5.1. Model construction
To estimate BMI trajectories over 'time', it is important to select an appropriate variable to reflect time in our model construction. The selection of the time variable and its origin must be clear in the context of a study. For example, in a quality control study of a copier, number of copies produced by the copier could be a better time variable than the calendar time from its year of manufacture. Similarly, in the present study there may be at least two alternative time variables: age of the subjects and time-on-study, the calendar time from the baseline. One can construct HLM using age for the key 'time' variables as discussed in the context of Cox proportional hazards regression model , although the origin of the time variable age, that is 0, may not be appropriate for the present study. In the present example, time-on-study may be a more appropriate variable because its time origin is clear and it is appealing from a clinical point of view to predict future BMI at different points in time.
Let us denote 'time' by Tj, the length of the time interval in years between the baseline and the consecutive ith (i =1,2,...,nj) follow-up for the jth (j =1,2,...,N) individual in the pooled data set. For notational convenience, i = 1 for the baseline, which implies T1j = 0, for all j. First, for the first level of time points for each individual, the BMI, say Yj, was modelled in terms of Ty as follows:
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