ABSTRACT
We address the problem of how COVID-19 deaths observed in an oncology clinical trial can be consistently taken into account in typical survival estimates. We refer to oncological patients since there is empirical evidence of strong correlation between COVID-19 and cancer deaths, which implies that COVID-19 deaths cannot be treated simply as non-informative censoring, a property usually required by the classical survival estimators. We consider the problem in the framework of the widely used Kaplan-Meier (KM) estimator. Through a counterfactual approach, an algorithmic method is developed allowing to include COVID-19 deaths in the observed data by mean-imputation. The procedure can be seen in the class of the Expectation-Maximization (EM) algorithms and will be referred to as Covid-Death Mean-Imputation (CoDMI) algorithm. We discuss the CoDMI underlying assumptions and the convergence issue. The algorithm provides a completed lifetime data set, where each Covid-death time is replaced by a point estimate of the corresponding virtual lifetime. This complete data set is naturally equipped with the corresponding KM survival function estimate and all available statistical tools can be applied to these data. However, mean-imputation requires an increased variance of the estimates. We then propose a natural extension of the classical Greenwood's formula, thus obtaining expanded confidence intervals for the survival function estimate. To illustrate how the algorithm works, CoDMI is applied to real medical data extended by the addition of artificial Covid-death observations. The results are compared with the estimates provided by the two naïve approaches which count COVID-19 deaths as censoring or as deaths by the disease under study. In order to evaluate the predictive performances of CoDMI an extensive simulation study is carried out. The results indicate that in the simulated scenarios CoDMI is roughly unbiased and outperforms the estimates obtained by the naïve approaches. A user-friendly version of CoDMI programmed in R is freely available.
Subject(s)
COVID-19 , Motivation , Humans , Survival Analysis , Kaplan-Meier Estimate , AlgorithmsABSTRACT
BACKGROUND/AIM: To report long-term survival results after trimodal approach for locally advanced rectal cancer (LARC) in the Covid-19 era. We herein illustrate a clinical application of Covid-death mean-imputation (CoDMI) algorithm in LARC patients with Covid-19 infection. PATIENTS AND METHODS: We analyzed 94 patients treated for primary LARC. Overall survival was calculated in months from diagnosis to first event (last follow-up/death). Because Covid-19 death events potentially bias survival estimation, to eliminate skewed data due to Covid-19 death events, the observed lifetime of Covid-19 cases was replaced by its corresponding expected lifetime in absence of the Covid-19 event using the CoDMI algorithm. Patients who died of Covid-19 (DoC) are mean-imputed by the Kaplan-Meier estimator. Under this approach, the observed lifetime of each DoC patient is considered as an "incomplete data" and is extended by an additional expected lifetime computed using the classical Kaplan-Meier model. RESULTS: Sixteen patients were dead of disease (DoD), 1 patient was DoC and 77 cases were censored (Cen). The DoC patient died of Covid-19 52 months after diagnosis. The CoDMI algorithm computed the expected future lifetime provided by the Kaplan-Meier estimator applied to the no-DoC observations as well as to the DoC data itself. Given the DoC event at 52 months, the CoDMI algorithm estimated that this patient would have died after 79.5 months of follow-up. CONCLUSION: The CoDMI algorithm leads to "unbiased" probability of overall survival in LARC patients with Covid-19 infection, compared to that provided by a naïve application of Kaplan-Meier approach. This allows for a proper interpretation/use of Covid-19 events in survival analysis. A user-friendly version of CoDMI is freely available at https://github.com/alef-innovation/codmi.