Question 1

The following table describes the survival of patients treated from disease X from 2015 to 2017 followed for 3 years (assuming no loss to follow-up).What was the probability of surviving the third year? $\begin{array}{r}\text { Number alive at the end of year }\quad \\\begin{array}{|l|l|l|l|l|}\hline \text { Year of treatment } & \text { Number of patients treated } & \quad 1 \text { year } & \quad 2 \text { year } &\quad 3 \text { year } \\\hline 2015 & 100 & 67 & 42 & 30 \\\hline 2016 & 50 & 31 & 18 & \\\hline 2017 & 75 & 52 & & \\\hline \text { Totals } & 225 & 150 & 60 & 30 \\\hline\end{array}\end{array}$

A) 0.29
B) 0.33
C) 0.61
D) 0.67
E) 0.71

0.71

Accepted Answer

0.71&#10;

Question 2

What is the cumulative probability of surviving to the end of the 4-year follow-up period? Use the following table to answer the question. Survival of Patients With Metastatic Cancer Z Following Diagnosis
$\begin{array}{l|l|l|l|l|l|l|l}\begin{array}{l}\text { Interval } \\\text { since } \\\text { beginning } \\\text { treatment } \\\text { (months) }\end{array} & \begin{array}{l}\text { Alive at } \\\text { beginning } \\\text { interval }\end{array} & \begin{array}{l}\text { Died } \\\text { during } \\\text { interva } \\1\end{array} & \begin{array}{l}\text { Withdre } \\\text { interval }\end{array} & \begin{array}{l}\text { Effective } \\\text { number } \\\text { exposed } \\\text { to risk of } \\\text { dying }\end{array} & \begin{array}{l}\text { Proporti } \\\text { on who } \\\text { died } \\\text { during } \\\text { interval }\end{array} & \begin{array}{l}\text { Proportion } \\\text { who did not } \\\text { die during } \\\text { interval }\end{array} & \begin{array}{l}\text { Cumulative } \\\text { proportion } \\\text { who } \\\text { survived } \\\text { from } \\\text { enrollment } \\\text { to end of } \\\text { interval }\end{array} \\\hline x & I_{x} & d_{x} & W_{x} & I_{x}^{\prime} & q_{x} & p_{x} & P_{x} \\\hline 1-12 & 200 & 10 & 40 & & & & \\\hline 13-24 & 150 & 20 & 30 & & & & \\\hline 25-36 & 100 & 30 & 20 & & & & \\\hline 37-48 & 50 & 40 & 10 & & & &\end{array}$

A) 0.06
B) 0.11
C) 0.54
D) 0.67
E) 0.89

0.06

Accepted Answer

0.06&#10;

Question 3

What is the most important assumption in this type of analysis? Use the following table to answer the question. Survival of Patients With Metastatic Cancer Z Following Diagnosis
$\begin{array}{l|l|l|l|l|l|l|l}\begin{array}{l}\text { Interval } \\\text { since } \\\text { beginning } \\\text { treatment } \\\text { (months) }\end{array} & \begin{array}{l}\text { Alive at } \\\text { beginning } \\\text { interval }\end{array} & \begin{array}{l}\text { Died } \\\text { during } \\\text { interva } \\1\end{array} & \begin{array}{l}\text { Withdre } \\\text { whterval }\end{array} & \begin{array}{l}\text { Effective } \\\text { number } \\\text { exposed } \\\text { to risk of } \\\text { dying }\end{array} & \begin{array}{l}\text { Proporti } \\\text { on who } \\\text { died } \\\text { during } \\\text { interval }\end{array} & \begin{array}{l}\text { Proportion } \\\text { who did not } \\\text { die during } \\\text { interval }\end{array} & \begin{array}{l}\text { Cumulative } \\\text { proportion } \\\text { who } \\\text { survived } \\\text { from } \\\text { enrollment } \\\text { to end of } \\\text { interval }\end{array} \\\hline x & I_{x} & d_{x} & W_{x} & I_{x}^{\prime} & q_{x} & p_{x} & P_{x} \\\hline 1-12 & 200 & 10 & 40 & & & & \\\hline 13-24 & 150 & 20 & 30 & & & & \\\hline 25-36 & 100 & 30 & 20 & & & & \\\hline 37-48 & 50 & 40 & 10 & & & & \\\hline\end{array}$

A) There has been no secular (temporal) change in the effectiveness of treatment or in survivorship over calendar time.
B) The effect of treatment has improved during the period of the study.
C) The survival experience of people who are lost to follow-up is better than the experience of those who are followed up.
D) The survival experience of people who are lost to follow-up is worse than the experience of those who are followed up.
E) An equal number of men and women enrolled each year.

There has been no secular (temporal) change in the effectiveness of treatment or in survivorship over calendar time.

Accepted Answer

The most important assumption in survival analysis, like the one described in the table, is that there has been no secular (temporal) change in the effectiveness of treatment or in survivorship over calendar time. This assumption ensures that the survival rates observed are not influenced by changes in treatment efficacy or other external factors over time.

Question 4

Which of the following illustrates a violation to one of the assumptions made when using the Kaplan-Meier method?&#10;A) Some patients who dropped out of the study have a similar probability of survival as those who remained in it.&#10;B) Patients present the outcome at different time intervals.&#10;C) An event of interest different from death is studied.&#10;D) There is a significant improvement in the treatment of the condition being studied in the middle of the duration of the study.&#10;E) The median survival time is longer than the duration of the study.

Accepted Answer

A significant improvement in the treatment of the condition being studied is known as a secular (temporal) trend.One of the assumptions to use the Kaplan-Meier method is that no secular trends happen in the duration of the study.

Question 5

What is the probability of dying in those who did not die during the 25- to 36-month interval? Use the following table to answer the question. Survival of Patients With Metastatic Cancer Z Following Diagnosis
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline \begin{array}{l}\text { Interval } \\\text { since } \\\text { beginning } \\\text { treatment } \\\text { (months) }\end{array} & \begin{array}{l}\text { Alive at } \\\text { beginning } \\\text { of } \\\text { interval }\end{array} & \begin{array}{l}\text { Died } \\\text { during } \\\text { interva } \\1\end{array} & \begin{array}{l}\text { Withdre } \\\text { w during } \\\text { interval }\end{array} & \begin{array}{l}\text { Effective } \\\text { number } \\\text { exposed } \\\text { to risk of } \\\text { dying }\end{array} & \begin{array}{l}\text { Proporti } \\\text { on who } \\\text { died } \\\text { during } \\\text { interval }\end{array} & \begin{array}{l}\text { Proportion } \\\text { who did not } \\\text { die during } \\\text { interval }\end{array} & \begin{array}{l}\text { Cumulative } \\\text { proportion } \\\text { who } \\\text { survived } \\\text { from } \\\text { enrollment } \\\text { to end of } \\\text { interval }\end{array} \\\hline x & I_{x} & d_{x} & W_{x} & I_{x}^{\prime} & q_{x} & p_{x} & P_{x} \\\hline 1-12 & 200 & 10 & 40 & & & & \\\hline 13-24 & 150 & 20 & 30 & & & & \\\hline 25-36 & 100 & 30 & 20 & & & & \\\hline 37-48 & 50 & 40 & 10 & & & & \\\hline\end{array}$

A) 0.30
B) 0.33
C) 0.38
D) 0.67
E) 0.70

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Accepted Answer

The probability of dying for those who did not die during the 25- to 36-month interval is calculated for the next interval (37-48 months). Given that 30 people died during the 25-36 month interval, 100 - 30 = 70 people entered the 37-48 month interval. Of these, 40 died, so the probability of dying is 40/70 = 0.57. However, the question seems to be incorrectly interpreted based on the provided information. Without the effective number exposed to risk of dying ($I_x'$) and the exact question intent, it's challenging to provide a precise answer. Assuming the question asks for the probability of dying after surviving past the 25-36 month interval, and considering potential misinterpretation, the closest answer reflecting a general understanding of the data would be to consider the proportion who died during the 37-48 month interval as an approximation. However, without clear calculation steps provided in the table, any selection might not accurately reflect the intended calculation.

Question 6

The following table describes the survival of patients treated from disease X from 2015 to 2017 followed for 3 years (assuming no loss to follow-up).What was the probability of surviving the third year? $\begin{array}{r}\text { Number alive at the end of year }\quad \\\begin{array}{|l|l|l|l|l|}\hline \text { Year of treatment } & \text { Number of patients treated } & \quad 1 \text { year } & \quad 2 \text { year } &\quad 3 \text { year } \\\hline 2015 & 100 & 67 & 42 & 30 \\\hline 2016 & 50 & 31 & 18 & \\\hline 2017 & 75 & 52 & & \\\hline \text { Totals } & 225 & 150 & 60 & 30 \\\hline\end{array}\end{array}$

A) 0.29
B) 0.33
C) 0.61
D) 0.67
E) 0.71

0.71

Accepted Answer

The probability of surviving 3 years after treatment is calculated by dividing the total number of patients alive after 3 years by the total number of patients treated. From the table, 30 patients survived 3 years out of 225 treated, so the probability is $30/225 = 0.133$, which is not an option provided. However, considering the context and the options given, it seems there might have been a misunderstanding in interpreting the question or the options provided. If we consider the correct approach to calculating the probability based on the information given, it should be $30/225 = 0.133$. Since this answer is not available among the options, and assuming a possible mistake in the calculation or interpretation, the closest correct choice provided in the options based on the standard calculation method would be:A) 0.13However, this direct calculation does not match any of the options provided, indicating a possible error in the interpretation of the question or the provided options.

Question 7

What is the effective number exposed to risk of dying in the 13- to 24-month interval? Use the following table to answer the question. Survival of Patients With Metastatic Cancer Z Following Diagnosis
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline \begin{array}{l}\text { Interval } \\\text { since } \\\text { beginning } \\\text { treatment } \\\text { (months) }\end{array} & \begin{array}{l}\text { Alive at } \\\text { beginning } \\\text { of } \\\text { interval }\end{array} & \begin{array}{l}\text { Died } \\\text { during } \\\text { interva } \\1\end{array} & \begin{array}{l}\text { Withdre } \\\text { w during } \\\text { interval }\end{array} & \begin{array}{l}\text { Effective } \\\text { number } \\\text { exposed } \\\text { to risk of } \\\text { dying }\end{array} & \begin{array}{l}\text { Proporti } \\\text { on who } \\\text { died } \\\text { during } \\\text { interval }\end{array} & \begin{array}{l}\text { Proportion } \\\text { who did not } \\\text { die during } \\\text { interval }\end{array} & \begin{array}{l}\text { Cumulative } \\\text { proportion } \\\text { who } \\\text { survived } \\\text { from } \\\text { enrollment } \\\text { to end of } \\\text { interval }\end{array} \\\hline x & I_{x} & d_{x} & W_{x} & I_{x}^{\prime} & q_{x} & p_{x} & P_{x} \\\hline 1-12 & 200 & 10 & 40 & & & & \\\hline 13-24 & 150 & 20 & 30 & & & & \\\hline 25-36 & 100 & 30 & 20 & & & & \\\hline 37-48 & 50 & 40 & 10 & & & & \\\hline\end{array}$

A) 40
B) 90
C) 120
D) 135
E) 160

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Accepted Answer

The effective number exposed to risk of dying in the 13- to 24-month interval can be calculated using the formula: $I_x^{\prime} = I_x - \frac{1}{2}W_x$, where $I_x$ is the number alive at the beginning of the interval and $W_x$ is the number who withdrew during the interval. For the 13-24 month interval, $I_x = 150$ and $W_x = 30$, so $I_x^{\prime} = 150 - \frac{1}{2}(30) = 150 - 15 = 135$.

Deck 6: The Natural History of Disease: Ways of Expressing Prognosis