Question

Chronic disease, such as type I diabetes can lead to observer medical complications. For a long time, the medical community was divided on whether or not to aggressively control the patients’ blood glucose levels. The Diabetes Control and Complications Trial (DCCT) randomly assigned volunteers with type I diabetes without retinopathy either to a conventional treatment or to a more intensive treatment aimed at maintaining blood glucose levels as close to normal as possible. The health of 378 patients in the conventional care group and 348 in the intensive care group was closely monitored for about 6 years. By the end of the study, 91 patients in the conventional treatment group had developed retinopathy, compared to only 23 in the intensive treatment group. 2 of 4 2 a. Briefly describe the objective of this study. b. Describe the parameter we are interested in making decision about. Determine the point estimation of the parameter. c. Construct 95% Confidence Interval (CI) for the parameter you cited in part (b) above. Interpret the CI in context. d. What conclusion can you draw from the CI in part (c) above?

Answer 1

a.

The objective of the study is to identify whether the blood glucose levels affects the the development of retinopathy.

b.

The parameter we are interested is the differences in the true proportion of patients developing retinopathy in intensive treatment group and conventional care group.

c.

Point estimation of the parameter are,

=  91/378 = 0.2407

= 23 / 348 = 0.0661

- = 0.2407 - 0.0661 = 0.1746

d.

Pooled proportion, p = (91 + 23) / (378 + 348) = 0.1570

Standard error of differences in proportions, SE =

= 0.027

Z score for 95% Confidence Interval is 1.96

95% Confidence Interval of differences in the true proportion is,

(0.1746 - 1.96 * 0.027 ,  0.1746 + 1.96 * 0.027)

(0.1217 ,  0.2275)

We are 95% confident that the interval (0.1217 ,  0.2275) contains the differences in the true proportion of patients developing retinopathy in intensive treatment group and conventional care group.

d.

Since the 95% Confidence Interval does not contain zero or negative values, we can conclude that the true proportion of patients developing retinopathy in conventional care group is larger than the true proportion of patients developing retinopathy in intensive treatment group.