key: cord-0817856-qlxg76t2
authors: Linli, Zeqiang; Chen, Yinyin; Tian, Guoliang; Guo, Shuixia; Fei, Yu
title: Identifying and quantifying robust risk factors for mortality in critically ill patients with COVID-19 using quantile regression
date: 2020-09-03
journal: Am J Emerg Med
DOI: 10.1016/j.ajem.2020.08.090
sha: c774c26c20e2ee104f4ebe76dce27e2c1142966f
doc_id: 817856
cord_uid: qlxg76t2

OBJECTIVE: Many laboratory indicators form a skewed distribution with outliers in critically ill patients with COVID-19, for which robust methods are needed to precisely determine and quantify fatality risk factors. METHOD: A total of 192 critically ill patients (142 were discharged and 50 died in the hospital) with COVID-19 were included in the sample. Quantile regression was used to determine discrepant laboratory indexes between survivors and non-survivors and quantile shift (QS) was used to quantify the difference. Logistic regression was then used to calculate the odds ratio (OR) and the predictive power of death for each risk indicator. RESULTS: After adjusting for multiple comparisons and controlling numerous confounders, quantile regression revealed that the laboratory indexes of non-survivors were significantly higher in C-reactive protein (CRP; QS = 0.835, p < .001), white blood cell counts (WBC; QS = 0.743, p < .001), glutamic oxaloacetic transaminase (AST; QS = 0.735, p < .001), blood glucose (BG; QS = 0.608, p = .059), fibrin degradation product (FDP; QS = 0.730, p = .080), and partial pressure of carbon dioxide (PCO(2)), and lower in oxygen saturation (SO(2); QS = 0.312, p < .001), calcium (Ca(2+); QS = 0.306, p = .073), and pH. Most of these indexes were associated with an increased fatality risk, and predictive for the probability of death. Especially, CRP is the most prominent index with and odds ratio of 205.97 and predictive accuracy of 93.2%. CONCLUSION: Laboratory indexes provided reliable information on mortality in critically ill patients with COVID-19, which might help improve clinical prediction and treatment at an early stage.

The outbreak of coronavirus-2019 (COVID- 19) , which the World Health Organization (WHO) labeled a "pandemic," has spread rapidly worldwide. [1] By the end of June, COVID-19 had spread to more than 200 countries and regions, and the number of confirmed cases worldwide exceeded 10 million, with nearly 200,000 deaths, according to statistics from Johnson Hopkins University (https://coronavirus.jhu.edu/). Even so, the number of cases, deaths, and affected countries is still increasing. The overall death rate of patients with COVID-19 is about 5%; however, this rises to more than 25% for critically ill patients. [2] The risk of death has usually been evaluated based on laboratory indexes. [3] [4] [5] Identification of reliable biomarkers associated with laboratory indexes may help clinicians assess risk and develop strategies for the prevention of early mortality in critical patients.

Recently, there have been many studies on the clinical course, outcomes, mortality, and risk factors of critically ill patients with COVID-19. For example, Zhou et al. [4] found that older age, higher sequential organ failure assessment score, and d-dimer greater than 1 μg/L at admission were associated with an increased probability of death. Yang et al. [6] demonstrated that the survival term of non-survivors is likely to be within 1-2 weeks after intensive care unit (ICU) admission and the older patients (>65 years) with comorbidities and ARDS are at increased risk of death. Older patients' conditions on admission such as dyspnea, lymphocytopenia, cardiovascular disease and chronic obstructive pulmonary disease (COPD), and the occurrence of acute respiratory distress syndrome (ARDS) during hospitalization were predictive of fatal outcomes.

[7] Although these retrospective observations or cohort studies indicated the clinical courses and risk factors of severe patients via exploratory and descriptive methods, few studies have described the association between case fatality and clinical indexes while adjusting for the false discovery rates (FDR).In addition, each patient's response to the virus is different, with considerable individual differences, for example, application of descriptive statistical methods might be limited, and robust methods are needed to precisely determine and quantify the quantify risk factors of fatality.

Quantile regression is a robust method for addressing outliers and heteroscedasticity in response measurements, and it can estimate the conditional quantiles of the response variable to capture more information about data. Different measures of central tendency and statistical dispersion can be useful to obtain a more comprehensive analysis of the relationship between variables. [9] The current study aimed to solve two important problems, as follows: (1) identification of differences in laboratory indicators between survivors and non-survivors in critically ill patients with COVID-19 using robust statistical methods; (2) determination of risk indicators for in-hospital death and prediction of the probability of death via risk indicators. Specifically, we built a quantile regression of laboratory indexes and outcomes (survival or death) together with some other co-variables to identify discrepant indicators. Then, we conducted post hoc logistic regressions to calculate the risk of fatality associated with abnormal index values.

Findings from this study might help clinicians better understand this disease and reduce mortality.

This single-center study was performed at the Dabie Mountain Regional Medical Center (Huanggang City, China), which is a designated hospital for the treatment of patients with Regional Medical Center before March 13, 2020. After excluding 1272 patients who were not critically ill or who were still hospitalized, 6 patients who died within 24 hours after admission, and 7 inpatients without available key information in their medical records, there were, in total 215 COVID inpatients who met our inclusion criteria ( Figure S1 ). Thus, those participating in this study comprised 51 patients who died during hospitalization and 164 who were discharged. Data on all patients, including demographic data, clinical symptoms, underlying diseases, and laboratory indexes were collected on admission. Laboratory indexes included information on routine tests at the time of admission, such as routine blood indexes.

Because not all patients had undergone all the laboratory examinations, we needed to preprocess the raw data. Specifically, subjects missing more than 15% clinical index values were excluded, and indexes missing more than 15% values were discarded. Accordingly, 192 patients (50 non-survivors and 142 survivors) and 30 laboratory indexes were included in the following analysis; see Table S1 for abbreviations of the laboratory indicators. Imputation of the remaining missing values was conducted utilizing multivariate imputation by chained equations (MICE) implemented in the R package "mice" [10] . We imputed missing data for CRP (2.11%), procalcitonin (PCT; 2.11%), erythrocyte sedimentation rate (ESR; 4.74%), etc. (Table S1 ). Furthermore, the outliers are reset as the boundaries of the data. Specifically, the quantiles of 1% and 99% for each continuous variable were calculated, replacing the data less than 1% quantile and more than 99% quantile, respectively (see Figure S2 for a visual representation).

The normality test and variance homogeneity test showed that laboratory indexes were highly skewed and that there was heteroscedasticity between the two groups (see Figure 1 for a visual sense). [11, 12] It therefore would be inappropriate to use ordinary linear regression (mean regression) to identify the indicators between the two groups in this analysis. Quantile regression is a robust statistical method to capture more information about our data and work well when the data have outliers as the median is much less affected by extreme values than J o u r n a l P r e -p r o o f Journal Pre-proof the mean (0.5 quantile). Therefore, quantile regression was used to identify the different laboratory indicators between the non-survival (= 0) group and survival group (= 1).

Specifically, we built the models as follows: 

In this section, logistic regression was used to 1) calculate the odds ratio, and 2) predict the probability of death.

Binary logistic regression was performed to quantify the risk of laboratory indicators contributing to fatality. Firstly, to avoid the effects of outliers, each laboratory index was divided into three subgroups (i.e., "Normal", "High", and "Low") according to their reference range (Table S1) . Then, single-index logistic regression models were built to calculate the odds ratio (OR) for fatality. Specifically, the logistic regression was as follows:

[ ( = 1)] = 0 + 1 * + 2 * + 3 * + 4 * lactate accumulation (higher lactate [Lat]), and respiratory impairment (lower oxygenation index (OI) values) in non-survivors than in the survival group. The levels of albumin (Alb) and lymphocyte counts (LYMPH) were significantly lower, and glutamic oxaloacetic transaminase (AST) and international normalized ratio (INR) were higher in the survival group than in the non-survival group (uncorrected P < 0.001).

Using quantile regression with = 0.1, 0.3, 0.5, 0.7, 0.9, we found that there were significant differences (P FDR < 0.05) in some indicators between the two groups after adjusting sex, age, Table S2 ). Univariate QS effect sizes of these indicators are shown in Figure2(B) and Table   S3 . QS effect sizes were big and significant in AST, CRP, SO2 and WBC (P < 0.05) and

trended towards significance in BG, Ca, and FDP (P < 0.1).

Logistic regression revealed that, after controlling for sex and duration (time from onset to admission), each additional year of age at admission was associated with a 9% increase in the odds of death (OR: 1.09). After controlling for sex and age, each additional day's duration before hospital admission was associated with a 33% increase in the odds of death (OR: 1.33); the gender effect was not significant (see Figure2(C), Table S4 for more information).

Single-index logistic regression demonstrated that increased odds of in-hospital death were Next, we examined whether these discrepant indexes could predict the probability of fatality using 5-fold CV logistic regression. To be more cautious and clinically significant, subjects with a probability of fatality of more than 0.3 were deemed non-survivors in the prediction procedures. The results suggested that, over the 10 under-sampling iterations, these indicators predicted probability of death with a mean accuracy of more than 81%, mean sensitivity more than 90%, and mean specificity more than 72.8% (Figure2(D) , Table S5 ), in which CRP had an optimal predictive ability with an accuracy of 93.2%, sensitivity of 94.2%, and specificity of 92.2%.

In this retrospective study, we focused on identifying and quantifying the relationship Moreover, the presence of underlying diseases can be seen among many critical patients, especially, digestive, cardiovascular, cerebrovascular and COPD diseases were more prevalent in the dead patients, which might greatly increase the vulnerability of critical patients when faced with COVID-19.

In addition to performing Wilcoxon tests for comparing laboratory variables, which discovered 14 (/30) significantly different indexes (P uncorrected < 0.001) using comparative statistics between the dead and survivors (Table 2) infection [19] , such as H1N1 [8] , H7N9 [20] and SARS [21] . Moreover, CRP was found to be the largest contributory factor among all lab-examination indexes in another analysis that used machine learning and distinguished between the two groups (non-survivor and survivors) J o u r n a l P r e -p r o o f Journal Pre-proof Table 2 

Index (Reference range.) Overall (n=192) a Non-survival (n = 50) Survival (n = 142) P-value b

) WHO announces COVID-19 outbreak a pandemic

Baseline Characteristics and Outcomes of 1591 Patients Infected With SARS-CoV-2 Admitted to ICUs of the Lombardy Region

Clinical Characteristics of 138 Hospitalized Patients With 2019 Novel Coronavirus-Infected Pneumonia in Wuhan

Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study. The Lancet

Clinical characteristics of 113 deceased patients with coronavirus disease 2019: retrospective study

Clinical course and outcomes of critically ill patients with SARS-CoV-2 pneumonia in Wuhan, China: a single-centered, retrospective

C-reactive protein as a biomarker of severe H1N1 influenza

Quantile regression

mice : Multivariate Imputation by Chained Equations in R

Efficient tests for normality, homoscedasticity and serial independence of regression residuals

Robust tests for equality of variances. Contributions to probability and statistics

A Robust Nonparametric Measure of Effect Size Based on an Analog of Cohen's <em>d</em>, Plus Inferences About the Median of the Typical Difference

Altered Cortical Brain Structure and Increased Risk for Disease Seen Decades After Perinatal Exposure to Maternal

Sex Differences in Severity and Mortality Among Patients With COVID-19: Evidence from Pooled Literature Analysis and Insights from Integrated Bioinformatic Analysis

Identification of a novel coronavirus causing severe pneumonia in human: a descriptive study

Clinical features of 2019 novel coronavirus pneumonia in the early stage from a fever clinic in Beijing

Immune responses in influenza A virus and human coronavirus infections: an ongoing battle between the virus and host

A new perspective on C-reactive protein in H7N9 infections

Severe acute respiratory syndrome in Taiwan: analysis of epidemiological characteristics in 29 cases

Critically Ill Patients with Middle East Respiratory Syndrome

Respiratory Virus Co-infection in Acute Respiratory Infections in Children

Viral-Bacterial Co-infections in the Cystic Fibrosis Respiratory Tract

Update on Diagnosis, Treatment, Chemoprophylaxis, and Institutional Outbreak Management of Seasonal Influenzaa

A comparative study on the clinical features of COVID-19 pneumonia to other pneumonias

Liver injury in COVID-19: management and challenges

COVID-19 in a Designated Infectious Diseases 6