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Regression Regression analysis is helpful in assessing specific forms of the relation- ship between variables discount viagra capsules 100 mg on line, and the ultimate objective when this method of analysis is employed usually is to predict or estimate the value of one variable corresponding to a given value of another variable order viagra capsules 100 mg online. The ideas of regression were first elucidated by the English scientist Sir Francis Galton (1822–1911) in reports of his research on heredity—first in sweet peas and later in human stature buy viagra capsules visa. He described a tendency of adult offspring, having either short or tall parents, to revert back toward the average height of the general population. He first used the word reversion, and later regression, to refer to this phenomenon. Correlation Correlation analysis, on the other hand, is concerned with measuring the strength of the relationship between variables. When we compute measures of correlation from a set of data, we are interested in the degree of the correlation between variables. Again, the concepts and terminology of correlation analysis originated with Galton, who first used the word correlation in 1888. In this chapter our discussion is limited to the exploration of the linear relationship between two variables. The concepts and methods of regression are covered first, beginning in the next section. In the next chapter we consider the case where there is an interest in the relationships among three or more variables. Regression and correlation analysis are areas in which the speed and accuracy of a computer are most appreciated. The data for the exercises of this chapter, therefore, are presented in a way that makes them suitable for computer processing. As is always the case, the input requirements and output features of the particular programs and software packages to be used should be studied carefully. Based on the results of their analysis of the sample data, they are interested in reaching decisions about the population from which the sample is presumed to have been drawn. It is important, therefore, that the researchers understand the nature of the population in which they are interested. They should know enough about the population to be able either to construct a mathematical model for its representation or to determine if it reasonably fits 9. A researcher about to analyze a set of data by the methods of simple linear regression, for example, should be secure in the knowledge that the simple linear regression model is, at least, an approximate representation of the population. It is unlikely that the model will be a perfect portrait of the real situation, since this characteristic is seldom found in models of practical value. A model constructed so that it corresponds precisely with the details of the situation is usually too complex to yield any information of value. On the other hand, the results obtained from the analysis of data that have been forced into a model that does not fit are also worthless. Fortunately, however, a perfectly fitting model is not a requirement for obtaining useful results. Researchers, then, should be able to distinguish between the occasion when their chosen models and the data are sufficiently compatible for them to proceed and the case where their chosen model must be abandoned. Assumptions Underlying Simple Linear Regression In the simple linear regression model two variables, usually labeled X and Y, are of interest. The letter X is usually used to designate a variable referred to as the independent variable, since frequently it is controlled by the investigator; that is, values of X may be selected by the investigator and, corresponding to each preselected value of X, one or more values of another variable, labeled Y, are obtained. The variable, Y, accordingly, is called the dependent variable, and we speak of the regression of Y on X. In this model, X is referred to by some writers as a nonrandom variable and by others as a mathematical variable. It should be pointed out at this time that the statement of this assumption classifies our model as the classical regression model. Regression analysis also can be carried out on data in which X is a random variable. Since no measuring procedure is perfect, this means that the magnitude of the measurement error in X is negligible. For the usual inferential procedures of estimation and hypothesis testing to be valid, these subpopulations must be normally distributed. In order that these procedures may be presented it will be assumed that the Y values are normally distributed in the examples and exercises that follow. Geometrically, b0 and b1 represent the y-intercept and slope, respectively, of the line on which all of the means are assumed to lie. In other words, in drawing the sample, it is assumed that the values of Y chosen at one value of X in no way depend on the values of Y chosen at another value of X. These assumptions may be summarized by means of the following equation, which is called the simple linear regression model: y ¼ b0 þ b1x þ e (9. As a consequence of the assumption that the subpopulations of Y values are normally distributed with equal variances, the e’s for each subpopulation are normally distributed with a variance equal to the common variance of the subpopulations of Y values. The variable designated by Y is sometimes called the response variable and X is sometimes called the predictor variable. In an effort to reach a decision regarding the likely form of this relationship, the researcher draws a sample from the population of interest and using the resulting data, computes a sample regression equation that forms the basis for reaching conclusions regarding the unknown population regression equation. Steps in Regression Analysis In the absence of extensive information regarding the nature of the variables of interest, a frequently employed strategy is to assume initially that they are linearly related. Determine whether or not the assumptions underlying a linear relationship are met in the data available for analysis. Evaluate the equation to obtain some idea of the strength of the relationship and the usefulness of the equation for predicting and estimating. If the data appear to conform satisfactorily to the linear model, use the equation obtained from the sample data to predict and to estimate. When we use the regression equation to predict, we will be predicting the value Y is likely to have when X has a given value. When we use the equation to estimate, we will be estimating the mean of the subpopulation of Y values assumed to exist at a given value of X. Note that the sample data used to obtain the regression equation consist of known values of both X and Y. When the equation is used to predict and to estimate Y, only the corresponding values of X will be known. We illustrate the steps involved in simple linear regression analysis by means of the following example. Their subjects were men between the ages of 18 and 42 years who were free from metabolic disease that would require treatment. This question is typical of those that can be answered by means of regression analysis. The variable waist measurement, knowledge of which will be used to make the predictions and estimations, is the independent variable. The points are plotted by assigning values of the independent variable X to the horizontal axis and values of the dependent variable Y to the vertical axis.

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Progressive intra-atrial conduction delay occurs in response to increasing prematurity of extrastimuli order viagra capsules now. Second generic viagra capsules 100 mg with visa, in those patients in whom atrial fibrillation was induced buy viagra capsules, a greater degree of delay was noted in the triangle of Koch than in those patients in whom no atrial fibrillation was induced. Third, the local electrogram duration in the posterior triangle of Koch was longer in those patients who developed atrial fibrillation in response to atrial stimulation than in those who did not (Fig. These data suggest the prolonged conduction times during high-right atrial stimulation are common to patients with palpitations regardless of whether or not atrial fibrillation is inducible. However, nonuniform anisotropy in the area of the posterior triangle of Koch, and perhaps elsewhere, is quite important since left atrial extrastimuli rarely induce atrial fibrillation or flutter and are rarely associated with intra-atrial conduction delay, particularly in the posterior triangle of Koch (Fig. Additional studies using high-density mapping in both atrial chambers would be critical to decide if any particular site of conduction delay is necessary for initiation of atrial fibrillation and/or flutter. Such studies suggest that the crista forms a functional arc of block in most cases. During slow pacing from these areas, no split potentials are usually seen; however, during rapid pacing from the low posterior right atrium split potentials with opposite activation sequences are 20 21 23 seen. The opposite activation sequence reflects activation caudocranially from the posterior to the crista terminalis and craniocaudally lateral to the crista terminalis. The longest cycle length at which transverse cristal 20 block appeared was increased slightly by propranolol and to a greater extent by procainamide. They suggested that this is the reason that counterclockwise flutter is more frequent than clockwise flutter. However, other factors must be involved since counterclockwise flutter is also induced in transplanted hearts in which the crista 24 terminalis cannot play a role. We have recently evaluated the presence and degree of anisotropy on intra-atrial conduction velocity measured from a high-density (240 poles; 2. Intra-atrial conduction velocity was measured in 16 radii during pacing from the center of the plaque at 600 msec, the fastest rate of 1:1 conduction (F max), and at a rate just above local atrial refractoriness. We found no differences in the degree of anisotropy in patients with chronic atrial P. This reduction was specifically related to a decrease in conduction velocity parallel to fiber orientation (in the so-called rapidly conducting direction) (Table 9-1). All patients showed significant direction-dependent conduction (anisotropy) with the fastest conduction perpendicular to the A-V groove (Fig. The relationship to this pattern of conduction to the activation patterns during atrial fibrillation will be discussed subsequently. In the diagrams, pacing is delivered medial to the potential barrier of the crista terminalis. In A, slow pacing propagates slowly across the crista, resulting in parallel activation on both sides of the crista. At faster rates (B) functional block occurs and activation proceeds around the block. This gives rise to split potentials with opposite activation sequences on either side of the line of block. C depicts a fixed barrier in which conduction never crosses the crista regardless of the rate of pacing. Conduction barriers in human atrial flutter: correlation of electrophysiology and anatomy. An isochronic map and conduction velocities in 16 radii in response to central stimulation from a 240-pole plaque are shown. The isochronic map shows an elliptical pattern with rapid conduction perpendicular to the A-V groove and slow conduction parallel to it. Atrial Refractoriness Changes in atrial refractoriness could and should have a marked influence on development of reentrant arrhythmias. Patients with a history of paroxysmal fibrillation or flutter appear to have different characteristics of 8 9 11 12 refractoriness than in control subjects. Similar observations 10 15 have been noted in patients in whom atrial fibrillation is inducible. Thus, patients with a history of atrial fibrillation and flutter are characterized by a failure of adaptation of high-right atrial refractoriness when short and long cycle lengths are compared. These findings 8 15 are similar to patients in whom atrial fibrillation was induced, as described by our group and Attuel et al. This failure of rate adaptation was noted even though many patients had been in sinus rhythm for days to weeks. They looked at the average induced atrial fibrillation interval at 35 to 40 sites in patients with and without paroxysmal atrial fibrillation during open heart surgery. The average fibrillation interval was 152 ± 3 msec measured at 247 sites in patients with atrial fibrillation and 176 ± 8. The variance of fibrillation at all recording sites was much larger in patients with a history of atrial fibrillation. The largest difference in atrial fibrillation intervals in adjacent sites was 22 msec in patients with prior atrial fibrillation and 7 msec in patients without a history of atrial fibrillation. The overall variance (difference between longest and shortest intervals) in 4-second snapshots was 31. While this measurement of refractoriness and dispersion refractoriness is much different than that of standard measurements, these investigators showed a linear relationship between the atrial fibrillation intervals and the refractory period determined by the extrastimulus technique at four of the measured sites. However, not surprisingly, the fibrillatory intervals were much shorter than the measured refractory periods determined by the extrastimulus technique. Thus, while the fibrillation interval does not measure the local refractory period, it is an indirect measure of refractoriness. Both methods demonstrate greater heterogeneity in patients with a history of atrial fibrillation. There has been recent interest in the role of remodeling of atrial electrophysiology by atrial fibrillation and its effect upon ease of induction and spontaneous recurrences of atrial fibrillation. This was correlated with an increased ease of inducibility and duration of atrial fibrillation. Following short periods of pacing for minutes only, brief episodes of atrial fibrillation could be induced as the refractory period shortened. By 24 hours of pacing, the refractory period had shortened maximally as measured by the standard atrial extrastimulus technique and by the fibrillation interval 26 method described by Misier et al. They found that during short periods of up to 7 hours of atrial pacing at 800 bpm, the effective atrial refractory period shortened despite autonomic blockade, absence of changes in atrial pressure, and pretreatment with glibenclamide. They found that the remodeling was blocked by verapamil and accentuated by hypercalcemia. Intracellular calcium loading during rapid atrial activation is believed to play an important role in remodeling, with subsequent downregulation in L-type calcium channels as well as sodium and 31 (transient outward current) potassium channels. This channel remodeling may lead to shortening of the action potential with subsequent shortening of refractory periods as well as conduction slowing. While verapamil blocked the remodeling phenomenon, there was a minimal effect of inducibility of atrial fibrillation by verapamil. Thus, while it is tempting to speculate that rapid pacing as well as atrial fibrillation causes remodeling, which begets atrial fibrillation, remodeling may be merely a secondary phenomenon and not causally related to atrial fibrillation.

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These independent variables may be either continuous or discrete or a combination of the two buy discount viagra capsules 100mg line. Subjects were classified as having either early (< 25 years) or late (> 25 years) onset of excessive alcohol use discount viagra capsules 100 mg on-line. Test of H0 that b1 ¼ 0 Tests for significance of the regression coefficients can be obtained directly from Figure 11 viagra capsules 100mg sale. Given the nature of the response variable in logistic regression, a coefficient of determination does not provide the same information as it does in linear regression. This is because in logistic regression values of the parameters are not derived to minimize sums of squares, but rather are iterative estimates; hence, there is no 2 equivalent measure of R in logistic regression. Below, we provide an explanation of some commonly used approaches to evaluate logistic regression models, and follow these explanations with two illustrative examples. In other words, they are comparative measures designed to indicate “how much better” a model with predictor variables is when compared to a model with no predictors. Two 2 commonly used pseudo-R statistics were developed by Cox and Snell (4) and Nagelkerke (5). The value of these measures is the fact that they may be useful for comparing models with different predictor variables, but provide little relative use for examining a single model. Both of these approaches are based on the idea of using a measure of fit known as the log-likelihood statistic. The log-likelihood for the intercept-only model is used to represent the total sum of squares, while the log-likelihood for the model with predictor variables is used to represent the error sum of squares. Interested readers may find an explanation of the log- likelihood statistic in Hosmer and Lemeshow (2). Using this method, one develops a contingency table that provides frequency counts of the number of data points that were observed to be either 0 or 1 in the raw data, along with whether the raw data were classified as 0 or 1 based on the predictive equation. As a general rule-of-thumb, correctly classifying 70 percent or greater is considered evidence of a satisfactory model from a statistical viewpoint. However, the model may not provide great enough predictive ability to be useful in a practice sense. A problem does arise, however, in that reclassifying the same data used to build a model with the model itself may bias the results. First, one may use part of the data set to construct the model and the other part of the data set to develop a classification table. This strategy, of course, requires a sample large enough to accommodate adequately the needs of both procedures. A second approach is to construct a model using the data in hand and then collect additional data to test the adequacy of the model using a classification table. This strategy, too, has its shortcomings, as the collection of additional data can be both time- consuming and expensive. A third approach that also has intuitive visual appeal is to develop a plot that shows the frequency of observations against their predicted probability. In this type of plot, one would hope to see a complete separation of 0 and 1 values. When there is misclassification of the outcome variable, this type of plot provides a means of determining where the misclassification occurred, and how frequently observations were misclassified. Finally, in a commonly used approach known as the Hosmer and Lemeshow test, one develops a table of observed and expected frequencies and uses a chi-square test to determine if there is a significant deviation between the observed and expected frequen- cies. In this 2 figure, we see that both the Cox and Snell and the Nagelkerke pseudo-R values are provided. Since they are both > 0, the model with the predictor provides more information than the intercept-only model. In this 2 figure, we see that both the Cox and Snell and the Nagelkerke pseudo-R values are provided, and since they are both > 0, the model with the predictors provides more information than the intercept-only model. The frequency distribution shows the large number of those without onset of excessive alcohol use predicted by the model to develop early onset of alcoholism. We may, for example, have subjects that are classified as positive, negative, and undetermined for a given disease (a standard polytomous response). The modeling process is slightly more complex and requires the use of a computer program. For those interested in exploring these valuable methods further, we recommend the book by Hosmer and Lemeshow (2). There are also techniques available for constructing confidence intervals for odds ratios. The reader who wishes to learn more about logistic regression may consult the books by Hosmer and Lemeshow (2) and Kleinbaum (3). Patients filled out a health history questionnaire that included a question about victimization. The following table shows the sample subjects cross-classified by gender and whether the subject self-identified as being “hit, kicked, punched, or otherwise hurt by someone within the past year. Victimization Women Men Total No victimization 611 308 919 Violently victimized 68 37 105 Total 679 345 1024 Source: John H. Severson, and Dunia Karana, “Violent Victimization of Women and Men: Physical and Psychiatric Symptoms,” Journal of the American Board of Family Practice, 16 (2003), 32–39. Another covariate of interest was a score using the Hospital Anxiety and Depression Index. Use the following data to predict whether a woman in the study participated in a cardiac rehabilitation program. We discuss the analysis that is appropriate when one or more of the independent variables is dichotomous. A second topic that we discuss is how to select the most useful independent variables when we have a long list of potential candidates. Finally, we present the basic concepts and procedures that are involved in logistic regression analysis. We cover two situations: the case in which the independent variable is dichotomous, and the case in which the independent variable is continuous. Since the calculations involved in obtaining useful results from data that are appropriate for analysis by means of the techniques presented in this chapter are complicated and time-consuming when attempted by hand, it is recommended that a computer be used to work the exercises. Why is a knowledge of variable selection techniques important to the health sciences researcher? Give an example in your field in which logistic regression analysis would be appropriate when the independent variable is dichotomous. Give an example in your field in which logistic regression analysis would be appropriate when the independent variable is continuous. Find a published article in the health sciences field in which each of the following techniques is employed: (a) Dummy variable coding (b) Stepwise regression (c) Logistic regression Write a report on the article in which you identify the variables involved, the reason for the choice of the technique, and the conclusions that the authors reach on the basis of their analysis. The study collected information on 71 community-dwelling older women with normal mental status. Perform stepwise regression with the data in the following table and report your final model, p values, and conclusions. Treat cardiac output as the dependent variable and use dummy variable coding and analyze the data by regression techniques.

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Te cases perhaps take much longer time to regress even mental dullness continues for several months 100 mg viagra capsules sale. Investigations should be aimed at fnding the Tis term refers to the sudden viagra capsules 100mg without a prescription, unexpected death of an extent and morphologic type of anemia purchase viagra capsules 100 mg free shipping, determining the apparently healthy infant, usually 2–3 months of age, who nutritional status and detecting coexisting infections and had been put to the bed without any suspicion of such an infestations. Allergy to cow milk, enlargement of thymus, sufocation, defciency of parathyroids or adrenals, hypernatremia and fulminant respiratory infection causing laryngeal obstruction and/or spasm fgure among the large number of conditions/factors that are incriminated in its etiology. Such states as prolonged sleep, apnea, (associated with central nervous system Fig. Te characteristic features include infantilism, respiration, heart rate and temperature, and postnatal remarkable absence or diminution of subcutaneous fat, growth retardation. Te parents must be questioned about generalized alopecia (including missing eyebrows) and other the infant’s feeding, medications, etc. Physical examination should concentrate on infant’s Physical development in infancy is not signifcantly afected. Te infant needs to be observed Manifestations such as scleroderma, midfacial while he is being fed. Investigations include: cyanosis and sculpted nose in early infancy may suggest Blood analysis for glucose, sodium, potassium, calcium, the existence of the syndrome. Urinalysis Since the patients do not become sexually mature, par- Microbiologic tests ent-to-child transmission is not noticed. Etiopathogenesis to believe that the pains have anything to do with physical 849 growth, epiphyseal closure or hormonal changes. Tere is Most pediatric subjects are adolescents, from both sexes good deal of consensus that these may well be “a reaction with predominance of girls. Te probable cause is an to emotional disturbances, family pain predisposition infection with replication of a known or new virus, including or environmental stress”. Te cornerstone of treatment is reassurance to the Clinical Features parents as well as the child that the problem is not organic and will be over in due course. Child’s emotional needs Chronic fatigue, varying from mild (subtle) to severe must receive adequate attention. Intestinal parasite(s), and anemia, if is often accompanied by deterioration in work or school present, should be treated. Intolerable pains may warrant performance, activities of daily living, exercise tolerance use of analgesics and local massage. Te term is applied to a group of rare, but severe disor- Diagnosis ders having signifcant proliferation or accumulation of cells of the monocyte-macrophage system of bone mar- It is primarily by exclusion. Tere is no mortality hypofbrinogenemias, high hepatic enzymes and very high though signifcant morbidity is a rule. In one-third cases, Etiopathogenesis there may be associated headache and abdominal pain. Te granulomatous lesions may Te pains are usually complained of toward the late involve any organ or system though lung is the most com- evening and during night. Excessive fatigue and activity monly afected organ with parenchymal infltrates, miliary precipitate them. Te afected subjects usually belong to nodules and hilar and paratracheal lymphadenopathy. In a signifcant Typically a granuloma contains epithelioid cells, mac- proportion, there is a family history of such pains. A large Later Infancy and Childhood proportion of the granulomas heal with complete preserva- Tongue-tie (Ankyloglossia) tion of the parenchyma. A true tongue-tie is characterized by a very short frenulum which may manifest as a prominent midline groove at the Clinical Features tip of the tongue as a result of traction and/or failure on the part of the child to lick his upper lip. Tis is not only Tese include chronic cough, easy fatigability, weight infrequent, but also of not known functional signifcance. At worst, it may cause little dyslalia but never delayed In older children, predominant manifestations may be speech. Only rarely it needs a surgical cut at 2–3 years of ophthalmic (uveitis, iritis), dermatologic (maculopapular age. Te child is in need of a hyperproteinemia, hypercalcemia, hypercalciuria, a high greater sensory stimulation. Defnitive diagnosis is from a biopsy of be told that some normal children do take 3 years or longer the granulomatous lesion. Differential Diagnosis Eating Problem It is from tuberculosis, pulmonary fungal infection Many otherwise normal and healthy-looking children (mycosis), lymphoma and infammatory bowel disease (some may be rather thin), according to the parents, are and phlyctenular conjunctivitis. It is primarily symptomatic and supportive, at times war- Such parents need to be told, after examination and ranting the use of steroids to suppress acute manifestations. Prognosis Tey must forthwith stop forcible feeding or any kind of Tose who fail to have spontaneous recovery, after months cajoling or bribing in which they may be indulging to make to years, may develop a progressive pulmonary disease the child eat in accordance with their wishes. Umbilical Hernia Te attending doctor is required to provide proper guid- A proportion of the babies (say 1 in 4) have umbilical ance, reassurance and support to the parents, the mothers hernia (1–5 cm diameter) in association with diastasis in particular, in allaying their concern and running from recti (divertication of abdominal recti muscles) as a result pillar to post. In this way, many unnecessary investiga- of imperfect closure or weakness of the umbilical ring. Most such hernias disappear by 1 year, practically all by Neonatal Period 3–5 years of age. Indications of surgery are as follows: Te benign problems that cause undue parental anxiety Persistence beyond 3–5 years include physiologic jaundice, vomiting, transitional stools, Rather than reduction, further increase in size after the constipation, toxic erythema, milia, Mongolian spots, age of 1 year salmon patches, benign neonatal hemangiomatosis, Rarely, when it gets strangulated. Irregular/Asymmetrical Skull Types 851 Some otherwise normal babies have an asymmetrical Two major types are recognized—intravascular hypov- head. If craniosynostosis is excluded, the parents should olemia and intravascular normovolemia or hypervolemia. Intravascular hypovolemia is caused by loss of volume assumes proper rounding by 3–4 months age. With the child’s growth, during the third and fourth caused by cardiac dysfunction (coronary artery disease, year, bowlegs are replaced by physiologic knock-knees myocarditis, cardiomyopathy, hypoxemia, metabolic which are more pronounced in obese children. Spontane- insult), infow obstruction (pericardial tamponade, ous improvement results during 4–10 years of age. In shock due to loss of resistance, patients extremities are Heat syncope refers to a situation in which a child unduly warm due to vasodilatation. In addition, postural standing in the sun for prolonged periods becomes hypotension may be remarkable. An important example of pale with fall in blood pressure and sudden collapse this type of shock is septic shock associated with septicemia. Interestingly, body temperature further progression, myocardial function decreases with may not be raised. Response to shifting the child to a reduced cardiac output together with secondary severe shady neighborhood and making him lie comfortably vasoconstriction. Diagnosis Heat cramps manifested by painful and spasmodic con- It is based on a good history, physical examination and tractions exercise in hot and humid environment due to laboratory support. As the laboratory results are likely to excessive loss of sodium and chlorides from body. Treatment consists in lowering the body temperature Swan-Ganz catheterization of pulmonary artery is of by ice-water baths until it falls to 102°F. For heat injury in value to demonstrate a reduced cardiac output or index case of newborn, See Chapter 17 (Neonatology).

T. Miguel. Baldwin-Wallace College.