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biostatistics

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

What does it mean when the effects of two variables are said to be confounded?
What is(a) an extraneous variable? (b) confounding variable?
What distinguishes an experiment from an observational study?
What is an observational study?
In the article“Validation of a melanoma prognostic model” published in the Archives of Dermatology (Margolis et al., 1998), the authors reported a logistic regression model for the 5-year probability of death for melanoma patients. The variables in the model are age coded as 1 if greater than
In the article “Predicting 10-year survival of patients with primary cutaneous melanoma: corroboration of a prognostic model” published in Cancer(Sahin, 1997), the authors reported a logistic regression model for the 10-year survival probability of melanoma patients. The variables in the model
For the logistic regression model logit = ????0+????1????1+????2????2 suppose that ˆ????1 = −1.49 and ????????(ˆ????1) = 0.18.(a) Test ????0 ∶ ????1 = 0 at the ???? = 0.05 level. Be sure to compute the ????-value for this test.(b) Compute a 95% confidence interval for ????1.(c) Estimate the
When fitting a logistic regression model, what is the large sample distribution ofˆ????????se(ˆ???????? )when ???????? = 0?
In the logistic regression model logit(????(⃗????)) = ????0 + ????1????1 + ????2????2 +⋯+ ????????????????what does(a) ???????? represent? (b) e???????? represent?
What are the differences between a logistic regression model of a survival probability and the proportional hazards model of the hazard function?
In terms of the logit function what is the survival probability at time ????⋆?
How are the observations that are censored before time ????⋆ used in a logistic regression model for estimating ????(????⋆)?
What is the response variable in a logistic regression model of the 5-year survival probability?
Under what conditions would it be appropriate to use a logistic regression model to model the survival probability at a fixed time ????⋆?
Under what conditions is a model a parametric model?
Use the results of the Bayes Information Criterion variable selection procedure for screening three explanatory variables in a proportional hazards model given in Table 13.17 to answer the following:(a) Which two models are the best fitting models according to the Bayes Information Criterion?(b) If
In the article “Risk Factors Associated With Ischemic Stroke in Japanese Patients With Nonvalvular Atrial Fibrillation” published in JAMA Network Open (Okumura, 2020), the authors reported the results of a study on the risk factors that are associated with ischemic stroke in Japanese patients
In the article “Increased Pulse Pressure and Risk of Heart Failure in the Elderly”published in JAMA (Chae, eta al.,1999), the authors reported the results of a study on pulse pressure, an index of arterial stiffening, and congestive heart failure (CHF)in the elderly. The information in Table
For the proportional hazards model ln[ℎ(????)] = ln[ℎ0(????)] + ????1????1 + ????2????2, suppose that ˆ????1 = 0.87, ????????(ˆ????1) = 0.91, ˆ????2 = −1.57, and ????????(ˆ????2) = 0.69.(a) Test ????0 ∶ ????1 = 0 at the ???? = 0.05 level. Be sure to compute the ????-value for this
For the proportional hazards model ln[ℎ(????)] = ln[ℎ0(????)] + ????1????1 + ????2????2, suppose that ˆ????1 = −0.73 and ????????(ˆ????1) = 0.26.(a) Test ????0 ∶ ????1 = 0 at the ???? = 0.05 level. Be sure to compute the ????-value for this(b) Compute a 95% confidence interval for
When fitting a proportional hazards model, what is the large sample distribution ofˆ????????se(ˆ???????? )when ???????? = 0?
In the proportional hazards model ln [ℎ(????)] = ln [ℎ0(????)] + ????1????1 + ????2????2 +⋯+ ????????????????what does(a) ???????? represent? (b) e???????? represent?
When a proportional hazards coefficient is negative, does this indicate that risk ratio increases or decreases when the value of the explanatory variable is increased?
What is the risk ratio in a proportional hazards model?
What is the risk ratio?
What is the proportional hazards model for(a) a single explanatory variable? (b) ???? explanatory variables?
What is the hazard function?
Under what conditions is a model a semiparametric model?
The Kaplan–Meier estimates of the survival functions for three treatments used in treating ovarian cancer are given in Figure 13.7, and the results of the log-rank test are given in Table 13.14. Use the information given in Figure 13.7 and Table 13.14 to answer the following:(a) Is there
Use the Kaplan–Meier estimates given in Figure 13.6 and the summary of the logrank test given in Table 13.13 to answer the following questions.(a) Is there sufficient evidence in the observed sample data to conclude the survival functions are different for the treatment and control groups?
What does it mean when the ????-value associated with the log-rank test for comparing two survival functions is(a) less than ????? (b) larger than ?????
Which hypothesis test is used to test the equality of two or more survival functions?
Use the Kaplan–Meier estimate given in Figure 13.5 to answer the following questions.(a) Estimate the median survival time.(b) Estimate ????(9).(c) If ????????(ˆ????(5)) = 0.052, compute an approximate 95% confidence interval for the value of S(5).
Use the Kaplan–Meier estimate in Figure 13.4 to answer the following:(a) Estimate the median survival time.(b) Estimate ????(50).(c) If se(ˆ????(50)) = 0.058, compute an approximate 95% confidence interval for the value of ????(50). 100 80- Percent 660 40- 20- 0. 0 10 20 20 50 60 T 50 60 60 30
Use the information in Table 13.12 to answer the following:(a) Estimate ????(????1), ????(????2), ????(????3), ????(????4), ????(????5), ????(????6), ????(????7), and ????(????8).(b) Plot the estimated survival function.(c) If se(ˆ????(30)) = 0.072, compute an approximate 95% confidence interval
Use the information in Table 13.11 to answer the following questions.(a) Estimate ????(????1), ????(????2), ????(????3), ????(????4), and ????(????5).(b) Plot the estimated survival function.(c) If se(ˆ????(24)) = 0.031, compute an approximate 95% confidence interval for the value of ????(24).(d)
Use the information in Table 13.10 to answer the following the questions.(a) How many patients were censored at time ????3?(b) Estimate ????1, ????2, ????3, ????4, ????5, and ????6.(c) Estimate ????(????1), ????(????2), ????(????3), ????(????4), ????(????5), and ????(????6).(d) Plot the estimated
Suppose the fifth survival time is ????5 = 10 weeks and there are 22 patients alive out of 40 who were at risk at time ????5. If ˆ????1 = 0.88, ˆ????2 = 0.86, ˆ????3 = 0.85, ˆ????4 = 0.82, and ˆ????5 = 0.75, compute the Kaplan–Meier estimate of the survival probability at 10 weeks.
Suppose the fourth survival time is ????4 = 4 years and there are 50 patients alive out of 75 who were at risk at time ????4. If ˆ????(????3) = 0.83, compute the Kaplan–Meier estimate of the survival probability at 4 years.
What is the formula for estimating the survival function with the Kaplan–Meier estimator?
Which estimator of the survival function is a nonparametric estimator?
Under what conditions is an estimator a nonparametric estimator?
What are two reasons that cause the censoring of a survival time?
What is a censored survival time?
If ????(25) = 0.55, is(a) ????(20) larger or smaller than 0.55? Explain.(b) ????(50) larger or smaller than 0.55? Explain.
What happens to the survival function as the value of ???? increases?
What is the survival function ????(????)?
Using the Exerbike2 data set with heart rate as the response variable(a) perform a completely randomized two-factor ANOV on the 2020 data with factors month and time as the factors,(b) determine whether there is a significant interaction between month and time,(c) separate the appropriate treatment
Using the Exerbike2 data set with speed as the response variable(a) perform a completely randomized two-factor ANOV on the 2020 data with factors month and time as the factors,(b) determine whether there is a significant interaction between month and time,(c) separate the appropriate treatment
Using the Exerbike2 data set with calories burned per minute as the response variable(a) perform a two-factor ANOV on the 2020 data with factors month and time as the factors, (b) determine whether there is a significant interaction between month and time, (c) separate the appropriate treatment
Using the Exerbike2 data set with calories burned per minute as the response variable(a) perform a completely randomized ANOV on the 2020 data with month as the treatment,(b) determine whether there is a significant difference between the mean number of calories burned per minute by month,(c)
Determine the number of replicates needed to achieve the prespecified power when???? = 0.05 and(a) there are five treatments, ???? = 10, a distance of ???? = 15 is to be detected, and the desired power is 0.80.(b) there are six treatments, ???? = 60, a distance of ???? = 80 is to be detected, and
Determine the number of replicates needed to achieve the prespecified Bonferroni distance ???? when the experimentwise error rate is ???????? = 0.05 and the number of comparisons is less than 10, when(a) ???? = 10 and ???? = 10.(b) ???? = 3 and ???? = 2.(c) ???? = 1.4 and ???? = 0.8.
In the article “Tensile strength of mineralized/demineralized human normal and carious dentin” published in Journal of Dental Research (Nishitani et al., 2005), the authors reported the results of a 23 three-factor experiment on the ultimate tensile strength (UTS) of human dentin. The factors
Use the partial ????-ratios and ????-values in Table 12.47 for a 3 × 2 × 3 randomized block experiment with five blocks to answer the following questions.(a) Based on the ????-ratios and the ????-values in Table 12.47, is the three-way interaction significant at the ???? = 0.05 level?(b) Based on
Use the partial ????-ratios and ????-values in Table 12.46 for a 2×2×4 experiment with five replicates of each treatment to answer the following questions.(a) Based on the ????-ratios and the ????-values in Table 12.46, is the three-way interaction significant at the ???? = 0.05 level?(b) Based
Use the partial ANOV table given in Table 12.45 for a 23 randomized block experiment with eight blocks to answer the following questions.(a) Fill in the missing entries in the ANOV table.(b) Estimate the variance of the experimental error.(c) On the basis of ????-ratios and their ????-values, is it
Use the partial ANOV table given in Table 12.44 for a 2×3×4 factorial study with five replicates of each treatment to answer the following questions.(a) Fill in the missing entries in the ANOV table.(b) Estimate the standard deviation of the experimental error.(c) Based on the ????-ratios and
Explain why the main effects in a three-factor analysis of variance should not be tested when there are significant interactions among the factors.
In terms of the parameters of a three-factor analysis of variance model, what is the(a) ????????????th treatment mean?(b) difference between the ????????????th and ????????????th treatment means when none of the factors interact with each other?
In a three-factor analysis of variance, what does(a) ????̄????????????• estimate?(b) ????̄????••• estimate?(c) ????̄•????•• estimate?
In a three-factor randomized block analysis of variance, what(a) is the model?(b) are the assumptions of the model?(c) does ???????????????????? represent?
In a three-factor analysis of variance, what(a) is the model?(b) are the assumptions of the model?(c) does ???????????????????? represent?
For a 4 × 5 two-factor analysis of variance with ???? = 5 replicates of each treatment, if ???????????? = 120, determine the estimated standard error of a(a) treatment mean.(b) factor A mean.(c) factor B mean.(d) the difference of two treatment means.(e) the difference of two factor A means.(f)
For a 5 × 3 two-factor analysis of variance with ???? = 4 replicates of each treatment, determine the number of replications of a(a) factor A mean.(b) factor B mean.(c) AB treatment mean.
In the article “Dose uniformity of samples prepared from dispersible aspirin tablets for paediatric use” published in the European Journal of Hospital Pharmacy Science(Broadhurst et al., 2008), the authors reported the results of a two-factor experiment on the dispersion of 75 mg aspirin
In the article “Effect of irradiation on grip strength” published in the Journal of Korean Academy of University Trained Physical Therapists (Sang-hyub, 1999), the author reported the results of a two-factor experiment on grip strength. The two factors in the experiment were dominant hand (Yes,
In the article “Modulation of Cutaneous Aging With Calorie Restriction in Fischer 342 Rats” published in JAMA Facial Plastic Surgery (Bhattacharyya, et al., 2005), the authors reported the results of an experiment with a 3 × 2 factorial design for studying the factors age and diet on
Use the information in the ANOV table given in Table 12.39 for a randomized block experiment with a 3 × 4 treatment structure and six blocks to answer the following questions.(a) Fill in the missing entries in the ANOV table.(b) Estimate the standard deviation of the experimental error.(c) Test
Use the information in the ANOV table given in Table 12.38 for a two-factor experiment with 2×3 treatment structure and eight replicates of each treatment to answer the following questions.(a) Fill in the missing entries in the ANOV table.(b) Estimate the standard deviation of the experimental
Explain why the main effects in a two-factor analysis of variance should not be tested when the interaction is significant.
In terms of the parameters of a two-factor analysis of variance model, what is the(a) ????????th treatment mean?(b) difference between the ????????th and ????????th treatment means when the factors interact?(c) difference between the ????????th and ????????th treatment means when the factors do not
In a two-factor analysis of variance what does(a) ????̄????????• estimate?(b) ????̄????•• estimate?(c) ????̄•????• estimate?
In a two-factor randomized block analysis of variance what(a) is the model?(b) are the assumptions of the model?(c) does ???????????????? represent?
In a two-factor analysis of variance what(a) is the model?(b) are the assumptions of the model?(c) does ???????????????? represent?
How many units are required for the experiment in each part of Exercise 12.44 when there are(a) five replicates of each treatment(b) three blocks of units(c) six replicates of each treatment(d) 10 blocks of units
How many treatments are there in a multi factor study when there is a(a) 4 × 2 treatment structure?(b) 3 × 6 treatment structure?(c) 3 × 3 × 3 treatment structure?(d) 24 treatment structure?
What is a multi factor treatment structure?
Suppose in a randomized block experiment designed to investigate the efficacy of four drugs for reducing the duration of migraine headaches, the observed ????-ratio for testing the equality of the treatment means is significant (???? = 0.003). Use the treatment means given in Table 12.37 to answer
Use the information in the ANOV table given in Table 12.36 for a randomized block experiment with five treatments and 12 blocks to answer the following questions,(a) Fill in the missing entries in the ANOV table.(b) Estimate the variance of the experimental error.(c) Test the equality of the
Use the information in the ANOV table given in Table 12.35 for a randomized block experiment with seven treatments and 12 blocks to answer the following questions.(a) Fill in the missing entries in the ANOV table.(b) Estimate the variance of the experimental error.(c) Test the equality of the
Suppose a randomized block experiment is performed with six treatments and eight blocks. If ???????????????? = 770, ???????????????? = 1200, and ???????????????????? = 3400, construct an ANOV table for this experiment.
How are the assumption of a randomized block model checked?
In terms of the parameters of a randomized block analysis of variance model, what is the(a) ????th treatment mean?(b) difference between the ????th and ????th treatment means?
In a single-factor randomized block design what(a) is the model?(b) are the assumptions of the model?(c) does ???????????? represent?
Why are randomized block designs used?
In the article “Caudal analgesia in paediatrics: a comparison between bupivacaine and ketamine” published in The Internet Journal of Anesthesiology (Siddiqui and Choudhury, 2006), the authors reported the results of a study on the mean time intervals between the recovery from anesthesia and the
In the article “The effect of hydrogel and solution of sodium ascorbate on the bond strength of bleached enamel” published in the Journal of Conservative Dentistry(Paul et al., 2007), the authors reported the results of an experiment studying the effects of four different bleaching treatments
In the article “Cigarette smoking and age at natural menopause of women in Poland” published in The Internet Journal of Biological Anthropology (Pawlinska-Chmara and Anita Szwed, 2008), the authors reported the results of a retrospective study on smoking and age of menopause for 1948 women. The
Use the ANOV table given in Table 12.28 for a balanced experiment having three treatments to answer the following questions.(a) How many replicates of each treatment were used in this experiment?(b) Test the hypothesis of the equality of the treatment means at the ???? = 0.01 level.(c) Estimate the
In the article “An in vitro comparative study of wettability of four commercially available saliva substitutes and distilled water on heat-polymerized acrylic resin”published in the Journal of Indian Prosthodontic Society (Sharma and Chitre, 2008), the authors reported a significant F-ratio (F
Use the MINITAB output for the Bonferroni procedure given in Table 12.26 to determine which of the treatment means is significantly different from the treatment 1 mean when ???????? = 0.02.
If the adjusted ????-value for comparing ????3 and ????5 is ???? = 0.158, is there sufficient evidence to reject ????0 ∶ ????3 = ????5 when the Bonferroni multiple comparison procedure is used with ???????? = 0.05? Explain.
If the adjusted ????-value for comparing ????1 and ????2 is ???? = 0.003, is there sufficient evidence to reject ????0 ∶ ????1 = ????2 when the Bonferroni multiple comparison procedure is used with ???????? = 0.05? Explain.
What is an adjusted ????-value and how is it used?
For a balanced single-factor study, determine the Bonferroni distance ???? for an experimentwise error rate of ???? = 0.05 when(a) there are four treatments replicated 10 times, MSE = 20, and ???????? = 0.06.(b) there are six treatments replicated eight times, MSE = 50, and ???????? = 0.03.(c)
Determine the Bonferroni critical ????-value for separating the means when there are(a) three treatments, 30 degrees of freedom for error, and ???????? = 0.06.(b) four treatments, 20 degrees of freedom for error, and ???????? = 0.06.(c) five treatments, 60 degrees of freedom for error, and ????????
Determine the number of pairwise mean comparisons that would need to be made in separating the treatment means with the Bonferroni procedure when there are(a) five treatments.(b) six treatments.(c) 10 treatments.
What is the(a) experimentwise error rate?(b) per comparison wise error rate?
The partial ANOV table given in Table 12.25 was extracted from the article “Effects of folic acid and combinations of folic acid and vitamin B-12 on plasma homocysteine concentrations in healthy young women” published in the American Journal of Clinical Nutrition (Brönstrup et al., 1998). The

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