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\begin{document}

\title{Should we wait or not? The preferable option for patients with stage IV
oral cancer in COVID-19 pandemic~~}



\author[1]{Pankaj Chaturvedi, MS, FACS}%
\affil[1]{Tata Memorial Centre and HBNI}%


\vspace{-1em}



  
  \date{May 20, 2024}


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\selectlanguage{english}
\begin{abstract}
Background

The coronavirus infection is rapidly spreading putting a strain on
healthcare services across the globe. Oral cancer patients are
susceptible often immunosuppressed due to the disease and/or the
treatment received.

Methods

We performed a simulationof the currently available data using a multi
state and hazards model to provide an objective model for counseling and
decision making for healthcare workers.

Results

Stage IV oral cancer patients that did not receive treatment had
progression of disease and an increased mortality rate than patients
that receive treatment but did not contract COVID-19. The patients that
received treatment and got affected with COVID-19 had a far worse impact
and higher mortality rate than all other groups.

Conclusion

Isolation and deferring treatment for stage IV oral cancer patients, so
as to avoid hospital visits and contration of COVID-19, is an advisable
strategy based on this model.%
\end{abstract}%



\sloppy




\textbf{Authors}

Atanu Bhattacharjee, PhD Section of Biostatistics Centre for Cancer
Epidemiology Tata Memorial Centre and HBNI Email:
\href{mailto:atanustat@gmail.com}{\nolinkurl{atanustat@gmail.com}}

Vijay M Patil , MD Department of Medical Oncology Tata Memorial Centre
and HBNI Email:
\href{mailto:vijaypgi@gmail.com}{\nolinkurl{vijaypgi@gmail.com}}

Rajesh Dikshit, PhD Centre for Cancer Epidemiology Tata Memorial Centre
and HBNI Email:
\href{mailto:dixr24@gmail.com}{\nolinkurl{dixr24@gmail.com}}

Kumar Prabhash, MD Department of Medical Oncology Tata Memorial Centre
and HBNI

Email:
\href{mailto:kprabhash1@gmail.com}{\nolinkurl{kprabhash1@gmail.com}}~

Arjun Singh, MDS, MFDS (Glasgow) Department of Head Neck Oncology Tata
Memorial Centre and HBNI Email:
\href{mailto:arjun193@gmail.com}{\nolinkurl{arjun193@gmail.com}}

Pankaj Chaturvedi*, MS, FACS Department of Head Neck Oncology Tata
Memorial Centre and HBNI Email:
\href{mailto:chaturvedi.pankaj@gmail.com}{\nolinkurl{chaturvedi.pankaj@gmail.com}}~*Corresponding
author

\textbf{Funding statement}

No funding was obtained from any sources.

\textbf{Conflict of Interest statement}

None of the authors have any conflict of interest to declare.

\textbf{Authors contribution statement}

All authors have made a significant contribution to this article from
concept to implementation and publication.

\par\null

\textbf{Introduction}

As of the beginning of April, over a million people acrossthe globe have
been tested positive for the novel severe acute respiratory syndrome
corona virus 2 (SARS-CoV-2) infection\textsuperscript{1}. Having begun
in Wuhan,China, the epicentre of this pandemic has shifted to the USA
over the past three months. Parallel large scale outbreaks have occurred
in Italy and Spain with a majority of countries struggling to contain
its spread.Cancer patients are believed to be one of the most vulnerable
populations due to the immune compromised state caused by both the
disease and its treatment.\textsuperscript{2}

India has one of the largest incidence of oral cacner in the world. With
the mounting evidence on COVID-19,there are no systematic reports of
cancer patients with COVID-19, let alone oral cancer. Patients with
these cancers are more likely to succumb to COVID-19 than the cancer
itself. It is believed that the SARS-COV-2 would accelerate cell death
in a relatively short span of time, especially in patients receiving
chemotherapeutic agents where the underlying immunity level is
substantially low. Most healthcare administrators are deferring early
stage diseases to be attended to after the situation subsides. The
biggest brunt is being borne by the advanced stage oral cancer patietns,
especially stage IV. Almost all of these tumors will progress to an
unresectable stage by the time the pandemic is contained.Hence,planning
of intervention and an adequate support strategy is required for the
best service to be established.\textsuperscript{3}

We present a simulation model using a multistate approach with
transition-specific hazard functions that would predict the outcomes
ofstage IV oral cancer patients thatreceive cancer directed treatment
and get infected with SARS-CoV-2, and the same patients if they do not
receive any cancer directed treatment and do not get infected with
SARS-CoV-2during the pandemic.This model will provide a unique approach
for setting suitable strategiestaking into account the current complex
scenario of social distancing, human physiology and heterogeneity of the
patients' disease status.

\textbf{Methods}

The conventional infectious disease model considers an exponentially
rise in cases during the transition period.\textsuperscript{4} The
ordinary differential equations are compatible to work with the
exponential transition period model. The methodology of exponential time
periodswasdoneusing the Gillespie algorithm.\textsuperscript{5} Since
the time gaps are based on the patient's disease status,we divided
theminto states based on the treatment received and infeced with
SARS-CoV-2 andno treatment received and not infected with SARS-CoV-2, so
that a hazard model could be applied.\textsuperscript{6} Model
structures were applied through agent-based stochastic
procedure.\textsuperscript{7}

We assumed that patients with progressive disease and those receiving
active treatment could not avoid a hospital vist and would continue
rendering further treatment. Any of the above treatments would decline
their immunity level from 0-100\%. Due to social distancing and
stringentmobility criteria, we assumed that there were no follow-up
visits and these patients would have a nil to minimal risk of
contracting COVID-19. The states are expressed as\(\text{\ E}^{1},E^{2},E^{3}\)and
\(E^{4}\)dipicted in a directed acyclic
graph(DAG).\textsuperscript{8}The corresponding time shift from one
state to another is defined by time \(T^{1},T^{2},T^{3}\)
and\(T^{4}\) respectively. (Figure 1)

A multistate model was used to specify the treatment initiation, disease
progression, COVID-19 transmission and death. A cohort of stage IV oral
cancer patients being treated or not were considered for analysis and
their data was simulated. The transmission time was generated assuming
that the transmission would occur during their hospital visit. The
transmission probabilities and cumulative incidence were generated. The
computation was performed using R software. The ''mstate'' and ''muhaz''
packages were used.

Multistate model

Multi-state models are often used to describe the life history of an
individual. It defines several possible events for a single individual
or the dependence between several individuals. Events are considered
when there is a transition between the states. This model is useful to
represent an extremely flexible approach that can model almost any kind
of longitudinal failure time data.\textsuperscript{9} Our model was
formulated with states and transition steps. The DAG is formulated to
describe the transition and time period for the transmission (Figure 2).

Patients that continue receiving treatment were defined as
\(E_{i}\), and there could be n number of patients
theoretically. Another state that received no treatment is defined
as\(E_{j}\).Here,\(E_{1}\),\(E_{2}\),\(E_{3}\),\(E_{4}\)
shows the transition from states\(E_{i}\) to
\(E_{j}\) while \(i<j\). We used the stochastic
process defined as \(\left(X_{\left(t\right)}\right),t\geq 0\) to explain the different states.
The superset of states was defined
as\(\varepsilon=\{E_{1},\ldots.E_{n}\}\).\(S_{i}=\inf\left\{t\geq 0\middle|X_{t}{=E}_{i}\right\}.\)

We thenformulated the transition times of state
\(E_{j}\)from\(E_{i}\)as\(T_{j}=S_{j}-S_{max\{k|k<j,S_{k}<\infty\}}\),assuming
that\(S_{0}\)=0. The entire process was then defined by the
transition time\(T_{j}\) to state \(E_{j}\).The
hazard functions \(h_{\text{ij}}\) for the transition from
\(i\) to \emph{j} was defined
as\(\text{\ T}_{\text{ij}}\sim F_{\text{ij}}=1-exp\{-\int_{0}^{t}{h_{\text{ij}}\left(u\right)du\}}\)and\(T_{j}=\min_{i\in\{1,\ldots.,J-1|T_{i}<\infty\}}T_{\text{ij}}\). The cumulative distribution
was presented as\(\text{\ F}_{\text{ij}}\)for the transition from
\(E_{i}\)to \(E_{j}\).Finally, all hazards were
considered as constant X using the Markovian structure.

Hazards model

Assuming that the primary setups of the patients are presented with
state\(\text{\ \ E}_{1}\), further two states would be formulated
as\(\text{\ \ E}_{2}\) and \(\text{\ \ E}_{3}\). The intermidiate and
absorbing state would be defined as \(E_{4}\).

The probability of transition from \(E_{i}\)at time s to state
\(E_{j}\)at time t is presented as\(p\left(s,t\right)=P\left[X=E_{j}|X_{s}=E_{i}\right]for\ s\leq\ t\).

If\(i<j\ \) and \(\neq j,\) it may be formulated
as\(p_{\text{ii}}\left(s,t\right)=exp\{-\int_{s-S_{i}}^{t-S_{i}}{h_{i4}(u)}du\}\). Transition from i=4 to i=4 was not possible, but
i=1 to j=2,3,4 were possible choices. Similarly, i=2 to j=3,4 were the
other possibilities, i.e.\(p_{i4}\left(s,t\right)=1-\exp\left\{-\int_{s-S_{i}}^{t-S_{i}}{h_{i4}\left(u\right)}\text{du}\right\}\)and\(p_{\text{ii}}\left(s,t\right)=0\).

Assuming that \(S_{1}\)=0, the transition probability can be
obtained through integration

\begin{equation}
p_{11}\left(s,t\right)=exp\{-\int_{s}^{t}{h_{12}\left(u\right)du-}\int_{s}^{t}{h_{13}\left(u\right)du-\int_{s}^{t}{h_{14}\left(u\right)\text{du}}}\nonumber \\
 \end{equation}\begin{equation}
p_{12}\left(s,t\right)=\int_{s}^{t}{p_{11}\left(s,u\right)h_{12}\left(u\right)p_{22}\left(u,t\right)\text{du}}\nonumber \\
 \end{equation}\begin{equation}
p_{13}\left(s,t\right)=\int_{s}^{t}{p_{11}\left(s,u\right)h_{13}\left(u\right)p_{23}\left(u,t\right)\text{du}}\nonumber \\
 \end{equation}\begin{equation}
p_{14}\left(s,t\right)=1-p_{11}\left(s,t\right)-p_{12}\left(s,t\right)-p_{13}(s,t)\nonumber \\
 \end{equation}

This process was defined as X for state \(E_{1}\) shifting
from time s to u. The states\(E_{2}\) or \(E_{3}\)
will move from time \(t\). The transition probability
\(p_{12}\) and \(p_{13}\) can be obtained by
calculating the integration over u.This integration can be obtained by
simulating the transition time linked to the probabilities (Figure 3).

Simulation of Hazards

We simulated the hazard function to understand the magnitude of
mortality. The transition specific hazard function was formulated with
the assumption that hazard withmean\(\mu=4\) will specify the
constant function with \(h\left(t\right)=\frac{1}{\mu}\) having
parameter\(\ \mu=4\). The time points \(T_{\text{ik}}\)by the
hazard functions can be explained in the DAG (Figure 2). The minimum
time period for shifting one state to another state is represented as
prefixed k.It was possible to take a minimum of k. If the transition
time is \(T_{j}\)and connecting state
\(E_{j}\).Therefore, we can simulate X from the initial state
\(T_{1k}\) to calculate the first transition within a minimum
period. The simulation then could be obtained by the corresponding state
\(E_{j}\). It was iterated until it became nil at the end of
the simulation.

The hazard function was formulated as \(h(t)\) with piecewise
constant function\(h_{\text{pc}}(t)\). Using the msm package for
simulation, the transition probabilities from the first state at time
\(t=0\) by the process X was calculated.\textsuperscript{10}
We then simulated for N (Figure 4). Similarly, we used real data
obtained from the website (https://ourworldindata.org/) and the data
available on the coronavirus positive cases in India. This data is
presented for the general population. The simulated portion for cancer
patients' data is included for comparison.\textsuperscript{11,12}
(Figure 4)

\textbf{Results}

Data simulated for cancer patients are plotted in Figure 3 and Figure 4.
This model is prepared for a oncology hospital setup and simultaneously
having the pressure to deal with COVID-19. The appearance of cancer
cases is natural and the cumulative number is presented by the red line
in Figure 3. This is a non-communicable disease that will report at its
own pace, and the mortality rate without treatment will merge in Figure
3. But an alarming situation is present as the presence of COVID-19 is
added. Probability of cancer patients getting infected by SARS-CoV-2for
the next sixty days is plotted as a red line in Figure 4. Similarly,
their probability of death is plotted as a black line in Figure 4.

Further, we separated them into two groups i.e. group A and group
B(Figure 5). Group-A represents patients undergoing cancer directed
treatment during the pandemic, and group B were those that were
restricted dueto health serveicesnot rendering treatment. The 30 day
mortality rate in our hosptial audit was 0.9\% after completion of
treatment.\textsuperscript{13} However, there is no data to suggest the
probability of death when no treatment is rendered to stage-IV oral
cancer patients. We accumulated the number of patients that join the
pool as untreated(Group B). Even if we consider all these patients
eventually die, the risk of death within the 60 days is lesser than
those that contract SARS-CoV-2 and die. In absence of treatment the
disease will progress and increase mortality, but does not exceed the
mortality of those infected with SARS-CoV-2. The simulated presentation
on group A and B demonstrated different scenarios. We should prefer to
defer cancer treatement in these patients restricting the mortality to
them.

The current patient load in our hospital is between 800-1000. Each day,
150 patients are registered on average. In the past 3 weeks, a total of
4150 should have been registered. The accumulated cancer mortality of
partients not being treated (Group B) will be inclined linearly and we
can expect that it can come close to 50. We assumed that Group B will
see a cumulative increase of 10\% in the rate of patients dying. In
contrast, once infected by COVID-19, we expect to see a 50\% cumulative
increasein patients dying in group A. The soultion could revoles around
treating the cancer patient efficiently with minimal clinic visits
reducing their chance of infection.

\textbf{Discussion}

Countries across the world are implementing measures from national
quarantines to school closures, to slow down the spread of the
coronavirus. More than a third of humanity is under some form of
restriction.\textsuperscript{14} A few reports have described cancer
patients in quarantined cities struggling to obtain cancer directed
services and essential medication.\textsuperscript{15} Over time, this
will exacerbate due to interruptions in scheduled surgeries,
chemotherapy and radiotherapy in order to prioritize hospital space and
care for the seriously ill COVID-19 patients.

Among the cancer patients who develop COVID-19, treatment of the cancer
will be delayed in order to prioritize treatment for the infection. Many
physicians and surgeons around the world are being forced to take this
tough call on an individual patient basis. With these limited resources
and capacity it is important to understand the implications it has on
cancer patients with and without COVID-19. Given the acute time frame of
COVID-19 infection and lack of any retrograde data, a prospective study
of scale cannot be accomplished. The challenge comes about when we need
to triage cancer care during this pandemic. In our analysis we assumed
that patients treated for cancer will have a lesser risk of contracting
the virus at the hospital due to the measures taken by the governments.
At the same time their chances of disease inflammation and death are
relatively high due to the cancer or the treatment received.

The simulated work presented here is to visualize the impact of COVID-19
in the worst case scenario so as to support policy makersmake the hard
decisions. Nonetheless, decisions on patients care is required to be
taken as per the case, rather than abide by blanket guidelines. Due to
the limitation of adequate real world data and follow up on COVID-19, we
cannot provide personalized recommendations regarding cancer care.The
increased mortality of patients seen in this model should caution
oncologists. The risk-benefit ratio should be discussed with patients
before administering any definitive treatment. We propose that forceful
steps are required to reduce the frequency of hospital visits for
patients having cancer during this time.Proper isolation techniques are
required to mitigate the risk of transmission. Risk factors like disease
severity, recent chemotherapy received can increase the chance of
illness and mortality due to COVID-19.It is also required to take steps
to eliminate cross-infection between the patients and healthcare
workers.

With the situation gradually unfolding, there is not much we can do as
health care providers but to adapt as best we can. In case of suspicion,
appropriate isolation techniques need to be instated. Among cancer
patients, receiving recent chemotherapy does increase the risk of severe
illness. This model helps us better understand the survival trajectory
of oral cancer patients that might be affected by COVID-19.

\textbf{References}

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\end{enumerate}

\textbf{Figure legend:}

\textbf{}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure1/Figure1}
\caption{{This is a caption
{\label{672835}}%
}}
\end{center}
\end{figure}

Figure 1: Overview of COVID-19 transmission among stage IV oral cancer
patients

\par\null\par\null\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure2/Figure2}
\caption{{This is a caption
{\label{261997}}%
}}
\end{center}
\end{figure}

Figure 2: Multistate model transmission of COVID-19 among stage IV oral
cancer patients

\par\null\par\null\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-3/Figure-3}
\caption{{This is a caption
{\label{710572}}%
}}
\end{center}
\end{figure}

Figure 3: Outcomes of patients with cancer and cancer mortality

\par\null\par\null\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-4/Figure-4}
\caption{{This is a caption
{\label{836531}}%
}}
\end{center}
\end{figure}

Figure 4: Comparison of patients affected by COVID-19 and cancer
patients mortality comparison

\par\null\par\null\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-5/Figure-5}
\caption{{This is a caption
{\label{172409}}%
}}
\end{center}
\end{figure}

Figure 5: Comparision of patients receiving treatment and being infected
by COVID-19 and patients not receiving and cancer directed treatment

\selectlanguage{english}
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\end{document}

