in a single surgeon's experience with carotid endarterectomy, varying only the method of closure between primary closure versus patch angioplasty, there is no statistically significant difference in the rate of early restenosis. No difference was noted in the perioperative morbidity and mortality between groups.