1. In a retrospective cohort study on the impact of low birth weight on the development of type 2 diabetes in middle and old age, 152 subjects with low birth weight (<2500 g)

were selected using medical records from a hospital, and 738 subjects with normal birth weight (≥2500 g) were selected as the control. Data on age, sex (1 = Male, 2 =

Female), birth weight, family history of type 2 diabetes (1 = Yes, 0 = No), serum lipid status (1 = Abnormal, 0 = Normal), and diagnosis of type 2 diabetes (1 = Yes, 0 = No) at investigation were collected and part of the data is shown in Table 16.17.

(a) In order to study the effect of low birth weight on type 2 diabetes, what model do you think is more suitable for analyzing this data? Please establish a suitable logistic regression equation.

(b) Write down the regression model structure and interpret the logit link function in your own words.

(c) How do you determine the partial regression coefficients? What is the difference with the least squares method?

(d) Perform significance tests of the partial regression coefficients and the overall fitted model. What are the differences between these tests? Can they replace each other?

(e) Is the regression model obtained by the stepwise regression method optimal?
Why?

(f) From what perspectives could you assess the goodness-of-fit of the model?
(g) Given a 69-year-old man who has no family history of diabetes, abnormal serum lipid profiles, and was of normal birth weight, predict his probability of having type 2 diabetes.
(h) Suppose the data are collected using a paired samples design. What is the difference in the estimation method? Why is a paired samples design more efficient than the present design?