Dynamic aspects of ORF1ab and N RNA cycle threshold values among COVID-19 patients in China

Abstract

The dynamics of viral loads among COVID-19 patients in Changzhou, China were evaluated using dynamic random effects models. The models were estimated by maximum likelihood methods allowing for between and within patient variations. Statistical criteria were developed for focusing on viral RNAs for clinical decision making. The empirical results showed that inflammation among patients were significant predictors of cycle threshold values for ORF1ab and N RNAs. Moreover, within subject variations were higher in Ct values of ORF1ab RNA indicating that assessment of N RNA may be adequate in resource-poor settings. The inter-relationships between ORF1ab and N RNAs were investigated and the need for developing comprehensive models for viral load dynamics is emphasized.

Highlights

• •It is important to account for between and within patient variations in Ct values of ORF1ab and N RNAs.
• •Statistical methods are useful for discriminating between alternative empirical models.
• •Ct values for ORF1ab RNA exhibit higher within-patient variations and N RNA may be adequate in many settings.
• •Inflammation among patients appear more important than their ages for the dynamics of viral loads.

1. Introduction

The SARS-CoV-2 pandemic has already claimed over a million lives worldwide (Coronavirus Resource Center, 2020; Sironi et al., 2020). This virus gains entry to cells by attaching to ACE-2 receptors and its ~30 kb positive sense single stranded RNA encodes multiple proteins. ORF1a mainly encodes proteases and proteins that interfere with the innate immune response, while ORF1b mostly encodes proteins involved in RNA synthesis. Proteins such as spike, viral envelope, membrane, and Nucleocapsid are encoded by sub-genomic RNAs (Costela-Ruiz et al., 2020). Note that for simplifying the terminology, PCR products corresponding to the RNAs encoding the ORF1ab and N proteins are abbreviated as ORF1ab and N RNAs, respectively. Further, there has been interest in monitoring the viral load kinetics among Covid-19 patients especially of ORF1ab and N RNAs (He et al., 2020, Xu et al., 2020).Typically, investigators report SARS-CoV-2 RNA copies and/or cycle threshold values from RT-PCR assays, with Ct values >40 indicating undetectable viral loads.

The investigation of four sets of conceptual and methodological issues can facilitate clinical decision making. First, SARS-CoV-2 appears to induce an “imbalanced host response”(Blanco-Melo et al., 2020) in terms of production of cytokines such as IL-1, IL-2, IL-4, IL-6, IL-10, IL-17, and TNF-α, and interferon INF-I, INF-II, INF-III. The cytokines can elevate C-reactive protein levels that are indicators of inflammation and are likely to affect viral dynamics. Second, the estimation of associations between viral loads or Ct values at different time points (i.e., autocorrelations) needs to account for between and within patient variations that can be large (Bhargava and Sargan, 1983; Bhargava et al., 2018). Third, it is important to investigate using statistical method the relative merits of analyzing viral loads and Ct values for ORF1ab and N RNAs, reflecting, respectively, non-structural and structural proteins, for the efficient utilization of medical resources. While the previous literature (Shi et al., 2020) has analyzed data for ORF1ab and N RNAs, the between and within-patient variations in viral loads are important for RNA selection. Fourth, the effects of explanatory variables such as patients' biomarkers for viral load kinetics need to be investigated using comprehensive empirical models. The estimation methods in this article are helpful for selection of viral RNA and for drawing robust inferences regarding the effects of biomarkers for viral load dynamics. The empirical results from Changzhou, China can facilitate the formulation of evidence-based policies.

2. Methods

Dynamic random effects models, accounting for between and within patient variations in natural logarithms of Ct values for ORF1ab and N RNAs, were estimated by maximum likelihood methods (Bhargava and Sargan, 1983) using a data set from Changzhou, China for 49 COVID-19 patients observed at 3 time points within a fortnight (Xu et al., 2020). The Specification 1 allowed Ct values to depend on patients' ages and its square to account for possible nonlinearities:

$$ln{\left(\mathrm{Ct}\mathrm{ORF}1\mathrm{ab}\right)}_{\mathrm{it}}={\mathrm{a}}_0+{\mathrm{a}}_{1}ln{\left(\mathrm{Age}\right)}_{\mathrm{i}}+{\mathrm{a}}_2{{\left[ln\left(\mathrm{Age}\right)\right]}^2}_{\mathrm{i}}+{\mathrm{a}}_{3}ln{\left(\mathrm{Ct}\mathrm{ORF}1\mathrm{ab}\right)}_{\mathrm{it}-1}+{\mathrm{u}}_{\mathrm{it}}\left(i=1,\dots ,49;t=2,3\right)$$ (1)

In eq. (1), “ln” represents natural logarithms and a₀, a₁, a₂, and a₃ are unknown coefficients, with a₃ being the coefficient of the “lagged dependent variable”. The u_it's can be decomposed in a random effects fashion as:

$${\mathrm{u}}_{\mathrm{it}}={\mathrm{\delta }}_{\mathrm{i}}+{\mathrm{v}}_{\mathrm{it}}$$ (2)

where δ_i are patient-specific random effects that were distributed with zero mean and constant variance, and v_it were distributed with zero mean and constant variance. Specification 2 replaced the age variable by C-reactive protein levels. A comparison of the maximized values of log-likelihood functions for Specifications 1 and 2 can afford insights into the adequacy of empirical models.

3. Results

The sample means and standard deviations of explanatory variables such as patients' age, gender, and C-reactive protein levels and for Ct values for ORF1ab and N RNAs at 3 time points are reported in Table 1 . Patients' C-reactive protein levels were generally elevated at admittance, and there were rapid increases in Ct values and they approached 40 at the time of the third survey for most patients.

Table 1.

Sample means and standard deviations of cycle threshold values for ORF1ab and N RNAs and for selected explanatory variables of COVID-19 patients in Changzhou, China ¹.

Survey round:	Survey round 1		Survey round 2		Survey round 3
Variable:	Mean	SD	Mean	SD	Mean	SD
Age, years	42.32	17.92
Gender, 0–1	1.50	0.50
C-reactive protein, mg/dL	3.28	1.89
Plasma Ca, mmo/L	2.25	0.12
Ct ORF1ab RNA, n	28.48	5.04	34.28	5.31	37.22	4.64
Ct N RNA, n	29.96	4.90	35.06	4.50	37.62	4.10

¹The 3 survey rounds were conducted within a fortnight for the 49 patients.

In Table 2 , the results from Specification 1 for Ct values for ORF1ab and N RNAs showed nonlinear effects with respect to age though the coefficients were not statistically significant at the 5% level, presumably due to small number of patients. This was also true for the ratios of between to within variances that require larger sample sizes. However, coefficients of the lagged dependent variables were significant (P < 0.05) and the estimates 0.346 and 0.288 for ORF1ab and N RNAs, respectively, showed rapid convergence of Ct values to 40. Moreover, within patient variances for Ct values for ORF1ab and N RNAs were 0.0163 and 0.0100, respectively, thereby showing 50% higher variations for ORF1ab RNA.

Table 2.

Maximum likelihood estimates of dynamic random effects models for cycle threshold values for ORF1ab and N RNAs for COVID-19 patients in Changzhou, China¹.

Dependent variable:	ln (Ct OFR1ab RNA), n				ln (Ct N RNA), n
	Specification 12		Specification 22		Specification 12		Specification 22
Explanatory variables:	Coefficient	SE	Coefficient	SE	Coefficient	SE	Coefficient	SE
Constant	2.394	0.494	2.314	0.430	2.564	0.462	2.551	0.335
ln (Age), years	−0.076	0.201	–		−0.025	0.207	–
[ln (Age)]2, n	0.020	0.030	–		0.009	0.031	–
ln (C-reactive protein), mg/dL	–		0.035⁎	0.017	–		0.030⁎	0.016
[ln(C-reactive protein)]2, n	–		−0.006	0.006	–		−0.007	0.005
Lagged dependent variable	0.346⁎	0.011	0.358⁎	0.124	0.288⁎	0.093	0.295⁎	0.096
Between/within variance, n	0.153	0.241	0.122	0.264	0.384	0.319	0.337	0.290
Within variance, n	0.0163		0.0166		0.0100		0.0101
2× Maximized log-likelihood function	557.10		559.01		598.98		601.43

¹Slope coefficients and standard errors are reported for 49 patients in 3 survey rounds ² Specifications 1 and 2 included, respectively, patients' ages and C-reactive protein levels and their respective squares. ^⁎P < 0.05.

The coefficients of CRP levels in Specification 2 were significantly associated with Ct values for ORF1ab and N RNAs, though the squared terms were not significant. Moreover, maximized values of log-likelihood functions were higher for Specifications 2 indicating the importance of inflammation rather than of age for the dynamics of viral loads. Lastly, the fit of models for Ct values for N RNA were better than those for ORF1ab RNA.

4. Discussion

The results from the empirical analyses showed the importance of modeling the dynamics of Ct values especially for N RNA among patients in Changzhou, China. The relatively high variations in Ct values underscore the importance of modeling viral load kinetics using data on large numbers of patients. Such analyses are essential, for example, when investigating the effects of plasma vitamin D levels (Grant et al., 2020) on viral loads. While patients' 25 (OH) D concentrations were not assessed in the study, plasma calcium levels were not significantly associated with Ct values; estimated coefficients in the models for ORF1ab and N RNAs were not statistically different from zero.

Lastly, for further comparisons of the empirical models for ORF1ab and N RNAs using statistical criteria, the bivariate correlations between Ct values of ORF1ab and N RNAs in the three survey rounds were 0.96, 0.91, and 0.92, respectively. Subsequently, enlarged models were estimated for Ct values of ORF1ab RNA that were explained by the Ct values for N RNA and vice versa. The estimated coefficient of Ct values for N RNA was 1.07 in the model for ORF1ab RNA and it was not statistically different from 1. In contrast, in the model for N RNA, coefficient of Ct values for ORF1ab RNA was 0.77 and was significantly less than 1. This was perhaps not surprising because the N protein is encoded on a sub-genomic RNA that is more abundant than the ORF1ab RNA. In view of the apparent lack of cross-reactivity of these RNAs with other coronaviruses (Yan et al., 2020), these results indicate that there may not be additional information in Ct values for ORF1ab RNA, and Ct values for N RNA can convey the essential information for clinical decision making and for policy formulation.

Declaration of Competing Interest

The research in this manuscript was not supported by any funding agency and there are no conflicts of interest

Credit author statement

Alok Bhargava is responsible for all aspects of this manuscript