Methods for joint modeling of longitudinal omics data and time-to-event outcomes: applications to lysophosphatidylcholines in connection to aging and mortality in the Long Life Family Study

Abstract

Studying the relationships between longitudinal changes in omics variables and event risks requires specific methodologies for joint analyses of longitudinal and time-to-event outcomes. We applied two such approaches (joint models [JM], stochastic process models [SPM]) to longitudinal metabolomics data from the Long Life Family Study, focusing on the understudied associations of longitudinal changes in lysophosphatidylcholines (LPCs) with mortality and aging-related outcomes. We analyzed 23 LPC species, with 5,066 measurements of each in 3,462 participants, 1,245 of whom died during follow-up. JM analyses found that higher levels of the majority of LPC species were associated with lower mortality risks, with the largest magnitude observed for LPC 15:0/0:0 (hazard ratio: 0.71, 95% CI (0.64, 0.79)). SPM applications to LPC 15:0/0:0 revealed that the JM association reflects underlying aging-related processes: a decline in robustness to deviations from optimal LPC levels, higher equilibrium LPC levels in females, and the opposite age-related changes in the equilibrium and optimal LPC levels (declining and increasing, respectively), which lead to increased mortality risks with age. Our results support LPCs as biomarkers of aging and related decline in biological robustness, and call for further exploration of factors underlying age-related changes in LPC in relation to mortality and diseases.

Keywords: aging; longitudinal omics; lysophosphatidylcholines; mortality; repeated measurements.

Figure 1

Applications of stochastic process models to measurements of LPC 15:0/0:0 and mortality data in the LLFS: Estimates of different components of the model. (A) quadratic hazard term (Q(t, c)); (B) adaptive capacity (|a(t, c)|); (C) volatility coefficient (b(t, c)); (D) equilibrium trajectory (f₁ (t, c)); (E) optimal trajectory (f₀ (t, c)); (F) measure of allostatic load (AL(t, c) = |f₀ (t, c)–f₁ (t, c)|); p-values shown on the graphs are for different null hypotheses (H0): H0: Q(t, c) = Q(c) (P_QnoT); H0: Q(t, c) = Q(t) (P_QnoC); H0: Q(t, c) = 0 (P_Q0); H0: a(t, c) = a(c) (P_AnoT); H0: a(t, c) = a(t) (P_AnoC); H0: b(t, c) = b(t) (P_BnoC); H0: f₁(t, c) = f₁(c) (P_F1noT); H0: f₁(t, c) = f₁(t) (P_F1noC); H0: f₀(t, c) = f₀(c) (P_F0noT); H0: f₀(t, c) = f₀(t) (P_F0noC); H0: f₁(t, c) = f₀(t, c), i.e., AL(t, c) = 0 (P_AL0); H0: f₁(t, c) = f₁(c) and f₀(t, c) = f₀ (c), i.e., AL(t, c) = AL(c) (P_ALnoT). LPC values were transformed (see Data).