Statistical analysis
Information on initiation was recorded at annual intervals
from age 12 to 16, then a 2-year interval to age 18 and
a 3-year interval to age 21. As a result, discrete-time survival
analysis was used to analyze the risk of initiating daily
smoking and the effects of predictors on the risk of initiation.
This method allows incorporation of both time-varying
and invariant predictors. It can also model possible developmental
differences in the effects of family factors by
including the interactions between the predictors and time
[28,29]. The complementary log-log model is more appropriate
than the logit model according to Allison [28], and
was employed in this study:
log[log(1Pit)]t Xit
where Pit is a conditional probability that an event occurs at
time t to an individual i, given that the individual is at risk at
time t and has not already experienced the event at time t.
We first identified the age-specific risk of daily smoking
initiation from age 13 to 21. This was accomplished by
comparing four models where time (age) was modeled as
having (a) no effect (the intercept only model), (b) a linear
effect (the linear model), (c) a constant effect from age 13
to 14 and a linear effect from age 15 to age 21 (the piecewise-
effect model), and (d) different effects at different ages
(the unrestricted model). Although the other three models
contained commonly hypothesized age effects, the piecewise
model was chosen as the best-fitting model from examination
of the coefficients of time (age) in the models
compared. The best-fitting model was considered to have
optimally modeled the change of risk in daily smoking
initiation by age. The predicted probability of daily smoking
initiation can be calculated from this model.