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Pairwise measures of causal direction in the epidemiology of sleep problems and depression - PubMed

Pairwise measures of causal direction in the epidemiology of sleep problems and depression

Tom Rosenström et al. PLoS One. 2012.

Abstract

Depressive mood is often preceded by sleep problems, suggesting that they increase the risk of depression. Sleep problems can also reflect prodromal symptom of depression, thus temporal precedence alone is insufficient to confirm causality. The authors applied recently introduced statistical causal-discovery algorithms that can estimate causality from cross-sectional samples in order to infer the direction of causality between the two sets of symptoms from a novel perspective. Two common-population samples were used; one from the Young Finns study (690 men and 997 women, average age 37.7 years, range 30-45), and another from the Wisconsin Longitudinal study (3101 men and 3539 women, average age 53.1 years, range 52-55). These included three depression questionnaires (two in Young Finns data) and two sleep problem questionnaires. Three different causality estimates were constructed for each data set, tested in a benchmark data with a (practically) known causality, and tested for assumption violations using simulated data. Causality algorithms performed well in the benchmark data and simulations, and a prediction was drawn for future empirical studies to confirm: for minor depression/dysphoria, sleep problems cause significantly more dysphoria than dysphoria causes sleep problems. The situation may change as depression becomes more severe, or more severe levels of symptoms are evaluated; also, artefacts due to severe depression being less well presented in the population data than minor depression may intervene the estimation for depression scales that emphasize severe symptoms. The findings are consistent with other emerging epidemiological and biological evidence.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Analytic strategy of the study.

First, a causality algorithm is applied to infer whether the variable Y is a weighted sum of the variable X and a residual term e (X causes Y), or vice versa. Second, assumptions of the applied causal model are evaluated. Third, a simulation study probes the model’s sensitivity for assumption violations that are difficult to evaluate directly; most importantly, the impact of the partial confounding on the algorithms ability to recognize causal association is evaluated.

Figure 2
Figure 2. Three linear (Ordinary Least Squares) regression models corresponding to causal directions estimated by DirectLiNGAM-algorithm.

Each row shows data for a model estimated in one data set. First panel of a row (A, D, or G) shows the linear (thick line) and quadratic (thin line) fits, superimposed on the data points. Jitter (a uniform random variable ranging from −0.1 to 0.1) was added to variables to enhance visibility of data points. Second panel is a scatterplot of the linear model residual against the independent variable. Last panel of each row shows a Gaussian probability density with mean and standard deviation equaling those of the observed residual distribution, and a kernel density estimate of the observed linear model residual.

Figure 3
Figure 3. Simulation study approximating the observed data.

The situation where mBDI was linearly modeled in the Young Finns data using Sleep problems as independent/predicting variable was modeled. Histograms of Sleep problems (A), Ordinary Least Squares residual of mBDI (B), and the dependent mBDI (C) are shown, together with probability distributions fitted to these data (thick lines, y-axis re-scaled for the number of observations), and (Gaussian-) kernel density estimates of the data (thin lines). First panel suggests that Mixture of Gaussians is not a good model for Sleep problems; a shifted Exponential distribution was chosen.

Figure 4
Figure 4. Simulation results by gradually perturbing the model of Figure 3.

The rows signify the applied causality statistic: DirectLiNGAM-based (panels A,B,C), Skew-based (D,E,F), and Tanh-based statistic (G,H,I). Two leftmost panels of each row show estimation success (proportion of correct estimates) as a function of the degree of latent confounding. Different types of confounding (linear or proportional) and different distributional conditions were tested: Gaussian mixture (GM), Exponential (Exp), and GM and Exp (different) residual, and with all GM distributions; see methods. Last panel shows estimation success when an amount of Gaussian ‘measurement error’ indicated by horizontal axis was added to independent variable.

Figure 5
Figure 5. Total Test Information for the items of BDI-II (solid line) and for those of mBDI (dashed line).

Units of the horizontal axis represent standard deviations of the latent/general depression as estimated by unidimensional Graded Response Model. Information per latent depression value holds no absolute meaning; it is estimated by integral over an adjacent step in 200 point discretization of horizontal axis. In addition to (Fisher) Information-content of the scales, the thin dotted line plots a Gaussian kernel density estimate from the factor scores of the estimated Graded Response Model, normalized to maximum of one; this serves to illustrate which severity-levels were actually present in the population-based Young Finns data set.

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