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biostatistics

Applied Biostatistics For The Health Sciences 2nd Edition Richard J. Rossi - Solutions

Notation When randomly selecting an adult, A denotes the event of selecting someone with blue eyes. What do P(A) and P1A2 represent?
Cell Phones and Cancer A study of 420,095 Danish cell phone users resulted in 135 who developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute). When comparing this sample group to another group of people who did not use cell phones, it was
Sleepiness In a clinical trial of OxyContin (oxycodone) used for pain relief, 227 subjects were treated with OxyContin and 52 of them experienced sleepiness (based on data from Purdue Pharma L.P.). If OxyContin has no effect on sleepiness, the probability of getting these sample results by chance
Clinical Trial of Tamiflu Clinical trials involved the use of Tamiflu (oseltamivir phosphate)for treating flu patients. Among 724 patients treated with Tamiflu, 72 (or about 10%)experienced nausea. (An untreated group experienced a 6% rate of nausea.) If Tamiflu really has no effect on nausea,
Predicting Gender A study addressed the issue of whether pregnant women can correctly predict the gender of their baby. Among 104 pregnant women, 57 correctly predicted the gender of their baby (based on data from “Are Women Carrying ‘Basketballs’…,” by Perry, DiPietro, Constigan, Birth,
Four Children Using the same sample space and assumption from Exercise 35, find the probability that when a couple has four children, all four are of the same gender.
Four Children Exercise 33 lists the sample space for a couple having three children. After identifying the sample space for a couple having four children, find the probability of getting three girls and one boy (in any order).
Three Children Using the same sample space and assumption from Exercise 33, find the probability that when a couple has three children, there are exactly two girls.
Three Children Use this sample space listing the eight simple events that are possible when a couple has three children (as in Example 2 on page 122): {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. Assume that boys and girls are equally likely, so that the eight simple events are equally likely. Find
X-Linked Genetic Disease Men have XY (or YX) chromosomes and women have XX chromosomes. X-linked recessive genetic diseases (such as juvenile retinoschisis) occur when there is a defective X chromosome that occurs without a paired X chromosome that is not defective.In the following, represent a
Genetics: Eye Color Each of two parents has the genotype brown>blue, which consists of the pair of alleles that determine eye color, and each parent contributes one of those alleles to a child. Assume that if the child has at least one brown allele, that color will dominate and the eyes will be
Car Rollovers In a recent year in the United States, 83,600 passenger cars rolled over when they crashed, and 5,127,400 passenger cars did not roll over when they crashed. Find the probability that a randomly selected passenger car crash results in a rollover. Is it unlikely for a car to roll over
Online Medicine In a survey, 933 respondents say that they seek medical information online and 139 other respondents say that they never seek medical information online. What is the probability that a randomly selected person never seeks medical information online? Is it unlikely for someone to
Guessing Birthdays On their first date, Kelly asks Mike to guess the date of her birth, not including the year.a. What is the probability that Mike will guess correctly? (Ignore leap years.)b. Would it be unlikely for him to guess correctly on his first try?c. If you were Kelly, and Mike did guess
Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the expected
YSORT Gender Selection MicroSort’s YSORT gender-selection technique is designed to increase the likelihood that a baby will be a boy. At one point before clinical trials of the YSORT gender-selection technique were discontinued, 291 births consisted of 239 baby boys and 52 baby girls (based on
Drug Testing Job Applicants Find the probability of selecting someone who does not use drugs. Does the result appear to be reasonable as an estimate of the proportion of the adult population that does not use drugs?25. XSORT Gender Selection MicroSort’s XSORT gender selection technique was
Drug Testing Job Applicants Find the probability of selecting someone who uses drugs. Does the result appear to be reasonable as an estimate of the “prevalence rate” described in the Chapter Problem?
Drug Testing Job Applicants Find the probability of selecting someone who got a result that is a false positive. Who would suffer from a false positive result? Why?
Drug Testing Job Applicants Find the probability of selecting someone who got a result that is a false negative. Who would suffer from a false negative result? Why?
Job Applicant Mistakes Based on an Adecco survey of hiring managers who were asked to identify the biggest mistakes that job candidates make during an interview, there is a 50-50 chance that they will identify “inappropriate attire.”19. Square Peg Sydney Smith wrote in “On the Conduct of the
Randomness When using a computer to randomly generate the last digit of a phone number to be called for a survey, there is 1 chance in 10 that the last digit is zero.
Sleepwalking Based on a report in Neurology magazine, 29.2% of survey respondents have sleepwalked.
Genes One of the four DNA bases of A, G, C, and T is randomly selected, and the result is G. Assume that the four DNA bases are equally likely.
MCAT Test When making a random guess for an answer to a multiple-choice question on an MCAT test, the possible answers area, b,c, d,e, so there is 1 chance in 5 of being correct.
Testing If you make a random guess for the answer to a true>false test question, there is a 50-50 chance of being correct.
5 girls. In Exercises 9–12, assume that 50 births are randomly selected. Use subjective judgment to describe the given number of girls as (a) significantly low, (b) significantly high, or (c) neither significantly low nor significantly high.
23 girls. In Exercises 9–12, assume that 50 births are randomly selected. Use subjective judgment to describe the given number of girls as (a) significantly low, (b) significantly high, or (c) neither significantly low nor significantly high.
26 girls. In Exercises 9–12, assume that 50 births are randomly selected. Use subjective judgment to describe the given number of girls as (a) significantly low, (b) significantly high, or (c) neither significantly low nor significantly high.
47 girls. In Exercises 9–12, assume that 50 births are randomly selected. Use subjective judgment to describe the given number of girls as (a) significantly low, (b) significantly high, or (c) neither significantly low nor significantly high.
Births Example 2 in this section includes the sample space for genders from three births.Identify the sample space for the genders from two births.
Avogadro Constant If you are asked on a quiz to give the first (leftmost) nonzero digit of the Avogadro constant and, not knowing the answer, you make a random guess, what is the probability that your answer is the correct answer of 6?
Penicillin “Who discovered penicillin: Sean Penn, William Penn, Penn Jillette, Alexander Fleming, or Louis Pasteur?” If you make a random guess for the answer to that question, what is the probability that your answer is the correct answer of Alexander Fleming?
Identifying Probability Values Which of the following are probabilities?0 3>5 5>3 -0.25 250% 7:3 1 50@50 5:1 0.135 2.017
Subjective Probability Estimate the probability that the next time a physician walks into a patient’s room and turns on a light switch, she discovers that the light bulb does work.
Births In Example 4 “Three Children of the Same Gender” it was noted that in reality, the probability of a boy is 0.512 instead of 0.5. Let A denote the event of getting a boy when a baby is born. What is the value of P1A2?
Probability Given that the following statement is incorrect, rewrite it correctly: “The probability of a baby being born a boy is 50-50.”
Probability Rewrite the following statement with the probability expressed as a number with a decimal format: “The probability of selecting someone with blue eyes is 35%.”
Using the Body Fat data set,(a) fit a logistic regression model for the response variable Obese using the explanatory variables Height, Chest, and Hip.(b) classify all of the observed values.(c) determine the overall error rate.(d) estimate ????1, the error rate for observations classified not
For the logistic classifier in Exercise 10.59(???? = 100), there were 26 misclassified observations. Of the 26 misclassifications, there were 14 misclassifications among the 59 classified as not having evidence of CHD, and among the 41 observations classified as having evidence of CHD there were 14
A linear logistic regression model was fit to the Body Fat data set for classifying an individual as obese or not obese based on the explanatory variables abdomen circumference and height. Use the fitted logistic regression model logit(????) = −20.2 + 0.43Abdomen − 0.37Height to classify an
A simple linear logistic regression model was fit to the Coronary Heart Disease data set for classifying an individual as having evidence of coronary heart disease(CHD) or not having evidence of coronary heart disease based on the explanatory variable age. Use the fitted logistic regression model
A simple linear logistic regression model was fit to the Body Fat data set for classifying an individual as obese (1) or not obese (0) based on the explanatory variable abdomen circumference. Use the fitted logistic regression model logit(????) = −41.99 + 0.39Abdomen to classify an observation as
For the Body Fat data set with Overweight as the response variable and Age, Height, Neck, Chest, Hip, Ankle, and Biceps as the explanatory variables, Table 10.23 contains the best models according to BIC for considering 0 to 8 explanatory variables in the model. Use the information in Table 10.23
Table 10.22 contains summary information on the fit of the best two logistic regression models based on a sample of ???? = 313 observations for models including???? = 1, 2,…, 7 explanatory variables. Use the information in Table 10.22 to answer the following questions.(a) Compute the value of BIC
Suppose the BIC statistic value for a logistic regression model with five explanatory variables is BIC5 = 234.56 and the BIC statistic value for a logistic regression model with only three of the five explanatory variables is ????????????3 = 235.19, which model would be best according to the Bayes
What is the formula for computing the BIC value associated with a logistic regression model?
Use the Birth Weight data set to answer the following:(a) Fit the logistic regression interaction model with birth weight classification(LOW) as the response variable with mother’s smoking status (SMOKE) and mother’s race (RACE) as the explanatory variables.(b) Test the goodness-of-fit of the
Use the Intensive Care Unit data set to answer the following:(a) Fit the logistic regression interaction model with vital status (STA) as the response variable with age (AGE), CPR prior to admission (CPR), systolic blood pressure at admission (SYS), and heart rate at admission (HRA) as the
The information in Figures 10.20 and 10.21 are based on the ICU data set. Figure 10.23 results from fitting the logistic regression interaction model with vital status(STA) as the response variable with age (AGE), CPR prior to admission (CPR), systolic blood pressure at admission (SYS), and heart
The information in Figures 10.18 and 10.19 are based on the ICU data set. Figure 10.18 results from fitting the logistic regression interaction model with vital status(STA) as the response variable with age (AGE) and CPR prior to admission(CPR) as the explanatory variables, and Figure 10.19 results
The MINITAB output given in Figure 10.17 summarizes the fit of the logistic regression models logit(????) = ????0 + ????1NDRUGTX + ????2RACE + ????3RACE*NDRUGTX + ????4TREAT and logit(????) = ????0 + ????1NDRUGTX + ????4TREAT Use the information in Figure 10.17 to test ????0 ∶ ????2 = ????3 = 0.
The MINITAB output given in Figure 10.16 summarizes the fit of the logistic regression modelslogit(????) = ????0 + ????1AGE + ????2SYS + ????3HRA and logit(????) = ????0 + ????1AGE Use the information in Figure 10.18 to test ????0 ∶ ????2 = ????3 = 0. Model: AGE, SYS, HRA Term Constant 1.06 AGE
How many degrees of freedom would the drop-in-deviance have in Exercise 10.46?
What is the form of the drop-in-deviance test statistic for comparing the models and logit(p) Bo+BX +X+ B3X3 + 4X4 logit(p) Bo+BX
In the article “Multivariate explanatory model for sporadic carcinoma of the colon in Dukes stages I and IIa ” published in International Journal of Medical Sciences(Villadiego-Sanchez, et al.,2009), the authors reported the fitted logistic model in Table 10.21. Use the information in Table
Using Prostate Cancer Study data set, fit a logistic regression model with capsule penetration (CAPSULE) as the response variable with explanatory variables age(AGE), prostatic specific antigen (PSA), and tumor volume (VOL). For the resulting fitted model,(a) determine whether or not there are
In the article “Hypoglycemia in patients with type 2 diabetes mellitu” published in the Archives of Internal Medicine (Miller et al., 2001), the authors reported the odds ratios for a logistic regression model for predicting the occurrence of hypoglycemia given in Table 10.20. Use Table 10.20
The MINITAB output given in Figure 10.15 resulted from fitting a logistic regression model to the binary response variable prostatic capsule tumor penetration(CAPSULE) and the explanatory variables age (AGE) and prostatic specific antigen(PSA) on the Prostate Cancer Study data set. Use the
The MINITAB output given in Figure 10.14 resulted from fitting a logistic regression model to the binary response variable vital status (STA) and the explanatory variables age (AGE), systolic blood pressure (SYS), and heart rate (HRA) on the Intensive Care Unit data set. Use the information in
For each of the scenarios in Exercise 10.39 test ????0 ∶ ????1 = 0 and compute the????-value associated with the test.
For the logistic regression model logit(????) = ????0 + ????1????1 + ????2????2 + … + ???????????????? and a sufficiently large sample, compute a 95% confidence interval for the odds ratio associated with the explanatory variable ????1 when maximum likelihood estimate is(a) ˆ????1 = −1.12 with
For the logistic regression model logit(????) = ????0 + ????1????1 + ????2????2 + … + ????????????????, what is the formula for computing a (1 − ????) × 100% confidence interval for(a) the intercept?(b) the logistic regression coefficient associated with the explanatory variable ????1?(c) the
Using the Birth Weight data set with the response variable LOW, fit the model logit(????) = ????0 + ????1AGE + ????2 LWT + ????3 SMOKE and then(a) test the goodness-of-fit for this model.(b) create and interpret a plot of the standardized residuals versus the observation index.(c) create and
What is the general rule for identifying points to be investigated using the Δ????2 andΔ???? model diagnostics?
What are the two model diagnostics that can be used to detect outliers and influential explanatory conditions?
Use the plot of the standardized Pearson residuals versus the observation index given in Figure 10.13 to answer the following questions.(a) Does this residual plot suggest there are observations for which the model is not fitting well?(b) How should the influence of an observation for which there
Why are the standardized Pearson residuals generally used instead of the Pearson residuals?
What is the formula for computing a Pearson residual?
Use the MINITAB output given in Figure 10.12 for the logistic regression model relating the variable Overweight,1 when BMI≥ 25 and 0 otherwise, with explanatory variables Abdomen and Height given in Figure 10.12 to answer the following questions.(a) Is there any evidence of a collinearity problem
Use the MINITAB output given in Figure 10.11 for the logistic regression model relating the variable Overweight, 1 when BMI≥ 25 and 0 otherwise, to answer the following questions.(a) Write down the equation of the fitted logistic regression model.(b) Write down the equation of the estimate of
In the article “Socioeconomic Gradients and Distribution of Diabetes, Hypertension, and Obesity in India” published in JAMA Network Open (Corsi and Subramanian, 2019), the authors reported the odds ratios given in Table 10.19 for a logistic regression model for the incidence of diabetes. Use
In the article “Racial Disparities in Route of Hysterectomy for Benign Indications Within an Integrated Health Care System” published in JAMA Network Open (Zaritsky, et al., 2019), the authors reported the odds ratio from a logistic regression model for individuals receiving a minimally
What is the relationship between the maximum likelihood estimates of the logistic regression coefficients and the likelihood function?
What is the likelihood function for a logistic regression model?
What method is used for fitting a logistic regression model?
What does it mean when there is extra-binomial variation in the response variable?
How can the explanatory variables be checked for collinearity?
What does it mean when the explanatory variables are collinear?
What are the steps that must be carried out before using a fitted logistic regression model for making statistical inferences?
What are the assumptions of a logistic regression model?
If the true logistic model is logit([????(???? = 1|⃗????)]) = 1.2− 0.8????, determine(a) the probability that ???? = 1 when ???? = 2.5.(b) the probability that ???? = 1 when ???? = 4.(c) the odds ratio for the probability that ???? = 1 when ???? = 2.5 and ???? = 4.(d) what happens to the
In a logistic regression model what is the form of(a) logit[????(???? = 1|⃗????)].(b) ????(???? = 1|⃗ ????).(c) ????(???? = 0|⃗ ????).
Write down the form of the logistic regression model in terms of logit(????) for(a) the model based on the explanatory variables ???? and ????2.(b) the model based on the explanatory variables ????1,????2, and ????3.(c) the interaction model based on a single dummy variable and explanatory
Compute the value of logit(????) when(a) ???? = 0.4.(b) ???? = 0.75.(c) ???? = 0.9.
What is the logit transformation for a probability ?????
Using the Birth Weight data set(a) create a 2×2 contingency table that summarizes the percentage of babies weight classification (LOW) by mother’s smoking status (SMOKE).(b) estimate the odds ratio for LOW=1 for comparing smoking status.
In the article “Tumor-associated antigen TA-90 immune complex assay predicts subclinical metastasis and survival for patients with early stage melanoma” published in the journal Cancer (Kelley et al., 1998), the authors reported the data given in Table 10.18 for a study investigating the
In the article “Improving the health of African-american men: experiences for the Targeting Cancer in Blacks (TCiB) Project” published in The Journal of Mens Health & Gender (Fort, 2007), the author reported the data given in Table 10.17 summarizing the responses of n = 937 African-American men
In the article “Identification of patients at low risk for recurrent venous thromboembolism by measuring thrombin generation” published in the Journal of the American Medical Association (Hron et al., 2006), the authors reported the data given in Table 10.16 on the recurrence of venous
Use the information in Table 10.15 to compute the odds ratio for ???? = Yes and???? = No.
Use the information in Table 10.14 to compute the odds ratio for ???? = 0 and ???? = 1.
What does it mean when the odds ratio is(a) less than 1.(b) equal to 1.(c) more than 1.
For a binary variable ???? and a dichotomous explanatory variable ????, how is the odds ratio computed.
For a binary variable ????, compute the odds that ???? = 1 when(a) ????(???? = 1) = 0.25.(b) ????(???? = 1) = 0.6.(c) ????(???? = 1) = 0.01.
For a binary variable ????, what does it mean(a) when the odds that ???? = 1 is 1?(b) when the odds that ???? = 1 is 3?
For a binary response variable ????, how are the odds that ???? = 1 computed?
In a study of obesity, a researcher is interested in factors that influence the probability that an individual has a body mass index (BMI) of 30 or more. Create a binary response variable that could be used in modeling the probability that an individual has a BMI of 30 or more.
What is the difference between the type of response variable that is modeled with a linear regression model and a logistic regression model?
What is a(a) dichotomous variable?(b) binary variable?

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