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Zorluk: ZorInferential Statistical Tests

A medical researcher is evaluating the relationship between the class of oral antidiabetic medication prescribed and the incidence of major adverse cardiovascular events (MACE) in a retrospective cohort of 1,250 patients with type 2 diabetes. The medication classes are categorized as SGLT2 inhibitors (n=450n = 450), GLP-1 receptor agonists (n=600n = 600), and DPP-4 inhibitors (n=200n = 200). The cardiovascular outcomes over the study period are classified into three mutually exclusive categories: myocardial infarction (n=150n = 150), ischemic stroke (n=100n = 100), and no MACE (n=1,000n = 1,000).

The researcher plans to use a Pearson chi-square test to determine if the choice of medication is independent of cardiovascular outcomes. A key assumption of this test is that no more than 20% of the expected cell frequencies are less than 5.

Under the null hypothesis of no association, what is the expected count of patients who were prescribed a GLP-1 receptor agonist and subsequently experienced a myocardial infarction? (Enter your answer as a whole number).

Cevap: 72 patients

Cevap

72
The expected frequency for any given cell in a contingency table under the null hypothesis of independence is calculated by multiplying the marginal row total by the marginal column total, and then dividing by the grand total. In this clinical scenario, the marginal total for GLP-1 receptor agonists is 600, and the marginal total for myocardial infarction is 150. With a grand total of 1,250 patients, the expected count is calculated as (600×150)/1250(600 \times 150) / 1250, which equals 72. This mathematical value represents the exact number of patients we would expect to observe taking a GLP-1 agonist and subsequently having a myocardial infarction if the choice of antidiabetic medication and the occurrence of cardiovascular outcomes were completely independent.

Adım Adım Çözüm

1
Identify the formula for expected cell frequency in a Pearson chi-square test.
Expected Frequency = (Row Total × Column Total) / Grand Total
To test the null hypothesis of independence, expected counts must be calculated based on the assumption that the row and column variables are completely independent.
2
Determine the relevant marginal totals for the cell of interest.
Row Total (GLP-1 agonists) = 600; Column Total (Myocardial infarction) = 150; Grand Total = 1,250.
These are the necessary values required to substitute into the expected frequency formula.
3
Calculate the expected frequency.
(600 × 150) / 1250 = 90,000 / 1250 = 72.
This yields the count of patients expected in this specific cell if medication choice and cardiovascular outcome are truly independent.

Anahtar Kavram

Calculating expected cell frequencies for a Pearson chi-square test of independence

Alternatif Yöntem

An intuitive way to solve this is to first find the overall rate of myocardial infarction in the entire cohort (150 / 1,250 = 12%). Under the null hypothesis of independence, this 12% risk should apply equally across all medication groups. Therefore, the expected number of events in the 600 patients taking GLP-1 agonists is simply 12% of 600, which equals 72.
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