Ratio maps and correspondence analysis

We compare two methods for visualising contingency tables and developa method called the ratio map which combines the good properties of both.The first is a biplot based on the logratio approach to compositional dataanalysis. This approach is founded on the principle of subcompositionalcoherence, which assures that results are invariant to considering subsetsof the composition. The second approach, correspondence analysis, isbased on the chi-square approach to contingency table analysis. Acornerstone of correspondence analysis is the principle of distributionalequivalence, which assures invariance in the results when rows or columnswith identical conditional proportions are merged. Both methods may bedescribed as singular value decompositions of appropriately transformedmatrices. Correspondence analysis includes a weighting of the rows andcolumns proportional to the margins of the table. If this idea of row andcolumn weights is introduced into the logratio biplot, we obtain a methodwhich obeys both principles of subcompositional coherence and distributionalequivalence.

The contributions of rare objects in correspondence analysis

Correspondence analysis, when used to visualize relationships in a table of counts(for example, abundance data in ecology), has been frequently criticized as being too sensitiveto objects (for example, species) that occur with very low frequency or in very few samples. Inthis statistical report we show that this criticism is generally unfounded. We demonstrate this inseveral data sets by calculating the actual contributions of rare objects to the results ofcorrespondence analysis and canonical correspondence analysis, both to the determination ofthe principal axes and to the chi-square distance. It is a fact that rare objects are oftenpositioned as outliers in correspondence analysis maps, which gives the impression that theyare highly influential, but their low weight offsets their distant positions and reduces their effecton the results. An alternative scaling of the correspondence analysis solution, the contributionbiplot, is proposed as a way of mapping the results in order to avoid the problem of outlying andlow contributing rare objects.

Asymptotic robustness in multi-sample analysis of multivariate linear relations

Standard methods for the analysis of linear latent variable models oftenrely on the assumption that the vector of observed variables is normallydistributed. This normality assumption (NA) plays a crucial role inassessingoptimality of estimates, in computing standard errors, and in designinganasymptotic chi-square goodness-of-fit test. The asymptotic validity of NAinferences when the data deviates from normality has been calledasymptoticrobustness. In the present paper we extend previous work on asymptoticrobustnessto a general context of multi-sample analysis of linear latent variablemodels,with a latent component of the model allowed to be fixed across(hypothetical)sample replications, and with the asymptotic covariance matrix of thesamplemoments not necessarily finite. We will show that, under certainconditions,the matrix $\Gamma$ of asymptotic variances of the analyzed samplemomentscan be substituted by a matrix $\Omega$ that is a function only of thecross-product moments of the observed variables. The main advantage of thisis thatinferences based on $\Omega$ are readily available in standard softwareforcovariance structure analysis, and do not require to compute samplefourth-order moments. An illustration with simulated data in the context ofregressionwith errors in variables will be presented.

Longitudinal and cross-sectional changes in active commuting to school among Brazilian schoolchildren.

OBJECTIVE: The objective of the study is to evaluate cross-sectional and longitudinal changes in children's commuting to school in a representative sample of a Brazilian city. METHODS: Two school-based studies were carried out in 2002 (n=2936; 7-10years old) and 2007 (n=1232; 7-15years old) in Florianopolis, Brazil. Cross-sectional data were collected from children aged 7 to 10years in 2002 and 2007. Longitudinal analyses were performed with data from 733 children participating in both surveys. Children self-reported their mode of transportation to school using a validated illustrated questionnaire. Changes were tested with chi square statistics and McNemar's test. RESULTS: Cross-sectional data showed a 17% decline in active commuting; a decrease from 49% in 2002 to 41% in 2007. On the other hand, active commuting among the 733 children increased as they entered adolescence 5years later, rising from 40% to 49%. CONCLUSION: Active commuting to school decreased in Brazilian children aged 7-10years over a five year period; whereas, it increased among children entering adolescence. Policies should focus on safety and environmental determinants to increase active commuting.

Power transformations in correspondence analysis

Power transformations of positive data tables, prior to applying the correspondence analysis algorithm, are shown to open up a family of methods with direct connections to the analysis of log-ratios. Two variations of this idea are illustrated. The first approach is simply to power the original data and perform a correspondence analysis this method is shown to converge to unweighted log-ratio analysis as the power parameter tends to zero. The second approach is to apply the power transformation to thecontingency ratios, that is the values in the table relative to expected values based on the marginals this method converges to weighted log-ratio analysis, or the spectral map. Two applications are described: first, a matrix of population genetic data which is inherently two-dimensional, and second, a larger cross-tabulation with higher dimensionality, from a linguistic analysis of several books.

Weighted metric multidimensional scaling

This paper establishes a general framework for metric scaling of any distance measure between individuals based on a rectangular individuals-by-variables data matrix. The method allows visualization of both individuals and variables as well as preserving all the good properties of principal axis methods such as principal components and correspondence analysis, based on the singular-value decomposition, including the decomposition of variance into components along principal axes which provide the numerical diagnostics known as contributions. The idea is inspired from the chi-square distance in correspondence analysis which weights each coordinate by an amount calculated from the margins of the data table. In weighted metric multidimensional scaling (WMDS) we allow these weights to be unknown parameters which are estimated from the data to maximize the fit to the original distances. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing a matrix and displaying its rows and columns in biplots.

Measuring subcompositional incoherence

Subcompositional coherence is a fundamental property of Aitchison s approach to compositional data analysis, and is the principal justification for using ratios of components. We maintain, however, that lack of subcompositional coherence, that is incoherence, can be measured in an attempt to evaluate whether any given technique is close enough, for all practical purposes, to being subcompositionally coherent. This opens up the field to alternative methods, which might be better suited to cope with problems such as data zeros and outliers, while being only slightly incoherent. The measure that we propose is based on the distance measure between components. We show that the two-part subcompositions, which appear to be the most sensitive to subcompositional incoherence, can be used to establish a distance matrix which can be directly compared with the pairwise distances in the full composition. The closeness of these two matrices can be quantified using a stress measure that is common in multidimensional scaling, providing a measure of subcompositional incoherence. The approach is illustrated using power-transformed correspondence analysis, which has already been shown to converge to log-ratio analysis as the power transform tends to zero.

Tying up the loose ends in simple correspondence analysis

Although correspondence analysis is now widely available in statistical software packages and applied in a variety of contexts, notably the social and environmental sciences, there are still some misconceptions about this method as well as unresolved issues which remain controversial to this day. In this paper we hope to settle these matters, namely (i) the way CA measures variance in a two-way table and how to compare variances between tables of different sizes, (ii) the influence, or rather lack of influence, of outliers in the usual CA maps, (iii) the scaling issue and the biplot interpretation of maps,(iv) whether or not to rotate a solution, and (v) statistical significance of results.

Subset correspondence analysis: Visualizing relationships among a selected set of response categories from a questionnaire survey

It is shown how correspondence analysis may be applied to a subset of response categories from a questionnaire survey, for example the subset of undecided responses or the subset of responses for a particular category. The idea is to maintain the original relative frequencies of the categories and not re-express them relative to totals within the subset, as would normally be done in a regular correspondence analysis of the subset. Furthermore, the masses and chi-square metric assigned to the data subset are the same as those in the correspondence analysis of the whole data set. This variant of the method, called Subset Correspondence Analysis, is illustrated on data from the ISSP survey on Family and Changing Gender Roles.

The Effect of Amifostine on Acute and Late Radiation Side Effects in Head and Neck Cancer Patients

Objective: We aimed to investigate the effect of amifostine on acute and late side effects, and its tolerability in head and neck cancer patients treated with radiotherapy (RT). Material and Methods: The study included 87 patients with primary head and neck cancers and cervical lymph node metastases from unknown primary cancers treated with RT alone or combined with chemotherapy (CT). Forty-one patients (47%) received amifostine combined with RT (ART group) and 46 patients (52%) received RT without amifostine (RT group). The patients were evaluated every week during the treatment and at month 1 and 2 after the completion of RT for acute side effects and month 3, 6, 9, 12, and 24 after the treatment for late side effects according to SOMA/LENT scale. Amifostine was administered prior to RT, along with anti-emetic prophylaxis. The two groups were compared with the Student's t and Mann-Whitney U and Chi-square tests. Results: The ART group had significantly less toxicity (grade! 1 mucositis, grade 2 fibrosis) than patients in the RT group (p=0.001, p=0.03, respectively). At week 3 of RT grade 2 mucositis developed in two patients (5%) in the ART group and 10 patients (22%) in the RT group (p=0.02). The protective effect of amifostine on skin reactions developed at week 4 of RT (p=0.05). Grade 3 xerostomia at 9, 12, and 15 months of follow-up (p=0.02, p=0.02, and p=0.02, respectively), grade 2 xerostomia at 18 and 24 months (p=0.02 and p=0.01, respectively) and fibrosis at 15, 18 and 24 months (p=0.05, p=0.02 and p=0.02, respectively) decreased markedly in the ART group compared with the RT group. Emesis was the most common adverse effect of amifostine. Conclusion: Daily administration of amifostine during RT was effective in avoiding late grade 2-3 xerostomia, as well as grade 2 fibrosis.

Three essays on liquidity risk

Preface In this thesis we study several questions related to transaction data measured at an individual level. The questions are addressed in three essays that will constitute this thesis. In the first essay we use tick-by-tick data to estimate non-parametrically the jump process of 37 big stocks traded on the Paris Stock Exchange, and of the CAC 40 index. We separate the total daily returns in three components (trading continuous, trading jump, and overnight), and we characterize each one of them. We estimate at the individual and index levels the contribution of each return component to the total daily variability. For the index, the contribution of jumps is smaller and it is compensated by the larger contribution of overnight returns. We test formally that individual stocks jump more frequently than the index, and that they do not respond independently to the arrive of news. Finally, we find that daily jumps are larger when their arrival rates are larger. At the contemporaneous level there is a strong negative correlation between the jump frequency and the trading activity measures. The second essay study the general properties of the trade- and volume-duration processes for two stocks traded on the Paris Stock Exchange. These two stocks correspond to a very illiquid stock and to a relatively liquid stock. We estimate a class of autoregressive gamma process with conditional distribution from the family of non-central gamma (up to a scale factor). This process was introduced by Gouriéroux and Jasiak and it is known as Autoregressive gamma process. We also evaluate the ability of the process to fit the data. For this purpose we use the Diebold, Gunther and Tay (1998) test; and the capacity of the model to reproduce the moments of the observed data, and the empirical serial correlation and the partial serial correlation functions. We establish that the model describes correctly the trade duration process of illiquid stocks, but have problems to adjust correctly the trade duration process of liquid stocks which present long-memory characteristics. When the model is adjusted to volume duration, it successfully fit the data. In the third essay we study the economic relevance of optimal liquidation strategies by calibrating a recent and realistic microstructure model with data from the Paris Stock Exchange. We distinguish the case of parameters which are constant through the day from time-varying ones. An optimization problem incorporating this realistic microstructure model is presented and solved. Our model endogenizes the number of trades required before the position is liquidated. A comparative static exercise demonstrates the realism of our model. We find that a sell decision taken in the morning will be liquidated by the early afternoon. If price impacts increase over the day, the liquidation will take place more rapidly.

Physical activity in daily life is associated with lower adiposity values than doing weekly sports in Lc65+ cohort at baseline.

BACKGROUND: Overweight and obesity prevalence is the highest at age 65-75 years in Lausanne (compared with younger classes). We aimed to describe 1) eating habits, daily physical activity (PA), and sports frequency in community-dwelling adults aged 65-70, 2) the links of these behaviors with socio-economic factors, and 3) with adiposity. METHODS: Cross-sectional analysis of Lc65+ cohort at baseline, including 1260 adults from the general population of Lausanne aged 65-70 years. Eating habits (8 items from MNA) and PA (sports frequency and daily PA: walking and using stairs) were assessed by questionnaires. Body mass index (BMI), supra-iliac (SISF), triceps skin-folds (TSF), waist circumference (WC), and WHR were measured. RESULTS: Prevalence of overweight (BMI 25.0-29.9 kg/m2), obesity (BMI ≥ 30.0 kg/m2), and abdominal obesity was 53%, 24%, and 45% in men; 35%, 23%, and 45% in women.Intake of fruits or vegetables (FV) ≥ twice/day was negatively associated with male sex (prevalence 81% versus 90%, chi-square P < 0.001). The proportion avoiding stairs in daily life was higher among women (25%) than among men (20%, chi-square P=0.003).In multivariate analyses among both sexes, eating FV, using stairs in daily life ("stairs"), and doing sports ≥ once/week were significantly negatively associated with financial difficulties (stairs: OR=0.54, 95% CI=0.40-0.72) and positively with educational level (stairs: OR=1.68, 95% CI=1.17-2.43 for high school).For all five log-transformed adiposity indicators in women, and for all indicators except SISF and TSF in men, a gradual decrease in adiposity was observed from category "no stairs, sports < once/week" (reference), to "no stairs, sports ≥ once/week", to "stairs, sports < once/week", and "stairs, sports ≥ once/week" (for example: WC in men, respectively: ß= -0.03, 95% CI= -0.07-0.02; ß= -0.06, 95% CI= -0.09- -0.03; ß= -0.10, 95% CI= -0.12- -0.07). CONCLUSIONS: In this population with high overweight and obesity prevalence, eating FV and PA were strongly negatively associated with financial difficulties and positively with education. Using stairs in daily life was more strongly negatively associated with adiposity than doing sports ≥ once/week.

Treatment of penile carcinoma: to cut or not to cut?

PURPOSE: The aim of this study was to assess the outcome in patients with penile cancer. METHODS AND MATERIALS: A total of 60 patients with penile carcinoma were included. Of the patients, 45 (n = 27) underwent surgery, and 51 underwent definitive (n = 29) or postoperative (n = 22) radiotherapy (RT). Median follow-up was 62 months. RESULTS: Median time to locoregional relapse was 14 months. Local failure was observed in 3 of 23 patients (13%) treated with surgery with or without postoperative RT vs. in 19 of 33 patients (56%) given organ-sparing treatment (p = 0.0008). Of 22 local failures, 16 (73%) were salvaged with surgery. Of the 33 patients treated with definitive RT (n = 29) and the 4 patients refusing RT after excisional biopsy, local control was obtained with organ preservation in 13 (39%). In the remaining 20, 4 patients with local failure underwent salvage conservatively, resulting in an ultimate penis preservation rate of 17 of 33 (52%) patients treated with definitive RT. The 5-year and 10-year probability of surviving with an intact penis was 43% and 26%, respectively. There was no survival difference between the patients treated with definitive RT and primary surgery (56% vs. 53%; p = 0.16). In multivariate analysis, independent factors influencing survival were N-classification and pathologic grade. Surgery was the only independent predictor for better local control. CONCLUSION: Based on our study findings, in patients with penile cancer, local control is superior with surgery. However, there is no difference in survival between patients treated with surgery and those treated with definitive RT, with 52% organ preservation.

Performance of panel-based criteria to evaluate the appropriateness of colonoscopy: a prospective study.

BACKGROUND: Prospective data describing the appropriateness of use of colonoscopy based on detailed panel-based clinical criteria are not available. METHODS: In a cohort of 553 consecutive patients referred for colonoscopy to two university-based Swiss outpatient clinics, the percentage of patients who underwent colonoscopy for appropriate, equivocal, and inappropriate indications and the relationship between appropriateness of use and the presence of relevant endoscopic lesions was prospectively assessed. This assessment was based on criteria of the American Society for Gastrointestinal Endoscopy and explicit American and Swiss criteria developed in 1994 by a formal panel process using the RAND/UCLA appropriateness method. RESULTS: The procedures were rated appropriate or equivocal in 72.2% by criteria of the American Society for Gastrointestinal Endoscopy, in 68.5% by explicit American criteria, and in 74.4% by explicit Swiss criteria (not statistically significant, NS). Inappropriate use (overuse) of colonoscopy was found in 27.8%, 31.5%, and 25.6%, respectively (NS). The proportion of appropriate procedures was higher with increasing age. Almost all reasons for using colonoscopy could be assessed by the two explicit criteria sets, whereas 28.4% of reasons for using colonoscopy could not be evaluated by the criteria of the American Society for Gastrointestinal Endoscopy (p < 0.0001). The probability of finding a relevant endoscopic lesion was distinctly higher in the procedures rated appropriate or equivocal than in procedures judged inappropriate. CONCLUSIONS: The rate of inappropriate use of colonoscopy is substantial in Switzerland. Explicit criteria allow assessment of almost all indications encountered in clinical practice. In this study, all sets of appropriateness criteria significantly enhanced the probability of finding a relevant endoscopic lesion during colonoscopy.

Plaque characteristics and arterial remodeling in coronary and peripheral arterial systems.

BACKGROUND: Few studies have examined plaque characteristics among multiple arterial beds in vivo. The purpose of this study was to compare the plaque morphology and arterial remodeling between coronary and peripheral arteries using gray-scale and radiofrequency intravascular ultrasound (IVUS) at clinical presentation. METHODS AND RESULTS: IVUS imaging was performed in 68 patients with coronary and 93 with peripheral artery lesions (29 carotid, 50 renal, and 14 iliac arteries). Plaques were classified as fibroatheroma (VH-FA) (further subclassified as thin-capped [VH-TCFA] and thick-capped [VH-ThCFA]), fibrocalcific plaque (VH-FC) and pathological intimal thickening (VH-PIT). Plaque rupture (13% of coronary, 7% of carotid, 6% of renal, and 7% of iliac arteries; P = NS) and VH-TCFA (37% of coronary, 24% of carotid, 16% of renal, and 7% of iliac arteries; P = 0.02) were observed in all arteries. Compared with coronary arteries, VH-FA was less frequently observed in renal (P < 0.001) and iliac arteries (P < 0.006). Lesions with positive remodeling demonstrated more characteristics of VH-FA in coronary (84% vs. 25%, P < 0.001), carotid (72% vs. 20%, P = 0.001), and renal arteries (42% vs. 4%, P = 0.001) compared with those with intermediate/negative remodeling. There was positive relationship between remodeling index and percent necrotic area in all four arteries. CONCLUSIONS: Atherosclerotic plaque phenotypes were heterogeneous among four different arteries; renal and iliac arteries had more stable phenotypes compared with coronary artery. In contrast, the associations of remodeling pattern with plaque phenotype and composition were similar among the various arterial beds.