**UFBA**

# Statistics for Epidemiology-Nicholas P. Jewell-1584884339-CRC-2003-352-$94

(Parte **7** de 7)

3.7 Problems

Question 3.1

The original data from the Chicago Western Electric Study (Shekelle et al., 1981) gave information on deaths from coronary heart disease (CHD) among middle-aged men who were free from CHD at entry into the study and who were followed for 25 years. There were 205 men who reported eating no fish at entry. Of these individuals, 42 subsequently died from CHD. Compute the 95% confidence interval for the unknown CHD mortality proportion for this group using both methods described in Section 3.3.

Repeat the calculations for the group of 261 men who reported consuming more than 35 g of fish per day at entry. Of these, 34 died from CHD during the study.

Question 3.2

Weitoft et al. (2003) investigated the impact of children growing up with a single parent in terms of the children’s mental health morbidity and mortality, both total and causespecific. Data were taken from Swedish national registries, covering almost the entire national population. Children were identified as living with (i) the same single adult or (i) with two adults if their living situation remained the same in 1985 and 1990, with no requirement that the adults be biological parents. All such children were then tracked from 1991 until the end of 1999, at which point the youngest child was 14 years old and the oldest 26. Table 3.5 describes a very small amount of their data and ignores key variables including the sex of the child, socioeconomic factors, and other demographic factors.

Suppose a child is randomly selected from this population; based on Table 3.5, compute the probability that this child (1) was raised by a single parent; (2) died during the follow-up period; and (3) committed suicide during the same period. Compute the mortality and suicide probabilities conditional on whether the child lived with one or two parents. Comment on the possibility of association between their living arrangement and both mortality and suicide risk.

Table 3.5 Mortality in children living with one or two parents in Sweden

Total Mortality Child’s Living Arrangement Death Survival Total

With single parent 56 65,029 65,085 With two parents 608 920,649 921,257

Total 664 985,678 986,342 Suicide

Child’s Living Arrangement Suicide No Suicide Total

With single parent 19 65,066 65,085 With two parents 96 921,161 921,257 Total 115 986,227 986,342

Source: Weitoft et al. (2003).

Question 3.3

Section 3.3 indicates that, in large samples, the standard deviation of a proportion

estimate of a population probability or proportion p is given by the square root of p(1!p)/n, where n is the sample size. Compute this standard deviation for n=16, 25, 100, 1000, 1500, and 2000 when p=0.5, 0.3, 0.1, and 0.01. At a fixed sample size, for which values of p does the estimate have the highest standard deviation? If p=0.5, how large a sample size is needed to guarantee that the width of a 95% confidence interval is no larger (i) than 0.05 and (i) than 0.02?

(Parte **7** de 7)