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  • CLUMP documentation
    cell has an expected value less than 5 then its column is lumped together with the column with the next smallest total This process is repeated until every cell has an expected value of 5 or more This probably represents the most conventional method of dealing with a sparse contingency table The significance of the chi squared value obtained from this table using the Monte Carlo method should closely correspond to the nominal significance of the chi squared statistic with m 1 degrees of freedom where m is the number of columns in the clumped table The statistic produced is called T2 For the Monte Carlo simulations tables with 2 by m cells are simulated with row and column totals constrained to be the same as for the clumped table not the original 2 by m table and the number of times a simulated table yields a chi squared value greater than or equal to that obtained from the clumped table is output 3 A 2 by 2 table obtained by comparing one column of the original table against the total of all the other columns This represents another fairly conventional way of dealing with a contingency table having several columns and tests the hypothesis that there is one particular column which has cells deviating from the expected values For each column in turn all the other m 1 columns are clumped into one to yield a 2 by 2 table and the column producing the maximum chi squared value is used The statistic produced is called T3 Columns containing expected values less than 5 are not allowed to be considered on their own but are clumped together with the other columns In order to assess the significance of the maximum chi squared value produced by this means one could consider it as a chi squared statistic with one degree of freedom and then apply a Bonferroni correction to the p value obtained This Bonferroni correction would assume that a number of trials had been performed equal to the number of columns which had been compared against all other columns i e the number of columns having cells with expected values greater than or equal to 5 One could argue that these trials were not in fact independent in which case the Bonferroni correction would result in a conservative significance value Assessing the significance using Monte Carlo simulations avoids these problems These simulations are performed by simulating 2 by m tables constrained to have the same row and column totals as the original table and then clumping each into a 2 by 2 table by comparing one column against the total of the others and using the column which produces the maximum chi squared value Again this must be a column in which the expected values are both at least 5 The number of times a clumped simulated table yields a chi squared value greater than or equal to that obtained from the clumped real table is output 4 A

    Original URL path: http://linkage.rockefeller.edu/soft/clump.html (2012-11-26)
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  • COMDS manual
    w x specifies a field of w digits with x decimal places to the right S and R fields are used in conjunction with the SI SD control cards The TR control card considers only the A and F fields as variables The PT field must be an A3 field left adjusted Blanks in F fields are treated as unknown values not as zeros Form FM format specification Example FM A5 F1 0 4X F2 0 F1 0 F1 0 SI SD control optional Selection and deletion See Morton et al 1983 NA control Names of variables after transformation if necessary are specified in order by NA Variables are F and A fields given on the FM control and additional variables created by transformation Depending on the job not all variables need be specified The variables are described in the Input Data section They are ID family identification PO position within the family AF affection status LI liability situational class DS diathesis SV severity PT pointer relationship PR proband TL marker locus example NA1 ID A5 NA2 PO F1 0 TR control optional Transformations See Morton et al 1983 COMDS job file Controls for the COMDS job file These controls are used in the following order CB PI LI DS SV TL PA IT RA RP CC CB control required CB is the header to indicate that a COMDS job file is being used PI control required only if the PR field is specified Ascertainment probability for corresponding sampling class Form PI c1 c2 cn If a child s PR field is coded I PI I will be assigned to that child s family The maximum number of pi s is 9 The value c 0 conditions likelihood on severity of the single proband child affected parents and pointers Other conditional likelihoods consider severity of parents and pointers but not proband children LI control required only if the LI field is specified Within a set of parentheses specify the affection risk for each liability class Form LI A1 A2 A3 An The maximum number of classes is 9 An individual is assigned to a liability class by his LI field TL control optional required only if there is a TL field Within a set of parentheses specify the gene frequencies that correspond to coupling frequencies C1 C2 Cn There may be a maximum of 9 values Form TL P1 P2 PN PA control required The parameter control supplies trial values to the 24 parameters that may be estimated or fixed The parameters are V U D T Q DM TM QM TH K B BS S SM P C1 C2 C3 C4 C5 C6 C7 C8 and C9 The default for each parameter is 0 except for V TM K and P whose defaults are 1 and for D DM and QM whose defaults are 5 The PA control provides the trial values for the first IT control immediately following it The trial values for all subsequent IT controls are

    Original URL path: http://linkage.rockefeller.edu/soft/comds.html (2012-11-26)
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  • crimap documentation
    disease loci Getting started File structures 4 1 gen file 4 2 par file 4 3 dat file 4 4 ord file Program options 5 1 all 5 2 build 5 3 chrompic 5 4 fixed 5 5 flips n 5 6 instant 5 7 merge 5 8 prepare 5 9 quick 5 10 twopoint Technical notes Changes incorporated in versions 2 2 2 4 Bibliography this document is converted

    Original URL path: http://linkage.rockefeller.edu/soft/crimap/ (2012-11-26)
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  • R 2004 Support files nbsp readme txt and ehp help S R built in help Key words EM algorithm pooled genotype missing values variance estimates Features This program provides variance estimates for haplotype frequency estimates it allows several kinds of missing information in the genotype data it also allows for combined genotype data of different pool sizes This program can be used for testing haplotype disease associations in case control

    Original URL path: http://linkage.rockefeller.edu/yyang/resources.html (2012-11-26)
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  • slink
    1 0 0 3 0 0 1 1 0 0 2 3 0 0 2 1 2 0 0 3 0 0 2 0 0 0 2 2 0 0 0 1 3 1 2 0 4 4 2 0 0 0 2 2 0 0 2 1 4 1 2 0 5 5 2 0 0 0 2 1 0 0 2 1 5 1 2 0 6 6 1 0 0 0 2 2 0 0 2 1 6 1 2 0 7 7 2 0 0 0 2 1 0 0 2 1 7 1 2 0 8 8 1 0 0 0 2 1 0 0 2 1 8 1 2 0 9 9 1 0 0 0 2 2 0 0 2 1 9 1 2 0 10 10 1 0 0 0 2 2 0 0 2 1 10 1 2 14 12 12 2 0 0 0 2 2 0 0 2 1 11 0 0 14 0 0 1 0 0 0 2 3 0 0 2 1 12 1 2 0 13 13 1 0 0 0 2 2 0 0 2 1 13 1 2 0 0 0 2 0 0 0 2 1 0 0 2 1 14 11 10 0 15 15 2 0 0 0 2 1 0 0 2 1 15 11 10 0 16 16 1 0 0 0 2 2 0 0 2 1 16 11 10 0 17 17 1 0 0 0 2 2 0 0 2 1 17 11 10 0 0 0 2 0 0 0 2 1 0 0 2 2 1 0 0 3 0 0 1 1 0 0 2 3 0 0 0 2 2 0 0 3 0 0 2 0 0 0 2 2 0 0 2 2 3 1 2 0 4 4 2 0 0 0 2 2 0 0 2 2 4 1 2 0 5 5 1 0 0 0 2 2 0 0 2 2 5 1 2 0 6 6 1 0 0 0 2 2 0 0 2 2 6 1 2 10 8 8 1 0 0 0 2 2 0 0 2 2 7 0 0 10 0 0 2 0 0 0 2 3 0 0 2 2 8 1 2 13 0 0 2 0 0 0 2 2 0 0 2 2 9 0 0 13 0 0 1 0 0 0 2 3 0 0 2 2 10 6 7 0 11 11 1 0 0 0 2 1 0 0 2 2 11 6 7 0 12 12 1 0 0 0 2 1 0 0 2 2 12 6 7 0 0 0 1 0 0 0 2 2 0 0 2 2 13 9 8 0 14 14 1 0 0 0 2 1 0 0 2 2 14 9 8 0 0 0 1 0 0 0 2 2 0 0 2 Step 3 Create the slinkin dat input file for SLINK holding the parameters defined in section 3 above Please note that the random number seed should be changed for every new simulation Step 4 Run SLINK to create a pedfile dat containing the simulated data As outlined in section 3 SLINK requires several parameters in an input file slinkin dat The input files for SLINK are simdata dat and simped dat see the flow chart in figure 1 SLINK outputs the simulated data in the file pedfile dat while the parameters as described above and the thetas are written to simout dat If one of the companion analysis programs is run it will put the information from the most recent simout dat into the output file it creates figure 1 Note that the pedfile dat is a bona fide LINKAGE pedigree file and can be analyzed by any of the regular LINKAGE programs However it may contain many replicates of the pedigrees one set after another so that in most cases it is more practical to use the modified versions of the LINKAGE programs MSIM ISIM LSIM that are designed to analyze the data a replicate at a time In our example we asked for simulated marker data while maintaining the original trait phenotypes Availability code 2 for all but two people Note that the two people with availability code 0 have unknown marker genotypes File pedfile dat first replicate of both families 1 1 0 0 3 0 0 1 1 1 3 2 3 1 2 2 Linked Mk Avail Tr orig 1 2 0 0 3 0 0 2 0 0 0 2 2 0 0 0 Linked Mk Unkno Tr orig 1 3 1 2 0 4 4 2 0 1 3 2 2 1 2 2 Linked Mk Avail Tr orig 1 4 1 2 0 5 5 2 0 1 3 2 1 1 1 2 Linked Mk Avail Tr orig 1 5 1 2 0 6 6 1 0 1 3 2 2 1 2 2 Linked Mk Avail Tr orig 1 6 1 2 0 7 7 2 0 3 3 2 1 2 2 2 Linked Mk Avail Tr orig 1 7 1 2 0 8 8 1 0 3 3 2 1 2 2 2 Linked Mk Avail Tr orig 1 8 1 2 0 9 9 1 0 1 1 2 2 1 1 2 Linked Mk Avail Tr orig 1 9 1 2 0 10 10 1 0 1 3 2 2 1 2 2 Linked Mk Avail Tr orig 1 10 1 2 14 12 12 2 0 1 1 2 2 1 1 2 Linked Mk Avail Tr orig 1 11 0 0 14 0 0 1 0 1 3 2 3 2 2 2 Linked Mk Avail Tr orig 1 12 1 2 0 13 13 1 0 1 1 2 2 2 1 2 Linked Mk Avail Tr orig 1 13 1 2 0 0 0 2 0 3 3 2 1 1 2 2 Linked Mk Avail Tr orig 1 14 11 10 0 15 15 2 0 1 3 2 1 1 2 2 Linked Mk Avail Tr orig 1 15 11 10 0 16 16 1 0 1 1 2 2 2 1 2 Linked Mk Avail Tr orig 1 16 11 10 0 17 17 1 0 1 3 2 2 1 2 2 Linked Mk Avail Tr orig 1 17 11 10 0 0 0 2 0 1 3 2 1 1 2 2 Linked Mk Avail Tr orig 2 1 0 0 3 0 0 1 1 0 0 2 3 0 0 0 Linked Mk Unkno Tr orig 2 2 0 0 3 0 0 2 0 1 2 2 2 2 2 2 Linked Mk Avail Tr orig 2 3 1 2 0 4 4 2 0 1 1 2 2 2 2 2 Linked Mk Avail Tr orig 2 4 1 2 0 5 5 1 0 1 1 2 2 2 2 2 Linked Mk Avail Tr orig 2 5 1 2 0 6 6 1 0 1 1 2 2 2 2 2 Linked Mk Avail Tr orig 2 6 1 2 10 8 8 1 0 1 2 2 2 2 2 2 Linked Mk Avail Tr orig 2 7 0 0 10 0 0 2 0 3 3 2 3 1 2 2 Linked Mk Avail Tr orig 2 8 1 2 13 0 0 2 0 1 2 2 2 2 2 2 Linked Mk Avail Tr orig 2 9 0 0 13 0 0 1 0 1 3 2 3 2 1 2 Linked Mk Avail Tr orig 2 10 6 7 0 11 11 1 0 2 3 2 1 2 1 2 Linked Mk Avail Tr orig 2 11 6 7 0 12 12 1 0 2 3 2 1 2 2 2 Linked Mk Avail Tr orig 2 12 6 7 0 0 0 1 0 1 3 2 2 2 1 2 Linked Mk Avail Tr orig 2 13 9 8 0 14 14 1 0 1 2 2 1 2 2 2 Linked Mk Avail Tr orig 2 14 9 8 0 0 0 1 0 1 1 2 2 2 2 2 Linked Mk Avail Tr orig Step 5 Create a datafile dat defining how the simulated data should be analyzed The analysis programs require five input files figure 1 Two are made by UNKNOWN ipedfile dat and speedfile dat see step 6 One is made by SLINK simout dat see step 4 The fourth datafile dat must be made using PREPLINK prior to running the desired analysis program The fifth input file limit dat contains three threshold values eg 1 2 3 used to determine the proportion of replicates exceeding a given lod score limit The datafile dat is a standard LINKAGE data file which determines how the analyses of the simulated data will be carried out It must be in MLINK format for MSIM ILINK format for ISIM and LINKMAP format for LSIM The example datafile dat below is in MLINK format and is thus appropriate for input into MSIM the modified version of MLINK File datafile dat 3 0 0 5 NOTE If you choose the increment size too small you will get an error message that maxpnt is too small Maxpnt is the number of é s or map positions in LSIM at which the lod score is evaluated You may fix this problem by either choosing a larger increment or by inreasing maxpnt and recompiling Step 6 Run UNKNOWN to create a speedfile dat and an ipedfile dat Once the pedfile dat has been created by SLINK then it is necessary to process this file with the program UNKNOWN of the LINKAGE package before running any of the analysis programs UNKNOWN creates the pedigree file ipedfile dat and the speedfile dat speedfil dat on DOS machines These two files are needed for input into MSIM ISIM or LSIM Step 7 Run the appropriate analysis program such as MSIM or LSIM 5 TYPICAL APPLICATIONS The analysis programs MSIM LSIM and ISIM each require three input files A parameter file called limit dat This file holds three thresholds limits for the maximum lod score the programs will approximate the probability with which the maximum lod score exceeds each of the three thresholds Typical threshold values are 1 2 and 3 Note that numbers must have at least one digit to the left of any decimal point for example 0 5 a number given as 5 would lead to an error A locus file datafile dat which is analogous to the one used for the LINKAGE programs You may simply copy simdata dat to datafile dat and modify the datafile dat file to correspond i to the analysis program to be used and ii to reflect the theta values at which analysis is to be carried out Note that datafile dat is also used as an input file to the UN KNOWN program A pedigree file ipedfile dat created by the UNKNOWN program Details of programs usage are given below 5A MSIM Approximating the expected lod score First we show how to use MSIM which summarizes its results in the file msim dat The first part of msim dat contains information defining the simulation such as the random number seed the number of replicates the requested proportion of unlinked families and the trait locus number This information is taken from the most recent simout dat Note that the thetas and the locus order presented in the simout dat section pertain to the model under which the simulation was carried out as previously specified in the simdata dat file These may differ from the thetas and locus order used in the analysis of the simulated data The rest of msim dat provides statistical information If two loci are used then the results are reported on the traditional lod score scale When three or more loci are used multipoint lod scores are computed as the log likelihood at the current thetas minus the log likelihood with the theta involving the trait locus set to 0 50 For this reason when MLINK or MSIM are used the trait locus must be either the leftmost or rightmost locus for these statistics to make sense Normally MSIM like MLINK will be used for analyses involving only two loci However in this example we use three loci but place the trait locus number 2 on the right by specifying the locus order to be 1 3 2 in the datafile dat file see above Lod scores for the position of a disease versus a map of markers are usually computed with the LINKMAP LSIM see next section MSIM is used here for demonstration purposes File msim dat Data from most recent SIMOUT DAT The random number seed is 25432 The number of replications is 20 The requested proportion of unlinked families is 0 000 The trait locus is locus number 2 Summary Statistics about simped dat Number of pedigrees 2 Number of people 31 Number of females 12 Number of males 19 There were 2 in category Marker Unknown Trait original There were 0 in category Marker Available Trait simulated There were 29 in category Marker Available Trait original There were 0 in category Marker Unknown Trait simulated LINKAGE V4 91 WITH 3 POINT AUTOSOMAL DATA LINKED ORDER OF LOCI 1 2 3 TRUE THETAS FOR LINKED ORDER 0 073900 0 053900 UNLINKED ORDER OF LOCI 2 1 3 TRUE THETAS FOR UNLINKED ORDER 0 500000 0 119834 Elapsed Time for one replicate 8 seconds Elapsed Time 162 seconds or 2 70 minutes Actual proportion of unlinked families 0 000 End of most recent SIMOUT DAT ORDER OF LOCI 1 3 2 Average Multipoint Lod Scores at Given Thetas Number of replicates 20 THETAS 0 120 0 125 Pedigree Average StdDev Min Max 1 0 928233 0 823127 0 499552 2 372393 2 0 581052 0 458913 0 066598 1 564117 Study 1 509285 0 725744 0 163738 3 215271 THETAS 0 120 0 250 Pedigree Average StdDev Min Max 1 0 673438 0 524425 0 170536 1 607466 2 0 355322 0 371757 0 404606 0 957419 Study 1 028760 0 507228 0 259767 2 132345 THETAS 0 120 0 375 Pedigree Average StdDev Min Max 1 0 313556 0 231926 0 036782 0 742686 2 0 140380 0 209244 0 369045 0 398341 Study 0 453935 0 265833 0 275562 0 937106 Brief explanation of the output The file msim dat contains information defining the simulation followed by some tables providing statistical information about the distribution of the simulated lod scores The Average column provides the expected or mean lod score by pedigree and by study i e set of families The StdDev column provides the standard deviation of the lod score The Min column lists the minimum lod score encountered in all the replicates and the Max column lists the maximum lod score encountered in all the replicates and when the pedigrees are used together in one study Note that the only column in which the Study value will equal the sum of the Pedigree values is the Average column If one is interested in approaching the absolute smallest or absolute largest lod score in the whole study one should add up the min or max values if all have the same sign over pedigrees rather than looking at the Study min or max value 5B LSIM Disease versus map of markers If we want to run LSIM the modified version of LINKMAP we need a different datafile dat than the one used above for MSIM because the data file for LSIM must be in standard LINKMAP format Like LINKMAP LSIM is most appropriate for calculating lod scores of the trait locus at various positions across a fixed map of marker loci As mentioned above a multipoint lod score requires calculation of the likelihood of the data with the trait off the map first Thus there are two requirements for getting accurate results out of LSIM 1 the trait locus must start out as the leftmost locus and 2 the trait locus must be placed off the map on the left at a recombination fraction of 0 50 This allows calculation of multipoint lod scores as the trait locus is moved across the whole map In this example the trait locus is number 2 and so the locus order must be specified as 2 1 3 in order to have the trait locus be off the map on the left Since the trait locus must be placed off the map the first recombination fraction is 0 50 File datafile dat 3 0 0 4 LSIM the modified version of LINKMAP creates the following output file which has been edited to conserve space Note how LSIM unlike LINKMAP automatically moves the trait locus across each interval in the fixed map of marker loci as indicated by the different locus orders in the tables below the middle number on the last line of the datafile dat is irrelevant for LSIM File lsim dat edited Data from most recent SIMOUT DAT LINKED ORDER OF LOCI 1 2 3 TRUE THETAS FOR LINKED ORDER 0 073900 0 053900 UNLINKED ORDER OF LOCI 2 1 3 TRUE THETAS FOR UNLINKED ORDER 0 500000 0 119834 Actual proportion of unlinked families 0 000 End of most recent SIMOUT DAT Average Multipoint Lod Scores at Given Thetas Number of replicates 20 Locus Order 2 1 3 THETAS 0 500 0 120 Number of replicates with a maximum at this location 0 Pedigree Average StdDev Min Max 1 0 000000 0 000000 0 000000 0 000000 2 0 000000 0 000000 0 000000 0 000000 Study 0 000000 0 000000 0 000000 0 000000 Locus Order 2 1 3 THETAS 0 125 0 120 Number of replicates

    Original URL path: http://linkage.rockefeller.edu/soft/slink.html (2012-11-26)
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  • Corrections to "Analysis of Human Genetic Linkage"
    59 line 3 from the bottom P 0 θ 1 22 not I 22 Page 60 lines 6 and 7 should read The i th segment i 1 s of length b i then contains the likelihood ratio L θ i where b 1 θ 2 θ 1 b i θ i 1 θ i θ i θ i 1 θ i 1 θ i 1 b s θ s θ s 1 Σb i 0 5 Pages 93 and 94 Arguments referring ot linear independence of probabilities are incorrect and will be corrected in the new book edition Formulas are correct Page 95 top line should read the maximum of the expected lod score the ELOD must occur at θ r Page 105 line 2 after equation 5 21 replace 11 10 by 11 9 Page 115 equation 6 7 Subscript J should be j Page 116 line 19 up Add reference as follows than does two point analysis Fisher 1954 Page 119 second line up from formula 6 10 2 θ AB 1 θ AB Page 126 table 6 6 column Kosambi line 4 0 0600 should read 0 0060 Page 151 In equation 7 1 there should be two summation signs one in the numerator and one in the denominator Thus the numerator should read Σ i k i 1 and the denominator should read Σ i n i 1 Also 2 lines above 7 1 replace 1912 by 1927 Page 169 line 13 up Replace figure 6 1 by figure 8 1 Page 171 line 12 Insert be after has to Page 171 lines 4 and 6 up P x i g j first superscript is i twice Page 183 line 5 up After 0 4343 insert the following for log e θ rather than Z

    Original URL path: http://linkage.rockefeller.edu/ott/corr-ott.htm (2012-11-26)
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  • Table of Contents (Ott, 1991)
    Inference Likelihood Maximum Likelihood Estimation Statistical Properties of Maximum Likelihood Estimates Significance Tests The Likelihood Method Interval Estimation Bayes Theorem Methods of Linkage Analysis A Brief Historical Review Prior and Posterior Distribution of Theta The Lod Score Method Testing for Linkage Equivalent Observations Exact Tests in Simple Family Types Multiple Comparisons The Likelihood of Family Data Nonparametric Approaches Some Special Methods The Informativeness of Family Data Measures of Informativeness Expected Lod Score Expected Information Mating Type Double Intercross with Two Alleles Double Intercross with More Than Two Alleles Phase known Double Backcross Phase unknown Double Backcross with Two Offspring Phase unknown Double Backcross with More Than Two Offspring The Number of Observations Required to Detect Linkage Multipoint Linkage Analysis Notation and Terminology Three point Analysis Phase unknown Triple Backcross with Two Offspring Interference Multilocus Map Functions Ordering Loci Mapping under Complete Inteference Other Methodologic Issues Penetrance Definition of Penetrance The Cost of Incomplete Penetrance Estimating Penetrance and Recombination Age dependent Penetrance The Factors Influencing Penetrance Quantitative Phenotypes Numerical and Computerized Methods Calculating Lod Scores Analytically The Elston Stewart Algorithm Computer Programs for Linkage Analysis Special Applications of Linkage Programs Linkage Utility Programs Paternity Calculations Computer Simulation Methods Variability of the

    Original URL path: http://linkage.rockefeller.edu/ott/booktoc.htm (2012-11-26)
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  • Genetic Linkage Analysis notes
    genomewide linkage scan by use of the peak length Am J Hum Genet 62 1561 1562 Page 164 append to paragraph Estimating Age of Onset Curves A recent analysis has applied sophisticated statistical methods for an unbiased estimation of penetrance in BRCA1 and BRCA2 Satagopan JM Offit K Foulkes W Robson ME Wacholder S Eng CM Karp SE Begg CB 2001 The lifetime risks of breast cancer in Ashkenazi Jewish carriers of BRCA1 and BRCA2 mutations Cancer Epidemiol Biomarkers Prev 10 467 473 Page 177 section 8 5 An early paper describing a variance components approach to the mapping of quantitative trait loci is Jayakar SD 1970 On the detection and estimation of linkage between a locus influencing a quantitative character and a marker locus Biometrics 26 451 464 Page 190 Another program for multipoint linkage analysis is Allegro Gudbjartsson et al 2000 Allegro a new computer program for multipoint linkage analysis Nat Genet 25 12 13 Page 223 Properties of testing for heterogeneity under the model discussed here have been addressed by Whittemore and Halpern 2001 Problems in the definition interpretation and evaluation of genetic heterogeneity Am J Hum Genet 68 457 465 Page 226 top Additional references to the irregularitiy of mixture models are for example Chernoff H Lander E 1995 Asymptotic distribution of the likelihood ratio test that a mixture of two binomials is a single binomial J Statist Plann Inference 43 19 40 Chen J 1998 Penalized likelihood ratio test for finite mixture models with multinomial observations Canadian Journal of Statistics 26 583 599 Page 278 See note for page 190 Page 286 An extended version of this program is available as EHPLUS It has simpler input requirements and approximates p values by a computer simulation algorithm Based on EH EHPLUS was developed by and is available at http www iop kcl ac uk IoP Departments PsychMed GEpiBSt software stm The reference is Zhao et al 2000 Model free analysis and permutation tests for allelic associations Hum Hered 50 133 139 Page 286 There has been a debate as to the relative efficiency of estimating haplotype frequencies based on phase unknown genotype data versus that based on phase known haplotype data For a lucid discussion of this matter with analytical solutions see P M McKeigue 2000 Efficiency of estimation of haplotype frequencies Use of marker phenotypes of unrelated individuals versus counting of phase known gametes Am J Hum Genet 67 1626 1627 Page 287 top A useful program on linkage disequilibrium MLD may be found at ftp statgen ncsu edu pub zaykin a brief manual is contained in the readme txt file in that directory Page 289 bottom Cattle represent a population in which it is most likely genetic drift that generates much disequilibrium estimates for effective population size are as low as 50 See Farnir et al 2000 Extensive genome wide linkage disequilibrium in cattle Genome Res 10 220 227 Page 302 last paragraph in section 14 1 Dr Michael Knapp Bonn Germany pointed out

    Original URL path: http://linkage.rockefeller.edu/ott/booknotes.html (2012-11-26)
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