Survival function from probabilities of no event at time t

In summary, the conversation discusses formulating a survival function from a sequence of probabilities of no event at different time intervals. It is clarified that survival means no event and the formula for calculating the survival probability is given as P(1)xP(2)x...xP(t).
  • #1
senit
2
0
Hello World,

How can I formulate a survival function from a sequence of probabilities of no event at every time t, i.e P(0), P(1), P(2),...,P(t) where P(i), for i=0,1,...,t is the probability of no event at time i?

Thanks
 
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  • #2
If you mean survival means no event and if the probabilities {P(i)} are all independent, then the probability of survival is simply P(1)xP(2)x...xP(t).
 
  • #3
mathman said:
If you mean survival means no event and if the probabilities {P(i)} are all independent, then the probability of survival is simply P(1)xP(2)x...xP(t).

Awesome Mathman, thanks
 

FAQ: Survival function from probabilities of no event at time t

What is the survival function?

The survival function is a statistical concept that represents the probability of surviving beyond a certain time point. It is used to analyze time-to-event data, such as how long it takes for an individual or group to experience an event.

How is the survival function calculated from probabilities of no event at time t?

The survival function is calculated by taking the cumulative product of the probabilities of no event at each time point. This means that the probability of surviving beyond time t is equal to the product of all the probabilities of no event from time 0 to time t.

What does the survival function tell us about the data?

The survival function provides information about the probability of surviving beyond a certain time point. It can also be used to estimate the median survival time, as well as the probabilities of survival at specific time points. Additionally, it can be used to compare survival between different groups or treatments.

How is the survival function typically presented?

The survival function is often presented graphically as a curve, with time on the x-axis and the probability of survival on the y-axis. This curve can be used to visualize the survival probabilities over time and to compare different groups or treatments. Additionally, the survival function can also be presented in a table format, showing the survival probabilities at specific time points.

What are some limitations of using the survival function for data analysis?

One limitation of the survival function is that it assumes that all individuals in the study are followed until the event of interest occurs. This may not always be the case in real-world scenarios. Additionally, the survival function may not accurately represent the survival probabilities in situations where there are censoring or competing risks present in the data.

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