Checking Model Assumptions II: Homoscedasticity/ Normality/Linearity

Meat intake and serum albumin levels: the data

Checking Model Assumptions II: Homoscedasticity/ Normality/Linearity

1. Meat intake and serum albumin levels: the data

Decreased body stores of protein and energy fuels are associated with diminished functional capacity, impaired quality of life, and increased morbidity and mortality in patients with chronic kidney disease (CKD). Serum albumin is the principal nutritional marker used to identify malnutrition in CKD patients.

In this study researchers investigated whether red meat intake was associated with increased levels of serum albumin in CKD patients. They randomly recruited 50 patients and they measured their serum albumin levels and their daily meat intake. Following their analysis regressing albumin on meat intake (i.e. lm(albumin~meat)), researchers reported no evidence of an association between meat intake and serum albumin levels.

1.1 Using the “albumin.csv” data

The “albumin.csv” data contain information for

• Serum albumin (g/dL)

• Meat intake (g/day)

• Sex (0: female; 1: male)

Task 1: Repeat the analysis similar to what researchers did and answer the following MSQs

MCQ1: Is there evidence of confounding?

[_] Yes.

[_] No. 

MCQ2: What assumption is contravened?

[_] Both the assumptions of homoscedasticity and linearity.

[_] Both the assumptions of normality and linearity.

[_] Both the assumptions of homoscedasticity and normality.

[_] The assumption of normality.

[_] The assumption of homoscedasticity.

[_] The assumption of linearity. 

MCQ3: The assumptions are satisfied if we apply:

[_] A log-transformation for serum albumin.

[_] A log-transformation for meat intake.

[_] A log-transformation for both the serum albumin and meat intake.

[_] An interaction term between meat intake and sex.

2. Measuring ethanol intake: the data

Cardiovascular disease is more prevalent in males and research has been shown that heavy drinking has been associated with manifestations of cardiovascular disease, such as coronary heart disease death, heart failure, cardiac arrest, transient ischaemic attack and ischaemic stroke. Researchers have randomly recruited healthy adults to investigate whether alcohol intake is also greater among male and thus provide a linkage between male sex alcohol intake and development of cardiovascular disease.

2.1 Using the “ethanol.csv” data

The “ethanol.csv” data contain information for the amount of alcohol (measured in gr of ethanol per day) that has been consumed in a day by 272 healthy adults. Additional data include:

• male sex (0: no; 1: yes)

• age in years

• smoking (0: no; 1: yes)

• body mass index, kg/m2

• energy intake, kcal

Task 2: Investigate the association between male sex and ethanol intake, also accounting for all other potential confounders.

MCQ4: Which of the following is correct for the interpretation of the regression coefficient for a male participant?

[_] Males are expected to have on average 4.12g grater intake of ethanol per day, compared to females, holding all the other factors constant.

[_] Males are expected to have on average 0.53g grater intake of ethanol per day, compared to females, holding all the other factors constant.

[_] Males, compared to females, are expected to have on average 70% grater increase in ethanol intake per day, holding all the other factors constant.

MCQ5: Did you observe any influential points? How many? Did the results change after exclusion of the influential points?Hint: You can use the function plot(modelname)

[_] No influential points were observed.

[_] Yes, two influential points were observed, results didn’t change

[_] Yes, two influential points were observed, results change (regression coefficient for male sex increased)

[_] Yes, two influential points were observed, results change (regression coefficient for male sex decreased)