Synchrony of biomarker variability indicates a critical transition: Application to mortality prediction in hemodialysis

Abstract

Critical transition theory suggests that complex systems should experience increased temporal variability just before abrupt state changes. We tested this hypothesis in 763 patients on long-term hemodialysis, using 11 biomarkers collected every two weeks and all-cause mortality as a proxy for critical transitions. We find that variability-measured by coefficients of variation (CVs)-increases before death for all 11 clinical biomarkers, and is strikingly synchronized across all biomarkers: the first axis of a principal component analysis on all CVs explains 49% of the variance. This axis then generates powerful predictions of mortality (HR95 = 9.7, p < 0.0001, where HR95 is a scale-invariant metric of hazard ratio; AUC up to 0.82) and starts to increase markedly ∼3 months prior to death. Our results provide an early warning sign of physiological collapse and, more broadly, a quantification of joint system dynamics that opens questions of how system modularity may break down before critical transitions.

Keywords: bioinformatics; biological sciences; computational bioinformatics; health informatics; health sciences; medicine.

Graphical abstract

Figure 1

Study population flowchart diagram Of the 2,565 patients having hemodialysis (HD) at the CHUS between January 1997 and December 2017, we excluded 1694 patients who had HD for less than six months and 73 patients who had both an irregular HD visit frequency and an acute or unspecified kidney failure (KF) diagnosis. Then, we selected visits with biomarker data at least three days apart, and excluded nine patients with incomplete biomarker data (including four without any biomarker profiles) and 26 patients with less than three visits in total. The final study population thus included 763 patients, among whom 413 died within 30 days from their last HD visit and 112 who died more than 30 days after their last HD visit. Within patients still alive at the end of the study period, 59 had a kidney transplant (KT) after which they stopped HD (within 30 days), 117 stopped HD for unknown reasons, and 62 were still on HD within 30 days from the end of the study period. See Tables S1 and S2 for demographic characteristics of patients excluded from analyses and of observations with incomplete data, respectively.

Figure 2

Prediction of death by biomarker levels and variability indices (A and B), HR95, together with 95% confidence intervals, are shown for the levels (means, red) and variability (CVs, blue) of each biomarker considered (A) and integrative multivariate indices (i.e. each principal component calculated on all biomarkers, (B). Levels of hemoglobin, hematocrit, MCH, MCHC, MCV, potassium, sodium, and RBC were inversed (1/x) to obtain HR95 above 1, for ease of representation. (C) Receiver operating characteristic curves for a basic model including only demographic and control variables (black) and for models sequentially adding PC1 (green), CVPC1 (red), and all 10 other CVPCs (blue) are shown. (D) Accuracy of mortality prediction for the first principal component of a PCA performed on means (PC1, blue) or CVs (CVPC1, red), or on either one controlling for the other PCs/CVPCs in the cox model (darker hues), by sequentially increasing the number of PCs/CVPCs added in the cox model. Cox proportional hazard models were performed with (dashed lines) or without (solid lines) including demographic control variables (age, sex, diabetes diagnosis, and length of follow-up). See Figures S1, S2 and S6 for results of sensitivity analyses and Figure S3 for effects of combining means and CVs on mortality prediction. See also Figures S7 and S10 for results with the 4-month variable list and Figure S13 for the effect of the number of observations included in CV calculation. Abbreviations: AUC, area under the curve; MCH, mean corpuscular hemoglobin; MCHC, mean corpuscular hemoglobin concentration; MCV, mean corpuscular volume; RBC, red blood cells; RDW, red cell distribution width; WBC, white blood cells.

Figure 3

Mortality prediction by PC1, PC2, PC6, CVPC1, and CVPC3 in different population subsets (A–E) HR95, i.e. the hazard ratio of being in the 97.5th percentile relative to the 2.5th percentile of the index, together with 95% confidence intervals are shown for PC1 (A), PC2 (B), PC6 (C), CVPC1 (D), and CVPC3 (E) in different subsets of the study population. All models control for age using a cubic spline (with 3 degrees of freedom when performed on a specific age group and five otherwise) and length of follow-up, clustering multiple observations per individual. Models also control for sex and diabetes diagnosis, except when population is stratified using this variable. P-values of proportional assumption tests for the given coefficients are indicated. See Figures S2 and S13 for results of sensitivity analyses using non-redundant biomarkers and at least five observations in CV calculation, respectively. See Figure S9 for results with the 4-month list.

Figure 4

Physiological variability shows a strong coordinated signal distributed evenly across all measured biomarkers (A) Variance explained by PCA on raw biomarkers (triangles) or coefficients of variation (circles), for different population subsets relative to time of death or by demography. (B) Relative biomarker contributions to CVPC1, ordered from largest contribution (hemoglobin) to smallest (MCHC) in the full dataset (see STAR Methods). Subsequent columns are based on loadings of the PCA run exclusively on the indicated subsets. Contribution for a given biomarker is the absolute value of the loading divided by the sum of the absolute values of all loadings. (C) Pearson correlations (Corr) among raw biomarkers, coefficients of variation, and composite indices (CVPC1-3: First through third axes of the PC on coefficients of variation). Blue indicates positive correlations, and red represents negative correlations. Xs represent correlations not significant at α = 0.05. Above the diagonal are the CVs, and below are the biomarker levels. (D) Histogram of pairwise Pearson correlation coefficients between CVs of individual biomarkers. See Figure S2 for results of sensitivity analyses using non-redundant biomarkers and Figure S4 for variable contributions to PC1, PC2, PC6, and CVPC3. See Figures S8 and S11 for results with the 4-month variable list. Abbreviations: MCH, mean corpuscular hemoglobin; MCHC, mean corpuscular hemoglobin concentration; MCV, mean corpuscular volume; RBC, red blood cells; RDW, red cell distribution width; WBC, white blood cells.

Figure 5

CVPC1 trend before death (A) CVPC1, the first principal component of a PCA performed on CVs calculated every 2 (red), 3 (blue), or 4 (green) months, is plotted against time before death. Change point analyses were applied to regression models between CVPC1 and time before death, allowing slopes to vary across individuals, and are represented by the vertical dashed lines with the respective colors. (B) Results from change point analyses applied to regression models between each CVPC (calculated every 3 months) and time before death are indicated with 95% confidence intervals. (C and D) Integrative multivariate indices for biomarker levels (PCs, C) and variability (CVPCs, D) calculated every 3 months are averaged and plotted against time before death, centering at 5 years before death for ease of comparison. Results from change point analyses performed on CVPCs are indicated as vertical dashed lines. (E and F) Biomarker levels (mean z-scores, E) and variability (CVs, F) were calculated every 3 months and averages are plotted against time before death, centering at 5 years before death. See Figure S5 for index trends after hemodialysis initiation and Figure S12 for results with the 4-month list. Abbreviations: MCH, mean corpuscular hemoglobin; MCHC, mean corpuscular hemoglobin concentration; MCV, mean corpuscular volume; RBC, red blood cells; RDW, red cell distribution width; WBC, white blood cells.

Figure 6

Individual CVPC1 trajectories before death or censoring The color represents the status at the end of follow-up (red for patients who died and blue for patients who were alive) and line type represents the diabetes diagnosis (a solid line for non-diabetics and a dashed line for diabetic subjects). Vertical green lines represent hospitalizations. Individuals were randomly chosen from among those with ≥6 years of follow-up.