The following inclusion criteria were applied to recruit COVID-19 patients for this study:
Patients’ demographic and health data were extracted from medical records. All medical records were screened by double opinion of two hospital doctors. Adjudication of any clinical interpretative diagnostic difference was performed by a pulmonologist. Missing clinical data were filled up by discussion with health care staff.
According to above selection criteria, COVID-19 patients were broken down as shown in Fig. 1:
This study was approved by the Ethical Committee of Baqiyatallah University of Medical Sciences (IR.BMSU.REC.1398435; IRCT registration number: IRCT20080901001165N58; Registration date: 2020-05-27) . All ethical guidelines for studies on human subjects were carefully observed and informed consent was obtained from study participants.
Risk factors. According to Centers for Disease Control and Prevention , older age, chronic obstructive pulmonary disease, cardiovascular disease, type 2 diabetes mellitus; obesity, sickle cell disease, chronic kidney disease, immunocompromised status and cancer are risk factors for severe Covid-19 . We considered these factors if they were actually found in the clinical records of the patients. We also included in the statistical analysis additional conditions for which the data were unclear: co-morbidity (grouping miscellaneous conditions); male sex (that is not currently included on the CDC list of risk factors); type 1 diabetes mellitus; hypertension; and smoking. All the above risk factors were considered dichotomous variables in the statistical analysis.
Criteria of classification. In the present study COVID-19 patients were categorized according to death or by TPE administration. For a same risk factor, we estimated the risk of death and/or the probability of being assigned to TPE.
Oxygen support. The disease is a severe pneumonia limiting the gas exchange of lung. Rather than chest CT scan imaging, we assumed as indicator of lung involvement the heaviest oxygen delivery support ever administered. The variable was categorized as 0 (high-flow nasal canula), 1 (noninvasive mechanical ventilation) and 2 (invasive mechanical ventilation with intubation). The variable was treated as ordered polytomous variable in the analysis.
TPE administration. Early initiation, duration and quantity of TPE could be related to better outcomes. Hence, TPE administration was categorized according to days - ranging from 1 to 12 - of treatment start since hospital admission, coding a new variable (timing) as follows:
- 0 (sample including the above Group 1);
- 1 (patients admitted to TPE on days 1 to 3);
- 2 (patients treated on day 4-5); and
- 3 (patients admitted to TPE 6 to 12 days since hospital admission).
We also coded a variable (n_treat) with 3 levels:
- 0 (including the above Group 1),
- 1 (patients pertaining to Group 2 who underwent 1 to 4 sessions of TPE); and
- 2 (Group 2 patients with 5 TPEs).
The latent variable Severity. The latter is not an observed variable but is estimated by SEM program (see below). As can be read in statistical package STATA 14 for SEM analysis, “a variable is latent if it is not in your dataset but you wish it were. You wish you had a variable recording the propensity to commit violent crime, or socioeconomic status, or happiness, or true ability, or even income. Sometimes, latent variables are imagined variants of real variables, variables that are somehow better, such as being measured without error. At the other end of the spectrum are latent variables that are not even conceptually measurable”. Severity is a single score summarizing a large number of measured pretreatment covariates that was particularly useful to adjust for confounders using Cox regression models (see below).
The risk factors of 73 COVID-19 patients, broken down by vital status or TPE treatment, were reported in rows and columns of table 1 to summarize the relationships among observations. At each row and column interception, there were numbers and percentages of subjects having a given trait; the denominator of the percentage was always 53 for patients survived, 20 for those deceased, 43 for patients treated with TPE and 30 for those not undergoing TPE (“Total” in last row of table 1). Risk factors for severe COVID-19 were mainly dichotomic variables (e.g., sex). Table 1 reports only one of the two possible values, the other being easily calculated by subtraction using the total figures (numbers) or 1.00 (percentages). Conversely, all the possible categories of polytomous variables (for example, oxygen support) were reported in table 1. Besides numbers and percentages, table 1 displays the odds ratios (OR), estimated with an exact method due to the relatively limited number of study subjects, with the 95% confidence interval (95%CI) and the two-tail p-value. By default, the conditional maximum likelihood estimates were used in the OR estimation, except for those parameters (e.g., ICU admission) for which a percentage was equal to 100% and the upper bound of 95%CI was infinite. In such a case OR was obtained by Median Unbiased Estimates (MUEs). OR is a measure of association between an exposure and an outcome. The OR represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure. The outcome was “death” in the analysis for columns 2 and 3, or “TPE treatment” for columns 5 and 6. The multiple categories of polytomous variables were coded as ordinal variables (0, 1, 2, etc.) but were considered as “continuous variables” in the context of exact regression analysis; therefore, only one OR was returned by the statistical program.
A numerical value of Severity was estimated by SEM program for each patient. Multiple summary statistics were calculated conditioned on a categorical variable that identified two groups: survived/deceased, or TPE treated/TPE untreated. The numerical statistics for Severity (min, max, median, 25th and 75th percentiles) were reported in table 2, together with the Wilcoxon rank sum test for the equality of the median distribution across the two groups. The distribution of the score Severity score was shown in figure 2 incorporating various vertical lines to mark the median, min and max values of the different samples.
Statistical analysis for assessing TPE effectiveness
The intervention (TPE) was not randomly allocated to study subjects. To rule out the possibility that any threats were responsible for the observed treatment effect, we used a conceptual framework based on knowledge of the relevant literature. We contrasted the two central aspects of the study: TPE therapy (including number and timing of administration) and the latent variable Severity, using mortality as outcome.
All the above assumption were converted into a SEM model. The STATA command syntax for the model was:
sem (Severity -> age sex smoking diabetes hypertension co_morbidities oxygen_support) (mortality <- Severity tpe n_treat timing), stand vce(oim)
“Severity” is capitalized because SEM program commands assume that variables are latent if the first letter of the name is capitalized. In the first and second set of parentheses we specified, respectively, the estimations of the latent variable “Severity” (i.e., identification of a plausible confounder) and the model for the final outcome (i.e., adjustment by illness severity of the mortality associated with number and timing of TPE treatment, and treatment as a whole). In STATA commands, “stand” specifies that the effects are expressed as standardized (or beta) coefficients that make comparisons easy by ignoring the independent variable’s scale of units, while “vce(oim)” is the default and specifies how the standard errors are calculated. We used two SEM goodness-of-fit statistics: (1) the chi square test for “model versus saturated” (the saturated model is the model that fits the covariances perfectly); and (2) the coefficient of determination (CD) that is like R2 for the whole model, a perfect fit corresponding to a CD of 1. SEM results were both tabulated and presented graphically (see figure 3).
The sample size required for SEM is dependent on model complexity. The best option is to consider the model complexity (i.e., the number of exogenous variables) and the following rules of thumb: minimum ratio 5:1, with a recommended ratio of 10:1, or a recommended ratio of 15:1 for data with no normal distribution . With four exogenous variables (tpe, n_treat, timing, Severity) used in the SEM model, we should have a minimum of 20 (= 4 × 5) to a maximum of 60 (= 4 × 15) subjects; in total we reached 73 subjects with complete data, thus fulfilling these requirements.
Furthermore, to examine how the above factors influenced the rate of mortality happening at a particular point in time, the survival analysis using the Cox proportional-hazards models was adopted. Since the test “rho” of proportional-hazards assumption was not statistically significant for each covariate and the global test was neither statistically significant (data not shown), we therefore started by computing univariate Cox analyses for all variables (overall TPE therapy, n_treat, timing, severity), then we fitted multivariate Cox analysis using various models (with different numbers of covariates) to describe how the factors jointly impacted on survival.
Assuming a HR of 0.4, the sample size for Cox proportional-hazard model was estimated to be 38.
Complete case analysis was adopted including all 73 patients. In all analyses 0.05 was set as threshold of statistical significance. All analysis were conducted with the statistical package STATA 14.