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##### HLTH501 WEEK 8 PROBLEMS

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Question;Week 8;Problems?30 points;15 points each.;Place answers within the Word document below.;1. A;study is conducted to estimate survival in patients following kidney;transplant. Key factors that adversely affect success of the transplant include;advanced age and diabetes. This study involves 25;participants who are 65 years of age and older and all have diabetes. Following;transplant, each participant is followed for up to 10 years. The following are;times to death, in years, or the time to last contact (at which time the participant;was known to be alive).;Deaths: 1.2, 2.5, 4.3, 5.6, 6.7, 7.3 and 8.1 years;Alive: 3.4, 4.1, 4.2, 5.7, 5.9, 6.3, 6.4, 6.5;7.3, 8.2, 8.6, 8.9, 9.4, 9.5, 10, 10, 10, and 10 years;Use the life;table approach to estimate the survival function. Use years intervals of;0?2;2?4;Complete;the table below.;Interval;in;Years;Number At Risk During Interval;Nt;Average Number At Risk During Interval;Nt* =Nt-Ct /2;Number of Deaths During Interval;Dt;Lost to Follow-Up;Ct;Proportion Dying;qt = Dt/Nt*;Proportion Surviving;pt = 1-qt;Survival Probability;St =;pt*St-1;0?2;25;25;1;0;0.04;0.96;0.96;2?4;24;23.5;1;1;0.042;0.958;0.919;4?6;22;20.5;2;3;0.0956;0.9044;0.8311;6?8;17;15;2;4;0.133;0.867;0.720;8?10;11;8.5;1;5;0.118;0.882;0.635;Use the;Kaplan-Meier approach to estimate the survival function.;Complete the;table below;Time, Years;Number at Risk;Nt;Number of;Deaths;Dt;Number;Censored;Ct;Survival;Probability;St+1=;St*((Nt-Dt)/Nt);0;25;--;--;1;1.2;25;1;0;0.96;2.5;24;1;0;0.92;3.4;23;0;1;0.92;4.1;22;0;1;0.92;4.2;21;0;1;0.88;4.3;20;1;1;0.836;5.6;19;1;0;0.792;5.7;18;0;1;0.792;5.9;17;0;1;0.792;6.3;16;0;1;0.792;6.4;15;0;1;0.792;6.5;14;0;1;0.792;6.7;13;1;1;0.731;7.3;12;1;0;0.670;8.1;11;1;0;0.609;8.2;10;0;1;0.609;8.6;9;0;1;0.609;8.9;8;0;1;0.609;9.4;7;0;1;0.609;9.5;6;0;1;0.609;10.0;5;0;4;0.609;Referring;to the graph above;What is the probability;of surviving 6.5 years?;A.;None;B.;0.85;C.;0.60;D.;0.90;Patients have an;85% chance of surviving how many years?;A.;6.0;B.;4.25;C.;3.2;D.;5.5;2. A clinical trial is conducted to;evaluate the efficacy of a new drug for prevention of hypertension in patients;with pre-hypertension (defined as systolic blood pressure between 120?139 mmHg;or diastolic blood pressure between 80?89 mmHg). A total of 20 patients are;randomized to receive the new drug or a currently available drug for treatment;of high blood pressure. Participants are followed for up to 12 months, and time;to progression to hypertension is measured. The experiences of participants in;each arm of the trial are shown below.;New Drug;Currently Available Drug;Hypertension;Free of;Hypertension;Hypertension;Free of;Hypertension;7;8;6;8;8;8;7;9;10;8;9;11;9;10;11;11;11;12;12;12;Estimate the;survival (time to progression to hypertension) functions for each treatment;group using the Kaplan-Meier approach.;New Drug;Complete the;table below.;Time, Months;Number at Risk;Nt;Number of;Events (Hypertension);Dt;Number;Censored;Ct;Survival;Probability;St+1=;St*((Nt-Dt)/Nt);0;10;1;7;10;3;0;0.7;8;7;2;0.5;9;5;2;0.3;10;3;0;0.3;11;2;0;0.3;12;1;0;0.3;Currently;Available Drug;Complete the;table below.;Time, Weeks;Number at Risk;Nt;Number of;Events (Hypertension);Dt;Number;Censored;Ct;Survival;Probability;St+1=;St*((Nt-Dt)/Nt);0;10;--;--;1;6;10;6;0.4;7;6;7;-0.07;8;5;9;-0.056;9;3;10;0.131;10;2;11;-0.59;11;--;12;--;To;answer the question as to whether or not there is a difference in time to;progression, a Chi square statistic is computed. The critical value for;rejection of the null hypothesis is 3.84. The computed Chi square is 0.335.;Based;on comparing the computed Chi square and the critical Chi square, which of the;following is (are) true?;A.;There;is not statistically significant evidence to show that thetime to progression is different between groups.;B.;There;is statistically significant evidence to show that thetime to progression is different between groups.;C.;The time to progression is;essentially the same for each group.;D.;a and c.;The hazard ratio;risk of progression to hypertension is 0.658. Based on this computation, which;of the following is (are) true?;A.;The risk of progression to;hypertension is reduced by 34.2% in patients assigned to the new drug as;compared to the currently available drug.;B.;The risk of progression to;hypertension is 1.52 times higher in patient?s current drug as compared to the;new drug.;C.;The risk of progression to;hypertension is 5.12 times higher in patient?s current drug as compared to the;new drug;D. a and b

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