Abstract
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.
Since the World Health Organization (WHO) declaration of 2019 coronavirus disease (Covid-19) on 2020 March 11, it has been proven that cancer patients have a higher risk of Covid-19 infection and death than individuals without cancer diagnosis (1-2). This new reality may introduce problems in survival estimates in oncologic clinical trials. Once pandemic data will be fully collected, trial populations are expected to include a relevant proportion of death observations secondary to Covid-19 infection. Therefore, there is a need to define a more suitable way to correctly categorize this information for the estimation of survival rates (3). A possible, and perhaps more appropriate, approach to survival analysis when Covid-19 deaths are present in an oncological clinical trial in addition to cancer deaths, could be based on the theory of competing risks, as detailed in (4). This would lead to dealing with sub-distributions (the marginal probabilities of each competing risk) and would require for more appropriate statistical tests. However, most clinical researchers perform survival analyses by routinely applying standard statistical tools, like the Kaplan-Meier estimator, which are actually not well suited for competing events. As noted in (5), “Kaplan-Meier curves have become familiar friends to medical researchers, a lingua franca for reporting clinical trial results”. When these standard tools cannot be directly applied, there is a danger that Covid-19 death observations will simply be discarded from the study sample, with serious loss of information. With this in mind, we limit ourselves to a more pragmatic approach, consisting in operating directly on the data through mean-imputation, transforming each observed competing event into a virtual event-of-interest or a censoring. This is performed by a recently proposed purpose-built algorithm. The advantage of this approach is that any statistical tool suitable for analysis of non-competing events can be used, without requiring additional skills. The cost of this choice is that it is necessary to accept some approximations and a certain level of bias.
In a traditional Kaplan-Meier approach, patients who died from Covid-19 could be: i) excluded from the cohort, or ii) counted as lost-to-follow-up, or iii) considered as died of disease. Yet all these three options are unsatisfactory. Option (i) represents loss of data (we know that Covid-19 patients were alive since the time of observed death); both options (ii) and (iii) imply substantial bias in survival estimates. A new statistical method recently presented allows for a more suitable option: iv) Covid-19 data are adjusted using the Kaplan-Meier model itself, so that the traditional model can be consistently applied to the entire sample of observations. This is realized by a freely available algorithm named Covid-death mean-imputation (CoDMI) (6). Essentially, in CoDMI algorithm the observed lifetime of each Covid-19 case is replaced by the corresponding expected lifetime in absence of the Covid-19 event, where the expectation is derived consistently with the Kaplan-Meier estimator (this replacement is usually referred to as mean-imputation).
Herein we present a first clinical application of the CoDMI algorithm in a radiation oncology scenario. This observational study was planned to describe a population (P) and observe outcomes (O). The aim is to provide an outlook of what happens in a group of subjects when researchers actively use the CoDMI algorithm in survival analysis. In the sample considered in this study, we had only one Covid-19 death out of 94 oncological patients. Therefore, the effect of the Covid-19 event on the survival estimates is expected to be marginal with any option considered. However, this simplified situation is interesting, because it makes it easier to interpret the effects of different options and illustrate how the CoDMI algorithm can be used.
Patients and Methods
Study design. An observational study was carried out with data prospectively collected from locally advanced rectal cancer patients, treated with curative intent, from July 2014 to September 2020, at the Department of Radiotherapy, Policlinico Umberto I “Sapienza” University of Rome Medical records of adult patients (≥18 years of age), who presented with a histologically confirmed diagnosis of adenocarcinoma of the rectum were collected. Approval for the study was obtained from Ethics Committee (ref. 6452) and written informed consent was obtained from all patients before treatment. Data were collected in a digital form and included patient-related, tumor-related, and follow-up-related variables. The possible diagnosis of the Covid-19 infection was recorded. All data were anonymized prior to analysis.
Treatment. All patients referred to a multidisciplinary gastrointestinal tumor board prior to treatment initiation. Clinical examinations – complete medical history and careful physical examination – were combined with imaging – trans-rectal ultrasound, total-body contrast-enhanced computed tomography (CT) and magnetic resonance imaging (MRI) of the pelvis – to properly define the local (T), regional nodal (N) and distant (M) extent of the disease. External beam definitive radiotherapy with an intensity modulated technique (IMRT) was delivered to a total dose of 50.4-54 Gy (1.8 Gy per fraction) to the tumor volume and 45 Gy (1.8 Gy per fraction) to the whole pelvis. Concurrent chemotherapy consisted of weekly oxaliplatin (50 mg/m2 on the first day of each week of RT) and 5-FU (200 mg/m2/5 daily continuous infusions) (7). Surgery was planned 7-9 weeks after the end of concomitant treatment and its type was left to the surgeon’s discretion. Induction chemotherapy was recommended in case of bulky primary or nodal disease from October 2015 (8).
Follow-up. According to the protocol undertaken (9), patients were followed-up at 3-month intervals for two years and every 6 months for subsequent years with a physical examination, complete blood count, blood chemistry and trans-rectal ultrasound. Patients were monitored closely to detect local recurrent disease and distant metastasis by clinical examination and imaging, including total body CT and pelvic MRI recommended annually for up to 5 years after treatment.
Statistical analysis. Statistical analysis was performed using R 4.0. In standard descriptive analysis, continuous variables were reported as means±1 standard deviation (SD) and categorical variables as frequencies or percentages.
As the study was designed to analyze the usefulness of the CoDMI algorithm, the primary outcome focused solely on overall survival (OS), which was defined as the time between the initial diagnosis to the first event (death from any cause). In the calculation of the OS rates, patients observed to die of Covid-19 (DoC) were taken into account following alternative options. They were: i) excluded from the data analysis; ii) censored at the time of death and counted as censored (Cen) and therefore lost-to-follow-up; iii) considered as died of disease (DoD); iv) “adjusted” using CoDMI algorithm (6). Survival rates were estimated using the Kaplan-Meier model directly in the first three cases and after mean imputation by CoDMI in the fourth case. Moreover, the mean imputation, that is the replacement of the observed lifetime with an estimated virtual life expectancy, was made under two additional options: iv.a) assuming a virtual death of disease (CoDMI applied in standard form); iv.b) assuming a virtual censoring (CoDMI with adjustment for censoring). A detailed analysis of the CoDMI algorithm, as well as the underlying model, is beyond the aim of this study; a comprehensive overview and a tutorial of the fundamental aspects of the algorithm is provided in (6). Briefly, we note that the CoDMI adjustment is obtained by running the Kaplan-Meier estimator itself starting from the no-DoC observations, then providing a consistent estimate of the life expectancy beyond the DoC date. A user-friendly version of CoDMI programmed in R is freely available at https://github.com/alef-innovation/codmi.
Results
Overall, 94 patient records were collected. All patients had been treated with a curative intent. Patient and tumor characteristics are listed in Table I. Mean age was 67.4 years and 47 patients (50.0%) were females. There were no patients with coexisting serious medical conditions. The vast majority of patients (n=85, 90.4%) had regional lymph node involvement at diagnosis. Most tumors were located in the low rectum (n=60, 63.8%).
Study population characteristics.
In the examined sample, the minimum and the maximum observed survival time was t=2 months and t=82 months, respectively. In the entire cohort, 17 patients (18.1%) died, and the last death event occurred 53 months after diagnosis. Of these 17 death events, one case (5.9%) was attributed to Covid-19 and was recorded after 52 months. Therefore, on the entire sample of 94 patients, there were 16 DoD patients, 1 patient DoC and 77 Cen cases, as summarized in Table II. The basic problem in this kind of samples is how to consider the DoC cases in order to obtain a usual sample composed of only DoD and Cen cases (as per traditional Kaplan-Meier approach) and to which the classical Kaplan-Meier estimator, as well as any statistical tool for survival analysis, can be applied.
Details of exit causes in the entire sample.
Let us consider the Kaplan-Meier estimator. Using the standard model, it is possible to estimate the survival probabilities in our sample according to three different options: i) excluding the DoC event from the data analysis (accounting for a total of 93 observations); ii) considering the DoC event as a Cen event at the same time point; iii) considering the DoC event as a DoD event at the same time point. The corresponding Kaplan-Meier survival plots are provided in Figure 1A. In the figure, the black curve (without DoC) corresponds to option (i), the green curve (DoC as Cen) refers to option (ii) and the red curve (DoC as DoD) corresponds to option (iii). Using CoDMI algorithm an additional option is available. This essentially consists in considering the DoC event as an “incomplete data” which is adjusted by mean imputation, that is the observed lifetime of the DoC patient is extended by an additional expected lifetime. The crucial point is that this lifetime extension is computed by the algorithm using the Kaplan-Meier model itself and therefore does not introduce inconsistencies in the survival estimates.
Overall survival Kaplan-Meier curves for alternative options on treatment of Covid-19 deaths. (A) Dead of Covid-19 (DoC) event imputed as dead of disease (DoD). (B) Dead of Covid-19 (DoC) event imputed as censored (Cen).
In Figure 1A, a blue curve (DoC Imputed) is also provided corresponding to option (iv.a), where the DoC event is considered as an “incomplete data” which is adjusted by mean imputation using CoDMI algorithm in its standard form, that is assuming that it would have been a virtual DoD event at a later time point. In this case, CoDMI algorithm estimates that the DoC patient that died due to Covid-19 at time t=52 months, without Covid-19 infection would have survived for additional 27.5 months and would have died of tumor at time t=79.5 months (52+27.5 months). Therefore, the observed DoC event at time 52, indicated by a red triangle on the blue line in the figure, is changed as a virtual DoD event at time 79.5, which is indicated by a circle.
If the virtual DoC event is considered unlikely, it is possible to modify the standard-form result by applying CoDMI algorithm with an additional option, called adjustment for censoring, where the survival estimate is obtained counting the DoC event as a virtual Cen rather than a virtual DoD. If this option is used, a reverse Kaplan-Meier estimate is computed by CoDMI, providing an expected survival of 13.98 months beyond the observed DoC event. In this case, the DoC event at time 52 is then changed as a virtual Cen event at time t=65.98 months (52+13.98 months). This is illustrated by the blue line in Figure 1B, where the circle on the blue curve (DoC Imputed) corresponds now to the time point of the virtual Cen event.
The choice between the standard and the no-standard mode of CoDMI application can be a matter of the clinician’s discretion, but it can also be made directly by the algorithm, which computes the probability of a virtual DoC event vs. that of a virtual Cen event.
The survival rates illustrated in Figure 1 are reported in Table III for two selected time points, 2 and 5 years, together with the corresponding 95% confidence intervals (CI). For options (i), (ii) and (iii) the confidence intervals are computed using the classical Greenwood’s formula. For options (iv.a) and (iv.b), where the observed DoC time point is replaced by the expected DoD and Cen time point, respectively, the confidence intervals must be computed taking into account that changing an observed value with an expected value (i.e., applying the mean imputation) provides an increase of the estimation uncertainty. This correction is provided by the CoDMI algorithm, which includes a built-in extension of Greenwood’s formula. Table III shows that the 2-year OS rate was 89.8% (CI=83.7-96.4) and the 5-year OS rate was 74.8% (CI=63.7-0.87.9), when the DoC event was not included in survival analysis (option i). Considering that Covid-19 patient died after 52 months of follow-up, the 2-year OS rate was equal (81.1%, CI=72.3-91.0) in all other cases (option ii, iii, iv.a, and iv.b). The 5-year OS where different in case of DoC as Cen, DoC as DoD, DoC as virtual DoD and DoC as virtual Cen, and survival rates were 75.1%, 71.9%, 75.3% and 75.3%, respectively. Concerning the confidence intervals, the differences between those provided by the classical Greenwood’s formula and those computed with the extended formula, result to be immaterial in this case with a single DoC event.
Survival rate estimates for different treatment of Covid-19 death event.
It should be noted that, independently of these survival rate estimates, the DoC imputations provided by CoDMI algorithm under option (iv.a) or (iv.b) provide, correspondingly, an adjusted sample including a total of 94 observations (the total number of original observations), where, however, only DoD and Cen events are now considered. This is summarized in Table IV for the two options. As shown in (5), the mean imputations provided by CoDMI are roughly unbiased. Therefore, all the usual statistical tools can be applied to these “standardized” samples and the information conveyed by DoC events is then consistently used. As an example, a standard proportional hazard model was applied to our data. Table V summarizes results from the Cox regression obtained according to the five possible DoC options. Several variables deemed to be relevant to overall survival (including clinical T stage, clinical N stage, tumor diameter and age) were included in the multivariate analysis. As expected, given the presence of only one DoC case in the sample, even in this application the differences between the estimates with the different options are almost immaterial. Obviously, in the estimation of the regression coefficients, options (ii) and (iv.b) provide exactly the same results.
Details of exit causes after Covid-death mean-imputation (CoDMI) imputation in standard form (option iv.a) and with adjustment for censoring (option iv.b).
Multivariate analysis of prognostic factors for overall survival according to dead of Covid-19 (DoC) options.
Discussion
The main clinical conclusion of this observational study is that the CoDMI algorithm can be easily applied taking into account the information conveyed by DoC events in a sample of LARC patients with Covid-19 infection. The data adjustments provided by the algorithm through mean imputation allow for consistent Kaplan-Meier estimates of the survival curve and, more generally, produce a complete sample of survival observations which can be safely used for any further statistical analysis, as illustrated in Table V. A possible alternative approach based on the theory of competing risks, would require a multidimensional point of view, characterized by more specific, and complex, statistical techniques.
The presence of just one DoC event in our study sample allows a better illustration of the effects of the CoDMI adjustments and a more direct comparison of these effects with those provided by simpler (and more naïve) options. Obviously, the usefulness of the algorithm is greater the greater the impact of Covid-19 deaths in the study sample and, correspondingly, the greater the potential loss of information caused by a poor treatment of this Covid-19 data.
This finding is new since there are no published studies on this topic. To further illustrate the clinical relevance of such a conclusion, direct applications of the CoDMI algorithm to larger number of Covid-19 death cases are welcome. The aim of this study was to simply describe a population descriptive. Data were obtained from patients with rectal cancer who have been treated with concomitant chemoradiotherapy due to their locally advanced stage disease at diagnosis. Toxicity and treatment compliance details were deliberately not included in the present analysis. Our first idea was to include OS data to strengthen CoDMI algorithm and thus overcome uncertainties in DoC classification. We aimed to demonstrate that our CoDMI algorithm represents an attractive and valid statistical tool to adequately perform survival analysis in the Covid-19 era. Therefore, we do not want to speculate on the relative efficacy of the treatment management, despite the homogeneity of the sample would allow to it. The main advantage of CoDMI algorithm – that combines Covid-19 and no-Covid-19 events over standard survival approaches – is to perform unbiased high-quality survival analysis in order to allow every possible data comparison. Undoubtedly, well-designed randomized clinical trials remain the reference to obtain level-one evidence. CoDMI algorithm should be used mostly to analyze data of these new trials presumably enrolling both Covid-19-positive and Covid-19-negative cases.
Conclusion
This is the first clinical application of the CoDMI algorithm in a radiation oncology scenario. We demonstrated that the CoDMI algorithm is a valid and easy to use statistical tool and offers a satisfactory interpretation of Covid-19 events in survival analysis. Based on a homogenous cohort of patients, it provides appropriate data adjustments resulting in consistent Kaplan-Meier estimates of survival curves overcoming the direction of bias (over- or under- estimation). A user-friendly version of the CoDMI algorithm is freely available (https://github.com/alef-innovation/codmi) to facilitate and ensure accurate data analysis in the near future.
Footnotes
Authors’ Contributions
Franco Moriconi: Conceptualization; Data curation; Formal analysis; Methodology; Software; Writing – review & editing; final approval. Francesca De Felice: Conceptualization; Data curation; Formal analysis; Writing - original draft; final approval. Luca Mazzoni: Software; final approval. Daniela Musio: Data acquisition; final approval. Vinncenzo Tombolini: Data acquisition; final approval.
Conflicts of Interest
The Authors declare no potential conflicts of interest with respect to the study.
- Received June 25, 2022.
- Revision received August 21, 2022.
- Accepted August 29, 2022.
- Copyright © 2022, International Institute of Anticancer Research (Dr. George J. Delinasios), All rights reserved
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY-NC-ND) 4.0 international license (https://creativecommons.org/licenses/by-nc-nd/4.0).
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