Survival Analysis is a collection of statistical procedures for data
analysis for which the outcome variable of interest is time until an
event occurs.
By time,we mean years, months,weeks,or days from the beginning
of follow-up of an individual until an event occurs;alternatively,time
can refer to the age of an individual when am event occurs.
By event,we mean death,disease incidence,relapse from remission,
recovery (e.g.,return to work) or any designated experience of interest
that may to an individual.
Although more than one event may be considered in the same analysis,
we will assume that only one event is of designated interest.
When more than one event is considered (e.g., death from any of
several causes), the statistical problem can be characterized as either
a recurrent event or a competing risk problem.
In a survival analysis, we usually refer to the time variable as survival
time, because it gives the time that an individual has “survived”
over some follow-up period. We also typically refer to the
event as a failure, because the event of interest usually is death, disease
incidence, or some other negative individual experience. However,
survival time may be “time to return to work after an elective
surgical procedure,” in which case failure is a positive event.Due
to presence of censoring,which is data whose event is not occurred
yet,survival analysis model require special consideration.
Cox proportional hazard(Cox PH) and accelerated failure time
model(AFT) are widely used to handle right censored data.Yet the
5
assumptions made by these model are violated in the real worlds .Recent
studies showed that the Ordinary Differential Equation(ODE)
modeling framework unifies many existing Survival analysis models
including Cox PH and AFT. They also showed that the ODE modeling
framework is flexible and widely applicable.
However, naively applying the ODE framework to survival analysis
problems may result in wildly oscillating density function that
may worsen the model’s performance. Regularization techniques
that can regularize this undesirable behavior are understudied.The
cluster assumption from semi-supervised learning states that the decision
boundaries should not cross high-density regions. Likewise,
survival analysis models need hazard functions that slowly change
in high-density regions.
In this paper ,we propose Cox Proportional Hazard Model to predict
exact Survival Time where the individuals are either incurred with
death or censored.Our method has several advantages 1)The model
is computationally efficient.2)The model is theoretically sound.3)It
is easy to implement.4)The model is applicable to any Survival analysis
problem containing censored data.
Arjun392
commented
1 year ago 
Survival Analysis is a collection of statistical procedures for data analysis for which the outcome variable of interest is time until an event occurs. By time,we mean years, months,weeks,or days from the beginning of follow-up of an individual until an event occurs;alternatively,time can refer to the age of an individual when am event occurs. By event,we mean death,disease incidence,relapse from remission, recovery (e.g.,return to work) or any designated experience of interest that may to an individual. Although more than one event may be considered in the same analysis, we will assume that only one event is of designated interest. When more than one event is considered (e.g., death from any of several causes), the statistical problem can be characterized as either a recurrent event or a competing risk problem. In a survival analysis, we usually refer to the time variable as survival time, because it gives the time that an individual has “survived” over some follow-up period. We also typically refer to the event as a failure, because the event of interest usually is death, disease incidence, or some other negative individual experience. However, survival time may be “time to return to work after an elective surgical procedure,” in which case failure is a positive event.Due to presence of censoring,which is data whose event is not occurred yet,survival analysis model require special consideration. Cox proportional hazard(Cox PH) and accelerated failure time model(AFT) are widely used to handle right censored data.Yet the 5 assumptions made by these model are violated in the real worlds .Recent studies showed that the Ordinary Differential Equation(ODE) modeling framework unifies many existing Survival analysis models including Cox PH and AFT. They also showed that the ODE modeling framework is flexible and widely applicable. However, naively applying the ODE framework to survival analysis problems may result in wildly oscillating density function that may worsen the model’s performance. Regularization techniques that can regularize this undesirable behavior are understudied.The cluster assumption from semi-supervised learning states that the decision boundaries should not cross high-density regions. Likewise, survival analysis models need hazard functions that slowly change in high-density regions. In this paper ,we propose Cox Proportional Hazard Model to predict exact Survival Time where the individuals are either incurred with death or censored.Our method has several advantages 1)The model is computationally efficient.2)The model is theoretically sound.3)It is easy to implement.4)The model is applicable to any Survival analysis problem containing censored data.