EXERCISE
9.1 Radioactive radon is an inert gas that can migrate from soil and rock and
accumulate in enclosed areas such as underground mines and homes. The
radioactive decay of trace amounts of uranium in Earth’s crust through
radium is the source of radon, or more precisely, the isotope radon-222.
Radon-222 emits alpha particles; when inhaled, alpha particles rapidly
di¤use across the alveolar membrane of the lung and are transported by
the blood to all parts of the body. Due to the relatively high flow rate of
blood in bone marrow, this may be a biologically plausible mechanism for
the development of leukemia. Table E9.1 provides some data from a
case–control study to investigate the association between indoor residen-
tial radon exposure and risk of childhood acute myeloid leukemia. The
variables are:
Disease (1, case; 2, control)
Radon (radon concentration in Bq/m^3 )
Some characteristics of the child: gender (1, male; 2, female), race (1,
white; 2, black; 3, Hispanic; 4, Asian; 5, others), Down’s syndrome (a
known risk factor for leukemia; 1, no; 2, yes)
Risk factors from the parents: Msmoke (1, mother a current smoker; 2,
no; 0, unknown), Mdrink (1, mother a current alcohol drinker; 2, no; 0,
unknown), Fsmoke (1, father a current smoker; 2, no; 0, unknown),
Fdrink (1, father a current alcohol drinker; 2, no; 0, unknown).
(Note: An electronic copy of this file is available upon request.)
(a) Taken collectively, do the covariates contribute significantly to sepa-
ration of the cases and controls? Give your interpretation for the
measure of goodness of fitC.
(b)Fit the multiple regression model to obtain estimates of individual
regression coe‰cients and their standard errors. Draw your conclu-
sion concerning the conditional contribution of each factor.
(c) Within the context of the multiple regression model in part (b), does
gender alter the e¤ect of Down’s syndrome?
(d) Within the context of the multiple regression model in part (b), does
Down’s syndrome alter the e¤ect of radon exposure?
(e) Within the context of the multiple regression model in part (b), taken
collectively, do the smoking–drinking variables (by the father or
mother) relate significanty to the disease of the child?
(f) Within the context of the multiple regression model in part (b), is the
e¤ect of radon concentration linear?
(g) Focus on radon exposure as the primary factor, taken collectively,
was this main e¤ect altered by any other covariates?
EXERCISE 341