Currently, I am working on a project that aims to predict a certain cancer-related outcome (y) using a number of control (c) and predictor (X) variables:

y(i) = a + c(it) + X(it) + u (1)

In Equation (1): y(i) is continuous in nature, data is available

*only*as means of values aggregated from 2009 to 2013; c(it) is a vector of several

*longitudinal*(yearly) control variables available from 2009 through 2013; and X(it) is a vector of several

*longitudinal*(yearly) predictor variables available from 2010 through 2013.

As you can see, the outcome does not vary over time as it is available only in the aggregated form of means; however the controls and predictors are in the panel form. Facing such a limitation, panel models do not seem applicable. Therefore, my approach is to firstly estimate:

y(i) = a + c(i) + X(i) + u (2), where c(i) and X(i) are aggregated as means

And secondly to (a) ensure consistency of the coefficients, and (b) test for lagged effects estimate:

y(i) = a + c(it-1) + X(it-1) + u (3), where c(it-1) and X(it-1) are from 2012 only

y(i) = a + c(it-2) + X(it-2) + u (4), where c(it-2) and X(it-2) are from 2011 only

y(i) = a + c(it-3) + X(it-3) + u (5), where c(it-3) and X(it-3) are from 2010 only

Please advice if my modeling approach seems plausible (considering the limitation related to DV data).