BME380J.5 Exam 3 Spring 2017

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University of Texas *

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380J

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Mechanical Engineering

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Dec 6, 2023

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Student# _______ BME 380J.5 Exam 3 Spring 2017 I understand that the exam proctors will watch for violations of the exam rules and that offending students will be reported to the Dean of Students. I understand that Scholastic Dishonesty can result in an automatic F in the course. I understand the exam rules. I know that … • I have 75 minutes to complete this exam • I may not communicate in any way with anyone other than exam proctors during the exam time • I may not consult textbooks, notes, or other reference material during the exam other that that which is provided by the exam proctor • I may not use any electronic devices during the exam including but not limited to laptops, tablets, calculators, cell phones, or smart watches • My answers must be legibly written and clearly demonstrate my thought process in order to earn full credit on the exam. I know that mathematical notation has been consistently used in this course and that I must follow that same convention on the exam. • I should not write my name or any other identifying information on any portion of the exam other than this face page. Writing my name or any other identifying information on any portion of the exam other than this face page will be interpreted as an attempt to gain any unfair advantage and may result in automatic failure of the exam. Print Name ____________________________________ Sign Name ____________________________________ Date _________________________________________

Student# _______ Problem #1 _______ / 10 points Problem #2 _______ / 10 points Problem #3 _______ / 10 points Problem #4 _______ / 10 points Problem #5 _______ / 10 points Problem #6 _______ / 10 points Problem #7 _______ / 10 points Problem #8 _______ / 10 points Problem #9 _______ / 10 points Problem #10 _______ / 10 points TOTAL _______ / 100 points

Student# _______ Problem # Problem Total = ___ / 10 1 Problem #1. [10 points] In each blank, write the letter from the flowchart that indicates the best location for the question/statement. Some questions/statements may be used more than once. ____ Two-way ANOVA ____ Survival analysis ____ Pearson correlation ____ Kappa statistic ____ Number of ways in which the categorical variable can be classified ____ Non-parametric ANOVA ____ Other covariates to be controlled for? ____ Rank correlation ____ One-way ANCOVA

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Student# _______ Problem # Problem Total = ___ / 10 2 Problem #2. [10 points] Fill in the letter corresponding to the name of the method that best fits in each blank below. Each method may be used zero, once, or more than once. If none of the listed methods fits the blank, write in “NONE.” The ANOVA F-test is a multi-sample extension of _____ A. Paired t-test B. t-test for two independent samples C. Wilcoxon Signed Rank D. Wilcoxon Rank Sum E. Chi-square test F. Kappa statistic G. Multiple linear regression H. Pearson correlation coefficient I. ANCOVA J. Kruskal-Wallis K. Dunn procedure L. Intraclass correlation coefficient The non-parametric analogue of the ANOVA F-test is ______ The non-parametric analogue of the ANOVA t-test is ______ The multi-sample extension of the Wilcoxon Rank Sum test is ______ The multi-sample extension of the Wilcoxon Signed Rank test is ______ ______ is used to quantify the agreement between categorical variables ______ is used to quantify the agreement between continuous variables ______ is used to quantify the association between continuous variables ______ is estimated using a one-way random effects ANOVA model ______ is used to compare group means, while controlling for covariates

Student# _______ Problem # Problem Total = ___ / 10 3 Problem #3. [10 points] (a) Annotate the diagram to explain the Within Sum of Squares (a) (b) Annotate the diagram to explain the Between Sum of Squares (b) (c) Annotate the diagram to explain why larger values for F = Between MS / Within MS provide evidence against the null hypothesis that all groups have the same mean. Recall that Between MS = Between SS / (k-1) and Within MS = With SS / (n- k). (c)

Student# _______ Problem # Problem Total = ___ / 10 4 Problem #4. [10 points] Consider a multiple regression model of the form ࠵? = ࠵? + ࠵? & ࠵? & + ࠵? ( ࠵? ( + ࠵? ) ࠵? ) + ࠵? * ࠵? * + ࠵? + ࠵? + where the x’s are dummy variables used to encode a categorical variable. (a) How many different values are there for the categorical variable, i.e., how many categories are there? Explain your answer. (b) How can ࠵? be interpreted? (c) How can ࠵? ) be interpreted? (d) Could the categorical variable be encoded using a different set of dummy variables? Explain your answer.

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Student# _______ Problem # Problem Total = ___ / 10 5 Problem #5. [10 points] (a) Using high-throughput techniques such as microarrays, it is possible to study the expression levels of thousands of genes in a study. If no correction is made for multiple comparisons, how many “significant” results would be expected by chance alone if one compares the expression levels of 1000 genes between a sample of healthy tissue and a sample of a cancerous tissue at a significance level of 0.05? (b) Suppose that the Bonferroni adjustment is applied to the comparison of the expression of 1000 genes for healthy vs. cancerous tissue. The adjusted significance level is given by ࠵? ∗ = . / . What is does ࠵? mean in this context? For (c) through (h), circle the correct answer. (c) Correction for multiple comparisons is often advised when [many | few] tests are conducted. (d) Correction for multiple comparisons is often advised when the tests [are | are not] specified before looking at the data. (e) Correction for multiple comparisons [is | is not] applied to analyses other than ANOVA. (f) The Bonferroni method [does | does not] assume that all of the tests to be conducted are statistically independent. (g) The goal of the False-Discovery Rate method [is | is not] to control the experiment-wide type I error. (h) The False-Discovery Rate method [is | is not] less conservative than the Bonferroni method.

Student# _______ Problem # Problem Total = ___ / 10 6 Problem #6. [10 points] Recall the example from the textbook by Rosner that used a multiple logistic regression model to relate sudden death (cardiovascular) to several risk factors (see table provided). [10 points] (a) Why was logistic regression used rather than the Mantel-Haenszel test? (b) The odds in favor of sudden death are _________ times higher for a person who is 65 years old than for a person who is 60 years old, all other factors being equal. [fill in the blank] (c) Recall that to test the hypothesis ࠵? 2 :࠵? 4 = 0 for all other ࠵? 6 ≠ 0 vs. ࠵? & :࠵? 4 ≠ 0 for all ࠵? 4 , we calculate the test statistic ࠵? = 9 : ; <=>9 : ; ? , which follows a standard normal distribution when the null hypothesis is true. Given that ࠵? = 2.27 for hematocrit, use a clearly annotated sketch of the distribution of test statistic under the null hypothesis to explain the definition of a p-value.

Student# _______ Problem # Problem Total = ___ / 10 7 Problem #7. [10 points] For questions (a), (b), and (c), circle the correct answer and provide a one-sentence explanation of your answer. (a) All else being equal, a cross-over design without carry-over effects will have [more | less] power than a parallel group design. (b) All else being equal, a cross-over design without carry-over effects will have [more | less] power than cross-over design with carry-over effects. (c) All else being equal, a cross-over design is better suited for a study in which the endpoint is measured after a [short (e.g., weeks) | long (e.g., years)] period of time, assuming no carry over effects. (d) Compare and contrast an equivalence study and a superiority study with respect to… the study goals. the sample size required. Ethical considerations. (e) Generally, a sample size calculation for a superiority study based on two independent samples requires the investigator to specify quantities such as the desired significance level, the desired power level, the expected effect size, the expected ratio of the sample sizes, and the expected variability of the data. What additional information must the investigator specify for sample size calculation for an equivalence study?

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Student# _______ Problem # Problem Total = ___ / 10 8 Problem #8. [10 points] Recall the example from the Rosner textbook on the efficacy of vitamin supplements in preventing vision loss (see provided table). Vision loss was defined as a 50% decline in a measure of the electrical activity in the retina. ࠵? D (࠵? G ) = I1 − ࠵? & ࠵? 2 M × I1 − ࠵? ( ࠵? & M × ⋯× I1 − ࠵? G ࠵? GP& M, ࠵? = 1,… , ࠵? ࠵? D (࠵? * ) = I1 − ࠵? ࠵? M × I1 − ࠵? ࠵? M × I1 − ࠵? ࠵? M × I1 − ࠵? ࠵? M A = ________ B = ________ C = ________ D = ________ E = ________ F = ________ G = ________ H = ________ (I) Based on the survival curve provided, what is the approximate probability of retaining one’s vision at year 2? (J) Explain how to estimate ℎ ] (࠵? * ) from the survival curve provided. Recall that the estimated hazard at time t i is 1 – Prob(survive to t i given that one has survived to t i-1 ). 0.5 0.6 0.7 0.8 0.9 1 0 2 4 6 SurivialProbability years Fail Censored Survive Total t 1 = 1 year 3 4 165 172 t 2 = 2 year 6 0 159 165 t 3 = 3 year 15 1 143 159 t 4 = 4 year 21 26 96 143 t 5 = 5 year 15 35 46 96 t 6 = 6 year 5 41 0 46

Student# _______ Problem # Problem Total = ___ / 10 9 Problem #9. [10 points] In each blank write the letters corresponding the methods for which the statement is true. There can be more than one letter per blank. Each letter may be used 0, 1, or more than 1 time. (i) ________ is more suitable than the log-rank test when there several risk factors and/or many strata per risk factor A. Log-Rank Test B. Kaplan-Meier C. Cox Proportional-Hazards Model (ii) ________ entails performing the Mantel-Haenszel test over a set of contingency tables corresponding to time intervals over which the incidence is homogeneous (iii) ________ can be used to analyzed censored data (iv) ________ is used to compare two survival curves (v) ________ can be thought of as an extension of multiple logistic regression where the time when an event occurs is taken into account (vi) ________ is a non-parametric method for estimating survival curves (vii) What is the key assumption of the log-rank test?

Student# _______ Problem # Problem Total = ___ / 10 10 Problem #10. [10 points] Write in the letter indicating the term that corresponds to the definition provided. ______ Probability that a person with no prior disease will develop a new case of the disease over some a specified time period. A. Censored B. Confounding C. Cumulative incidence D. Experimental study E. Hazard rate F. Incidence rate G. Observational study H. Prevalence I. Prospective study J. Retrospective study ______ Probability of currently having a disease regardless of the duration of time that one has had it ______ Number of events in a group divided by the total person-time accumulated in the study ______ Incidence rates that vary substantially over time ______ Investigator assigns interventions to subjects ______ Investigator does not assign interventions to subjects ______ Longitudinal study in which subjects are followed over time ______ Longitudinal study in which subjects’ prior circumstances are studied ______ subject doesn’t have event during follow-up period ______ A variable that is related to both the independent and dependent variables being studied

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