91Ó°ÊÓ

A case-control study was performed among 145 subjects with macular degeneration and 34 controls, all of whom were \(70-\) to 79 -year-old women. A genetic risk score was developed to help differentiate the cases from the controls. The risk score was categorized into six groups \((1,2,3,4,\) 5, 6), with 6 being the highest risk and 1 being the lowest risk. The data in Table 10.48 were obtained relating the risk score to case/control status. What test can be performed to study the association between case/control status and risk score? Specifically, we are interested in testing whether cases tend to have consistently higher risk scores or consistently lower risk scores than controls.

Step by step solution

01

Understand the Variables

We have two main variables: the case/control status and the genetic risk score. The case/control status is dichotomous (either case or control), and the genetic risk score is ordinal, ranging from 1 to 6.

02

Identify the Hypothesis

The hypothesis is whether there is an association between the case/control status and the risk score, specifically if cases tend to have higher or lower risk scores than controls.

03

Choose the Appropriate Test

Since we're testing the association between an ordinal variable (risk score) and a dichotomous variable (case/control), we use the Mann-Whitney U test (also known as the Wilcoxon rank-sum test) to compare the distributions of risk scores between the two groups.

04

Conclusion

The Mann-Whitney U test will indicate if there is a statistically significant difference in the distributions of risk scores between cases and controls, thereby showing whether the cases have consistently higher or lower scores.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Case-Control Study

A case-control study is a type of observational study frequently used in epidemiology. It helps scientists understand causes of diseases by comparing two groups: one with the disease (cases) and one without (controls). This study design is retrospective, meaning researchers look back in time to find common exposures or risk factors.

• The cases in our exercise have macular degeneration, while the controls do not.
• Both groups consist of women aged 70 to 79, lending consistency to the study.

In our exercise, the main focus was to explore the connection between the genetic risk score and the presence of macular degeneration through these groups.

Ordinary Variable

In statistics, an ordinary (or ordinal) variable is one that represents data with a natural order. However, ordinal variables do not have a consistent difference between their values, unlike interval or ratio variables. A typical example of an ordinary variable is a ranking system.

• In the exercise, the genetic risk score is an ordinal variable categorized into six levels, 1 through 6.
• This risk score helps differentiate the severity of risk, with higher numbers indicating higher risk.

Since this score ranks the level of genetic risk, it is crucial in determining statistical tests that can assess its relationship with another variable, like case/control status.

Statistical Association

Statistical association refers to a relationship between two or more variables where changes in one variable relate to changes in another. Determining a statistical association is essential in understanding possible cause-effect connections.

• In the context of our exercise, we want to know if a higher risk score is statistically associated with being a case (having macular degeneration) as opposed to a control.
• Such associations are usually examined through statistical tests that evaluate if the observed patterns in the data are due to chance.

To explore this in our exercise, we use a Mann-Whitney U test. This test checks if there is a significant difference between the risk scores of cases versus controls, thus indicating whether a statistical association exists.