Find the Probability of time of death occurring after right censoring time

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SUMMARY

The discussion focuses on calculating the probability P(T > C) where T is a random variable following an exponential distribution with hazard rate 'a', and C is a right censoring time uniformly distributed between 0 and 'b'. The independence of T and C is crucial for accurate probability assessment. The conversation highlights the importance of understanding the implications of censoring on statistical results, referencing the Cox proportional hazard model as a foundational resource for further exploration.

PREREQUISITES
  • Understanding of exponential distribution and hazard rates
  • Familiarity with uniform distribution concepts
  • Knowledge of right censoring in statistical analysis
  • Basic grasp of the Cox proportional hazard model
NEXT STEPS
  • Study the properties of exponential distributions and their applications
  • Learn about right censoring techniques in survival analysis
  • Explore the Cox proportional hazard model in detail
  • Review statistical papers on the implications of censoring in data analysis
USEFUL FOR

Statisticians, data analysts, and researchers working with survival analysis and censored data, particularly those interested in the implications of censoring on statistical results.

artbio
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Hi. I have the following problem I am finding very difficult to solve.

Assume that the lifetime T is an r.v. that follows an exponential distribution with hazard rate a (Note: the hazard rate is the parameter of the exponential distribution) and that the right censoring time C is Uniform(0,b). Suppose that T and C are independent r.v. Find P(T>C).

Any help would be appreciated.
Thanks.
 
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artbio said:
Hi. I have the following problem I am finding very difficult to solve.

Assume that the lifetime T is an r.v. that follows an exponential distribution with hazard rate a (Note: the hazard rate is the parameter of the exponential distribution) and that the right censoring time C is Uniform(0,b). Suppose that T and C are independent r.v. Find P(T>C).

Any help would be appreciated.
Thanks.

I don't know how experienced you are with censored data. The assumption is that censoring is randomly distributed between comparison groups. If this assumption does not hold, the result can be biased.

The following paper is fairly basic and easy to follow. It mainly discusses the Cox proportional hazard model. If you want something more advanced, I can supply other links.

http://www.amstat.org/sections/SRMS/proceedings/y2002/Files/JSM2002-000406.pdf
 

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