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

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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  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)  40B)  90C)  120D)  135E)  160

uzair imran · Accepted Answer

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

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