Modeling Clinical Trials 1 punto posible (calificable) In a clinical trial, a pharmaceutical company wants to determine the efficacy of a cold remedy. To do so, they recruit 2n individuals to participate in a study, (randomly) placing n individuals in the treatment group and n individuals in the control group. Throughout the study, the treatment group will receive the actual drug, while the control group will only receive a placebo (for example, a sugar pill). To statistically model this scenario, we let X1,..., Xn be random variables that denote the number of coughs per hour of individuals 1,..., n, respectively in the treatment group, and Y1,..., Yn be random variables that denote the number of coughs per hour of individuals 1,..., n, respectively, in the control group. Let's assume that the individuals participating in the trial are separated throughout the trial, so that it's reasonable to expect the coughs per hour of one individual in the study will not affect the coughs per hour of some other individual in the study. Moreover, we expect the administered drug to induce the same distribution of coughs for each individual in the treatment group. We will also assume that the distribution of coughs in the control group is the same for each individual. What collection of mathematical assumption(s) below would capture exactly all of the assumptions stated in the previous paragraph, but nothing more? (Choose all that apply.) X1,..., Xn are independent, but may not all have the same distribution. The same holds for Y1,..., Yn. X1,..., X, all have the same distribution, but some of them are correlated. The same holds for Y1, ..., Yn. The random variables X1, ..., Xn are iid and the random variables Y1,..., different distribution from X1,..., Xn). Yn are iid (though perhaps from a The random variables X1,..., Xn, Y1,..., Yn are all iid (in particular, the X;'s and Y,'s are sampled from the same distribution). The random variable X; for any i is independent of Y; for any j.
Modeling Clinical Trials 1 punto posible (calificable) In a clinical trial, a pharmaceutical company wants to determine the efficacy of a cold remedy. To do so, they recruit 2n individuals to participate in a study, (randomly) placing n individuals in the treatment group and n individuals in the control group. Throughout the study, the treatment group will receive the actual drug, while the control group will only receive a placebo (for example, a sugar pill). To statistically model this scenario, we let X1,..., Xn be random variables that denote the number of coughs per hour of individuals 1,..., n, respectively in the treatment group, and Y1,..., Yn be random variables that denote the number of coughs per hour of individuals 1,..., n, respectively, in the control group. Let's assume that the individuals participating in the trial are separated throughout the trial, so that it's reasonable to expect the coughs per hour of one individual in the study will not affect the coughs per hour of some other individual in the study. Moreover, we expect the administered drug to induce the same distribution of coughs for each individual in the treatment group. We will also assume that the distribution of coughs in the control group is the same for each individual. What collection of mathematical assumption(s) below would capture exactly all of the assumptions stated in the previous paragraph, but nothing more? (Choose all that apply.) X1,..., Xn are independent, but may not all have the same distribution. The same holds for Y1,..., Yn. X1,..., X, all have the same distribution, but some of them are correlated. The same holds for Y1, ..., Yn. The random variables X1, ..., Xn are iid and the random variables Y1,..., different distribution from X1,..., Xn). Yn are iid (though perhaps from a The random variables X1,..., Xn, Y1,..., Yn are all iid (in particular, the X;'s and Y,'s are sampled from the same distribution). The random variable X; for any i is independent of Y; for any j.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Transcribed Image Text:Modeling Clinical Trials
1 punto posible (calificable)
In a clinical trial, a pharmaceutical company wants to determine the efficacy of a cold remedy. To do so, they recruit 2n
individuals to participate in a study, (randomly) placing n individuals in the treatment group and n individuals in the control
group. Throughout the study, the treatment group will receive the actual drug, while the control group will only receive a
placebo (for example, a sugar pill).
To statistically model this scenario, we let
X1,..., Xn be random variables that denote the number of coughs per hour of individuals 1,..., n, respectively in the
treatment group, and
• Y1,..., Yn be random variables that denote the number of coughs per hour of individuals 1,..., n, respectively, in the
control group.
Let's assume that the individuals participating in the trial are separated throughout the trial, so that it's reasonable to expect
the coughs per hour of one individual in the study will not affect the coughs per hour of some other individual in the study.
Moreover, we expect the administered drug to induce the same distribution of coughs for each individual in the treatment
group. We will also assume that the distribution of coughs in the control group is the same for each individual.
What collection of mathematical assumption(s) below would capture exactly all of the assumptions stated in the previous
paragraph, but nothing more? (Choose all that apply.)
X1,..., Xn are independent, but may not all have the same distribution. The same holds for Y1, ..., Yn.
X1,..., Xn all have the same distribution, but some of them are correlated. The same holds for Y1,..., Yn.
The random variables X1,..., Xn are iid and the random variables Y1,..., Y, are iid (though perhaps from a
different distribution from X1,..., Xn).
The random variables X1,... , Xn, Y1,..., Yn are all iid (in particular, the X;'s and Y;'s are sampled from the
same distribution).
The random variable X; for any i is independent of Y; for any j.
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