F17-MLR-Applications

# F17-MLR-Applications - PubH 7405 REGRESSION ANALYSIS MLR...

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PubH 7405: REGRESSION ANALYSIS MLR: BIOMEDICAL APPLICATIONS

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Multiple Regression allows us to get into two new areas that were not possible with Simple Linear Regression : (i) Interaction or Effect Modification , and (ii) Non-linear Relationship .
This lecture today is devoted to biomedical applications; we cover two topics: (1) For interactions, we re-visit and expands the topic of bioassays , and (2) As an example of non-linear models, I’ll show you how to study “ seasonal diseases ”- a case similar to that of quadratic regression - with two predictor terms representing the same “predictor source” where we search for an optimal condition for the outcome.

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DEFINITION “Biological assays” or “ bioassays are a set of methods for estimating the potency or strength of an “ agent by utilizing the “ response caused by its application to biological material or experimental living “ subjects ”.
COMPONENTS OF A BIOASSAY The subject is usually an animal, a human tissue, or a bacteria culture, The agent is usually a drug, The response is usually a change in a particular characteristic or even the death of a subject ; the response could be binary or on continuous scale .

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DIRECT ASSAYS In direct assays , the doses of the standard and test preparations are “directly measured for an “event of interest”. When an (pre-determined) event of interest occurs, e.g. . the death of the subject, and the variable of interest is the dose required to produce that response/event for each subject. In other words: (Binary) Response is fixed , Dose is a Random Variable .
INDIRECT ASSAYS In indirect assays , the doses of the standard and test preparations are are applied and we observe the response that each dose produces; for example, we measure the tension in a tissue or the hormone level or the blood sugar content. For each subject, the dose is fixed in advance, the variable of interest is not the dose but the response it produces in each each subject. Doses are fixed, Response is a Random Variable ; statistically, indirect assays are more interesting and also more difficult.

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For Indirect Assays, depending on the measurement scale for the response – our Random Variable, we have: (1) Quantal assays , where the response is binary : whether or not an event (like the death of the subject) occur, (2) Quantitative assays , where measurements for the response are on a continuous scale. This is our main focus; the dependent variable Y .
The common indirect assay is usually one in which the ratio of equipotent doses is estimated from “curves” or “lines” relating quantitative responses and doses for the two preparations. The shape of these curves or lines further divides Quantitative Indirect Assays into : (1) Parallel-line assays are those in which the response is linearly related to the log dose , (2) Slope ratio assays are those in which the response is linearly related to the dose itself.

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PARALLEL-LINE ASSAYS Parallel-line assays are those in which the
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## This note was uploaded on 11/21/2011 for the course PUBH 7405 taught by Professor Staff during the Fall '08 term at Minnesota.

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F17-MLR-Applications - PubH 7405 REGRESSION ANALYSIS MLR...

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