An exploration of the dynamic longitudinal relationship between mental health and alcohol consumption: a prospective cohort study

Background Despite intense investigation, the temporal sequence between alcohol consumption and mental health remains unclear. This study explored the relationship between alcohol consumption and mental health over multiple occasions, and compared a series of competing theoretical models to determine which best reflected the association between the two. Methods Data from phases 5 (1997 to 1999), 7 (2002 to 2004), and 9 (2007 to 2009) of the Whitehall II prospective cohort study were used, providing approximately 10 years of follow-up for 6,330 participants (73% men; mean ± SD age 55.8 ± 6.0 years). Mental health was assessed using the Short Form (SF)-36 mental health component score. Alcohol consumption was defined as the number of UK units of alcohol drunk per week. Four dynamic latent change score models were compared: 1) a baseline model in which alcohol consumption and mental health trajectories did not influence each other, 2) and model in which alcohol consumption influenced changes in mental health but mental health exerted no effect on changes in drinking and 3) vice versa, and (4) a reciprocal model in which both variables influenced changes in each other. Results The third model, in which mental health influenced changes in alcohol consumption but not vice versa, was the best fit. In this model, the effect of previous mental health on upcoming change in alcohol consumption was negative (γ = -0.31, 95% CI -0.52 to -0.10), meaning that those with better mental health tended to make greater reductions (or shallower increases) in their drinking between occasions. Conclusions Mental health appears to be the leading indicator of change in the dynamic longitudinal relationship between mental health and weekly alcohol consumption in this sample of middle-aged adults. In addition to fuelling increases in alcohol consumption among low-level consumers, poor mental health may also be a maintaining factor for heavy alcohol consumption. Future work should seek to examine whether there are critical levels of alcohol intake at which different dynamic relationships begin to emerge between alcohol-related measures and mental health.


Description of latent change score methodology
Here we will describe LCS models based on two processes with observed variables Y and X at time t for individual i (represented in graphical form in Supplementary Figure 1A with parameters defined in Supplementary Table 1A).
To begin, it is important to detail how latent difference scores are defined. Under classical true score theory it is assumed that each observed raw score (Y) can be disintegrated into a true underlying latent score y or x plus a source of unrelated error e. Therefore, one can express the observed score at any time point t, as:

Equation 1
These true scores can then be used to define the present state of each variable as a function of its preceding state plus changes, using:

Equation 2
From this equation, the development of observed variables Y and X for a person i at a specified time t can be expressed as a function of an originally observed score (y0 and x0) 3 plus the linear accumulation of latent changes (∆y and ∆x) until that point in time in addition to residual error (e y and e x ), using:

Equation 3
Following from this a model for the latent change scores can be written as a product of multiple components. One common specification is:

Equation 4
Whereby change in a variable (∆) is a function of three main components: a constant amount (α) which is associated with the additive scores/slopes of y is and x is (the sum of latent changes over time), a quantity proportional to the previous state of itself (β)in many ways representing a self-feedback loop, and an amount proportional to the previous state of the alternative variable (γ). Placing certain constraints on parts of this model allow for specific hypotheses to be tested.
For example, constraining the coupling parameter (γ) from x to y to be zero, while estimating the parameter from y to x, would model a leading effect of y to changes in x. Alternatively, one is able to use Equation 4 above (both coupling parameters freed) to explore whether there 4 is a reciprocal dynamic relationship over time between both variables. Note that the dynamics of the system are brought about by jointly estimating and interpreting these equations together as the model parameters are dependent on each other [1][2][3][4].
It is also important to note that while LCS models are usually specified as linear models,  Mean of initial conditions for variables Y and X µys, µxs Mean of additive scores for variables Y and X σ 2 y0, σ 2 x0 Variance of initial conditions of Y and X σ 2 ys, σ 2 xs Variance of additive scores of Y and X σ 2 ey, σ 2 ex Residual variance of initial conditions of Y and X σy0, x0 Covariance of initial conditions of Y and X σys, xs Covariance of additive scores of Y and X σey, ex Covariance of residuals from Y and X K Constant to estimate means and intercepts (set to 1)