Question

Day care centers expose children to a wider variety of germs than the children would be exposed to if they stayed at home more often. This has the obvious downside of more frequent colds and other illnesses, but it also serves to challenge the immune system of children at a critical stage in their development. A study by Gilham et al. (2005) tested whether social activity outside the house in young children affected their probabilty of later developing the white blood cell disease acute lymphoblastic leukemia (ALL), the most common cancer of children. They compared 1272 children with acute lymphoblastic leukemia to 6238 children without acute lymphoblastic leukemia. Of the acute lymphoblastic leukemia kids, 1020 had significant social activity outside the home (including day care) when younger. Of the kids without acute lymphoblastic leukemia, 5343 had significant social activity outside the home. The rest of the children in both groups lacked regular contact with children who were not in their immediate surroundings.

a.) Is this an experimental or observational study?

b.) What are the proportions of children with significant social activity in children with and without acute lymphoblastic leukemia?

c.) What is the odds ratio for acute lymphoblastic leukemia, comparing the groups with and without significant social activity?

d.) What is the 95% confidence interval for this odds ratio?

e.) Does this confidence interval indicate that the amount of social activity is associated with acute lymphoblastic leukemia? If so, did the children with more social activity have a higher or lower occurence of acute lymphoblastic leukemia?

f.) The researchers interpreted their study results in terms of the differing immune system exposure of the children, but gave several alternative explanations for the pattern. Can you think of any possible cofounding variables?

Answer 1

a) The study is an observational study

b) The proportion of children with significant social activity in children with acute lymphoblastic leukemia is approximately 0.802

The proportion of children with significant social activity in children without acute lymphoblastic leukemia is approximately 0.8565

c) The odds ratio is approximately 0.6780

d) The 95% CI is approximately 0.523 < OR < 0.833

e) i) Yes

ii) Children with more social activity have a higher occurrence of acute lymphoblastic leukemia

Explanation:

a) An experimental study is a study in which the researcher adds inputs to the study and then monitors the outcomes

An observational study is one in which the researcher observes risk factors and does not intervene in the process

Therefore, the study is an observational study

b) The proportion of children with significant social activity in children with acute lymphoblastic leukemia is
`\hat p_1` = 1020/1272 = 85/106 =
`0.8\overline {0188679245283}` ≈ 0.802

The proportion of children with significant social activity in children without acute lymphoblastic leukemia is
`\hat p_2` = 5343/6238 ≈ 0.8565

c) We have the following two way table;

`\begin{array}{ccc}Lymphoblastic \ Leukemia &With \ Social \ Activity & Without \ Social \ Activity\\With&1020 \ (a)&252 \ (b)\\Without&5343 \ (c)&895 \ (d) \end{array}`

`The \ odds \ ratio = (1,020 * 895)/(5,343 * 252) \approx 0.6780`

The odds ratio ≈ 0.6780

d) The 95% confidence interval for the odds ratio is given as follows;

`95 \% \ CI = OR \ \pm \ 1.96 * \sqrt{(1)/(a) +(1)/(b)+(1)/(c)+(1)/(d)}`

Where;

a = 1020, b = 252, c = 5343, d = 895

Therefore;

`95 \% \ CI \approx 0.6780 \ \pm \ 1.96 * \sqrt{(1)/(1,020) +(1)/(252)+(1)/(5,343)+(1)/(895)} \approx 0.678 \pm0.155`

The 95% CI ≈ 0.523 < OR < 0.833

e) i) Given that the observed Odds Ratio is within the Confidence Interval, therefore, there is an indication that the amount of social activity is associated with acute lymphoblastic leukemia

ii) Based on the proportion of the study findings, children with more social activity have a higher occurrence of acute lymphoblastic leukemia