By E. Flint. University of Pittsburgh. 2018.

Confidence Interval for the Difference between Two s Above we found a difference of 13 between our sample means buy 10 mg alavert otc, so if we could exam- ine the corresponding 1 and 2 buy alavert 10 mg low cost, we’d expect their difference would be around 13 alavert 10 mg with mastercard. To more precisely define “around,” we can compute a confidence interval for this difference. We will compute the largest and smallest difference between s that our difference between sample means is likely to represent. Then we will have a range of The Independent-Samples t-Test 269 differences between the population s that our difference between Xs may represent. The confidence interval for the difference between two s describes a range of dif- ferences between two s, one of which is likely to be represented by the difference between our two sample means. The formula for the confidence interval for the difference between two s is 1sX 2X 212tcrit2 1 1X1 2 X22 # 1 2 2 # 1sX 2X 211tcrit2 1 1X1 2 X22 1 2 1 2 Here, 1 2 2 stands for the unknown difference we are estimating. The tcrit is the two- tailed value found for the appropriate at df 5 1n1 2 12 1 1n2 2 12. In essence, if someone asked us how big a difference hyp- nosis makes for everyone in the population when recalling information in our study, we’d be 95% confident that the difference is, on average, between about. Performing One-Tailed Tests with Independent Samples As usual, we perform a one-tailed test whenever we predict the specific direction in which the dependent scores will change. Thus, we would have performed a one-tailed test if we had predicted that hypnosis would increase recall scores. Everything dis- cussed previously applies here, but to prevent confusion, we’ll use the subscript h for hypnosis and n for no hypnosis. If we expect a positive difference, it is in the right-hand tail of the sampling distribution, so tcrit is positive. If we predict a negative differ- ence, it is in the left-hand tail and tcrit is negative. Compute tobt as we did previously, but be sure to subtract the Xs in the same way as in Ha. Compare tobt to tcrit: If tobt is beyond tcrit, the results are significant; describe the relationship. If tobt is not beyond tcrit, the results are not significant; make no conclusion about the relationship. Compute the confidence interval: Describe the represented by each condition and/or the difference between the s. Subtracting cramming from no cramming, what dence interval for the difference between the s is are H0 and Ha? The related-samples t-test is the parametric procedure used with two related samples. Related samples occur when we pair each score in one sample with a particular score in the other sam- ple. Researchers create related samples to have more equivalent and thus more compa- rable samples. In a matched-samples design, we match each participant in one condition with a participant in the other condition. For example, say that we want to measure how well people shoot baskets when using either a standard basketball or a new type of ball (one with handles). If, however, by luck, one condition contained taller people than the other, then differences in basket shooting could be due to the differences in height instead of the different balls. We do this by matching pairs of people who are the same height and assigning a member of the pair to each condition. Thus, if two participants are 6 feet tall, one will be assigned to each condition. Likewise, a 4-foot person in one condition is matched with a 4-footer in the other condition, and so on. This will pro- duce two samples that, overall, are equivalent in height, so any differences in basket shooting between them cannot be due to differences in height. Likewise, we might match participants using age, or physical ability, or we might use naturally occurring pairs such as roommates or identical twins. The other, more common, way of producing related samples is called repeated meas- ures. In a repeated-measures design, each participant is tested under all conditions of the independent variable. For example, we might first test people when they use the standard basketball and then measure the same people again when they use the new ball. In Chapter 9, two events were dependent when the probability of one is influenced by the occurrence of the other. Related samples are dependent because the probability that a score in a pair is a particular value is influenced by the paired score. For exam- ple, if I make zero baskets in one condition, I’ll probably make close to zero in the other condition. This is not the case with independent samples: In the hypnosis study, whether someone scores 0 in the no-hypnosis condition will not influence the probabil- ity of anyone scoring 0 in the hypnosis condition. We cannot use the independent-samples t-test in such situations because its sampling distribution describes the probability of differences between means from independent samples. With related samples, we must compute this probability differently, so we cre- ate the sampling distribution differently and we compute tobt differently. However, except for requiring related samples, the assumptions of the related-samples t-test are the same as those for the independent-samples t-test: (1) The dependent variable involves an interval or ratio scale, (2) the raw score populations are at least approxi- mately normally distributed, and (3) the populations have homogeneous variance.

A long plastic tubing ﬁlled with a radioactive solution is placed in the ﬁeld of view of the detec- tor buy 10mg alavert with mastercard. Line spread function of a gamma camera equipped with a low-energy all- purpose parallel hole collimator obtained in (a) air and (b) water at different dis- tances using a 99mTc-line source cheap alavert 10 mg otc. Such a distribution gives a spatial frequency ( ) in cycles per centimeter or cycles per millimeter cheap 10 mg alavert with visa. The contrast, or modulation (Ms), in the source activity is given by A max − min Ms = (10. Because the imaging devices are not absolutely perfect, it will portray the distribution of activity in the image with Cmax for the peak and Cmin for the valley, which are smaller in magnitude than Amax and Amin. This is true if the sinusoidal cycles are well sepa- rated and if the imaging device reproduces the image of each cycle faith- fully. Performance Parameters of Gamma Cameras When the distribution of activity is such that spatial frequency increases, the peaks and valleys come closer. It is important to note that small objects are better imaged at higher frequencies and large objects at lower frequencies. The mathematical expression of these functions is quite complex and can be found in reference physics books. System A gives better spatial resolution than systems B and C, and system B pro- vides better resolution than system C. Brieﬂy, (a) the intrinsic photopeak efﬁciency of a detector decreases with increas- ing photon energy and with increasing source-to-detector distance (see Fig. The photo- peak efﬁciency of these crystals is about 90% for 140-keV photons of 99mTc and about 30% for 364-keV photons of 131I. Sensitivity of a gamma camera is most affected by the collimator efﬁ- ciency, which is described next. Variation of geometric efﬁciency with source-to-collimator distance for various collimators. The constant K is a function of the shape and arrangement of holes in the collimator and varies between 0. The collimator efﬁciency for parallel-hole collimators increases with increasing diameter of the collimator holes and decreases with increasing collimator thickness (t) and septal thickness (a), which is quite opposite to Uniformity 129 spatial resolution [see Eq. Thus, for a given collimator, as the spatial resolution of a system increases, its sensitivity decreases, and vice versa. Note that collimator efﬁciency, Eg, for parallel-hole collimators is not affected by the source-to-detector distance for an extended planar source; that is, it essentially remains the same at different distances from the detector. Collimator efﬁciency varies with different types of colli- mators, and the values are shown as a function of source-to-collimator dis- tance in Figure 10. Uniformity It is always expected that a gamma camera should yield a uniform response throughout the ﬁeld of view. That is, a point source counted at different locations in the ﬁeld of view should give the same count rate by the detec- tor at all locations. However, even properly tuned and adjusted gamma cameras produce nonuniform images with count density variations of as much as 10%. Such nonuniformity adds to the degradation of the spatial resolution of the system. Although factor (c) is preventable as discussed below, factors (a) and (b) are the leading causes of deterioration in uniformity and special attention is needed to remedy them. An intrinsic image (without the col- limator) is acquired using the appropriate window and stored in a 128 × 128 matrix. The pulse height in each (X, Y) pixel is determined and stored in a 128 × 128 look-up table. In subsequent patient studies, a microprocessor compares the pulse height in each pixel of the patient image with the cor- responding value in the look-up table, and then either moves the energy 130 10. Performance Parameters of Gamma Cameras window or adjusts the pulse height to compensate for the variations. This is performed in real-time during the data collection in patient studies and should be carried out for each radionuclide. Nonlinearity The spatial nonlinearities are systematic errors in the positioning of X-, Y-coordinates of pulses in the image and result from local count compres- sion or expansion. The spatial distortions due to nonlinearity are corrected by micro- processors built into modern cameras that use correction matrices. Nonlin- earity correction factors are generated by calculating the spatial shift of the observed position of an event from its actual position. The test pattern is placed directly on the detector, and an image is stored in a 128 × 128 matrix. The actual location (X, Y) of each pixel is known and the corresponding location on the image is measured. These variations in X, Y for all pixels are calculated as correction factors and are normally supplied by the manufacturer in the form of a look-up table. These correction factors are subsequently applied in real-time to each detected event to move it to the actual position during patient imaging. As stated above, modern cameras include two look-up matrices, the pulse-height correction and the linearity correction, to compensate for vari- ations in the overall uniformity of images. As the camera slowly drifts over time, the correction tables have to be updated for proper correction of the patient scan. The exact frequency of reacquiring the correction tables depends on stability of the camera and varies with the manufacturer. The pulse-height correction tables require more frequent acquisitions, whereas the linearity correction tables are typically performed by a service engineer. Different manufacturers recommend monthly to quarterly acquisition of these correction factor maps. Even though the uni- formity corrections at times can correct for large nonuniformities, frequent retuning of the gamma camera is essential as these corrections affect lin- earity, resolution, and overall sensitivity of the camera.

There bowel sounds buy discount alavert 10mg line, a nontender abdomen order 10mg alavert with visa, no organomeg- is no guarding or rebound buy alavert 10 mg with visa, but she is tender throughout. Several cutaneous le- Review of her records reveals no bowel movement over sions are noted on her lower extremities, bilateral the past 72 h and no stool is palpable in the rectal vault. Abdominal plain ﬁlm of her current disease state except shows what is read as a probable ileus in the right lower quadrant. A 36-year-old man with a history of hypertension plaining of several days of worsening burning and pain with presents complaining of a 3-year history of constant fa- urination. She describes an increase in urinary frequency tigue, diffuse myalgias, and memory deﬁcits. He was diag- has no past medical history with the exception of two prior nosed with Lyme disease 4 years ago and was brieﬂy ad- episodes similar to this in the past 2 years. Urine analysis mitted to a cardiac care unit for transient third-degree shows moderate white blood cells. Symptoms at that time included fever, mal- the most likely causative agent of her current symptoms? Ceftriaxone, 2 g daily × 1 month thema and warmth over the thigh with notable woody, C. Empirical antibiotic therapy for continuous ambu- tinin (H) and neuraminidase (N) antigens. Antigenic shift is deﬁned by an exchange of hemag- tis should be directed towards which organisms? Inﬂuenza C virus infections, while uncommon, are plus yeast more virulent on a population basis due to its in- creased ability to undergo antigenic shift. Hepatic necrosis in pregnant women of the following factors on history and laboratory exami- D. Isospora infection may cause biliary tract disease, ments is accurate in reference to diagnosis of malaria? Isospora is more likely to infect immunocompetent comparison to a thin smear but can only be per- hosts than Cryptosporidium. Isospora is less challenging to treat and generally sonnel and has a longer processing time. Isospora occasionally causes large outbreaks among and morphology of the erythrocytes. In the absence of rapid diagnostic information, empiri- cal treatment for malaria should be strongly considered. A 27-year-old man presents to your clinic with 2 ness of breath but denies any gastrointestinal symptoms, weeks of sore throat, malaise, myalgias, night sweats, fe- urinary retention, or loss of bowel or bladder continence. He visited an urgent care center and was Physical examination reveals a frustrated, nontoxic ap- told that he likely had the ﬂu. He was told that he had a pearing man who is alert and oriented but noticeably dys- “negative test for mono. Cranial nerve states that he is in a monogamous relationship and has examination reveals bilateral cranial nerve six deﬁcits and unprotected receptive and insertive anal and oral inter- an inability to maintain medial gaze in both eyes. He had several partners prior to mild bilateral ptosis, and both pupils are reactive but his current partner 4 years ago but none recently. He is and deep tendon reﬂexes are within normal limits in all otherwise healthy with no medical problems. Giardiasis is self-limited and requires no antibiotic shows no likely resistance mutations. Which of the fol- therapy lowing is now considered an acceptable ﬁrst-line regimen D. All of the following clinical ﬁndings are consistent bacilli consistent with Mycobacterium avium complex. Sensitive and speciﬁc serum or urine diagnostic and medical nonadherence to therapy is admitted to the tests exist for all of the following invasive fungal infec- hospital with 2–3 weeks of increasing dyspnea on exer- tions except tion and malaise. Chest radiograph shows bilateral alveo- lar inﬁltrates and induced sputum is positive for A. Invasive aspergillosis curs a needle stick from a patient with known active hep- D. Hepatitis B immunoglobulins gency room with crampy abdominal pain and watery di- B. Hepatitis B vaccine plus hepatitis B immunoglobulins returned from a volunteer trip to Mexico. Hepatitis B vaccine plus lamivudine medical history and felt well throughout the trip. Lamivudine plus tenofovir examination shows small cysts containing four nuclei, and stool antigen immunoassay is positive for Giardia. Which of the following is not a common feature of Which of the following is an effective treatment regimen? Polymicrobial content with gram-positive cocci in mentia with severe memory loss and decline in intellec- chains, enteric gram-negative rods, and anaerobic tual function. These symptoms were preceded by 2–3 pleomorphic forms months of labile mood, weight loss, and headache. A 64-year-old man in Wisconsin develops a high rently he is awake but unable to answer questions. He has spent his weekends logic examination is notable for normal cranial nerves over the past month chopping wood in his backyard. A peripheral blood smear reveals chemistries, negative serologic tests for syphilis, and nor- prominent morulae in neutrophils. A previously healthy 19-year-old man presents quent use of albuterol over the past few months. Persistent with several days of headache, cough with scant sputum, inﬁltrates are seen on chest roentgenogram.

There is progressive confluence of the opacities resulting in lobar opacification cheap alavert 10mg line. Abscess formation occurs late in the infection and is demonstrated by increasing demarcation of an initially ill-defined opacity with evolution into a round cavity with an irregular thick wall and possibly an air-fluid level (37) buy 10mg alavert overnight delivery. Gram-negative agents include Klebsiella and Pseudomonas 10mg alavert with visa, each of which has relatively specific radiographic features that can facilitate diagnosis, in addition to clinical history and sputum culture. In general, Gram-negative pneumonia can present as ill-defined pulmonary 96 Luongo et al. Infection is usually bilateral and multifocal, with the lower lobes affected more often. The infection manifests as lobar opacification with an exuberant inflammatory reaction, resulting in bulging fissures and a high incidence of effusion and empyema compared with other organisms. Infection may occur via the tracheobronchial tree, resulting in patchy opacities and abscess formation, or hematogenously, which is seen as diffuse, bilateral ill-defined nodular opacities (37). Aspergillosis Invasive pulmonary aspergillosis is another entity that frequently results in focal lung infarctions and cavitary formation. Additional nodular lesions with surrounding ground-glass opacity, some of which were cavitating, were also seen through- out both lungs. The findings combined with the clinical information are highly compatible with invasive aspergillosis. There is also tracheal dilatation and preexistent bronchiectasis as well as architectural distortion of the upper lobes. Aspergillomas, which are not frankly angioinvasive in contrast to invasive aspergillosis, but which may cause hemoptysis or may be asymptomatic, move freely within the cavity and thus should change position between prone and supine imaging, a helpful identifying feature (37,38). The inner wall of a tuberculous lesion can be either smooth or irregular in appearance (Fig. Clinical and Radiologic Diagnosis of Diffuse Bilateral Pneumonia Truly diffuse pneumonias are often viral in etiology. In the elderly or debilitated patient, infection can be fulminant and potentially fatal within a matter of days. Over the course of days to weeks, depending on the condition of the patient, diffuse consolidation may develop. In a healthy host, the findings should resolve within approximately three weeks (37,43). Herpes simplex virus is a rare entity, occurring primarily in the immunocompromised or those with airway trauma, such as the chronically intubated. Infection occurs either via aspiration, via extension from oropharyngeal infection, or hematogenously in cases of sepsis. Addi- tional opacities are seen diffusely in both lungs, some of which demonstrate a “tree-in-bud” configuration. On radiographs, the most common findings are patchy segmental or subsegmental areas of air- space disease. Mixed alveolar and interstitial abnormalities; consolidation; nodules; small, ill-defined centrilobular nodules; bronchial dilatation; and thickened interlobular septa are all potential findings. Progressive disease results in formation of confluent areas of air- space opacification. Asymmetric or focal areas of interstitial disease are also highly suggestive of pneumocystis pneumonia in the correct clinical context. Significant adenopathy and pleural effusions are highly unusual, and their presence usually indicates an alternate diagnosis. Thin- walled cysts or pneumatoceles can also be seen with pneumocystis pneumonia, as can pneumothorax (25,38,43). Mimics of Diffuse Bilateral Pneumonia Congestive Heart Failure Congestive changes occur in two phases: interstitial edema and alveolar flooding or edema. With increased transmural arterial pressure, the earliest findings are loss of definition of subsegmental and segmental vessels; enlargement of peribronchovascular spaces; and the appearance of Kerley A, B, and C lines, reflecting fluid in the central connective septa, peripheral septa, and interlobular septa, respectively. If allowed to progress, increasing accumulation of fluid results in spillage into the alveolar spaces, which is exhibited by confluent opacities primarily in the mid and lower lungs. A potentially helpful differentiating feature from other causes of diffuse bilateral air-space opacities is the rapid time frame in which these changes occur. Common associated findings are cardiomegaly, pulmonary venous distention, and pleural effusion (37,45). Pulmonary Hemorrhage Pulmonary hemorrhage may result from trauma, bleeding diathesis, infection, and auto- immune causes. Radiographic findings include bilateral coalescent air-space opacities that develop rapidly and that commonly improve rapidly with a time course of hours, as opposed to days or weeks, such as with most cases of pneumonia (37). Leakage of protein-rich fluid from damaged capillary membranes into the interstitial and alveolar spaces leads to decreased inflated lung volumes and decreased lung compliance (37). On chest radiographs, there are diffuse bilateral opacities located more peripherally due to predominance of capillaries in the periphery of the lung. Presumably, proteinaceous fluid remains in the periphery rather than migrating centrally due to poor diffusion, and there is decreased clearance of the material leading to persistence of the opacities for days to weeks with little change in appearance. There are many classifications of the disease, describing both etiology and pattern of pulmonary change. The time course is also more likely to be chronic, based on months to years, rather than acute or subacute as with pneumonia (37). Bilateral Massive Aspiration Aspirated material may include food, water, or sand (as in near drowning) or other foreign objects such as dental material. On chest radiographs, the characteristic appearance is of dependent pulmonary opacities, which then typically coalesce. In healthy individuals, the opacities should resolve rapidly because of mucociliary clearance. Also, sand or gravel particles may become lodged in small airways, leading to the diagnostic appearance of sand or gravel bronchograms (37,47).

All people with the disease are 56 years and older and all people aged less than 56 do not have the disease buy alavert 10 mg without prescription. Therefore cheap alavert 10 mg with amex, age group 3 predicts the presence of the disease and the age groups of 1 and 2 predict the absence of the disease 10 mg alavert amex. Here, the outcome groups (presence or absence of a disease) can be separated by the explanatory variable. Complete separation results in large standard errors as a result of overﬁtting the regression model. The Cox and Snell R square is similar to the multiple correlation coefﬁcient in linear regression and measures the strength of the association. This coefﬁcient which takes sample size into consideration is based on log likelihoods and cannot reach its maximum value of 1. Consequently, the Nagelkerke R square is generally higher than Cox’s and has values that range between 0 and 1. To evaluate the contribution of an explanatory variable to the model, the Wald statis- tic can be used. This statistic has a chi-square distribution and is the result of dividing the B value by its standard error and then squaring the result. This value is used to cal- culate the signiﬁcance (P) value for each factor in the model. In logistic regression, the constant is used in the prediction of probabilities but does not have a practical interpre- tation. It should be noted that when the absolute value of the B coefﬁcient is large, the standard error increases which results in the Wald statistic being underestimated. In this case, other methods such as a sequential method of entering variables should be used to assess the contribution of the variable to the model. In this model, the comparison model is no predictors, with only the constant (intercept) included. The Variables in the Equation table shows the model coefﬁcients but the interpretation of the coefﬁcients is different to those obtained in linear regression. A positive coefﬁcient indicates that the predicted odds increase as the explanatory variable increases. A negative coef- ﬁcient indicates that the predicted odds decrease as the explanatory variable increases. When adding further variables to the model, it is important that this standard error does not inﬂate by more than 10%. This value indicates the changes in odds associated with a unit increase in the explanatory variable and when there is only one explanatory variable in the model is the same as the estimate from the 2 × 2 crosstabulation. Model Summary Step −2 Log likelihood Cox & Snell R square Nagelkerke R square 1 2130. The Omnibus Tests of Model Coefﬁcients table indicates the change in the chi-square value from the previous model and whether this change is signiﬁcant. The odds ratio for infection, which is the exponential of the beta coefﬁcient (B) 0. The Omnibus Tests of Model Coefﬁcients table shows that the chi-square value has slightly changed, which is not signiﬁcant indicating that adding gender to the model did not improve the ﬁt of the model. Crosstabs Early infection * Gender Crosstabulation Gender Female Male Total Early infection No Count 1016 1005 2021 % within gender 85. Examination of the Crosstab- ulation tables shows that males have a higher percentage of allergy and early respiratory infections compared to females. Thus, gender was a risk factor in the unadjusted esti- mates because of confounding between gender and the other two risk factors. The logistic regression shows that once the effects of confounding are removed, gender is no longer a signiﬁcant independent risk factor for diagnosed asthma. Separating out the confounding and identifying the independent effects of risk factors makes an invaluable contribution towards identifying pathways to disease. In this research question, the data were derived from a cross-sectional study and thus it is important to report the proportion of children who had asthma in the groups that were exposed or not exposed to the risk factors of interest as shown in Table 9. In a case–control study, it would be important to report the per cent of par- ticipants in the case and control groups who were exposed to the factors of interest. It is also important to report the unadjusted and adjusted values so that the importance of confounding factors is clear. The adjusted odds ratios from the binary logistic regression are smaller but provide an estimate that is not biased by confounding. The estimates of odds ratios and conﬁdence interval widths can be entered into SigmaPlot worksheet with the odds ratio in column 1, the lower endpoint of the 95% conﬁdence interval in column 2 and the upper endpoint in column 3 as follows: Column 1 Column 2 Column 3 8. The sequence is then repeated in Graph Page → Add Plot with column 1 again as the data for the bar and column 3 as the data for the error. Once this basic graph is obtained, the labels, symbols, axes, ticks and labels can be customized under the Graph Page options menus to obtain Figure 9. The x-axis needs to be a logarithmic base 10 scale, the ﬁrst plot should have negative error bars only and the second plot should have positive error bars only. The errors bars can be changed by clicking on a bar and altering the attributes in the Page Objects box on the right hand side of the screen. For gender, the odds ratio is close to unity and the conﬁdence intervals lie on either side of the line of unity indicating a possible effect from protection to risk, which is therefore ambiguous. Relative risk can only be used when the sample is randomly selected from the population and cannot be used in other studies, such as case–control studies or some clinical trials, in which the percentage of the sample with the disease is determined by the sampling method. A relative risk of 2 indicates that the prevalence of the outcome (present) in the exposed group is twice as high as the prevalence of the outcome (present) in the non-exposed group. That is, people in the exposed group are two times more likely than people in the non-exposed group to have the disease, indicating that the exposure confers a risk for disease. A relative risk of 1 indicates equal risk in the two exposure groups and therefore that the outcome is not related to the exposure.

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