Reference no: EM132389537

Linear Models (LMR) Assignment -

Instructions: The assignment on linear regression model for consideration. Answer the questions in an essay-style approach when appropriate. Make sure to include all relevant computer output (and exclude irrelevant output), that is presented neatly and integrated through the discussion and interpretation. Do not include an appendix.

Part A -

Journal paper: A comparison of sLASER and MEGA-sLASER using simultaneous interleaved acquisition for measuring GABA in the human brain at 7T by Donghyun Hong, Seyedmorteza Rohani Rankouhi, Jan-Willem Thielen, Jack J. A. van Asten, and David G. Norris.

Background: The paper above was just published (last week in fact on 11^th October, 2019). In brief, this article is comparing two methods to measure the neurological biomarker "GABA" (the level of γ-Aminobutyric acid in the brain). The two methods being compared are called sLASER (semi-LASER) and MEGA-sLASER (MEsher-GArwood semi-LASER). Measurements using both techniques were taken from 12 healthy volunteers and from 6 different regions of the brain.

Task: Your task for this Part of the assignment is to review some of the statistics in this article to make sure everything was done appropriately. The main analysis in this article is linear regression and ANOVA, and so is perfect for re-analysis in LMR. Note that you do not need to read the entire paper, and you do not need to understand the clinical or biological processes involved. The background above is all the context that you need to understand and complete this assignment.

Data preparation instructions:

Access the above article and download the supporting information - the excel dataset used in this article. Format this data appropriately so that it can be imported into STATA or R, and then import this data. Note that you only need the following columns for this assignment:

• Column A - Subject ID
• Column B - Brain region
• Column C - grey matter tissue sample volume fraction
• Column G - sLASER GABA concentration
• Column L - MEGA-sLASER GABA concentration

All other columns can be ignored.

Question 1: Look at figure 3 in the article. Here the y-axis is GABA concentration (as measured by sLASER or MEGA-sLASER for blue and grey dots respectively) and the x-axis is grey matter volume (Column C). The authors also carried out the two corresponding regressions (one for sLASER and one for MEGA- sLASER, described in the caption) where GABA concentration is the outcome and grey matter volume is the explanatory variable. Perform the same two simple linear regressions as the article has done, and report on your results. Do you have any concerns regarding the results reported in the article? If so, what are these concerns and how do you think they have arisen? No assumption checking is needed in this question.

Question 2: The caption of figure 3 states that

"Linear regression lines of the two methods are almost identical".

Use the methods taught in this course to test this statistically, and report on your results. Do you agree with the authors conclusions that the two regression lines are almost identical? No assumption checking is needed in this question.

Question 3: The authors carry out an ANOVA to compare the GABA concentration levels across brain regions. They do this twice, once for each GABA concentration measurement method (sLASER and MEGA- sLASER). They report that:

"Regional GABA concentrations showed statistically significant differences between group means as determined by a one-way ANOVA (F(5,36) = 0.302, p = 0.019) for the sLASER method, and (F(5,36) = 6.015, p < 0.001) for the [MEGA-sLSER] method"

Perform the same two ANOVAs (or appropriate regressions) and report on your results. Do you have any concerns regarding the results reported in the article? If so, what are these concerns and how do you think they have arisen?

No assumption checking is needed in this question.

Question 4: Check and report on the assumptions of your analysis in question 2 and 3.

Question 5: Before an article is published in an academic journal, it must be reviewed by three subject matter experts to ensure the results are appropriately justified. Sometimes one of these experts is a statistician to ensure the statistics is appropriate. Based on your answers to questions 1-4, if you were such a statistical reviewer, would you recommend that the article be published as it is currently presented? In two to four sentences, explain why.

Optional and unmarked question: Has this analysis changed how you view scientific publications?

Part B -

Background: Part B uses the same data and context as Part A. However in this Part, you are not reviewing the statistical analysis presented in the article, but rather carrying out a new statistical analysis as per the questions below. For the purposes of this part, you can ignore any issues you identified with the analysis in Part A (if you identified any issues). For this Part we will only consider GABA concentration as measured by sLASER (and so you can totally ignore MEGA-sLASWER).

Question 1: You have decided you would like to compare GABA concentration levels between three different groupings of brain regions. The three comparisons of interest are:

Comparison	Group 1		Group 2
	Anterior cingulate cortex (AC) Dorsolateral prefrontal cortex (DLPFC) Motor cortex (MC)	versus	Occipital cortex (OCC) Posterior cingulate cortex (PC) Precuneus (PRC)
	Anterior cingulate cortex (AC) Dorsolateral prefrontal cortex (DLPFC)		Motor cortex (MC)
	Occipital cortex (OCC) Motor cortex (MC)		Posterior cingulate cortex (PC) Precuneus (PRC)

Write the algebraic formula for the regression equation where GABA concentration is the outcome, and brain region is the exposure variable. Define each parameter and each indicator variable used in this equation. Using these regression parameters, write algebraically the contrasts used to test each of the three comparisons above. Finally, estimate the numerical value and confidence interval for these contrasts, and their associated P-values using STATA or R (for sLASER method only). No assumption checking is needed in this question.

Question 2: Use multiple regression analysis to test for a difference of GABA concentration levels( as measured by the sLASER method) across brain regions after adjusting for grey matter volume fraction.

Interpret the important results.

No assumption checking is needed in this question.

Question 3: Write the algebraic formula for the regression equation with GABA concentration as the outcome, and where there is effect modification between brain regions and grey matter volume. Now test for this effect modification with STATA or R. Interpret the important results. Also, explain/interpret the meaning of each regression parameter in this output. No assumption checking is needed in this question.

Part C -

Data: regurge.dta

Background: A study in clinical cardiology examined patients before and after surgery for isolated aortic regurgitation. The aortic valve is the heart valve between the left ventricle where blood is pumped from the heart and the aorta, the large artery beginning the arterial system. When the valve is not functioning and closing properly some of the blood pumped from the heart returns (or regurgitates) as the heart relaxes before its next pumping action. To compensate for this, the heart volume increases to pump more blood out (since some of it returns). To correct for this, open-heart surgery is performed and an artificial valve is sewn into the heart. Data on left ventricular ejection fraction (LVEF) for 20 patients with aortic regurgitation before and after corrective surgery are provided in the dataset regurge.dta.

Question 1: Do the data provide evidence for a systematic change between preoperative and postoperative regurgitation rates? Explain your answer. When presented with this evidence your cardiologist is very eager to see whether the size of the change depends on the baseline value for each patient-what do you advise on this question?

Question 2: Suppose you hypothesise that the measurement error model described on pages 224-226 in Module 6 (with a constant shift ????) is a reasonable way of explaining the observed correlation between change in LVEF and baseline (preoperative) value. Under this model, write the algebraic formula for the regression coefficient from the regression of changes in LVEF on baseline values and describe what this regression coefficient tells us about the relative contribution of measurement error variance to the total variance of preoperative LVEF values?

Question 3: Under the measurement error model, how would the results for the regression of the changes D_i = Y_i - X_i (= post-op LVEF minus pre-op LVEF) on baseline X_i be altered if the cardiologist had taken k repeated measurements X_ij(j = 1, . . . , k) at baseline and instead of using a single X value to define the baseline value, he used the average of these k values, X^-_I = (_j-1Σ^k - X_ij)/k? What value of k would be needed in order to reduce the absolute value of the regression coefficient between D_i and X^-_i from 2/3 to 1/3? Does this depend on any other parameters or features of the data?

Derive a general expression for the number of replicates that are required in order to reduce the regression coefficient, for the regression of the change value D_i on the mean of a set of k baseline values X_i, from a value of γ down to a target value of γ*.

Attachment:- Linear Models Assignment Files.rar