This question is in the library, but has multiple answers making it confusing. I understand that the probability of surviving 1 year after being diagnosed with a slow-growing form of prostate cancer is 0.85, but where I'm confused is who does this apply to - only the study participants or study participants and everyone else who decide not to seek treatment. This tail-end is where there are multiple answers in the library. Can you explain? (I am going to be sending an additional question that is very similar). Thank you. **Title: Survival Probability Analysis Using the Kaplan-Meier Approach****Description:**In this study, we analyze survival probabilities for individuals diagnosed with a slow-progressing form of prostate cancer who opted out of any treatment. We use the Kaplan-Meier approach to determine survival probabilities at different time intervals. Here's a breakdown of the data and analysis:**Data Table:**| Time in Years | Number at Risk ($N_t$) | Number of Deaths ($D_t$) | Number Censored ($C_t$) | Survival Probability ||---------------|--------------------------|--------------------------|--------------------------|----------------------|| 0 | 20 | | | 1 || 1 | 20 | 3 | | || 2 | 17 | | 1 | || 3 | 16 | 2 | 1 | |**Interpretation:**a. The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is 0.85.b. The probability remains 0.85 for individuals followed in this study.c. This probability applies to those who have decided against all forms of treatment.d. The probability of surviving 1 year is consistent for the study participants and those opting out of all treatment forms.**Further Notes:**- **Censoring:** Refers to individuals leaving the study or being lost to follow-up.- **Deaths:** These are recorded events of death within the study period at specific time points.- **Survival Probability:** This measures the likelihood of survival over time, given the conditions outlined at the start of the study.This analysis helps in understanding the disease progression under non-treatment conditions, offering insights into patient decision-making and health outcomes.

Answered: This question is in the library, but…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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This question is in the library, but has multiple answers making it confusing. I understand that the probability of surviving 1 year after being diagnosed with a slow-growing form of prostate cancer is 0.85, but where I'm confused is who does this apply to - only the study participants or study participants and everyone else who decide not to seek treatment. This tail-end is where there are multiple answers in the library. Can you explain? (I am going to be sending an additional question that is very similar). Thank you.

**Title: Survival Probability Analysis Using the Kaplan-Meier Approach**

**Description:**

In this study, we analyze survival probabilities for individuals diagnosed with a slow-progressing form of prostate cancer who opted out of any treatment. We use the Kaplan-Meier approach to determine survival probabilities at different time intervals. Here's a breakdown of the data and analysis:

**Data Table:**

| Time in Years | Number at Risk ($N_t$) | Number of Deaths ($D_t$) | Number Censored ($C_t$) | Survival Probability |
|---------------|--------------------------|--------------------------|--------------------------|----------------------|
| 0 | 20 | | | 1 |
| 1 | 20 | 3 | | |
| 2 | 17 | | 1 | |
| 3 | 16 | 2 | 1 | |

**Interpretation:**

a. The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is 0.85.

b. The probability remains 0.85 for individuals followed in this study.

c. This probability applies to those who have decided against all forms of treatment.

d. The probability of surviving 1 year is consistent for the study participants and those opting out of all treatment forms.

**Further Notes:**

- **Censoring:** Refers to individuals leaving the study or being lost to follow-up.
- **Deaths:** These are recorded events of death within the study period at specific time points.
- **Survival Probability:** This measures the likelihood of survival over time, given the conditions outlined at the start of the study.

This analysis helps in understanding the disease progression under non-treatment conditions, offering insights into patient decision-making and health outcomes.

Expert Solution

Step 1

Given the life table constructed from following individuals who were diagnosed with a slow-progressing form of prostate cancer and decided not to receive treatment of any form :