Linkage Analysis: An Application of the Likelihood Ratio Test .

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Points for Discussion. Mendel\'s Contribution to the Understanding the Distribution of Genetic Material in Genetic CrossesWhat is the Goal of Linkage Analysis? Why is a Likelihood Approach Appropriate? Optimal?How is Linkage Analysis Performed?Abraham Wald\'s Contribution to the Optimization of Linkage Analysis Methods .
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Linkage Analysis: An Application of the Likelihood Ratio Test by Debbie Goldwasser STAT600 November 8,2004

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Topics for Discussion Mendel\'s Contribution to the Understanding the Distribution of Genetic Material in Genetic Crosses What is the Goal of Linkage Analysis? Why is a Likelihood Approach Appropriate? Ideal? How is Linkage Analysis Performed? Abraham Wald\'s Contribution to the Optimization of Linkage Analysis Methods

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Mendel: Brief Biography Gregor Johann Mendel was conceived on July 22, 1822, in Heinzendorf, Austria The main child of a worker agriculturist, his gifts were perceived and he went to the Olmutz Philosophical Institute as a young fellow At age 21, Mendel entered the Augustinian religious community of St. Thomas in Brunn, Austria, a site of noteworthy learning in numerous zones of study It was as a friar that Mendel built up an enthusiasm for the characteristic sciences and picked up acknowledgment as an especially generally welcomed educator among his understudies Published his milestone paper "Analyses in Plant Hybridization" in 1865, in which he established the trial framework for the laws of free collection and the law of isolation After Mendel\'s passing in 1882, his work was rediscovered in 1902, after which his thoughts increased across the board acknowledgment for their pertinence in clarifying fundamental components of heredity.

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Mendel and His Peas: The Law of Segregation Isolated immaculate types of plants with reciprocal attributes then crossed them to produce half breeds. Characterizes "Predominant" and "Latent" properties: prevailing properties constitute the whole character of the crossover though passive properties are lost in the half breed era (i.e. Axa - �� A) Crossed crossovers and found a proportion of 3:1 amongst predominant and latent characteristics (I.e. (3:1 A:a) Key understanding lie in Mendel\'s capacity to recognize overwhelming types of the half and half cross. The proportion of variation overwhelming structures to invariant predominant structures is 2:1 (Aa will be Aa OR An in a proportion of 2:1) Therefore he inferred that the proportion of peas coming about frame the half breed cross has a genuine proportion of 1:2:1 (A:Aa:a) These discoveries inevitably prompted to the law of isolation which in the year 2004 states that "diploid life forms have qualities in sets, and just a single individual from this match is transmitted to every posterity".

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Mendel and His Peas: The Law of Independent Assortment Next, Mendel took a gander at mixture crosses from doubly steady various characteristics (i.e. AbXaB) Again, he characterizes the latent properties as those that are lost in the half and half era (lowercase letters) The phenotypic proportion coming about because of the crossover cross is 9:3:3:1 for blends of characteristics (AB:Ab:aB:ab) Again, Mendel recognized these posterity by their capacity to create variation shapes keeping in mind the end goal to locate a genuine proportion of (AB,Ab,ABb,AaB,AaBb,Aab,aBb,aB,ab) among the mixtures to be 1:1:2:2:4:2:2:1:1 The law of autonomous arrangement in the year 2004 states that alleles at various loci isolate freely of each other.

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Relevance of Mendel\'s Findings Mendel\'s discoveries shape the reason for the investigation of hereditary qualities. It has been demonstrated that qualities, truth be told, do lie on chromosomes, of which we get a full set from both of our folks, bringing about a sum of two duplicates each. In the parent era, unlinked qualities isolate freely of each other amid meiosis and gamete development. We can show the dispersion of qualities transmitted to posterity as a progression of Bernoulli trials. Every duplicate of a quality is transmitted with likelihood ½ The law of free arrangement is the invalid theory we will test in linkage investigation. We will along these lines test the presumption that impartial hereditary material and an ailment quality isolate freely. On the off chance that we presume that a specific quality and ailment attribute don\'t isolate autonomously, then we allude to them as "connected" A probability approach is utilized on the grounds that the invalid speculation is a settled parameter.

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The Law of Likelihood: As cited by Royall in "On the Probability of Observing Misleading Statistical Evidence": Hacking (1965) characterizes the law of probability: If one theory, H1, infers that an arbitrary variable X brings the esteem x with likelihood f1(x), while another speculation, H2, suggests that the likelihood is f2(x), then the perception X=x is proof supporting H1 over H2 if f1(x) > f2(x), measures the quality of that confirmation. A Neyman-Pearson approach asks, for a given theories, how likely is it that this information may have happened? An evidential probability approach asks, given the information, which of my theories best clarifies the information?

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The probability proportion test can support comes about that the Neyman-Pearson test would dismiss Case Example: Let the basic esteem for the probability proportion = R.

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The Universal Bound Links Neyman-Pearson Results with Likelihood Ratio Tests Pr(Misleading Evidence) + Pr(Weak Evidence) +Pr(Strong Evidence)=1 Conclusion: The Probability of Misleading Evidence is Bounded by 1/R where R is the chosen basic esteem for the probability test. As the specimen estimate turns out to be extensive the Pr(Misleading Evidence)

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Linkage Analysis: Intuitive Case Example of Linkage: dd 1 2 3 4 5 6 7 8 9 10 dd Suppose Children 2,5,6,9,10 have the infection and youngsters 1,3,4,7,8 don\'t. Instinctively presume that Gene D is unequivocally identified with the ailment.

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Linkage Analysis: Intuitive Case Example of Non-Linkage: ff 1 2 3 4 5 6 7 8 9 10 ff Suppose Children 1,3,5,7,9 have the sickness and kids 2,4,6,8,10 don\'t. Naturally reason that quality F is not identified with the ailment.

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Mathematical Model: Key Features Case: We have distinguished an infection that we are sure has a hereditary segment. Subsequently, we accept that a quality or qualities identifying with the malady exist. Accordingly, it or they should be situated on one of the 23 chromosomes. Our occupation is to discover them! Linkage examination involves testing the speculation that an obscure illness quality is at a close position to a known bit of hereditary material by taking a gander at the isolation proportion from the youngsters. Elective Hypothesis (Linkage): Gamete Probabilities: d? f D? F D? F d? f D? f d? F Null Hypothesis (Independence): Gamete Probabilities: f D? d? D? d? D? d?

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LOD Scores for a Single Family: Assumption: We can decide with assurance which youngsters result from a recombination occasion under H1 (i.e. the instructive parent is stage known) LOD SCORE: Typically, a bend is plotted for the scope of theta qualities extending from 0 to 0.5.

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Why the Computation of LOD Scores is More Complicated in Practice The example estimate for a specific family is too little to accomplish noteworthiness from a solitary family. (i.e. likelihood of 3 Heads in succession is 1/8). N is obliged by the quantity of youngsters in a given family A basic method for joining various information sets is given underneath. Be that as it may, this measurement is not promptly interpretable for a few reasons: Data is not disseminated i.i.d. since family/family information arrives in an assortment of sizes. The period of the information for an arrangement of guardians is not generally known. Regularly, this relies on upon increasing amplified family data (i.e. grandparents), which is not generally accessible

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Abraham Wald: Brief Biography Born into a Jewish scholarly family in Hungary in 1902, Wald was self-taught through essential and auxiliary schools by his folks Attended the University of Cluj (Romania) and showed extraordinary capacity in arithmetic Continued his learns at the University of Vienna with Karl Menger and was granted his doctorate in 1931. Proceeded with his exploration while serving as an arithmetic guide to the affluent Karl Schlesinger, a main broker and market analyst. Wald built up an enthusiasm for financial matters and econometrics After the Nazi control of Austria in 1938, Wald\'s position got to be distinctly dubious, so he emigrated to the United States to end up distinctly a Fellow of the Carnegie enterprise contemplating measurements at Columbia University under Hotelling Made key commitments in the region of choice hypothesis, time arrangement, successive examination.

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Abraham Wald\'s Theory on Sequential Probability Testing Wald: "By a successive trial of a factual speculation is implied any measurable test technique which gives a particular manage at any phase of the examination for making one of the accompanying three choices: (1) to acknowledge the speculation being tried (invalid theory) (2) to dismiss the invalid speculation, (3) to proceed with the investigation by mentioning an extra objective facts". Wald designed the subject of successive examination in light of the interest for more productive strategies (i.e. diminished cost) of modern quality control amid World War II.

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Decision Rule in Wald\'s Sequential Probability Testing Scheme

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Sequential Probability Testing and Linkage Analysis Wald claims that his test is most productive when utilized for testing a basic speculation against a solitary option. S and S* are two unique strategies for testing with a similar quality (Type I and Type II Error rates). Productivity: It is alluring when hunting down potential biomarkers to minimize the opportunity to a choice, given the vast measure of potential quality targets.

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Mendel\'s energetic reflections… Yes, his shrubs should never blur, however time might suck around its vortex Whole eras into the chasm, Though nothing yet greenery develop parts Shall stay of the age In which the virtuoso showed up… May the might of fate concede me The preeminent joy of natural satisfaction The most noteworthy objective of natural fate That of seeing, when I emerge from the tomb, My specialty flourishing gently Among the individuals who are to come after me. Gregor Mendel, around 1830-1840

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References Hodge, Susan E. (Spring 2004) Course Notes, "Hypothetical Genetic Modeling" Columb

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