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 Interval since beginning treatment (months) Alive at beginning of interval Died during interva 1 Withdre w during interval Effective number exposed to risk of dying Proporti on who died during interval Proportion who did not die during interval Cumulative proportion who survived from enrollment to end of interval x I x d x W x I x ′ q x p x P x 1 − 12 200 10 40 13 − 24 150 20 30 25 − 36 100 30 20 37 − 48 50 40 10 \begin{array}{|l|l|l|l|l|l|l|l|}\hline \begin{array}{l} ext { Interval } \ ext { since } \ ext { beginning } \ ext { treatment } \ ext { (months) }\end{array} & \begin{array}{l} ext { Alive at } \ ext { beginning } \ ext { of } \ ext { interval }\end{array} & \begin{array}{l} ext { Died } \ ext { during } \ ext { interva } \1\end{array} & \begin{array}{l} ext { Withdre } \ ext { w during } \ ext { interval }\end{array} & \begin{array}{l} ext { Effective } \ ext { number } \ ext { exposed } \ ext { to risk of } \ ext { dying }\end{array} & \begin{array}{l} ext { Proporti } \ ext { on who } \ ext { died } \ ext { during } \ ext { interval }\end{array} & \begin{array}{l} ext { Proportion } \ ext { who did not } \ ext { die during } \ ext { interval }\end{array} & \begin{array}{l} ext { Cumulative } \ ext { proportion } \ ext { who } \ ext { survived } \ ext { from } \ ext { enrollment } \ ext { to end of } \ ext { 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} Interval since beginning treatment (months) x 1 − 12 13 − 24 25 − 36 37 − 48 Alive at beginning of interval I x 200 150 100 50 Died during interva 1 d x 10 20 30 40 Withdre w during interval W x 40 30 20 10 Effective number exposed to risk of dying I x ′ Proporti on who died during interval q x Proportion who did not die during interval p x Cumulative proportion who survived from enrollment to end of interval P x A) 0.30B) 0.33C) 0.38D) 0.67E) 0.70

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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  Interval   since   beginning   treatment   (months)    Alive at   beginning   of   interval   Died   during   interva  1  Withdre   w during   interval   Effective   number   exposed   to risk of   dying   Proporti   on who   died   during   interval   Proportion   who did not   die during   interval   Cumulative   proportion   who   survived   from   enrollment   to end of   interval  x I x d x W x I x ′ q x p x P x 1 − 12 200 10 40 13 − 24 150 20 30 25 − 36 100 30 20 37 − 48 50 40 10 \begin{array}{|l|l|l|l|l|l|l|l|}\hline \begin{array}{l}	ext { Interval } \	ext { since } \	ext { beginning } \	ext { treatment } \	ext { (months)  }\end{array}  &  \begin{array}{l}	ext { Alive at } \	ext { beginning } \	ext { of } \	ext { interval }\end{array}  &  \begin{array}{l}	ext { Died } \	ext { during } \	ext { interva } \1\end{array}  &  \begin{array}{l}	ext { Withdre } \	ext { w during } \	ext { interval }\end{array}  &  \begin{array}{l}	ext { Effective } \	ext { number } \	ext { exposed } \	ext { to risk of } \	ext { dying }\end{array}  &  \begin{array}{l}	ext { Proporti } \	ext { on who } \	ext { died } \	ext { during } \	ext { interval }\end{array}  &  \begin{array}{l}	ext { Proportion } \	ext { who did not } \	ext { die during } \	ext { interval }\end{array}  &  \begin{array}{l}	ext { Cumulative } \	ext { proportion } \	ext { who } \	ext { survived } \	ext { from } \	ext { enrollment } \	ext { to end of } \	ext { 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}  Interval   since   beginning   treatment   (months)   ​ x 1 − 12 13 − 24 25 − 36 37 − 48 ​  Alive at   beginning   of   interval  ​ I x ​ 200 150 100 50 ​  Died   during   interva  1 ​ d x ​ 10 20 30 40 ​  Withdre   w during   interval  ​ W x ​ 40 30 20 10 ​  Effective   number   exposed   to risk of   dying  ​ I x ′ ​ ​  Proporti   on who   died   during   interval  ​ q x ​ ​  Proportion   who did not   die during   interval  ​ p x ​ ​  Cumulative   proportion   who   survived   from   enrollment   to end of   interval  ​ P x ​ ​ ​ A)  0.30B)  0.33C)  0.38D)  0.67E)  0.70

Morgan Michel · Accepted Answer

Final Answer : D, Explanation :   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 ′ I_x ' 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.

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