5.95-5.98 Ophthalmology A previous study found that people consuming large quant

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5.95-5.98 Ophthalmology A previous study found that people consuming large quantities of vegetables containing lutein (mainly spinach) were less likely to develop macular degeneration, a common eye disease among older people (age 65+) that causes a substantial loss in visual acuity and in some cases can lead to total blindness. To follow up on this observation, a clinical trial is planned in which participants 65+ years of age without macular degeneration will be assigned to either a high-dose lutein supplement tablet or a placebo tablet taken once per day. To estimate the possible therapeutic effect, a pilot study was conducted in which 9 people 65+ years of age were randomized to placebo and 9 people 65+ years of age were randomized to lutein tablets (active treatment). Their serum lutein level was measured at baseline and again after 4 months of follow-up. From previous studies, people with serum lutein 10mg/dL are expected to get some protection from macular degeneration. However, the level of serum lutein may vary depending on genetic factors, dietary factors, and study supplements. 5.95 Suppose that among people randomized to placebo, at a 4-month follow-up mean serum lutein level=v6.4 mg/dL with standard deviation =3mg/dL. If we presume a normal distribution for serum lutein, then what percentage of placebo subjects will have serum lutein in the therapeutic range ( 10mg.dL)? (For the following problems, assume that lutein can be measured exactly, so no continuity correction is necessary) 5.96 Suppose that among people randomized to lutein tablets, at a 4 month follow-up the mean serum lutein level =21 mg/dL with standard deviation = 8mg/dL. If we presume a normal distribution for serum-lutein values among lutein-treated participants, then what percentage of people randomized to lutein tablets will have serum lutein in the therapeutic range? Suppose for the sake of simplicity that the incidence of macular degeneration is 1% per year among people 65+ years of age in therapeutic range (10 mg/dL) and 2% per year among people 65+ years of age with lower levels of lutein (< 10 mg/dL). 5.97 What is the expected incidence rate of macular degeneration among lutein treated participants? (Hint: Use the total-probability rule) 5.98 What is the expected relative risk of macular degeneration for lutein-treated participants versus placebo-treated participants in the proposed study? Please I only need the two last ones!

Explanation / Answer

Let lb be the variable that denotes lutein levels in placebo group and lt be lutein levels in luteins tablets treated group

5.95 Probability that lb is greater than 10 mg follows distribution N(6.4,3)

P(lb>10) = 1-p(lb<10) = 1 - z( (10-6.4)/3 ) = 1-88.5% = 11.5%

Only 11.5% of placebo subjects with have levels in the therapeutic range (>10mg)

5.95 Probability that lt is greater than 10 mg follows distribution N(21,8)

P(lt>10) = 1-p(lt<10) = 1 - z( (10-21)/3 ) = 1-8.5% = 91.5%

91.5% of those treated with lutein tablets with have levels in the therapeutic range (>10mg)

5.97 P( mucular generation in levels >10mg pop) = 1%

P(mucular generation in levels <10mg pop) = 2%

Probability (macular degeneration in lutein tablets group) = 1%* P( therapeutic levels in lutein tablets group) + 2%*P(non-therapeutic levels in lutein tablets group)

= 1%*91.5%+2%*8.5%=1.09%

5.98

Probability (macular degeneration in placebo group) = 1%* P( therapeutic levels in placebo group) + 2%*P(non-therapeutic levels in placebo group)

= 1%*11.5%+2%*88.5%=1.89%

Relative risk of macular degeneration lutein treated vs placebo = 1.09/1.89 =58%

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