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

In summary, the conversation discusses a problem involving an exponential distribution with a given hazard rate and a Uniform right censoring time. The goal is to find the probability that the lifetime is longer than the censoring time. The assumption is that censoring is randomly distributed between comparison groups. A paper is recommended for further understanding and more advanced resources can be provided if needed.
  • #1
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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  • #2
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
 

1. What is the concept of right censoring in time of death data?

Right censoring in time of death data refers to situations where the exact time of death is unknown for some individuals in a study. This can occur if the study ends before all individuals have died, or if some individuals drop out of the study before their death occurs. In these cases, the time of death is said to be censored or incomplete.

2. How is the probability of time of death after right censoring time calculated?

The probability of time of death occurring after right censoring time is typically calculated using survival analysis methods. This involves estimating the survival function, which represents the probability of an individual surviving beyond a certain time point. The probability of death after right censoring time can then be estimated using this survival function.

3. What factors can affect the probability of time of death after right censoring time?

Several factors can affect the probability of time of death after right censoring time, including the length of the study period, the number of individuals who drop out of the study, and the characteristics of the study population (e.g. age, health status, etc.). Additionally, the type of censoring (e.g. random vs. non-random) and the assumptions made in the analysis can also impact the estimated probability.

4. How is right censoring handled in statistical analysis?

Right censoring is typically handled using specialized statistical methods, such as survival analysis or time-to-event analysis. These methods take into account the incomplete nature of the data and allow for the estimation of probabilities and survival curves despite censoring. It is important for researchers to carefully consider the type of censoring in their study and choose appropriate methods for analysis.

5. Can the probability of time of death after right censoring time be used to make predictions?

Yes, the probability of time of death after right censoring time can be used to make predictions about future outcomes. For example, this information can be used to estimate the average lifespan of a particular population or to assess the effectiveness of a medical treatment in prolonging survival. However, it is important to note that these predictions are based on statistical models and may not accurately reflect individual outcomes.

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