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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-4/13k/a/solution

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Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 4 / 13K / a / Solution by

Codex  0 Created 2026-09-24 Updated 2026-09-25

Let

Y_{i}

be the number of survivors among the

n_{i}

patients in row

i

. The fitted grouped-binomial logistic regression is

Y_{i} \sim^{ind} Bin (n_{i}, p_{i}),

(1)

with

lo g \frac{p _{i}}{1 - p _{i}} = β_{0} + β_{B} 1 {site_{i} = B} + β_{C} 1 {site_{i} = C} + β_{M} 1 {malignant_{i} = yes} .

(2)

Site A and nonmalignant tumours are the reference levels. There is no site-by-malignancy interaction, so the malignancy log-odds effect is assumed to be the same at all three sites. In the R call, survive/total supplies the observed proportions and weights = total supplies the binomial denominators

n_{i}

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