Medical Statistics 4th Edition Michael J. Campbell, David Machin, Stephen J. Walters - Solutions

Unlock the full potential of "Medical Statistics 4th Edition" by accessing our comprehensive online resources. Discover a complete answers key and solution manual, featuring detailed solutions in PDF format. Our collection of solved problems provides clear and concise step-by-step answers, perfect for students and instructors alike. Utilize our extensive test bank, offering diverse questions and answers to enhance your understanding of each chapter. With our instructor manual and textbook resources, achieving academic success has never been easier. Enjoy the convenience of a free download and take your learning to the next level with our expertly curated content.

Explain the relationship between a random effects model and a Bayesian analysis of a fixed eff’ects model.
Explain why an analysis of variance and an analysis of covariance can be handled analytically in the m e way.
13.1 Show that conditional distribution for y, given the other, kj and Y is Bernoulli. Describe how to implement a Gibbs sampler to explore the posterior distribution of models.
13.2 Consider the linear regression model, with Zellner's g-prior and the noninformative prior on 0'. p ( d ) = I/&.(a) Find the predictive distribution of Y at X = X, under model averaging in the linear regression model.(b) What is the mean of the predictive distribution?(c) What is the variance
Let M denote the model Y = /?X + u and consider comparing &I to the niodel where M' : /I = 0.13.3 Using a noninfonnative prior distribution for 02, p(a2) = l / d , and Zeliner's g-prior for /?. p - N ( 0 , o*g(X'X)-' ), find the marginal like-Ilhood for Y under model JM.Find the marginal likelihood
13.4 Consider an improper prior distribution for jl and y given 02:p(By,y )proportional to I gX& lo?(a) What happens to the prior distribution of p, if g is multiplied by an arbitrary constant?(b) Find the posterior distribution for f i r . What happens to the posterior distribution for /3, if g is
14.1* Prove expression (14.2). with the associated defirution of a,, c,. (Recall that o2 and T? are assumed known. Hint: first derive the distributions of y I y and 8, I p, y and then integrate out p wing the formula for a normal mixture of normals.) Show that this equation can be written in the
14.2 Derive all of the conditional distributions required to implement a Gibbs sampler for the model (1 4.4).
I4.3* Consider the hierarchical model (14.5).(a) Draw a summary version of the hierarchical diagram as in Figure 14.1(a).(b) Assumc that L j , and k each have two leveIs and show the detailed diagram as in Figure 14,1(b].(c) Describe (in words) the exchangeability relationships that characterize
14.4 Consider the collapsed hierarchical model (14.6).(a) Write out the matrices J, K. I,, as in Equation (14.3). Assume that i. j , and k each have two levels; make clear thc ordering of the indices(iJ, k) labeling each row and column of these matrices.(b) Write the marginal covariance matrix of y
Each coin in a collection of bent coins has a different probability of coming up heads when tossed; the probability for each coin i s drawn h m a Beta distribution. Each coin is tossed several times with outcome recorded as I if heads, 0 if tails. Because the lighting is poor, the coin tosser
14.6 The genetic composition (genome) of a person is derived from that of the parents, but the way they are combined involves a random process. We will consider the process for a small group of' related individuals. Elaine and Juan have two children. Fred and Rosalia. Shanti and Nur have a child
Consider the model (14.10) and suppose that there is a single observation=y, from each Level 2 unit i, and thatb, = b is the same for every unit(i.e., the regression is a constant).(a) Derive the negative binomial marginal distribution of y, I ( I , h. Show that the probability parameter of this
Consider the random coefficient model (14.7).(a) Write the Level 1 conditional likelihood (given the variance components)for fit, i.e., the density of the part of the data that depends on /Il.(b) What is the posterior distribution of 8, I y,. A, 02,T ? (Hint:c ombine a normal prior and a normal
14.9 Consider the following three-level hierarchical model Y y - N O , , var,o‘,>, 0, - “P,, T 2 h of - IG(v,, V Z ) , pt -” “1. CU2L T2 I ~ ( V I t 112h where j e l l , ..., n ) , j e { l ., . . * r , } , and ( r . , ,v2,1.w2,~f , ,q2i)s known.(a) Derive the closed-form conditional
14.10 In a subject area that interests you, find a data set that has a hierarchical(clustered) structure and analyse it using any convenient software
15.1 Suppose you have data that consist of n = 10 independent and joint normally distributed random vectors representing multivariate data intensities.The data might correspond to the output of micro arrays, as used in biology, gray levels, as used in spatial analysis and imaging, or any other
Explain how you might assess the hyperpararrteters of the Bayesian factor analysis model when sample sizes are large.
What might be the advantages of standarkkg the data vectors (with respect to location and scale) before carrying out a Bayesian factor analysis?
Of what use might factor scores be in: marketing analysis; a political science voting context; an astronomy context; a sociology context; a biology context; and a medical context?
Suppose you carry out an exploratory Bayesian factor analysis (you had no idea in advance of collecting data of how many factors there might be) and you find there are four factors; but the four factors do not seem to correspond to anything real. What would you conclude?
Explain how you would go about fmding interval estimates of factor loadings in a Bayesian factor analysis containing a large number of data vectors.Why should you not be concerned about the possible biases of Bayesian estimators in the factor analysis model?What is the main advantage of using MCMC
Suppose a Bayesian factor analysis is contemplated but some of the observable variables in the data vectors are jointly continuous, and others are jointly discrete. What ways might you explore to carry out the analysis?Suppose that examination in each dimension, separately, of the data vectors
16.1 Suppose there are two normal populations that are each two-dimensional with unknown parameters. We want to classify an observation z. Suppose the training samples give x = (2,3)' S = x = (3,1)' == 3 (14) S = (22) based upon N = N = 10 observations. Let the observed vector be given by z =
16.2* Suppose there are three bivariate normal populations with training sample statistics as in Exercise 16.1, but, in addition, we know N = N = N = N = 10, and x = (0, 0), S = ( }). 3 Assuming the prior odds for all three populations are the same, classify z = (2.2)' into one of the three
16.3* For the classification problem in Section 16.1 adopt a natural conjugate prior family for (0,, A), instead of the vague prior family used there, and find: (a) The joint posterior density of 0,, A,, given (;, V, ;); (b) The predictive density of (z | x, V, ); (c) The posterior classification
16.4* Explain the classification concept behind the notion of "second guessing undecided respondents," as discussed in Section 16.8.
16.5* In what types of situations would we be likely to encounter large fractions of "undecided" respondents, in the sense presented in Section 16.8? 16.7
16.6* While it is a general principle that it is better to have more information than less, why might it be better to have very few subsidiary questions in the undecided respondents problem? (Hint: see Press and Yang, 1974.)
What are the arguments for and against merging observations already classified into say, , with its training sample, and using them to better estimate the parameters of r, in order to classify new observations?
Suppose you would like to classify an unknown observation vector (px 1) into one of two populations or for which both ", and 16.8
16.9 2 are multinomial populations with probability mass functions /(x) and f2(x). How would you develop a Bayesian classification procedure for classifying z into ?
You would like to use Bayesian classification methods to classify an unknown observation vector z: (px 1) into o , where ~ N(0,2),i=1,2. You have training data with N, observation vectors believed to come from , and N believed to come from 2. Suppose there are errors in the training data so that
Consider a survey of nurses’ opinions of their working conditions. What type of variables are: (i) length of service (ii) staff grade (iii) age (iv) salary(v) number of patients seen in a day (vi) possession of a degree.
What differences do you think are there in a discrete measurement such as shoe size, and a discrete measurement such as family size?
Many continuous variables are dichotomised to make them easier to understand e.g. obesity (body mass index >30 kg/m2) and anaemia(haemoglobin level
If a relative risk is quoted, what is the absolute risk difference? Is this a very small number? Beware of reports that only quote relative risks and give no hint of the absolute risk!
If an odds ratio is quoted, is it a reasonable approximation to the relative risk? (Ask what the size of the risk in the two groups are.)
The blood group of 55 women diagnosed as suffering from thromboembolic disease and 145 healthy women are displayed in Table 2.7.Table 2.7 Blood group distribution for healthy women and those with thromboembolic disease Blood Women with Healthy women Total group thromboembolic disease A 32 51 83 B 8
Ninety-nine pregnant women, with dystocia (diffi cult childbirth or labour), were allocated at random to receive immersion in water in a birth pool(Intervention group: Labour in water 49 women) or standard augmentation for dystocia (Control group: Augmentation 50 women) in a randomised controlled
A newspaper headline states that a new drug for early stage breast cancer reduces the risk of recurrence of the disease by 50%. What other information would you like before deciding to take the drug?
Is the number of subjects involved clearly stated?
Are appropriate measures of location and variation used in the paper?For example, if the distribution of the data is skewed, then has the median rather the mean been quoted? Is it sensible to quote a standard deviation, or would a range or interquartile range, be better? In general do not use SD
On graphs, are appropriate axes clearly labelled and scales indicated?
Do the titles adequately describe the contents of the tables and graphs?
Do the graphs indicate the relevant variability? For example, if the main object of the study is a within-subject comparison, has within-subject variability been illustrated?
Does the method of display convey all the relevant information in a study?For example if the data are paired, is the pairing shown? Can one assess the distribution of the data from the information given?
The age (in years) of a sample of 20 motor cyclists killed in road traffi c accidents is given below.18 41 24 28 71 52 15 20 21 31 16 24 33 44 20 24 16 64 24 32(i) Draw a dot plot and histogram. Is this distribution symmetric or skewed?(ii) Calculate the mean, median and mode.(iii) Calculate the
The table below shows the height of 12 fathers and their fully-grown sons.Father’s height Son’s height(cm) (cm)190 189 184 186 183 180 182 179 179 187 178 184 175 183 174 171 170 170 168 178 165 174 164 165(i) Draw a scatter plot of father’s height versus son’s height.(ii) From the graph
To whom has the diagnostic test been applied? It is possible that characteristics of the patients or stage and severity of the disease can infl uence the sensitivity of the test. For example, it is likely that a test for cancer will have greater sensitivity for advanced rather than early disease.
How has the group of patients used in the analysis been selected, and in particular how has the decision to verify the test by the gold standard been made? A common error is to select patients in some manner for verifi cation of a previous diagnosis; this usually leads to positive tests being
How have the investigators coped with specimens they were not able to interpret? If the reason for failure to interpret is essentially random, and is unrelated to disease status, then the test characteristics can be estimated.If it is related to disease status then these results cannot be ignored
Did the investigator who provided the diagnostic test result know other clinical results about the patients? Diagnostic tests are usually carried out during or, in conjunction with, the clinical examination. Where there is an element of subjectivity in a test, such as an ECG stress test, a
Was the reproducibility of the test result determined? This could be done by repeating the test with different operators, or at different times, or with different machines, depending on the circumstances.
Did the patients who had the test actually benefi t as a consequence of the test?
How good is the gold standard? An ideal gold standard either may not exist or be very expensive or invasive and therefore not carried out. In this case, the test used as the gold standard may be subject to error, which turn will make the estimates of sensitivity and specifi city problematical.
In a group of patients presenting to a hospital casualty department with abdominal pain, 30% of patients have acute appendicitis. Seventy per cent of patients with appendicitis have a temperature greater than 37.5°C, 40% of patients without appendicitis have a temperature greater than 37.5°C.(a)
A new laboratory test is developed for the diagnosis of rectal cancer.(a) A sensitivity of 85% implies that 15% of patients with rectal cancer will give negative fi ndings when tested.(b) A specifi city of 95% implies that 5% of patients with a negative test will actually have rectal cancer.(c) A
Three tests (A, B and C) for the diagnosis of breast cancer in premenopausal women were assessed against a ‘gold standard’ taken to be 100%accurate. Their sensitivities were A 90%, B 85%, C 80%. Their specifi cities were A 100%, B 90%, C 95%. All three tests carried the same cost, and none was
What is the population from which the sample was taken? Are there any possible sources of bias that may affect the estimates of the population parameters?
Have reference ranges been calculated on a random sample of healthy volunteers? If not, how does this affect your interpretation? Is there any good reason why a random sample was not taken?
For any continuous variable, are the variables correctly assumed to have a Normal distribution? If not, how do the investigators take account of this?
A GP estimates that about 50% of her patients have ‘trivial’ problems.What is the probability that four out of fi ve patients in one evening’s surgery have trivial problems?
Suppose a hospital Accident and Emergency department has an average of 10 new emergency cases per hour. Calculate the probability of observing exactly 10 new emergency cases in any given hour.
The systolic blood pressure of 16 middle age men before exercise has a Normal distribution with a mean of 141.1 mmHg and a standard deviation of 13.62 mmHg. What is the probability having a systolic blood pressure of 160 mmHg or higher?
The diastolic blood pressures (DBP) of a group of young men are Normally distributed with mean 70 mmHg and a standard deviation of 10 mmHg.Decide whether the following statements are true or false.(i) About 95% of the men have a DBP between 60 and 80 mmHg.(ii) About 50% of the men have a DBP of
Given the sample described in question 4.(i) What is the probability of a young man having a DBP of 95 mmHg or above?(ii) What is the probability of a young man having a DBP of 55 mmHg or less?(iii) What proportion of young men have a DBP between 55 mmHg and 95 mmHg?
A GP and partners have 6000 patients and refer 27 patients to neurology in one year. In the health authority region, there are 1400 neurology referrals from a population of 500 000.Is this GP’s referral rate unusually high?
When authors give the background information to a study they often quote fi gures of the form a ±b. Although it is usual that a represents the value of the sample mean, it is not always clear what b is. When the intent is to describe the variability found in the sample then b should be the SD.When
A useful mnemonic to decide which measure of variability to use is: ‘If the purpose is Descriptive use Standard Deviation, if the purpose is Estimation, use the Standard Error’.
What is the population from which the sample was taken? Are there any possible sources of bias that may affect the estimates of the population parameters?
Have reference ranges been calculated on a random sample of healthy volunteers? If not, how does this affect your interpretation? Is there any good reason why a random sample was not taken?
Have confi dence intervals been presented? Has the confi dence level been specifi ed (e.g. 95%)?
Has a Normal approximation been used to calculate confi dence intervals for a Binomial proportion or Poisson rate? If so, is this justifi ed?
As the size of a random sample increases:(a) The standard deviation decreases.(b) The standard error of the mean decreases.(c) The mean decreases.(d) The range is likely to increase.(e) The accuracy of the parameter estimates increases.
A 95% confi dence interval for a mean(a) Is wider than a 99% confi dence interval.(b) In repeated samples will include the population mean 95% of the time.(c) Will include the sample mean with a probability of 1.(d) Is a useful way of describing the accuracy of a study.(e) Will include 95% of the
Assume that the mid-upper arm circumference in a population of rural Indian children aged 12 to 60 months follows a Normal distribution with unknown mean, m. Ten samples each of four children are drawn from this population by a formal process of random sampling with replacement. The results are
Table 6.6 shows ten random samples of size 16 drawn from the same population of Indian children.(a) Display as a dot plot alongside the previous one, the means of the ten random samples of size 16 shown in Table 6.6.(b) Calculate the standard error of the mean using the standard deviation of random
(a) Estimate the 95% confi dence interval for one selected sample of size 4 (sample number 10 in Table 6.5) and display this on the dot plot for n = 4.(b) Estimate the 95% confi dence interval for one selected sample of size 16 (sample number 4 in Table 6.5) and display this on the dot plot for n =
A surgeon in a large hospital is investigating acute appendicitis in people aged 65 and over. As a preliminary study he examines the hospital case notes over the previous 10 years and fi nds that of 120 patients in this age group with a diagnosis confi rmed at operation 73 were women and 47 were
Have clinical importance and statistical signifi cance been confused?
Is it reasonable to assume that the continuous variables have a Normal distribution?
Have confi dence intervals of the main results been quoted?
Is the result medically or biologically plausible and has the statistical signifi cance of the result been considered in isolation, or have other studies of the same effect been taken into account?
Gaffney et al (1994) compared 141 babies who developed cerebral palsy to a control group of (control) babies made up from the babies who appeared immediately after each cerebral palsy case in the hospital delivery book. The corresponding hospital notes were reviewed by a researcher, who was blind
A randomised controlled trial was conducted to investigate the cost-effectiveness of community leg ulcer clinics (Morrell et al 1998). A total of 233 patients were randomly allocated to either intervention (120 patients, treatment at a leg ulcer clinic) or control (113, usual care at home by
A study by Taylor et al (2002) investigated whether the measles, mumps and rubella (MMR) vaccination was associated with bowel problems and developmental regression in children with autism. The authors reviewed the case notes for 278 children with core autism and 195 with atypical autism from fi ve
A UK study by Peacock et al (1995) of factors affecting the outcome of pregnancy among 1513 women reported that the overall incidence of preterm births was 7.5%, SE 0.68% and 95% CI 6.1 to 8.8%.(a) What is meant by SE = 0.68%?(b) What is meant by 95% CI 6.1 to 8.8%?(c) How would the confi dence
Have clinical importance and statistical signifi cance been confused?
Has the sample size been taken into account when determining the choice of statistical tests; that is, are small-sample tests used when appropriate?
Is it reasonable to assume that the continuous variables have a Normal distribution?
Have paired tests been utilised in the appropriate places?
Have confi dence intervals of the main results been quoted?
Is the result medically or biologically plausible and has the statistical signifi cance of the result been considered in isolation, or have other studies of the same effect been taken into account?
Table 8.12 shows the 24 hour total energy expenditure of groups of lean and obese women. The aim of this study was to compare total energy expenditure between the lean and obese women.(a) Write out a suitable null and alternative hypothesis for this problem and data.(b) Do these data suggest that
Table 8.13 shows the results of a randomised, double-blind, placebo-controlled trial examining whether patients with chronic fatigue syndrome (CFS) improved 6 weeks after treatment with intramuscular magnesium.The group who received the magnesium were compared to a group who received a placebo and
A prospective double-blind clinical trial was conducted in 11 young, health, normally menstruating female subjects to detect any differences in energy intake in the pre and post phases of the menstrual cycle. The data is shown in Table 8.14.(a) Write out a suitable null and alternative hypothesis
When a correlation coeffi cient is calculated, is the relationship likely to be linear?
Are the variables likely to be Normally distributed?
Is a plot of the data in the paper? (This is a common omission.)

Showing 4300 - 4400 of 6202

First
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
Last

Medical Statistics 4th Edition Michael J. Campbell, David Machin, Stephen J. Walters - Solutions

Step by Step Answers