Investigating Symptom Duration Using Current Status Data: A Case Study of Postacute COVID-19 Syndrome

Abstract

Background: For infectious diseases, characterizing symptom duration is of clinical and public health importance. Symptom duration may be assessed by surveying infected individuals and querying symptom status at the time of survey response. For example, in a severe acute respiratory syndrome coronavirus 2 testing program at the University of Washington, participants were surveyed at least 28 days after testing positive and asked to report current symptom status. This study design yielded current status data: outcome measurements for each respondent consisted only of the time of survey response and a binary indicator of whether symptoms had resolved by that time. Such study design benefits from limited risk of recall bias, but analyzing the resulting data necessitates tailored statistical tools.

Methods: We review methods for current status data and describe a novel application of modern nonparametric techniques to this setting. The proposed approach is valid under weaker assumptions compared with existing methods, allows the use of flexible machine learning tools, and handles potential survey nonresponse. Our method relies on the assumption that the survey response time is conditionally independent of symptom resolution time within strata of measured covariates, and we propose an approach to assess the sensitivity of results to deviations from conditional independence.

Results: From the university study, we estimate that 19% of participants experienced ongoing symptoms 30 days after testing positive, decreasing to 7% at 90 days. We found the estimates to be more sensitive to violations of the conditional independence assumption at 30 days compared with 90 days. Female sex, fatigue during acute infection, and higher viral load were associated with slower symptom resolution.

Conclusion: The proposed method and accompanying sensitivity analysis procedure provide tools for investigators faced with current status data.

Keywords: Interval censoring; Long COVID; Machine learning; Nonparametric; Survival analysis.

Figure 1:

Standardized survival curve for time from positive test until symptom resolution, estimated using the proposed extended causal isotonic regression method (top panel), along with the distribution of survey response times between 28 and 95 days (bottom panel). The solid black line shows the estimated proportion with ongoing symptoms at times from 30 days to 90 days after the positive test. The black points show the estimated proportion with ongoing symptoms at 30, 60, and 90 days. The dashed lines represent a pointwise 95% confidence interval. The gray vertical lines denote 30, 60, and 90 days.

Figure 2:

Sensitivity analysis for deviation from conditionally uninformative response time assumption. From top to bottom, the rows correspond to the estimated proportion with ongoing symptoms at 30, 60, and 90 days after the positive test. The x-axis represents the value of Kendall’s rank correlation coefficient τ used to encode conditional dependence in each sensitivity analysis. At τ = 0, in black, we give the estimate and confidence interval obtained from the proposed extended causal isotonic regression procedure assuming conditional independence (primary analysis). Gray crosses represent estimates corresponding to different values of τ.