tSymPerturb converts longitudinal symptom networks into time-indexed intervention strategies

Abstract

Longitudinal symptom networks encode directed prediction across measurement occasions, but outgoing connectivity does not by itself identify which symptom should be modified, how strongly it should be changed, or how a perturbation would propagate to later symptoms. We introduce tSymPerturb, a temporal extension of SymPerturb for cross-lagged panel networks (CLPNs). The framework separates source-state operators (temporal virtual knockout and knockdown), transition operators (directed edge and source-node communication blocking), and strategy procedures (dosage perturbation, combination analysis and sequence optimisation). For a two-wave linear CLPN, the central propagation identity is $Δμ_2 = B(μ_1 - μ_1^*)$, which makes the source time, outcome time and transition operator explicit. The formulation also yields three falsification constraints: dose response is exactly linear under a fixed linear transition model and linear dose map; independent source-state perturbations are additive at the mean level; and genuine treatment order is not identified from a single two-wave transition. In a known 22-node, four-module generating system, analytical temporal-knockout responses agreed with 250,000-draw Monte Carlo estimates within 0.0057 standard deviations. Across 200 independently generated datasets, median Spearman correlation with the population tVPPS ranking increased from 0.76 at n=250 to 0.88 at n=500 and 0.93 at n=1,000; median top-five recovery was 0.60, 0.80 and 0.80, respectively. Multi-wave simulations showed that target profiles can change across propagation horizons despite high overall rank concordance. tSymPerturb therefore converts longitudinal network structure into auditable, time-indexed intervention hypotheses while retaining the distinction between prediction and causal treatment effects.