Clomid 100mg, 50mg, 25mg
R. Grimboll. Columbia Southern University.
The total dose from all planned procedures plus all doses in excess of the limits must not exceed the dose limit (5rem or 50mSv) in a given year clomid 100mg without a prescription, nor must it exceed ﬁve times the annual dose limits in the indi- vidual’s lifetime discount 50mg clomid. Radiation Regulations and Protection The annual occupational dose limits for minors is 10% of the annual dose limits for adults 100mg clomid overnight delivery. The dose limit to the fetus/embryo during the entire preg- nancy (gestation period) due to occupational exposure of a declared preg- nant woman is 0. Under this concept, techniques, equipment, and procedures are all critically evaluated. Principles of Radiation Protection Of the various types of radiation, the a-particle is most damaging because of its charge and great mass, followed in order by the b-particle and the g- ray. Heavier particles have shorter ranges and therefore deposit more energy per unit path length in the absorber, causing more damage. On the other hand, g-rays and x-rays have no charge or mass and therefore have a longer range in matter and cause relatively less damage in tissue. Knowl- edge of the type and energy of radiations is essential in understanding the principles of radiation protection. The cardinal principles of radiation protection from external sources are based on four factors: time, distance, shielding, and activity. Time The total radiation exposure to an individual is directly proportional to the time of exposure to the radiation source. Therefore, it is wise to spend no more time than necessary near radiation sources. Distance The intensity of a radiation source, and hence the radiation exposure, varies inversely as the square of the distance from the source to the point of expo- sure. It is recommended that an individual should keep as far away as prac- tically possible from the radiation source. Procedures and radiation areas should be designed so that individuals conducting the procedures or staying in or near the radiation areas receive only minimum exposure. The G values are derived from the number of g-ray and x-ray emissions from the radionuclide, their energies, and their mass absorption coefﬁcients in air. The exposure rate X from an n-mCi radionuclide source at a distance d cm is given by a The G value of photon-emitting radionuclides can be calculated from the expres- sion G = 199ΣN Ei imi, where Ni is the fractional abundance of photons of energy Ei in MeV, and m is the mass absorption coefﬁcient (cm2/g) of photons of energy E in air. Shielding Various high atomic number (Z) materials that absorb radiations can be used to provide radiation protection. Because the ranges of a- and b- particles are short in matter, the containers themselves act as shields for these radiations. Therefore, highly absorbing material should be used for shielding of g-emitting sources, although for economic reasons, lead is most commonly used for this purpose. The radiopharmaceuti- cal dosages for patients should be carried in shielded syringes. Radionu- clides emitting b-particles should be stored in containers of low-Z material such as aluminum and plastic because in high-Z material, such as lead, they produce highly penetrating bremsstrahlung radiations. For example, 32P is a b− emitter and should be stored in plastic containers instead of lead containers. Activity It should be obvious that the radiation exposure increases with the inten- sity of the radioactive source. Therefore, one should not work unnecessarily with large quantities of radioactivity. Occupational workers including minors and pregnant women likely to receive in 1 year a dose in excess of 10% of the annual limit of exposure from the external radiation source 2. Three devices are used to measure the exposure of ionizing radiations received by an individual: the pocket dosimeter, the ﬁlm badge, and the thermoluminescent dosimeter. Film Badge The ﬁlm badge is most popular and cost-effective for personnel monitor- ing and gives reasonably accurate readings of exposures from b-, g- and x- radiations. The ﬁlm badge consists of a radiation-sensitive ﬁlm held in a plastic holder (Fig. Filters of different metals (aluminum, copper, and cadmium) are attached to the holder in front of the ﬁlm to differentiate 278 16. Filters of metals of different densities stop different energy radiations, thus discriminating exposures from them. After exposure the optical density of the developed ﬁlm is measured by a densitometer and compared with that of a calibrated ﬁlm exposed to known radiation. Film badges are usually changed monthly for each radiation worker in most institutions. The main disadvantage of the ﬁlm badge is the long waiting period (a month) before the exposed personnel know about their exposure. The ﬁlm badge also tends to develop fog resulting from heat and humidity, particularly when in storage for a long time, and this may obscure the actual exposure reading. The ﬁlm badges of all workers are normally sent to a commercial ﬁrm that develops and reads the density of the ﬁlms and sends back the report of exposure to the institution. When these crystals are exposed to radiation, electrons from the valence band are excited and trapped by the impurities in the forbidden band. If the radia- tion-exposed crystal is heated to 300°C to 400°C, the trapped electrons are raised to the conduction band; they then fall back into the valence band, emitting light. It should be noted that exposure resulting from medical procedures and background radiations are not included in occupational dose limits. These devices should be taken off during any medical procedures involv- ing radiation such as radiographic procedures and dental examinations, and also when leaving after the day’s work. Also radiation workers should not wear these badges for certain period of time after undergoing a diagnostic or therapeutic nuclear medicine procedure or radiation therapy permanent implant procedure. Dos and Don’ts in Radiation Protection Practice Do wear laboratory coats and gloves when working with radioactive materials. For iodine radionuclides, bioassay is performed by the thyroid uptake test within 72hr and at 14 days after handling the radioactivity. Radiation Regulations and Protection required for other radionuclides, depending on the amount and type of radionuclides. The suppliers require documentation of licensing of the user as to the types and limits of quantities of radioactive material before shipping. Monitoring of packages is required if the packages are labeled as con- taining radioactive material to check if the packages are damaged or leaking. A radioactive shipment must be monitored as soon as possible after receipt but no later than 3hr after delivery if the delivery takes place during normal hours, or not later than 3hr from the beginning of the next working day if it is received after working hours. Two types of monitoring are per- formed: survey for external exposure and wipe test for contamination on the surface of the package resulting from potential leakage of liquid. The survey reading of external exposure should not exceed 200mrem/hr (2mSv/hr) on the surface of the container or 10mrem/hr (100mSv/hr) at 1m from the surface of the container. The wipe test is performed by swab- bing an area of 300cm2 of the package and should show less than the limit 2 of 6600dpm or 111Bq/300cm. Advice should be sought from these authorities as to whether the shipment should be returned. The information logged in includes the date of the receipt, the man- ufacturer, the lot number, name and quantity of the product, date and time of calibration, and survey data along with the name of the individual pro- cessing the receipt. Radioactive Waste Disposal Radioactive waste generated in nuclear medicine or pharmacy (e. Radionuclides with half-lives less than 120 days usually are disposed of by this method. These radionuclides are allowed to decay in storage and monitored before disposal. If the radioactivity of the waste cannot be distinguished from back- ground, it can be disposed of in the normal trash after removal or defacing of all radiation labels. This method is most appropriate for 99m 123 201 111 67 131 shortlived radionuclides such as Tc, I, Tl, In, Ga and I. Radioac- tivities should be stored separately according to half-lives for convenience of timely disposal of each radionuclide. Excreta from humans undergoing medical diagnosis or treatment with radioactive material are exempted from these limitations. To adopt this method of radioactive disposal, one must determine the total volume and the ﬂow of sewer water in the institution and the number of users of a speciﬁc radionu- clide so that for each individual user, a limit can be set for sewer disposal of the radionuclide in question. Transfer to Authorized Recipient This method of transfer to an authorized recipient is adopted for longlived radionuclides and usually involves transfer of radioactive wastes to autho- rized commercial ﬁrms that bury or incinerate at approved sites or facilities. Although the columns of the 99Mo–99mTc generators may be decayed to background for disposal to normal trash, a convenient method of disposing of this generator is to return them to the vendors, who let them decay and later dispose of them. Normally, the used generator is picked up by the authorized carrier when a new one is delivered. Radiation Regulations and Protection Other Disposal Methods A licensee may adopt methods of radioactive waste disposal different from those mentioned here, provided regulatory agency approval is obtained. Impact of such disposal methods on environment, nearby facilities, and population is heavily weighed before approval. Incineration of solid radio- active waste and carcasses of research animals containing radioactive 133 materials is allowed by this method. Records must be maintained as to the date of storage and the amount and kind of activity stored in a waste disposal log book. The date of disposal and the amount of disposed activity must also be recorded in the log book, along with the initials of the individual disposing of the waste. Radioactive Spill Accidental spillage of radioactivity can cause unnecessary radiation exposure to personnel and must be treated cautiously and expeditiously.
Calciﬁc aortic stenosis is the most common cause of aortic stenosis and most commonly presents in the seventh or eighth decade buy clomid 25mg with visa. Rheumatic heart disease as a result of rheumatic fever is also commonly associated with aortic valve disease generic clomid 50 mg without a prescription. The age of presentation of rheumatic heart disease falls between that of bicuspid aortic valve and calciﬁc aortic stenosis generic 100mg clomid with mastercard, usually around the sixth or seventh decade. Severe heart failure with refrac- tory symptoms is the main indication for cardiac transplantation and may be caused by a variety of underlying diseases. In general, cardiac transplantation is reserved for younger individuals without signiﬁcant comorbidities. The patients given highest priority for transplant are those requiring vasopressor support with concomitant use of a pulmonary artery catheter or those requiring mechanical circulatory support. Individuals requiring vasopressor support managed without pulmonary artery catheter are given second high- est priority. Acute rejection and infection are the commonest causes of early transplant failure and death. Most programs perform routine endomyocardial bi- opsies to detect rejection for a period of 5 years after transplant. Mortality that occurs >1 year after transplant is most likely related to coronary artery disease, which is accelerated posttransplant due to immunosuppression. Average ef- ﬁcacy of these drug classes are as follows: nicotinic acid, 20–40%; ﬁbrate, 35–50%; statin, 7–30%). They lower choles- terol but often increase triglyceride levels and should not be used in patients with triglyc- erides >200 mg/dL. Nicotinic acid is effective for treating hypertriglyceridemia but may worsen glucose control and therefore should be used cautiously in patients with the metabolic syndrome. Balloon angioplasty reocclusion rates are up to two times higher com- pared to restenosis with stenting. This type of restenosis is mediated by hyperproliferation of smooth muscle cells into the intima as they react to the vascular injury induced by the balloon angioplasty. However, due to the delayed endothelial healing that is achieved with drug-eluting stents, the patient is exposed to a higher risk of subacute in-stent restenosis. This type of restenosis is mediated by thrombus formation as the denuded endothelium is exposed to the circulation. T-wave notching, or “humps,” may be common in asymptomatic patients and are of prognostic importance. Anti-ischemic therapy (nitrates, beta blockers) is important for symptom relief and to prevent recurrence of chest pain. Anti- thrombotic therapy is directed against the platelet aggregation at the site of the ruptured plaque. Continuation of treatment for up to 12 months confers addi- tional beneﬁt in patients treated conservatively and among those who underwent percutaneous coronary intervention. The major advantage of a bioprosthetic valve is the low incidence of thromboembolic phenomena, particularly 3 months after implantation. Although in the immediate postoperative period some anticoagulation may occur, after 3 months there is no further need for anticoagulation or monitoring. Therefore, these valves are useful in patients with contraindications to anticoagulation, such as elderly patients with comorbidities and younger patients who desire to become pregnant. Elderly people may also be spared the need for repeat surgery as their life span may be shorter than the natu- ral history of the bioprosthesis. Hemody- namic parameters are improved with double-disk valves compared with single-disk or ball-and-chain valves. Younger patients with no contraindications to anticoagulation may be better served by mechanical valve replacement. This designation is applied to patients with communications between the right and left circulations, pulmonary hypertension, and a predominantly right-to-left shunt. Eisen- menger’s syndrome can develop in patients with communication at the atrial, ventricu- 222 V. These shunts are initially left to right and therefore do not present with cyanosis. Pulmonary hypertension develops over years as a result of in- creased pulmonary ﬂow, increased vascular tone, and erythrocytosis. Cyanosis develops when the pulmonary hypertension becomes so severe that it reverses the shunt. Atrial septal defects are most common in adults presenting with Eisenmenger’s syndrome. Ebstein’s anomaly, tetralogy of Fallot, and truncus arteriosis all cause cyanosis. In this patient, the mitral regurgitation worsened during exercise and was due to occult coronary artery disease. The patient’s dyspnea improved with following an- gioplasty and stenting of the left circumﬂex artery. The pulmonary capillary wedge pres- sure reﬂects the left-ventricular end-diastolic pressure in the absence of mitral stenosis or pulmonary venous hypertension. In mitral stenosis, there is a signiﬁcant drop between left-atrial and left-ventricular diastolic pressures and elevation of the pulmonary capil- lary wedge pressure. Pulmonary arterial hypertension would have a normal pulmonary capillary wedge pressure but an elevated pulmonary artery mean pressure, which is not shown in these tracings. In aortic stenosis, the pulmonary capillary wedge pressure may be elevated if heart failure is present, but no abnormal wave forms would be expected. Congestive heart failure causes an elevated pulmonary capillary wedge pressure, which is not present here. The large v waves of mitral regurgitation should not be read as the pul- monary capillary wedge pressure. The most likely diagnosis in this patient is primary hyperaldosteronism, also known as Conn’s syndrome. The patient has no physical features that suggest con- genital adrenal hyperplasia or Cushing’s syndrome. In addition, there is no glucose intol- erance as is commonly seen in Cushing’s syndrome. The lack of episodic symptoms and the labile hypertension make pheochromocytoma unlikely. The ﬁndings of hypokalemia and metabolic alkalosis in the presence of difﬁcult to control hypertension yield the likely diagnosis of Conn’s syndrome. Diagnosis of the disease can be difﬁcult, but the preferred test is the plasma aldosterone/renin ratio. Selective adrenal vein renin sampling may be performed after the diagnosis to help determine if the process is unilat- eral or bilateral. Although ﬁbromuscular dysplasia is a common secondary cause of hy- pertension in young females, the presence of hypokalemia and metabolic alkalosis should suggest Conn’s syndrome. Thus, magnetic resonance imaging of the renal arteries is un- necessary in this case. Measurement of 24-h urine collection for potassium wasting and aldosterone secretion can be useful in the diagnosis of Conn’s syndrome. These patients often have a variety of su- praventricular and ventricular arrhythmias and are at risk for sudden death due to the in- trinsic cardiomyopathy as well as the low ejection fraction. Implantable cardioverter deﬁbrillators should be considered in the appropriate patient. Global left ventricular dys- function is a common ﬁnding in dilated cardiomyopathies, whereas focal wall motion abnormalities and angina are more common if there is ischemic myocardium. This pa- tient is at risk for venous thromboembolism; however, chronic thromboembolism would V. Amyotrophic lateral sclerosis is a disease of motor neurons and does not involve the heart. An advanced atrial septal defect would present with cyanosis and heart failure (Eisen- menger’s physiology). During inspiration, it is normal to hear the closing of the aortic valve (A2) before the closing of the pulmonic valve (P2). A ﬁxed split of the second heart sound occurs in the setting of an atrial septal defect. With this congenital heart defect, the volume of blood that is shunted from the left atrium to the right atrium results in a stable right-ventricular stroke volume. Thus, there is no difference between inspiration and expiration, resulting in a ﬁxed split of the second heart sound. Thickened myocardium increases back pressure in the coronary circulation thereby reducing coronary perfusion, leading to ischemia. In addition, diastolic pressures are lower when there is severe aortic regurgitation, which further decreases coronary perfu- sion. Myocardial oxygen consumption increases when there is ventricular hypertrophy as a result of increased mass and contractility. In chronic aortic regurgitation, the equilibration of end-diastolic left-ventricular and aortic pressures exacerbates left-ventricular remodeling and will cause premature closure of the mitral valve or functional mitral regurgitation. Diagnosing paroxys- mal atrial ﬁbrillation with a 24-h monitor is an option if there is no evidence of pulmonary hypertension. There is no evidence that percutaneous or surgical repair of mitral stenosis is beneﬁcial for slight or no functional impairment.
However clomid 25mg on-line, for some children impairment is a permanent feature in their lives clomid 100mg with mastercard, although it may become a disability only if they are unable to take part in everyday activities buy 25 mg clomid with mastercard, such as communicating with others, climbing stairs, and toothbrushing. There are a number of reasons why children with disabilities merit special consideration for dental care: 1. The oral health of some children with disabilities is different from that of their normal peers, for example, the greater prevalence of periodontal disease in people with Down syndrome and of toothwear in those with cerebral palsy. The prevention of dental disease in disabled children needs to be a higher priority than for so-called normal peers because dental disease, its sequelae, or its treatment, may be life-threatening, for example, the risk of infective endocarditis from oral organisms in children with congenital heart defects (Fig. Most of the studies which have been undertaken on disabled children have indicated that the majority can in fact be treated in a dental surgery in the normal way, together with the rest of their family. Key Points The need for special dental care arises because of: • differences in dental disease prevalence; • dental disease/treatment may be life-threatening; • the modifications required to treatment plans; • the need for special facilities; • treatment may be time-consuming. This normality is desirable, provided the disabled person actually receives good dental care. The evidence from many studies is that, although the overall caries experience is similar between disabled children and their so-called normal contemporaries, the type of treatment they have experienced is different: disabled children have similar levels of untreated decay, but more missing teeth and fewer restored teeth. A minority of children with complex disabilities need special facilities, usually only available in dental or general hospitals, or from specialized community dental clinics. What is needed by all patients with disabilities is a very aggressive approach to the prevention of dental disease. Because of the potential for dental disease, or its treatment, to disable an impaired child, priority must be given to preventive dental care for such individuals from a very young age. These terms, used synonymously, encompass a wide variety of impairments, but three main areas ⎯ intellectual, physical, and sensory impairments⎯predominate and will now be considered in more detail. Medical compromise, considered in more detail in Chapter1115H 16, may also be imposed on these impairments. The way in which some of these present to a dentist are given below, together with the dental management issues relevant to each. Approximately, 25 per 1000 of the child population are affected, and the majority, as with other impairments, will be males. Children with intellectual impairment can be divided broadly into those who are either mentally retarded or have a learning difficulty. These are broad groups, often without a well-defined aetiology or consistent presenting features, but there are two distinct subgroups where the cause is known and the features are well described, namely Down and Fragile X syndromes. Intellectual impairment may be present in some children with cerebral palsy and those who have suffered birth anoxia, and severe infections, for example, meningitis and rubella. Intellectual impairment is also a feature of autism, microcephaly, and metabolic disorders (e. Not every condition will have specific dental features like Down syndrome, but an understanding of the underlying impairment will help the dentist plan treatment more effectively. Mental retardation, pervasive developmental disorders (autism and schizophrenia), learning disabilities, dyslexia, attention-deficit disorders, and hyperactivity are all controversial categories whose definition and processes of assessment are not universally agreed. Key Points Classification of children with impairments • intellectually impaired⎯mentally retarded, learning difficulties; • physically impaired⎯developmental, degenerative; • sensory impairment; • medically compromised; • combination of impairments. Mental retardation This is sometimes called mental handicap, mental subnormality, or mental deficiency. It is a general category characterized by low intelligence, failure of adaptation, and early age of onset. Affected children are slow in their general mental development and they may have difficulties in attention, perception, memory, and thinking. They may be stronger in some skills than others, for example, music and computing, but generally they are of low intellectual attainment. Children with low intelligence are not called mentally retarded unless they also have some problem in adaptation. That is, they are unlikely to be able to live independently and will always depend inappropriately on others as a source of income and support for daily living. The simplicity of the classification is somewhat illusory with great individual differences among people with mental retardation. Key Points Intellectual impairment may occur in: • cerebral palsy; • birth anoxia; • severe infections; • autism; • microcephaly; • metabolic disorders; • major trauma; • some syndromes. Down syndrome Down syndrome is a chromosomal disorder, trisomy 21, with distinct clinical features. The prevalence is approximately 1 in 600 births but there is variation with maternal age, so that at 40 years of age the incidence is about 1 in 40 births. However, the numbers seen in any one country will vary depending on the prevailing attitude towards prenatal screening and termination. The general physical features associated with Down syndrome are a greater predisposition to cardiac defects, leukaemia of the myeloid type, infective hepatitis infection (especially in institutionalized males), although most children will have been vaccinated against viral forms. Coeliac disease as well as thyroid disorders are also clinical features of this condition. Increasingly, a form of early dementia, entitled disintegrative disorder is being recognized in adolescents with Down syndrome. The features seen are of a progressive loss of skills, both cognitive and physical and have obvious relevance in dentistry because of the impact on personal oral care. Varying degrees of mental retardation occur, and upper respiratory tract infections and an inability to withstand infections generally are common. Physically, predominant features are a rounded, small face with an under-developed mid-face (Fig. The hands of children with Down syndrome are stubby with a pronounced transverse palmar crease. There is usually a delay in the exfoliation of primary teeth and in the eruption of permanent teeth, while some teeth may be congenitally missing. There is a high prevalence of periodontal disease in the anterior alveolar segments, especially in the mandible. This is probably due to impaired phagocyte function in neutrophils and monocytes, combined with poor oral hygiene. Key Points Oral and dental features in Down syndrome: • mid-face hypoplasia; • large, fissured tongue; • narrow, high-vaulted palate; • delay in exfoliation/eruption; • congenitally absent teeth; • microdont/hypoplastic teeth; Fragile X syndrome Next to Down syndrome this is the most common cause of mental retardation. The condition is of particular significance because a high proportion of affected individuals have congenital heart defects, usually mitral valve prolapse, that may require antibiotic prophylaxis. Although males are predominantly affected, milder versions of the disability may be seen in females. Pervasive developmental disorders This group encompasses autism and childhood schizophrenia. The former is characterized by its early onset, usually before 30 months of age, whereas childhood schizophrenia presents later. They are conditions that represent profound adaptive problems in thinking, language, and social relationships. Autism in particular has the distinctive feature of restricted and stereotypical behaviour patterns. The more severely delayed children seem oblivious to their parents or carers, express themselves minimally, show a low level of interest in exploring objects, avoid sounds, and engage in ritualistic behaviour. These features need to be taken into consideration when attempting dental care, and underlines the particular importance of acclimatization and familiarity of routine (rituals) as part of that process. The causes of autism are unknown but are thought to be prenatal and not social in origin. A major malformation in the cerebellum has recently been implicated as a possible causative factor. Learning difficulties Learning difficulty is associated with dyslexia, minimal brain damage, attention- deficit disorder, and hyperactivity. All these categories are controversial, mainly because they have been overextended. Thus the impairment is restricted in its range and there is a discrepancy between academic performance and tested general ability. In these two ways a learning difficulty differs from mental retardation because the latter is characterized by general delay and academic performance is usually at the level expected from ability. In practice, learning difficulty has been used to characterize any child with a learning problem who cannot be labeled mentally retarded, no matter how broad the range of impairment or the discrepancy from the tested ability level. This overextension of the definition has not only increased the apparent prevalence of learning disability but has also made the whole area rather confusing. In general, the prevalence of learning difficulties is estimated on average to be about 4. There is overlap between learning difficulties and other problems, for example, higher levels of classroom behavioural problems and an increased risk of delinquency. In part, this accounts for the greater predominance of males in groups with intellectual impairment as they are more likely than females to be disruptive at school and thus be referred for assessment by educational psychologists. Dyslexia This widely discussed form of learning disability is a specific problem with cognition. The broadest definition of dyslexia includes those children whose reading skills are delayed for any reason, and it is usually associated with a number of cognitive deficits. Prevalence varies from 3% to 16% depending on the breadth of the definition and the country. For example, prevalence rates are higher in the United States than they are in Italy, perhaps due to the complexity of the English language as compared with Italian! Minimal brain damage This category of impairment is used to describe the child who has minor neurological signs, which are often transitory. Attention disorder and hyperactivity These disorders are often confused with one another. Children who cannot sit still are thought to be inattentive to their lessons in school. A child who does not pay attention often: fails to finish activities; acts prematurely or redundantly; infrequently reacts to requests and questions; has difficulties with tasks that require fine discrimination, sustained vigilance, or complex organization; and improves markedly when supervised intensively. A child who is hyperactive: engages in excessive standing up, walking, running, and climbing; does not remain seated for long during tasks; frequently makes redundant movements; shifts excessively from one activity to another; and/or often starts talking, asking, or making requests.
Cook’s distances are a measure of inﬂuence discount 50 mg clomid free shipping, that is buy clomid 100 mg otc, a product of leverage and discrep- ancy buy clomid 25 mg lowest price. Inﬂuence measures the change in regression coefﬁcients (see Chapter 7) if the data point is removed. Therefore in practice, Cook’s distances above 1 should be investigated because these cases are regarded as inﬂuential cases or outliers. A leverage value that is greater than 2(k + 1)/n,wherek is the number of explanatory variables in the model and n is the sample size, is of concern. As with Cook’s distance, this leverage calculation is also inﬂuenced by sample size and the number of explanatory variables in the model. Leverage is also related to Mahalanobis 158 Chapter 5 distance, which is another technique to identify multivariate outliers when regression is used (see Chapter 7). Deciding whether points are problematic will always be context speciﬁc and several factors need to be taken into account including sample size and diagnostic indicators. If problematic points are detected, it is reasonable to remove them, rerun the model and decide on an action depending on their inﬂuence on the results. Possible solutions are to recode values to remove their undue inﬂuence, to recruit a study sample with a larger sample size if the sample being tested is small or to limit the generalizability of the model. In addition, it is important to report how any univariate or multivariate outliers were treated in the analysis and which interactions were tested. Other statistics to report are the total amount of variation explained and the signiﬁcance of each factor in the model. Time is commonly measured as weeks, months or years but may be represented by other estimates such as age or school grade. When the outcome variable is continuous, two of the statistical methods that can be used to investigate changes in outcome and trends over time, both within and between study groups are: i. For analyzing data from cohort studies, models which offer the ability to compare differences at time points and/or between-exposure groups are ideal. In general, the sample size should be calculated on the basis of the number of vari- ables to be tested in the model including the outcome (dependent) variable. The number of participants needs to be much larger than the number of repeat measures because when the number of measurements exceeds the number of participants, the model used to analyze the data will have low statistical power. Calculation of the sample size required for repeated measures and linear mixed models can be complex and there are a few computing packages available (see Useful Websites). However, the calculation of power and sample size is not available for all types of mixed models. Generally the information that is required to calculate sample size for repeated measures or longitudinal analysis is an estimated effect size, the num- ber of repeated measures and an estimate of the correlations among pairs of the repeated measures. Cell size, that is the number of participants in each group of a ﬁxed factor or in each sub-group if there are two or more factors, is an important consideration. Groups with small numbers may need to be combined with other groups if the theory is logical. If combining cells is not logical, groups with small cell sizes can be omitted from the model, although this may reduce the generalizability of the results. When the sample size is small, alternative outcome measurements such as area under the curve or average values should be considered rather than using a repeated measures or longitudinal analysis. Including all potentially predictive variables into a single model may introduce multicollinearity and may result in a number of small or empty cells and therefore reduce the statistical power. A sequential approach in which variables are Analyses of longitudinal data 163 added into the model one at a time in order of clinical importance or univariate evidence of effect conserves power because variables can be removed from the model if they are not signiﬁcant predictors. At each step, the model can be examined for ﬁt and signs of mulitcollinearity which can provide important insights into relationships between explanatory variables and developmental pathways. Any degree of error in measuring a variable is likely to increase variance and reduce statistical power. On the other hand, variables that explain a signiﬁcant proportion of the variance and improve the ﬁt of a model increase statistical power. There is obviously a trade-off between including all variables that improve the ﬁt of a model and reducing the number of variables in order to maximize cell sizes and the precision that can be gained from the sample size. For example, when weight increase of infants is mod- elled, body length is an important covariate. In longitudinal data sets in which the covariate is measured at each time point the measurements may be highly correlated, and a time varying covariate such as age will also increase with time. In linear mixed models, if a covariate such as body length is included for each time point, the default option is that the mean value of the covariate across the model will be used. If the assumption of normality of residuals is not met, the direction of bias is not always clear. This may not be too important if the P value is large and clearly non-signiﬁcant or if the P value is small and clearly signiﬁcant. However, bias is a major problem if the P value is close to the margin of signiﬁcance or the sample size is small. Outliers can have an important effect on the perceived differences between groups by making the groups seem more different or more alike. The direction of bias caused by outliers is usually to artiﬁcially skew the mean value of a group in the direction of the outlier. Inﬂuential outliers can be recoded with a nominal value to remove their inﬂuence – a value that is commonly used is one that is marginally outside the range of the remainder of the data. An advantage of this method is that the results are readily understood and easily communicated. However, a disadvantage is that no allowance is made for measurements taken closer together in time to be more correlated than measurements taken further apart. The within-subject factor, which is related to time, is generally of most interest as the outcome variable. However, differences in between-subject ﬁxed fac- tors such as gender or treatment group can also be tested. However, sometimes the results of the univariate and multivariate repeated measures tests will disagree. The multivariate test statistics are based on transformed variables, not the original variables. In addition, the presence of Analyses of longitudinal data 165 outliers, sample size and violations of the test assumption may inﬂuence the test results. Sphericity requires that the variances of the differences for all pairs of repeated measures are constant. Sphericity should be checked for when there are three or more repeated measures conditions. The assumption of sphericity can be tested using Mauchly’s test which gives an estimate of epsilon ( ), a measure of sphericity. This statistic has a value of 1 when sphericity is met and values less than 1 indicate further deviation from sphericity. However, the Mauchly’s test is inﬂuenced by the sample size, in that, in small samples this test often fails to detect departures from sphericity and in large samples over detects sphericity. Another assumption is that the variances of the repeated measures are the same in each group, that is, there is homogeneity. The F test of the univariate model is robust to some violations of the assumption of normality of residuals but not to the sphericity assumption. When sphericity is not met, the F value is inﬂated and the P value is biased towards signiﬁcance. In this situation, the estimate of sphericity is adjusted using the Greenhouse-Geisser or the less conservative Huynh–Feldt methods. With these methods, the degrees of freedom are multiplied by the estimate of sphericity, consequently the degrees of freedom are decreased, making the F ratio more conservative. Thus, the original outcome values across time are trans- formed to contrast values and the model is applied only to these variables. This method of transforming the data bypasses the problem of dealing with covariance between time points rather than addressing it directly as in a linear mixed model. Interactions that are statistically signiﬁ- cant indicate that the pattern of change over time is different between groups. Thus missing values reduce the effective sample size, compromise statistical power and affect the generalizability of the results. If the number of missing values is small and the values are randomly missing, they can be replaced with a nominal value such as a mean value or the last value carried forward for each participant. The time point at which the increase is no longer signiﬁcant indicates where the plateau begins. Analyses of longitudinal data 167 • Polynomial, which tests for a trend across the time points. Tests of signiﬁcance for a linear trend through the data and for orders such as quadratic effects are included. For pairwise post hoc comparisons, the Tukey’s test is powerful when sphericity is met. When sphericity is violated, the Bonferroni is recommended since it maintains the type I error rate. The outlying values are few and are not extreme and therefore the values are left unchanged in the analyses. Between-Subjects Factors Value label N Group 1 Control 21 2 Intervention 26 Box’s Test of Equality of Covariance Matricesa Box’s M 22. A signiﬁcant interaction indicates that effect of 172 Chapter 6 one variable depends on the level of another variable. As an estimate of effect size the multivariate partial eta-squared was requested, which is the ratio of variance accounted by a factor to the variance accounted by a factor and its associated error.