Pairwise linkage disequilibrium measures ---------------------------------------- ^pwld^ varlist [weights] [^if^ exp] [^in^ range][, ^ht^ype ^gt^ype ^me^asure^(^string^)^ ^min(^number^)^ ^dp(^number^) noml qt^ol^(^#^) it^er^(^#^)^ ^p^attern^(^numlist^) s^ymbols^(^string^)^ ^gr^aph ^col^ors^(^numlist^)^ ^mat^rix^(^string^) sav^ing^(^filename^) rep^lace ] ^fweight^s and ^aweight^s are allowed Description ----------- This program calculates various measures of linkage disequilibrium between pairs of diallelic loci. The data may be in three formats: allele pairs: Pairs of variables containing alleles at each locus. Alleles coded 1 or 2. This is the default coding "gtype": For each locus, a single variable codes genotype as 0, 1, or 2 "htype": In each of the above formats, each line represents one subject. In htype coding, each line represents a haplotype. For each locus, one variable codes the allele carried as 1 or 2 If data are in either of the first two forms, the method of estimation assumes Hardy--Weinberg equilibrium. In this case, the default method of estimation is maximum likelihood but a method of moments can also be used. This is less accurate but somewhat faster. For all methods, each pairwise index is estimated using all pairs which have data for both loci. The measures of LD which may be calculated are: D (equivalent to the covariance between alleles) Cov (eqivalent to D) D' (Levwontin's D', a scaled version of D, constrained to lie between 0 and 1 given the allele frequencies) Delta (equivalent tp product-moment correlation coefficient) r (equivalent to Delta) delta* (attributable risk, equivalent to rho) rho (probability of association, equivalent to delta*) OR (odds ratio) R2 (R-squared, the square of r, Delta) Q (Yule's Q) These indices have been reviewed by Devlin and Risch, 1995 (Genomics, ^29^:311-322,1995). The index rho (delta*) and its role in the Malecot model is discussed by Morton et al. (PNAS, 98:5217-5221, 2001). Another index, termed either lambda or delta, has been described by several authors. This is asymmetric, relevant when one locus has "disease" and "normal" forms and invariant under case-control sampling on this locus. In my opinion It is not relevant or useful as a measure of LD between markers and is not calculated by this program. The direction of association is indicated for all measures except rho (delta*), D', and R2. Positive or negative association is indicated by the sign, except for the odds ratio where direction of association is indicated by values greater than or less than one. A minimum value may be specified for the minor allele frequency at a locus, and LD measures will not be calculated for any locus not achieving this. The matrix of measures can either be printed out numerically, or shown as a "pattern". This may either be shown as a character pattern on the standatd output, with a single character representing each pairwise comparison, or as a color plot in the graphics screen. Each character, or color, in the pattern represents a defined range of values for the LD measure. In this form of output the direction of association is ignored and the pattern represents only strength of association. If desired, the matrix of LD measures can be saved for later processing, or written to a file. Options ------- ^htype^ haplotype coding ^gtype^ genotype coding ^measure^ LD measure to be calculated (default is "Delta") ^min^ Minimum minor allele frequency (%) ^dp^ Number of decimal places in listing ^noml^ Do not use maximum likelihood estimation ^qtol^ Covergence criterion for ML estimation (change in Yule's `Q' between iterations). Default is 0.001. ^iter^ Maximum iterations to find each ML estimate (default 10) ^pattern^ Visualise matrix as a pattern.The option should specify a list of cut-points to define bands of POSITIVE LD. The list should be in ascending order. ^symbols^ A string containing, in sequence and without blanks, the characters to represent each band of the LD measure. The character "blank" is used automatically to denote LD weaker than the first number specified by ^pattern^. Default is the sequence ^.:+*#@^ ^graph^ Show LD matrix as colors in a graphical plot ^colors^ A list of colors to represent strength of LD. These are specified as pen numbers (2 thro 9) ^matrix^ Name of a matrix in which to save the results ^saving^ File in which to store the results ^replace^ If an existing file should be overwritten when saving results Example ------- ^pwld A_1 A_2 B_1 B_2 C_1 C_2, me(Delta) p(0.5 0.75 0.9 0.95) s(-=+#)^ ^pwld A_1-Z_2, me(OR) p(2 5 10 50 100 500)^ ^pwld A-Z, ht me(Q) ml mat(LDmat)^ Author ------ David Clayton Diabetes and Inflammation Laboratory Tel: 44 (0)1223 762669 Cambridge Institute for Medical Research Fax: 44 (0)1223 762102 Wellcome Trust/MRC Building david.clayton@cimr.cam.ac.uk Addenbrooke's Hospital, Cambridge, CB2 2XY www-gene.cimr.cam.ac.uk/clayton