Comparison of Clinical Characteristics of Patients with Asymptomatic vs Symptomatic Coronavirus Disease 2019 in Wuhan, China
Authors: Xien Gui
Yong Xiong
Rongrong Yang
Journal: JAMA Network Open (2020)
Discipline: CLINICAL MEDICINE
Keywords: clinical characteristics; patients; asymptomatic; symptomatic; coronavirus disease 2019
Affiliations: Department of Infectious Diseases, Zhongnan Hospital, Wuhan University, Wuhan, China.

Abstract:  This case series examines clinical characteristics of patients with asymptomatic vs symptomatic coronavirus disease 2019 in Wuhan, China. 

Retracted: No

PubPeer comments:
 Authors state in Methods that u201cMeans for continuous variables were compared using independent group t tests when the data were normally distributed; otherwise, the Mann-Whitney U test was used.u201d This contradicts the data they present in the singular table which reports results of comparisons on their continuous variables using an F test. No results of any Mann-Whitney U or t tests are reported. The F test is inappropriate for non-normal data and comparing mean values of two groups which is the difference the authors are aiming to detect. **Could the authors please provide either the raw data or the p values for the associations when the data is analyzed using Mann-Whitney U or t tests?** This paper as currently published contains results of an incorrect statistical test applied to almost every element in the singular table. The test as applied yields significant p values for associations which are likely insignificant if analyzed as the authors stated they did in the Methods. This articleu2019s results are misleading. Since this piece is getting significant media attention from places such as NBC, Business Insider, Yahoo News, etc a prompt response from the authors is appreciated. , 
 Thank you very much for your questions. After checking with other authors, we confirmed that the data about means for continuous variables present in the singular table were used t tests. , 
 Thank you for your reply. **I canu2019t find any evidence that t tests were applied but there is strong evidence that one-way ANOVA, while still inappropriate, was the test used to compare the continuous variables**. I can show this by calculating the p values that would result from the reported test statistics assuming the values you report are either 1) an F ratio from one-way ANOVA, 2) a chi-squared test, or 3) a two-way t test. Comparing these to the p values you report, itu2019s clear that the most likely situation is that a one-way ANOVA was applied. See here: (*Note:* I ve rounded to same number of significant figures that you all have in your table and bolded which distribution(s) gave the same p values as the table): |Characteristic | Table 1 reported statistic | Table 1 reported P value | Two-tailed P value assuming statistic is from t distribution | P value assuming statistic is from chi-square distribution | P value assuming statistic is from F distribution | |:---------------------------| :-----------------------------------: |:----------------------------:| :----------------------------------------:| :-------------------------------: | :----------------------------:| |Age| 10.221| 0.001 |NA| NA | 0.002| |Women|9.685|0.002|NA|**0.002**|NA| |Baseline liver injury|4.905|0.03|NA| **0.03**| NA | |Duration of viral shedding|7.022|0.001|8e-10 |NA | 0.01 | |Duration of lung recovery|6.914|0.001|1e-9|NA| 0.01| |Maximum difference of CD4 lymphocytes during treatment|4.570|0.04|2e-5|NA | **0.04** | |CD4 lymphocyte count during recovery|7.203|0.009|4e-10|NA|**0.009**| |Fluctuated results of SARS-CoV-2 test|4.649|0.03|1.4e-5|NA|**0.03**| |Deaths|1.505|0.22|NA|**0.22**|NA| Ignoring potential errors, methodology info I am missing, or incorrect assumptions I am making re: categorical vs. continuous for u201cAgeu201d, u201cDuration of viral sheddingu201d, and u201cDuration of lung recoveryu201d, 3 of the 6 p values in the table for continuous variables can be reproduced exactly assuming a one-way ANOVA and corresponding F statistic (F ratio). #### Notes: - For t distribution, given `nu2081 = 33` asymptomatic and `nu2082 = 45` symptomatic patients, degrees of freedom for independent t test comparing means we have `df = nu2081 + nu2082 - 2 = 76` degrees of freedom. - I made the assumption here that a pooled variance, i.e. classical two-group t-test was used. I recognize you all may have incorporated unequal variances (e.g. through a Welch t-test) in your t-test calculations. I can t calculate that since I don t have the raw data. Even if this was the case, to get a two-tailed p value of 0.001 for the 10.221 t statistic reported for  Age the degrees of freedom for the t distribution would have had to be between 3 and 4. I don t think this is appropriate since to achieve Welch degrees of freedom this small (using the Welchu2013Satterthwaite equation [[1]] ) one of the groups in the comparison would have had to have an extremely small variance with the other relatively large. I don t see any examples of this among the IQRs reported for the continuous variables. *Note*: Although I donu2019t believe a t test of any manner was applied, if it had been, it would still be **an inappropriate test.** Two of its fundamental assumptions are violated: the assumption of normality and the assumption of independence. The data for several of the continuous variables are clearly non-normal, as evidenced by the skew shown in the medians + IQRs. The data also violate the independence assumption. The asymptomatic and symptomatic patients as described in the Methods came from clusters discovered through testing and tracing of contacts of COVID-19 patients so they all share at least one link to someone in the other group through a mutual contact. Quoted from the manuscript:  Routine chest CT scans and SARS-CoV-2 testing from nasopharyngeal swab were performed on their [the source patients] close contacts ... The median (IQR) number of patients per cluster was 3 (2-3) patients, and the range was 2 to 10 patients per cluster - For the F distribution of a one-way ANOVA given `k = 2` groups and `n = 78` total patients, we have `k - 1 = 1`  between groups degree of freedom and `n - k = 78 - 2 = 76`  within groups degrees of freedom - There is likely a mistake that occurred when reporting the p value for duration of viral shedding and duration of lung recovery. The p values from one-way ANOVA (rightmost column) for the statistics are 0.01 for both but the reported p value is 0.001. Is it possible an additional 0 was inadvertently added? - For chi-square distribution, given `k = 2` groups, we have `k - 1 = 1` degree of freedom #### Demonstration calculations for above table values (R `{stats}` package v 3.3.2) ##### u201cAgeu201d * reported test statistic = 10.221 * reported p value = 0.001 ###### Assuming a 2-tailed t statistic with pooled variance, p value is ` 2*pt(10.221, 76, lower.tail=FALSE)` `[1] 7.981569e-10` ###### Assuming a F statistic, p value is ` pf(10.221, df1=1, df2=76, lower.tail=FALSE)` `[1] 0.002024163` ##### u201cWomenu201d * reported test statistic = 9.685 * reported p value = 0.002 ###### Assuming a chi-square statistic, p value is ` pchisq(9.685, df=1, lower.tail=FALSE)` `[1] 0.001857784` ,