Biomarkers for predicting COVID-19 mortality using the joint modelling approach

doi:10.21203/rs.3.rs-2496703/v1

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Biomarkers for predicting COVID-19 mortality using the joint modelling approach

https://doi.org/10.21203/rs.3.rs-2496703/v1

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Background

Evidence showed the role of biomarkers in predicting severity and mortality of coronavirus disease 2019 (COVID-19). We evaluated associations between several biomarkers measured throughout the follow-up and COVID-19 mortality using the joint modelling (JM) approach, the candidate tool for this kind of data.

Methods

Between February and May 2020, a total of 403 COVID-19 patients were admitted. Baseline characteristics included sex and age, whereas biomarkers included lymphocytes, neutrophils, D-dimer, ferritin, C-reactive protein, glucose and lactate dehydrogenase (LDH). Hazard ratios (HR) and 95% confidence interval (CI) were estimated through JM using a Bayesian approach. We fitted univariable and multivariable JMs including a single biomarker and the set of all biomarkers, respectively.

Results

In univariable JMs, all biomarkers were significantly associated with COVID-19 mortality. In the multivariable JM, HRs were 1.78 (95% CI: 1.13–2.87) per doubling of neutrophils levels, 1.49 (95% CI: 1.19–1.95) per doubling of C-reactive protein levels, 2.66 (95% CI: 1.45–4.95) per an increase of 100 mg/dL of glucose, and 1.31 (95% CI: 1.12–1.55) per an increase of 100 U/L of LDH. No evidence of association was observed for ferritin and lymphocytes in the multivariable JM. Men had a higher risk of COVID-19 mortality than women (HR = 1.75; 95% CI: 1.07–2.80) and age showed the strongest effect with risk starting to rapidly increase from 60 years.

Conclusions

These findings using JM confirm the usefulness of biomarkers in assessing COVID-19 severity and mortality. Monitoring trend patterns of such biomarkers can provide additional help in tailoring the more appropriate care pathway.

COVID-19 mortality

biomarkers

time-varying covariates

joint modelling approach

survival analysis

The coronavirus disease 2019 (COVID-19) pandemic, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), emerged in late 2019, and since then, have been threating human health. As of 10 April, 2022, COVID-19 has affected more than 496 million people and more than 6 million died globally (1). Italy was the first European country to be hit by COVID-19 pandemic outbreak, with clusters of cases detected in Lombardy and the first COVID-19 attributed deaths registered on 22 February 2020.

By the time, evidence has shown that older age is the main predictor of COVID-19 severity and mortality (2, 3). In addition, a meta-analysis comprising more than 36,000 patients reported that men experienced more severe disease (approximately 20% more) and were at higher risk of death from COVID-19 (50% higher risk) than women (4). The presence of pre-existing comorbidities such as obesity (5–9), cardiovascular diseases (10–13), hypertension (11, 13–16), diabetes (13, 17–20), chronic obstructive pulmonary diseases (11, 12, 14, 21), and cancer (12, 14, 22) are more common in patients with severe COVID-19, impacting on their survival (23). Limited evidence suggested a role of pre-existing chronic kidney diseases (24) and cerebrovascular diseases (11) in developing severe stage of COVID-19. Other recognized predictors for COVID-19 severity and mortality include haematological, coagulation, hematic, and biochemical markers (25–27). The most investigated were lymphocytes, neutrophils, eosinophils (haematological), D-dimer, prothrombin time, and activated partial-thromboplastin time (coagulation), aspartate aminotransferase, alanine aminotransferase (hematic), ferritin, C-reactive protein, procalcitonin, and lactate dehydrogenase (biochemical).

During the first wave of COVID-19 pandemic, physicians at Istituto Clinico Città Studi in Milan collected a set of biomarkers, measured repeatedly over the follow-up period, in order to understand whether changing in their levels might be used as prognostic factors for severity and mortality of COVID-19.

Thus, we evaluated here the association between a set of biomarkers measured throughout the follow-up and COVID-19 mortality using the joint modelling (JM) approach, the candidate tool for this kind of data.

Study design and patients

Between 24 February and 26 May 2020, a total of 403 COVID-19 patients were admitted at Istituto Clinico Città Studi in Milan. Patients aged 21–100 years (mean of 72.4 and standard deviation of 17.0 years) and 58.3% were men. Baseline characteristics included sex and age of patients, whereas the set of biomarkers included haematological, coagulation and biochemical markers. Haematological markers included lymphocytes (count x 10³/µL) and neutrophils (count x 10³/µL), coagulation markers included D-dimer (ng/mL), and biochemical markers included ferritin (ng/mL), C-reactive protein (mg/L), glucose (mg/dL) and lactate dehydrogenase – LDH (U/L). The biomarkers data was extracted from the patient’s clinical charts and stored in a database.

Person-time at risk (expressed in days) was computed as the time elapsed from the day of hospital admission to the day of COVID-19 death (event time), either to the day of hospital discharge, or to the day of moving in other structure (right-censoring time), whichever came first.

Statistical analyses

We evaluated the association between biomarkers and COVID-19 mortality using JM proposed by Rizopoulos (28). Particularly in the first epidemic outbreak, physicians did not have standard clinical protocols for management of COVID-19 patients and for this reason, measurements of biomarkers were highly incomplete especially at the baseline. In this context, the classical time-to-event analysis using Cox regression (29, 30) and baseline characteristics is unfeasible whereas the time-dependent Cox model (31) would likely lead to biased estimates in assessing the association between such incomplete time-varying covariates and mortality risk.

When time-varying covariates are incomplete, the JM is suitable to estimate the effect of such covariates (i.e. biomarkers) on a time-to-event outcome (i.e. the death from COVID-19). Briefly, the JM consists of two sub-models: (i) the survival sub-model used to predict hazards for a set of time-invariant covariates (i.e. baseline characteristics) and (ii) the longitudinal sub-model used to predict the complete trajectories of time-varying covariates during the follow-up, possibly considering a set of time-invariant covariates. The two sub-models are interdependent by means a set of random effects, also called shared parameters. The shared parameters (i.e. patient-specific predicted trajectories of time-varying covariates) derive from the longitudinal sub-model and they are plugged-in the survival sub-model. We used a Bayesian approach for fitting JMs. In particular, estimation of JM’s parameters proceeded using Markov chain Monte Carlo (MCMC) algorithm. The posterior distribution of the model parameters is derived under the assumptions that given the shared parameters, both longitudinal and survival sub-models are assumed independent, and the longitudinal outcomes of each patient are assumed independent. For explorative purposes, we set independent and non-informative priors for baseline characteristics and for the shared parameters.

We fitted univariable and multivariable JMs. In addition to sex and age, univariable JMs included a single biomarker, whereas the multivariable JM included the set of all biomarkers. The logarithmic transformation was used to account for the skewness in the distribution of lymphocytes (log-lymphocytes), neutrophils (log-neutrophils), D-dimer (log-D-dimer), ferritin (log-ferritin), and C-reactive protein (log-C-reactive protein). In addition, glucose (glucose/100) and LDH (LDH/100) levels were rescaled by dividing by 100 for numerical stability. In order to account for possible non-linear effects, we modelled age and patient-specific biomarkers trajectories through the follow-up time by means of natural cubic splines with two knots. Two knots are generally sufficient to detect mild non-linear relationships and to avoid over-parametrization of the model considering the available sample size. Due to the high number of patients (78; 19%) with missing values for D-dimer during the whole follow-up period, we excluded it from the set of biomarkers in the multivariable JM. Analyses were performed using JMbayes (32) package in R Statistical Software, version 4.0.5 (R Core Team 2021).

Among 403 COVID-19 patients admitted at Istituto Clinico Città Studi, 140 died during the follow-up. Among 263 patients survived, 99 were discharged and 164 were moved in other structures. The median of follow-up was 14 days (range: 0–78 days).

Table 1 reported the distribution of COVID-19 patients according to age group and sex. A higher mortality was observed for elderly patients compared with patients aged < 60 years (reference category), with a similar trend for men and women. Among men, the hazard ratios (HRs) run from 3.55 (95% confidence interval – CI: 1.07, 11.81) for patients aged 60–69 years to 26.88 (95% CI: 8.52, 84.81) for patients aged 90 years or older; among women the corresponding figures were 1.84 (95% CI: 0.11, 29.41) and 18.74 (95% CI: 2.51, 139.91).

Table 1

Distribution of 403 COVID-19 patients according to age and sex.
Age (years)	Men (n = 235; 58.3%)				Women (n = 168; 41.7%)
Age (years)	Patients at risk	Mortality rate^a		HR (95% CI)^b	Patients at risk	Mortality rate^a		HR (95% CI)^b
< 40	14	0.00	3.18^c	Ref	6	0.00	2.27^c	Ref
40–49	26	0.00			6	0.00
50–59	29	7.59			17	3.32
60–69	41	10.85		3.55 (1.07, 11.81)	15	4.37		1.84 (0.11, 29.41)
70–79	50	26.72		8.34 (2.86, 24.32)	26	28.44		12.12 (1.58, 93.30)
80–89	62	30.55		9.27 (3.27, 26.32)	71	23.67		10.29 (1.40, 75.49)
≥ 90	13	88.71		26.88 (8.52, 84.81)	27	43.86		18.74 (2.51, 139.91)
^aCalculated per 1000 person-days; ^bHazard ratios (HR) and corresponding 95% confidence intervals (CI) were calculated using Cox regression with age < 60 years as reference category separately for men and women; ^cMortality rate for age < 60 years.

Table 2 reported estimates of univariable and multivariable JMs. With regard to the longitudinal sub-model of univariable JMs, the predicted log-lymphocytes count significantly increased through the follow-up time according to the positive coefficients of time at measurement. Conversely, the predicted log-lymphocytes count significantly decreased with increasing age (negative spline coefficients for age) and men showed lower predicted log-lymphocytes count than women (negative coefficient for sex), though not significant. Instead, the predicted log-neutrophils count decreased during the follow-up time, it increased with age and men showed higher levels than women. Likewise, the predicted log-D-dimer and log-ferritin levels decreased through time, increased with age and men had higher levels. For log-C-reactive protein, predicted levels showed a mixed trend through time. In particular, levels initially decreased according to the negative spline coefficient of time at measurement concerning the first part of follow-up and increased thereafter. The predicted log-C-reactive protein levels increased with age and men showed higher levels than women. Predicted levels of glucose and LDH significantly decreased during the follow-up. Only for LDH, predicted levels significantly increased with age and men had higher levels.

Table 2

Univariable and multivariable joint models^a (JM) estimates.
Variables	Univariable JM		Multivariable JM
Variables	Effect (95% CI)	p-value	Effect (95% CI)	p-value
Haematological biomarkers
Longitudinal sub-model: log-lymphocytes (count x 10³/µL)
Intercept	0.68 (0.29, 1.05)	p < 0.01	0.64 (0.38, 0.90)	p < 0.01
ns(time at measurement in days, 2)1	1.11 (0.95, 1.27)	p < 0.01	1.23 (0.98, 1.49)	p < 0.01
ns(time at measurement in days, 2)2	0.52 (0.40, 0.65)	p < 0.01	0.93 (0.47, 1.43)	p < 0.01
ns(age in years, 2)1	-1.47 (-2.20, -0.72)	p < 0.01	-1.32 (-1.81, -0.82)	p < 0.01
ns(age in years, 2)2	-0.69 (-0.97, -0.39)	p < 0.01	-0.53 (-0.74, -0.30)	p < 0.01
Sex (male vs female)	-0.11 (-0.25, 0.03)	p = 0.14	-0.13 (-0.23, -0.04)	p < 0.01
Longitudinal sub-model: log-neutrophils (count x 10³/µL)
Intercept	0.90 (0.57, 1.22)	p < 0.01	1.09 (0.79, 1.41)	p < 0.01
ns(time at measurement in days, 2)1	-1.10 (-1.40, -0.78)	p < 0.01	-0.81 (-1.21, 0.41)	p < 0.01
ns(time at measurement in days, 2)2	-2.89 (-3.55, -2.15)	p < 0.01	-2.15 (-2.98, -1.36)	p < 0.01
ns(age in years, 2)1	1.24 (0.65, 1.85)	p < 0.01	0.94 (0.32, 1.54)	p < 0.01
ns(age in years, 2)2	0.89 (0.64, 1.15)	p < 0.01	0.62 (0.35, 0.89)	p < 0.01
Sex (male vs female)	0.25 (0.13, 0.37)	p < 0.01	0.23 (0.12, 0.34)	p < 0.01
Coagulation biomarkers
Longitudinal sub-model: log-D-dimer (ng/mL)
Intercept	4.34 (3.62, 5.01)	p < 0.01	-	-
ns(time at measurement in days, 2)1	-1.72 (-2.02, -1.39)	p < 0.01	-	-
ns(time at measurement in days, 2)2	-2.99 (-3.47, -2.57)	p < 0.01	-	-
ns(age in years, 2)1	4.18 (2.93, 5.52)	p < 0.01	-	-
ns(age in years, 2)2	1.57 (1.01, 2.09)	p < 0.01	-	-
Sex (male vs female)	0.35 (0.10, 0.61)	p = 0.01	-	-
Biochemical biomarkers
Longitudinal sub-model: log-ferritin (ng/mL)
Intercept	5.18 (4.67, 5.67)	p < 0.01	5.27 (4.74, 5.82)	p < 0.01
ns(time at measurement in days, 2)1	-1.05 (-1.32, -0.77)	p < 0.01	-1.16 (-1.66, -0.71)	p < 0.01
ns(time at measurement in days, 2)2	-1.69 (-2.23, -1.08)	p < 0.01	-2.07 (-3.25, -1.05)	p = 0.01
ns(age in years, 2)1	2.13 (1.15, 3.06)	p < 0.01	1.93 (0.82, 2.97)	p < 0.01
ns(age in years, 2)2	0.20 (-0.18, 0.59)	p = 0.31	0.16 (-0.29, 0.63)	p = 0.52
Sex (male vs female)	0.53 (0.34, 0.70)	p < 0.01	0.56 (0.35, 0.76)	p < 0.01
Longitudinal sub-model: log-C-reactive protein (mg/L)
Intercept	-0.19 (-0.71, 0.34)	p = 0.47	0.29 (-0.32, 0.91)	p = 0.36
ns(time at measurement in days, 2)1	-4.23 (-5.09, -3.35)	p < 0.01	-5.16 (-6.47, -3.90)	p < 0.01
ns(time at measurement in days, 2)2	1.03 (-0.65, 2.64)	p = 0.23	-0.84 (-3.67, 1.79)	p = 0.51
ns(age in years, 2)1	4.31 (3.30, 5.32)	p < 0.01	3.67 (2.51, 4.83)	p < 0.01
ns(age in years, 2)2	0.98 (0.57, 1.40)	p < 0.01	0.70 (0.20, 1.24)	p < 0.04
Sex (male vs female)	0.50 (0.31, 0.68)	p < 0.01	0.38 (0.13, 0.61)	p < 0.01
Longitudinal sub-model: glucose/100 (mg/dL)
Intercept	0.94 (0.45, 1.44)	p < 0.01	0.99 (0.75, 1.25)	p < 0.01
ns(time at measurement in days, 2)1	-0.33 (-0.45, -0.20)	p < 0.01	-0.40 (-0.64, -0.17)	p < 0.01
ns(time at measurement in days, 2)2	-0.35 (-0.52, -0.20)	p < 0.01	-0.61 (-1.23, -0.04)	p = 0.04
ns(age in years, 2)1	0.57 (-0.42, 1.49)	p = 0.25	0.41 (-0.08, 0.88)	p = 0.11
ns(age in years, 2)2	0.08 (-0.30, 0.46)	p = 0.66	0.05 (-0.15, 0.24)	p = 0.64
Sex (male vs female)	0.02 (-0.16, 0.21)	p = 0.80	0.04 (-0.04, 0.14)	p = 0.33
Longitudinal sub-model: LDH/100 (U/L)
Intercept	2.09 (1.56, 2.63)	p < 0.01	2.65 (1.76, 3.49)	p < 0.01
ns(time at measurement in days, 2)1	-2.45 (-2.70, -2.19)	p < 0.01	-2.45 (-3.21, 1.69)	p < 0.01
ns(time at measurement in days, 2)2	-3.74 (-4.77, -2.80)	p < 0.01	-3.32 (-5.36, -1.35)	p < 0.01
ns(age in years, 2)1	2.39 (1.36, 3.40)	p < 0.01	1.16 (-0.47, 2.91)	p = 0.16
ns(age in years, 2)2	0.86 (0.46, 1.25)	p < 0.01	0.44 (-0.33, 1.21)	p = 0.23
Sex (male vs female)	0.27 (0.07, 0.47)	p = 0.01	0.29 (-0.01, 0.61)	p = 0.05
Variables	HR (95% CI)	p-value	HR (95% CI)	p-value
Survival sub-model
Baseline characteristics
ns(age in years, 2)1^b	-	-	9.12 (2.17, 16.30)	p < 0.01
ns(age in years, 2)2^b	-	-	3.96 (2.53, 5.38)	p < 0.01
Sex (male vs female)^c	-	-	1.75 (1.07, 2.80)	p = 0.03
Haematological biomarkers		-
lymphocytes (count x 10³/µL)^d	0.58 (0.46, 0.74)	p < 0.01	1.01 (0.74, 1.43)	p = 0.96
neutrophils (count x 10³/µL)^d	2.95 (2.31, 3.76)	p < 0.01	1.78 (1.13, 2.87)	p = 0.02
Coagulation biomarkers
D-dimer (ng/mL)^d	1.39 (1.24, 1.56)	p < 0.01	Excluded due to the high number of missing values
Biochemical biomarkers
ferritin (ng/mL)^d	1.46 (1.26, 1.73)	p < 0.01	0.92 (0.73, 1.16)	p = 0.46
C-reactive protein (mg/L)^d	2.53 (2.07, 3.18)	p < 0.01	1.49 (1.19, 1.95)	p < 0.01
glucose (mg/dL)^e	3.16 (2.18, 4.53)	p < 0.01	2.66 (1.45, 4.95)	p < 0.01
LDH (U/L)^e	1.80 (1.63, 1.99)	p < 0.01	1.31 (1.12, 1.55)	p < 0.01
^aUnivariable and multivariable JMs included age modelled by means of a natural cubic spline with 2 knots, and sex (baseline characteristics) and biomarkers (time-varying covariates). In the longitudinal sub-models, time at measurement of biomarkers was modelled by means of a natural cubic spline with 2 knots. The HR estimates and 95% CI of the association between biomarkers and COVID-19 mortality are reported in the survival sub-model section. The HR estimates and 95% CI for age and sex of the univariate models are not reported; ^bEstimates are reported as log-hazard and 95% CI; ^cEstimates are reported as HR and 95% CI for men compared than women; ^dEstimates are reported as HR and 95% CI for doubling of biomarker levels; ^eEstimates are reported as HR and 95% CI for an increase of 100 unit of biomarker level. Abbreviations: CI, confidence interval; HR, hazard ratio.

With regard to survival sub-model of univariable JMs, all biomarkers were significantly associated with COVID-19 mortality. An increase in the levels of biomarkers was associated with an increased in the mortality risk, except for lymphocytes. In particular, doubling of lymphocytes was associated with approximately halving mortality risk with an HR of 0.58 (95% CI: 0.46–0.74). The strongest associations were observed for neutrophils (HR = 2.95; 95% CI: 2.31–3.76 per doubling of levels), C-reactive protein (HR = 2.53; 95% CI: 2.07–3.18 per doubling of levels), and glucose (HR = 3.16; 95% CI: 2.18–4.53 for an increase of 100 mg/dl).

In the multivariable JM, there was no more evidence of association with COVID-19 mortality for ferritin and lymphocytes. Furthermore, the strength of the association was attenuated for the other biomarkers considered. In particular, the HRs were 1.78 (95% CI: 1.13–2.87) per doubling of neutrophils, 1.49 (95% CI: 1.19–1.95) per doubling of C-reactive protein levels, 2.66 (95% CI: 1.45–4.95) per an increase of 100 mg/dL of glucose, and 1.31 (95% CI: 1.12–1.55) per an increase of 100 U/L of LDH. Lastly, men had a risk nearly 2-fold higher than women (HR = 1.75; 95% CI: 1.07–2.80; survival sub-model of multivariable JM in Table 2) and age showed the strongest effect on COVID-19 mortality (according to the high log-hazard estimate in the survival sub-model of multivariable JM in Table 2) with HRs starting to rapidly increase approximately from 60 years for both men and women (Fig. 1, last panel).

We used the JM approach to evaluate the association between a set of biomarkers and COVID-19 mortality including some baseline patients’ characteristics. Patients were admitted to a hospital in Milan during the first wave of COVID-19 pandemic outbreak. In the multivariable JM, increasing levels of some of the investigated biomarkers (i.e. neutrophils, C-reactive protein, glucose, and LDH) were significantly associated with a higher mortality. In addition, men were at higher risk of dying than women and the strongest association was observed for increasing age.

Previous findings on biomarkers showed their association with the severity and mortality of COVID-19 (2, 3, 25, 27). In particular, there was a wide evidence of lymphopenia among COVID-19 patients (17, 33–39). Furthermore, some studies also reported a lower absolute number of lymphocytes in patients with more severe illness, compared with patients with mild illness (37, 40, 41). Accordingly, we found a lower mortality risk for increasing the number of lymphocytes. A higher neutrophils count at hospital admission was reported in patients with severe or critical disease stage compared with patients with mild or moderate stage of COVID-19 (35, 38). Progressive increase in the number of neutrophils was associated with death (38). Our predicted means of neutrophils count for patients died followed a similar trend during the follow-up. In particular, the predicted means were 8.02 (95% CI: 6.59, 9.76) at baseline, 9.39 (95% CI: 7.72, 11.43) at 7-day, and 10.07 (95% CI: 8.27, 12.25) at 15-day follow-up; no further increase in predicted means was observed for subsequent follow-up times. Elevated D-dimer levels were frequently reported in COVID-19 patients (40, 42–44). Several meta-analyses showed the prognostic value of D-dimer for disease severity and mortality (1, 45–54). In addition, two studies reported that a baseline level of > 2 µg/mL was associated with a higher mortality (55, 56). Among patients died in the present study, the predicted mean of D-dimer at 7-days follow-up was 1.75 µg/mL and increasing the levels resulted in a higher mortality risk. Elevated levels of ferritin were associated with the progression to severe stages of COVID-19, as well as mortality (54, 57–59). A meta-analysis investigated the prognostic value of different biomarkers of anaemia and iron metabolism (including ferritin) in COVID-19 patients (60). Based on findings of 18 observational studies, comprising more than 7,000 patients, the authors showed approximately 2-fold higher pooled mean of ferritin levels in non-survivors (1303.08 ng/mL; 95% CI: 1072.26, 1533.90 ng/mL) than survivors (650.67; 95% CI: 541.84, 759.51 ng/mL). Likewise, our predicted mean levels of ferritin at 7-days follow-up were nearly 2 times higher in patients died (1058.22; 95% CI: 740.25, 1512.77 ng/mL) than in patients survived (556.90; 95% CI: 481.32, 644.35 ng/mL). In the multivariable JM, however, there was no evidence of association between ferritin and the risk of COVID-19 mortality. High levels of C-reactive protein were associated with developing of severe COVID-19 and higher mortality (1, 46, 49, 51, 53, 54, 57). A level of > 10 mg/L have been shown to be a predictor of poor outcome (54). In our analysis, the predicted mean levels of C-reactive protein were 10.71 mg/L (95% CI: 6.60, 17.38 mg/L) for non-survivors and 2.22 mg/L (95% CI: 1.66, 2.98 mg/L) for survivors. Furthermore, a meta-analysis showed a 4-fold higher risk of severe disease for levels of C-reactive protein > 10 mg/L (61). We estimated a mortality risk of approximately 2.5 times (univariable JM) and 1.5 times (multivariable JM) higher per doubling of C-reactive protein levels. Higher levels of glucose were observed in the severe and critical groups of COVID-19 patients (25, 51). Among the biomarkers considered in the present analysis, glucose showed the strongest association with COVID-19 mortality taking into account the effect of other biomarkers (HR from multivariable JM = 2.66; 95% CI: 1.45–4.95 per an increase of 100 mg/dL). Lastly, elevated LDH levels have been reported in COVID-19 patients with the highest levels for patients with severe disease (1, 46, 51, 62). A meta-analysis included more than 3,000 COVID-19 patients showed a pooled mean level of LDH 1.54 times higher for severe illness compared to mild severity (63). Similarly, our predicted LDH mean level at 7-day follow-up were approximately 2 times higher in patients died (478.68 U/L; 95% CI: 397.50, 559.87 U/L) than survivors (259.24; 95% CI: 244.49, 273.98 UI/l). Additionally, elevated baseline LDH levels were associated with higher mortality risk with a HR of 1.30 (95% CI: 1.11, 1.52) per an increase of 100 U/L (64) which is almost the same found in the present study (HR from multivariable JM = 1.31; 95% CI: 1.12–1.55 per an increase of 100 U/L).

To sum up, decreased lymphocytes count, increased neutrophils count, D-dimer, ferritin, C-reactive protein, glucose, and LDH levels were shown to be associated with the severity of the disease. It has been well assessed that high level of inflammation is characteristic of COVID-19 pneumonia and the observed biomarker trends might be the manifestation of this inflammatory reaction and the subsequent cell damages (65). In particular, significantly lower lymphocytes and higher neutrophils counts have been widely observed in patients with severe than in those with mild COVID-19: the lymphopenia might be caused both by the inflammatory mediators which directly damage the immune system cells, and by the migration of the circulating lymphocytes into inflammatory lung tissues (66, 67). Along with these, persistent stimulation by SARS-CoV-2 might lead to lymphocytes exhaustion. High levels of ferritin might reflect the macrophage activation, since the synthesis of ferritin is responsive to alteration in cytokine status (68), whereas the increase of LDH in serum is the manifestation of the cell necrosis, strongly increased in severe pneumonia (69).

The traditional time-to-event analysis using Cox regression can be extended to encompass time-varying covariates (i.e. covariates that are repeatedly measured over the follow-up and their values can change across time), as long as time-varying covariates are exogenous. In this study, the time-varying covariates appear endogenous. The main features of such covariates are that: (i) their existence (and/or future measurements) is directly related to the occurrence (or non-occurrence) of the event of interest, and (ii) they are measured intermittently (i.e. incomplete information occur at random points during the follow-up because, for instance, individuals may skip schedule visits and dropout from the study) (28). In order to properly incorporate endogenous time-varying covariates, the JM framework for the simultaneously analysis of the survival data of the event and the longitudinal data of the time-varying covariates was proposed. All biomarkers considered in the present study were typical examples of endogenous time-varying covariates and it was desirable to use the JM approach. In such case, using the time-dependent Cox model could lead to underestimated effect size (i.e. shrink HRs).

The lack of information on patients’ treatment should be counted as a limitation of the present study. Different treatments may have differently modified biomarkers levels and consequently their association with the risk of COVID-19 mortality. However, a standard treatment protocol for COVID-19 did not yet implemented at the time of data collection, minimaxing the variability due to different drugs administration deriving from tailored care management. In addition, information on other baseline characteristics such as body mass index, smoking habits, and pre-existing comorbidities were not available. The inclusion of these variable in the model could modify the HR estimates introducing further limit of the present analysis. Nevertheless, this is the first work using the JM approach to analyse jointly several biomarkers measured longitudinally during the follow-up for predicting survival time of COVID-19 patients.

Increasing levels of some biomarkers, i.e. neutrophils, C-reactive protein, glucose, and LDH were significantly associated with a higher COVID-19 mortality. Men were at higher risk of dying than women and the strongest association was observed for age with COVID-19 mortality risk starting to rapidly increase approximately from 60 years. Nevertheless, findings of the present study using the JM approach confirm the usefulness of biomarkers in assessing COVID-19 severity and mortality. Consequently, prognosis definition and therapy, and outcome prediction can benefit from the trend pattern analysis of such biomarkers.

CI, confidence interval; COVID-19, coronavirus disease 2019; HR, hazard ratio; JM, joint modelling; LDH, lactate dehydrogenase; MCMC, Markov chain Monte Carlo; SARS-CoV-2, severe acute respiratory syndrome coronavirus 2.

Acknowledgments

Not applicable

Authors’ contributions

P.F. and M.S. designed the research idea and supervised data collection; A.M. and S.D. supervised the laboratory testing; F.A. and M.D.M. conducted the statistical analysis; P.F., S.D., F.A., and M.D.M. interpreted the results; S.D., F.A., M.D., and M.D.M. drafted the manuscript; all authors read and approved the final version of the manuscript.

Funding

This work was partially supported by Italian Ministry of Education, Universities and Research project PRIN 2017, prot.20178S4EK9004, entitled “Innovative statistical methods in biomedical research on biomarkers: from their identification to their use in clinical practice”; PF and SD were supported by Grant PRIN 2017 prot.KM79NN, from Italian Ministry of Education, Universities and Research; SD and FA were supported by Grant Seal of Excellence (SOE) 2019, from University of Milan.

Availability of data and materials

Anonymized patient data are available for use in collaborative studies to researchers upon reasonable request to the corresponding author ([email protected]). Data will be provided following the review and approval of a research proposal (including a statistical analysis plan) and the completion of a data‑sharing agreement.

Ethics approval and consent to participate

Clinical specimens and patients' data were collected upon approval of the Local Ethical Committee and signature of the informed consent (Fondazione Ca’ Granda, Ospedale Maggiore, Milano, Italy, approved the protocol 456_2020, on May 2020)

Consent for publication

Not applicable.

Competing interests

The authors have no conflicts of interest to declare.

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Biomarkers for predicting COVID-19 mortality using the joint modelling approach

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