MPH5041 Introductory Biostatistics/Biostatistics Concepts & Applications - Assignment Help

Assignment Help on Formulation and Evaluation of Research Hypothesis

Study Description: A cross-sectional study was conducted in 2017 to determine the factors related to Health Related Quality of Life (HrQoL) and depression among people with type 2 diabetes mellitus (T2DM) in Bangladesh. The HrQoL was measured for each of the 1253 study participants in continuous scale between 0 and 1, where “0” represent the worst HrQoL and “1” represent the best HrQoL. The description of some selected variables are given in Table 1 below.

Table 1: Variable description with statistical code

Variable	Description	Statistical code (if any)
Gender	Gender of patient	0 for male and 1 for female
Age	Age of patient	N/A
Location	Area of residence	0 for rural and 1 for urban
Education	Education level	0 for up to year 12 and 1 for graduate and above
Duration_dm	Duration of diabetes	N/A
HbA1c	Glycaemic level (HbA1c)	0 for controlled and 1 for uncontrolled
PA*	Physical activity	0 for active and 1 for inactive
No_complic	Number of complications	N/A
HTN	Hypertension	0 for no and 1 for yes
HrQoL	Health Related Quality of life score	N/A
Cog_func	Cognitive function	0 for not-impaired and 1 for impaired
Anxiety	Presence of anxiety	0 for no-anxiety and 1 for anxiety
Depression	Presence of depression	0 for no-depression and 1 for depression

Macro- and micro-vascular complications (CAD, stroke, diabetic foot, retinopathy, nephropathy and neuropathy) are related to type 2 diabetes mellitus. Internationally standard questionnaires were used to assess patients’ physical activity, HrQoL, cognitive function, anxiety and depression. Hypertension was defined either as known previous detection, patient on anti- hypertensive medication or newly discovered blood pressure (BP) reading with systolic>140mmHg and diastolic >90mmHg. Glycaemic status was considered ‘good controlled’ for HbA1c <7% and ‘uncontrolled’ for HbA1c >= 7%.

Using the data described in the above table answer the Questions 1-3 below.

Question 1 [5 marks]: Perform appropriate statistical analysis and evaluate the strength of relationship of HrQoL with patients’ age, duration of diabetes and number of complications.

Question 2 [30 marks]: Perform appropriate simple as well as multiple regression analyses with stepwise variable selection method (use backward elimination method) to find the variables (from the list in Table 1 above) those are significantly related to HrQoL. For this analysis make an initial assumption that HrQoL approximately follows the normal distribution, i.e., you do not need to evaluate pre-analysis normality of HrQoL.

Present the above simple and stepwise multiple regression analyses results in a table (follow Module 8 Formative Assessment- MUST Attempt) and interpret the beta coefficients and 95% CI of both simple and multiple regression for the variables duration of diabetes and depression only. Then provide a summary discussion of the results followed by a conclusion and implication. Address all other (if any) relevant issues/results in your presentation.

Note: (1) for presentation please follow all necessary steps discussed in lecture; (2) please do not repeat the steps for each variable – follow Question 2 in AT2; (3) evaluation of model adequacy is not required for simple regression.

Consider that you submitted the above analysis results for a journal publication and a reviewer has recommended to forcefully adding the variables hypertension, systolic blood pressure, creatinine level (a measure of kidney function), and diastolic blood pressure into your multiple regression model. Assume that these variables are available in your database. Briefly discuss how do you address and/or reply reviewer’s comment.

Question 3 [15 marks]: Perform appropriate simple as well as multiple regression analyses with stepwise variable selection method (use backward: Wald) to find the variables those are significantly related to depression. Exclude HrQoL from your analysis. Present the results in a table (follow the Formative Assessment in Module 10) and provide a summary discussion of the results followed by a conclusion. Address all other (if any) relevant issues/results in your presentation.

Using the above results, predict the risk of depression for a physically active patient who completed graduate degree and have five complications, and also have anxiety and impaired cognitive function.

Note: (1) for presentation please follow all necessary steps discussed in lecture; (2) please do not repeat the steps for each variable – follow Question 2 in AT2.

Note: For Questions 4 & 5 you do not need to follow the steps outlined in the lecture and/or tutorial.

Question 4 [25 marks]:

Objectives: To examine the effect of different stages of chronic kidney disease (CKD) on patients’ risk of post-operative mortality and complications following isolated coronary artery bypass grafting (CABG) in a large cohort of patients who had cardiac surgery.

Description: All patients who underwent isolated CABG in the cohort were reviewed, and their preoperative glomerular filtration rates (eGFR) were estimated using the Chronic Kidney Disease Epidemiology Collaboration creatinine equation.

The CKD stages were classified as follows: normal: eGFE ≥ 90 ml/min/1.73m² and not on dialysis, mild: eGFR 60-89 ml/min/1.73m² and not on dialysis, moderate: eGFR 30 - 59 ml/min/1.73m² and not on dialysis, severe: eGFR < 30 ml/min/1.73m² and not on dialysis; and dialysis dependent.

Analysis Method: The descriptive statistics for various post-operative outcomes were reported as percentages (see Table 2). The effect of CKD stages on each of the outcomes following isolated CABG were examined using multiple logistic regression method. In the multiple logistic regression analysis the CKD variable was adjusted for other 12 predictors (please see the list below the Table 3), i.e., there were 13 predictors in each of the regression models including CKD stages. However, the OR, 95% CI and p-value were reported only for CKD stages (see Table 3). Normal CKD stage was considered as the reference category in the multiple logistic regression analysis. Thus, the ORs in the Table 3 quantify the odds of various CKD stages (moderate to severe) as compared to normal CKD stage. Please see the Appendix for a brief description of post-operative mortality and complications.

Discuss the results in Tables 2 and 3 and make a summary conclusion followed by the impact of the findings. Your answer must have only the following three separate sections:

Section 1: Summary (overall) discussion of descriptive statistics (presented in Table 2) of post-operative outcomes by CKD
Section 2: Summary (overall) discussion of multiple logistic regression analysis results presented in Table
Section 3: Make a brief summary conclusion about the effect of CKD on post-operative mortality and complications (see column 1 in Table 3 for the list of these variables) followed by the impact of the findings.

Table 2: Descriptive statistics (%) of post-operative outcomes following CABG by CKD stages.

		Kidney function (GFR ml/min/1.73m²)
Post-operative outcomes	Normal function (≥ 90)	Mild dysfunction (60-89)	Moderate dysfunction 30-59)	Severe dysfunction (< 30)	Dialysis
30-day mortality	0.5	1.4	2.8	5.5	4.3
Post-op Stroke	0.7	1.2	2.3	2.1	1.9
Reoperation for bleeding	1.8	2.4	2.9	2.6	1.5
MI within 21 days	29.5	26.3	29.8	37.1	31.8
New renal failure	1.2	2.6	7.1	7.6	3.8
Return to theatre	3.6	4.6	6.9	7.8	8.0
Prolonged ventilation> 24 hrs	6.0	7.2	12.4	16.1	15.6
Septicemia	0.6	0.7	1.4	2.2	2.5
Post-operative stay > 14 days	18.9	23.9	36.3	46.9	50.8
Readmission within ≤ 30 days from surgery	8.4	9.1	11.3	13.1	25.2
New cardiac arrhythmia	20.7	29.9	34.7	32.7	32.1
Deep sternal infection	0.6	0.5	1.1	1.3	2.3
Reoperation for deep sternal infection	0.4	0.4	0.8	0.8	1.5
Red blood cells transfusion	28.7	35.5	52.7	61.8	65.3
Pneumonia	3.6	3.7	5.1	5.2	6.5

Note: the data in the above table shows the % of outcome (yes) within each category of kidney function. For example percentages of death (30-day mortality) among sever kidney dysfunction was 5.5% and that among the dialysis

was 4.3%, etc. You don’t have to discuss every single %s in the table.

Table 3: Multiple logistic regression analysis of various post-operative outcomes following CABG.

Kidney function (GFR ml/min/1.73m²)
Outcome / Complications	Mild dysfunction (60-89) n=15,626	Moderate dysfunction (30-59) n=7,037	Severe dysfunction (< 30) n=720	Dialysis n=475
OR (P-value, 95% CI)
30-day mortality	1.8 (0.002, 1.3 – 2.6)	2.2 (<0.001, 1.5 – 3.3)	3.6 (<0.001, 2.2 – 6.1)	4.4 (<0.001, 2.4 – 8.2)
Post-operative Stroke	1.3 (0.094, .98 – 1.9)	2.0 (<0.001, 1.4 – 2.8)	1.6 (0,147, 0.8 – 3.0)	2.0 (0.061, 0.89 – 4.2)
Reoperation for bleeding	1.3 (0.011, 1.1 – 1.6)	1.6 (<0.001, 1.3 – 2.1)	1.5 (0.137, 0.9 – 2.5)	0.8 (0.669, 0.4 - 1.8)
New renal failure	2.1 (<0.001, 1.7 – 2.7)	5.1 (<0.001, 4.0 – 6.6)	4.7 (<0.001, 3.2 – 6.8)	2.5 (0.001, 1.4 – 4.3)
MI within 21 days	0.9 (0.016, .82 – .95)	0.9 (0.020, 0.8 – 0.99)	1.2 (0.121, 0.99 – 1.5)	1.0 (0.726, 0.8 – 1.4)
Return to theatre	1.2 (0.018, 1.01 – 1.4)	1.6 (<0.001, 1.3 – 1.9)	1.6 (0.004, 1.2 – 2.3)	2.0 (<0.001, 1.4 – 2.9)
Prolonged ventilation	1.1 (0.091, .96 – 1.3)	1.7 (<0.001, 1.4 – 1.9)	2.0 (<0.001, 1.6 – 2.6)	2.5 (<0.001, 1.8 – 3.3)
Post-operative stay > 14 days	1.1 (0.002, 1.01 – 1.2)	1.6 (<0.001, 1.4 – 1.7)	2.3 (<0.001, 1.9 – 2.8)	3.5 (<0.001, 2.9 – 4.3)
Red blood cells transfusion	1.1 (0.008, 1.01 – 1.2)	1.7 (<0.001, 1.5 – 1.8)	2.3 (<0.001, 1.9 – 2.7)	3.7 (<0.001, 3.0 – 4.5)
Pneumonia	1.0 (0.630, 0.8 – 1.1)	1.2 (0.045, 1.01 – 1.5)	1.1 (0.608, 0.8 – 1.6)	1.5 (0.069, .92 – 2.2)
Deep sternal infection	0.8 (0.322, 0.6 – 1.2)	1.6 (0.043, 1.01 – 2.4)	1.4 (0.412, 0.6 – 3.2)	3.4 (<0.001, 1.7 – 6.8)
Reoperation for deep sternal infection	0.9 (0.650, 0.5 – 1.5)	1.6 (0.106, 0.9 – 2.7)	1.5 (0.460, 0.5 – 4.0)	3.6 (0.004, 1.5 – 8.6)
Septicemia	1.2 (0.455, 0.8 – 1.7)	1.9 (0.002, 1.3 – 2.8)	2.7 (0.002, 1.4 – 5.0)	3.2 (0.001, 1.6 – 6.3)

Note: Variables in the logistic model: CKD stages (reference category: normal function), age, gender, heart ejection fraction, previous heart surgery, urgency status, New York Heart Association class, previous MI, peripheral vascular disease, cardiogenic shock, inotropes at day of surgery, anticoagulation at day of surgery, IV nitrates at day of surgery. You may not have to discuss every single ORs in the table.

Question 5 [25 marks]: Short Answer Questions

[5 marks] Consider that the creatinine level (measured in continuous scale) of patients with type 2 diabetes mellitus follows the normal If you construct a sampling distribution of sample mean for small samples, what would be its distribution? No data analysis required.
[5 marks] Consider 4 groups (A, B, C and D) of diabetic patients who were treated by four different Their fasting HbA1c mmol/L levels were as follows.

Group A	Group B	Group C	Group D
5.6	4.3	4.8	6.1
7.2	4.9	4.4	7.2
10.3	6.9	6.8	5.1
8.4	7.8	5.8	6.1
6.3	8.8		5.3
9.1	5.4		5.6
7.5	8.1		6.6
6.2	5.7		8.1
	6.3		7.2
	5.3		5.2

If the data in groups A and C are non-normal but normal in groups B and D, what are the statistical methods that could have been used to analyse the difference between these four treatment groups? Justify your answer. No data analysis required.

[6 marks] A clinician is performing a multiple logistic regression analysis to identify predictors of hypertension (yes/no) among patients with type 2 diabetes mellitus in Bangladesh. He is considering gender, age, body mass index, education level (up to year 11/above year 11), area of residence (urban/rural), duration of diabetes, adherence to treatment (yes/no), creatinine level, and kidney function (normal or mild, moderate, severe or dialysis) as the potential predictors into the multiple regression model. Do you think that the clinician is correctly justifying his analysis? Discuss briefly. No data analysis

[6 marks] The following graph shows the regression model “Birth-Weight = 6 + 0.596*Oestriol Level” where the data points A and B were excluded from the analysis. If you rerun the regression with all data points including A and B, what would be the possible effects of these two new data points (A and B) on the constant (baseline effect) and beta coefficient of the regression model? No data analysis required.
[3 marks] The regression model “Birth-Weight = 21.6 + 0.596*Oestriol Level” shown in the following graph was obtained excluding data point A from the analysis. If the data point A is included in the analysis how would you describe its effect on the constant (baseline effect) and beta coefficient of the regression model? No data analysis