STATISTICAL ANALYSIS FOR GENETIC EPIDEMIOLOGY (S.A.G.E.) INTRODUCTION

Transcription

1 STATISTICAL ANALYSIS FOR GENETIC EPIDEMIOLOGY (S.A.G.E.) INTRODUCTION Release 3.1 December 1997

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3 Table of Contents 1 Changes Since Last Release Purpose Using the Programs Machine Specific Limitations Data File Structure Maximum Likelihood Estimations Global and Local Maxima Initial Estimates of Parameters for Segregation Analysis Programs REGTN:Truncated (Censored) Trait with Normal p.d.f.-model REGTL : Truncated (Censored) Trait with Logistic p.d.f.-model References iii -

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5 1 Changes Since Last Release Please see the Release Notes and Installation Guide for the most up to date information about program changes

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7 2 Purpose The Statistical Analysis for Genetic Epidemiology (S.A.G.E.) package consists of a set of computer programs for use in the analysis of family data. All of the programs have been tested for the platforms we support. (Please contact us for a list of platforms supported.) The system in which S.A.G.E. will be stored must have at least 30 MB of free disk space to install it. It will require at least 32 MB of RAM to run these programs, and it is recommended that you have 40 MB of free disk space to store any output files or temporary files. In addition to the software itself, a full set of manuals is included with this package. The manuals covering the analysis programs are grouped into four volumes. There are also 2 additional booklets, one entitled Release Notes and Installation Guide, which covers system dependent elements of the packages such as installation, file names, etc., and one entitled Graphical User Interface Guide which provides instructions and information about using our GUI. Note: To become familiar with S.A.G.E., we strongly recommend you read chapter 3 - General Description, chapter 4 - Using the Programs, chapter 5 - Data File Structure in this manual, as well as the FSP manual. The programs available in the current S.A.G.E. release are: a) Estimating the Distribution of Age-of-Onset (AGEON) - This program estimates the susceptibility parameters and the parameters of a power-normal age of onset distribution, in the presence of non-susceptible persons, for up to six classes of susceptibility determined by parental affection status or some other variable. These estimates may then be used in SIBPAL for linkage analysis of a disease trait with variable age of onset. b) Marker-Trait Associations in Pedigree Data (ASSOC) - This program, using the method of George and Elston (1987), allows one to estimate and test the association between a quantitative trait and a genetic marker, in the presence of covariates, allowing for the dependent nature of pedigree data. It assumes that all residual familial correlations are proportional to degree of relationship. A power transformation is incorporated to induce approximate normality of the residuals. c) Genetic Hypotheses for Quantitative Data on Inbred Strains, Their F 1 and Backcross(es) (BCROSS) - This program allows one to test one-locus, two-locus, or polygenic models, or mixtures of these hypotheses, using the methods in Elston (1984). The methods assume normality, but not necessarily homoscedasticity, conditional on genotype. d) Power Transformation to Obtain Normality and Homoscedasticity from Clustered Data (CLUSTR) - This program can be used to obtain an appropriate transformation for data that is to undergo analysis with BCROSS, using the method in Elston (1984), but has been written in a more general manner. We assume k groups of measurements are available, each with its own mean, and we wish to find a transformation that will lead to an approximate normal distribution with the same variance within each group. It is further possible for the measurements within a group to be clustered into subgroups (to allow for e.g. common litters or pens), subgroup members having a common correlation

8 - 4 - INTRODUCTION e) Design of Linkage Studies that are Based on Affected Pairs of Relatives (DESPAIR) -The purpose of this program is to help in the DESign of linkage studies that are based on affected PAIRs of relatives (sibs, grandparents-grandchildren, aunts/uncles-nieces/nephews, half-sibs or first cousins). On the assumption of a known cost ratio (the cost of recruiting an individual into a study to the cost of determining one polymorphic marker), a desired significance level and power, and a value of the relative risk 8 to first degree relatives (due to the locus to be linked - see Risch, 1990a,b), the program can be used to determine the optimal two-stage study design - i.e., how many equally-spaced markers should be used for an initial search of the whole autosomal genome, and what criterion (p-value) should be chosen to decide around which markers further searching should be done. f) Familial Correlations (FCOR) - This program first generates all possible relevant pairs of relatives and classifies them into the following ten main types (and 88 subtypes defined by the sexes of the individuals involved): 1) Marital (spouse) 2) Parental (four subtypes) 3) Sibling (three subtypes) 4) Half-Sibling (six subtypes) 5) Grandparental (eight subtypes) 6) Avuncular (eight subtypes) 7) Cousin (ten subtypes) 8) Great-Grandparental (sixteen subtypes) 9) Great-Avuncular (sixteen subtypes) 10) Half-Avuncular (sixteen subtypes) Univariate and/or multivariate familial correlations for up to 5 traits are then computed for the main and/or sub-types of relatives. Three different weightings are used in the analysis (Karlin et al., 1981): equal weights to pairs of individuals, equal weights to nuclear families, and equal weights to pedigrees. The mean is assumed to be sex-specific. The user has the option to designate the mean to be also age and/or user-specified class specific. g) Family Structure Program (FSP) - This program checks pedigree data for twenty common structural errors, such as married individuals having the same sex code, an individual who is his own ancestor, or two or more individuals having the same identification number. It also identifies certain types of consanguineous matings and loops in the pedigree and sends an error message if the pedigree structure is too complex to be analyzed by the current programs in the package. It generates a linked list Pointer Table File with pointers to the father, mother, sibling, mate, offspring and multiple secondary records for each individual record. This flexible Pointer Table is then used to generate the appropriate pointer structure for the other programs in the package. h) Lod Score Linkage Analysis (LODLINK) - This program performs two-point linkage analyses between a trait and each of a set of markers, calculating lod scores at specified values of the recombination fraction(s). The trait may follow any arbitrary individual-specific phenotypic distribution, conditional on each of the three genotypes at a two-allele autosomal locus. In particular, the program can accept output from the programs REGC, REGD, REGTL and REGTN to allow the trait to follow any segregation model implemented in these programs. There are options to obtain maximum likelihood estimates of the recombination fraction, in males and females separately or pooled, to perform admixture and heterogeneity tests, and to obtain trait genotypic probabilities conditional on all the data available.

9 INTRODUCTION i) Mapping a Disease-Related Trait Relative to a Set of Linked Markers (MAPLOC) -This program assumes a fixed map for a set of markers to find the best relative position for a trait locus, utilizing as input the pairwise maximum likelihood estimates of the recombination fractions between the trait and each marker, together with the corresponding maximum lod scores. The general mapping function of Rao et al. (1977) can be used. j) Segregation Analysis Programs - This set of four programs, based on regressive models (Bonney, 1984, 1986), assumes that any major gene inheritance is through a single two-allele autosomal locus. An option to allow for single ascertainment (simplex or multiplex) is available in each program. 1. Segregation Analysis of a Continuous Trait under Regressive Models A, B, C and D (REGC) - Pedigree discriminant analysis (Zlotnik et al., 1983) under Class A, B, C and D regressive models is included as a special case. Alternatively, covariates may be included in the analysis. 2. Segregation Analysis of a Discrete Trait under a Regressive Logistic Model (REGD) - This program performs segregation analysis of a discrete trait coded as either a dichotomy or a trichotomy under a regressive logistic Class A model. Covariates may be included in the analysis. 3. Segregation Analysis of a Truncated (Censored) Trait with Logistic p.d.f. - Models 1 and 2 (REGTL) - This program performs segregation analysis of a disease trait under a regressive Class A model allowing for a logistically distributed age of onset (after transformation). Under Model 1, genotype is presumed to influence age of onset through location and scale parameters, but not to affect susceptibility (defined as the probability of being affected by age "infinity"). Susceptibility may be different for up to two affection classes. Under Model 2, genotype is presumed to influence susceptibility to the affected state, but not to affect age of onset. Covariates affecting age of onset may be included in the analysis under either model. 4. Segregation Analysis of a Truncated (Censored) Trait with Normal p.d.f. - Models 1 and 2 (REGTN) - This program performs segregation analysis of a disease trait under a transmission probability model allowing for a normally distributed age of onset (after transformation). Under Model 1, genotype is presumed to influence age of onset through location and scale parameters, but not susceptibility. Susceptibility may be different for up to two affection classes. Under Model 2, genotype is presumed to influence susceptibility to the affected state, but not age of onset. k. Relationship to Proband Program (RELATE) - This program determines, for single proband pedigrees, the relationship to the proband of each individual in the pedigree. It then creates corresponding dummy (0,1) variables that can be used to represent this relationship as independent variables in regression analyses (see, for example, George and Elston, 1989). l. Relative Pair Analysis Program (RELPAL) - This is a general program to screen for genetic linkage of a continuous trait to markers on the basis of relative pair relationships (Olson and Wijsman, 1993), combining information from sibling, half-sibling, avuncular, grandparental and cousin pairs. It does not assume a specific genetic model for the trait. m. Sib-Pair Linkage Analysis Program (SIBPAL) - This is a general program to screen for genetic linkage on the basis of the sib-pair relationship (Haseman and Elston, 1972), combining information from full- and half-sib pairs. It can be used for ordering marker loci (Keats and Elston, 1986), and for robust linkage analysis between putative genes and a set of marker loci. It does not assume a specific genetic model. This program can also be used to estimate, for each sib pair, the proportion of genes that are shared identical by descent at each of a set of marker loci.

10 - 6 - INTRODUCTION n. Exact Test for Transmission Disequilibrium (TDTEX) - This program implements several asymptotic and exact versions of the transmission disequilibrium test (TDT) (Spielman et al. 1993) for detecting linkage between marker and disease loci in the presence of linkage disequilibrium. The exact tests are useful in cases where little data are available or there are many alleles at the marker locus. Different types of tests are available, including an exact test by pruned enumeration and a Markov chain Monte Carlo randomization test, as well as several exact marginal homogeneity tests. o. Toolkit Programs (DBSORT, RENUM, SPLIT, PEDCHK) - The Toolkit currently consists of three programs designed to perform certain common data manipulation tasks for the user, and one program designed to check pedigree structure pointers prior to analysis. DBSORT sorts by family identification number and by birth order or birth date within pedigrees. This sorting is useful for preparing data for segregation analysis under regressive model classes B and C. RENUM renumbers family and individual identification numbers and recodes discrete traits to 0,1 or 0,1,2 codes. SPLIT divides data files by family and/or individual identification number. PEDCHK checks a sample data file in "SEG" format (as described in Sorant and Bonney, 1994) to detect invalid pedigree structure pointers. It should be run on Seg files containing pedigrees that have more than one set of original parents (complex pedigrees) before they are analyzed using ASSOC or LODLINK. (The REG programs include this check automatically.)

11 3 Using the Programs The FSP program must be run first on any set of data to prepare them for the analysis by any other programs (other than BCROSS, CLUSTR or MAPLOC) in the package (unless the program AGEON is being used to analyze non-family data). System specific information on running the programs can be found in the Release Notes and Installation Guide. The documentation for each program describes in detail all input and output files. Users should refer to the appropriate document before attempting to execute any program. 3.1 Machine Specific Limitations This program is limited by the accuracy of the system on which it runs. This is due to the precision of the floating point numbers and the sizes of values that can be stored. The information is system specific, and can be determined from its documentation or from the appropriate vendor. However, modern systems are capable of extensive floating point calculations and this should not be a problem for individuals running the software

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13 4 Data File Structure Data for S.A.G.E. should meet the requirements outlined in this section. The first 7 variables (study code through trait) should be in the order specified here. The maximum record length is 132 characters. Required data for each individual in the raw data file: Field Description Study code Up to 5 characters, or it may be left blank. Family ID This can be up to 5 digits and must be an integer. Each distinct pedigree must have a different family identification number. All persons in the same pedigree share the same family ID. Individual ID This can be an alphanumeric code of up to 8 characters. Each person within a pedigree must have a distinct individual ID, but these codes do not have to be distinct across pedigrees. Thus, it is the combination of family ID and individual ID that uniquely identifies each person. Legal Illegal Family ID Individual ID Family ID Individual ID people with the same family number 2 1 can not have the same individual number A Field Description Parent 1 ID For each individual, there must be the individual IDs of both parents (up to 8 Parent 2 ID characters each). If a person has no information on either parent or on any siblings, then the parent ID column can be left blank. If the person has data on siblings, but no data on parents, dummy parent IDs and dummy records that have missing value codes for all data values (except sex) must be added to the Family Data File. Similarly, if there is only information on one parent, a dummy parent ID and record must be made up for the missing parent. Parent refers to biological parents. Sex A character or numeric code (one digit or character) indicating whether the person is male or female. Trait(s) Numeric codes for each trait. A discrete trait is coded as 0: unaffected 1: affected status 1 2: affected status 2 (if present) Proband Status 0: non-proband 1: proband - 9 -

14 INTRODUCTION Age-at-onset Age at examination Covariates Marker Data The age at onset (in years) for all affected individuals; use a missing value code (e.g., -1) if individual is unaffected or age-at-onset is unknown. Use the current age at the time the data were collected, or the age at death if deceased when the data were collected. Use a missing value code if this information is unknown. As desired As desired For an example of a raw data file see section 7.2 of the FSP manual.

15 5 Maximum Likelihood Estimations The segregation analysis programs in the S.A.G.E. package use maximum likelihood estimation (MLE) techniques for parameter estimation. Certain characteristics of this statistical technique may not be familiar to novice users of these programs and will be discussed briefly in this section. 5.1 Global and Local Maxima It is well known that a likelihood function may have more than one (local) maximum, and that for this reason maximum likelihood estimates are not unique. At any maximum, the first derivatives of the log likelihood are all equal to zero. The individual who wishes to find estimates corresponding to the global (or overall largest) maximum must employ a strategy of multiple trials, using many different sets of initial estimates of the parameters to be estimated. It is to the investigator's advantage to ensure that biologically reasonable values are selected as initial estimates of the parameters. 5.2 Initial Estimates of Parameters for Segregation Analysis Programs Unacceptable initial estimates may be a cause of problems in the use of MLE techniques. The user must ensure that the initial estimate of each parameter to be estimated falls within the upper and lower boundary values for that parameter. Sometimes, certain parameter estimates (or combinations of parameter estimates) may cause the log likelihood to be undefined, or may cause the likelihood to become zero or so close to zero that the computer hardware cannot distinguish it from zero. In such a case, changing the initial estimates may resolve the problem. The segregation analysis programs allow a wide variety of models to be used in analysis. However, this flexibility means that a single model may involve a large number of parameters. When a user attempts to estimate too many parameters from too little data there is a greater chance of arriving at a meaningless local maximum. It is always wise to use biologically meaningful initial estimates of parameters, and to start by using the most restricted models, i.e., models with the fewest parameters to be estimated. Final parameter estimates from these previous analyses can then be used as initial estimates for models in which more parameters are estimated. Examples of initial estimates for two segregation analysis models are given in the following sections. Initial parameter estimates can be similarly chosen for the other segregation programs in this package REGTN:Truncated (Censored) Trait with Normal p.d.f.-model 1 Consider simple Mendelian models for a rare disease with late age of onset, incomplete penetrance, "sporadic" cases with on average a later age of onset than "familial" cases, and similar frequencies and ages of onset in males and females. If the mean age of onset among the affected persons in the sample to be analyzed is approximately 50 years old, the standard deviation is about 10 years, and if we let A be the disease susceptibility allele and B the normal allele, then the following initial estimates might be reasonable ones:

16 INTRODUCTION Dominant Recessive Arbitrary Major Gene Major Gene Major Gene Parameter Effect Effect Effect Frequency of Allele A Transmission Prob., J AA fixed Transmission Prob., J AB fixed Transmission Prob., J BB fixed Mean of age of onset, µ AA Mean of age of onset, µ AB Mean of age of onset, µ BB Var. age of onset, F Susceptibility, ( Other values of the allele frequency, such as 0.001, 0.1, 0.2, 0.3, 0.4, and 0.5 should be tried in subsequent runs, as should other initial values of the means, variance and susceptibility. Sometimes, something as simple as increasing the value of the initial estimate of the common variance can make a substantial difference in the final result REGTL : Truncated (Censored) Trait with Logistic p.d.f.-model 1 This program assumes that age of onset has a logistic distribution with age coefficient " and baseline parameter $ rather than the normal distribution with mean µ and variance F 2. It also allows one to analyze data under a regressive model with optional covariates, thus introducing three additional parameters for familial effects (spouse and parental regressive coefficients) and one additional parameter for each covariate included in the model. For the novice user, unused to thinking of ages of onset in these terms, the following correspondence is helpful. Consider a Mendelian logistic model specified such that there are no covariates and the spouse and parental regressive coefficients are fixed to zero. Suppose the baseline coefficients $ u (where u represents major genotype) are allowed to have a major gene effect, but the age coefficient " has no major gene effect. Then, letting µ u and F 2 be the parameters for the example given in the previous section, $ u Ñ &1.8µ u and " Ñ 1.8 F F. Thus, if the arbitrary major gene effect example above were to be converted to this logistic model, the initial estimates would be: Arbitrary Major Gene Parameter Effect Frequency of Allele A 0.01 Transmission Prob., J AA 1 fixed Transmission Prob., J AB 0.5 fixed Transmission Prob., J BB 0 fixed Spouse adjustment coef., * S 0 fixed Mother adjustment coef., * M 0 fixed Father adjustment coef., * F 0 fixed Baseline coef., $ AA -7.2 Baseline coef., $ AB -9.0 Baseline coef., $ BB Age of onset coef., " 0.18 Susceptibility, ( 0.7 After a successful run using these initial estimates, the next step might well be to allow the

17 INTRODUCTION spouse, mother and father coefficients to be estimated. The initial estimates for the new run would be zero for these new parameters, plus the final estimates obtained from the above run for the other parameters.

18 INTRODUCTION

19 References Bonney GE. [1984]: On the statistical determination of major gene mechanisms in continuous human traits: regressive models. Am J of Med Genet; 8: Bonney GE. [1986]: Regressive logistic models for familial disease and other binary traits. Biometrics; 42: Elston RC. [1984]: The genetic analysis of quantitative trait differences between two homozygous lines. Genetics; 108: Elston RC, Bailey-Wilson JE, Bonney GE, Keats BJ, Wilson AF. [1986]: S.A.G.E. - A package of computer programs to perform Statistical Analysis for Genetic Epidemiology. Presented at the Seventh International Congress of Human Genetics, Berlin. Elston RC, Keats BJB. [1985]: Genetic Analysis Workshop III: Sib pair analyses to determine linkage groups and to order loci. Genet Epidemiol; 2: George VT, Elston RC. [1987]: Testing the association between polymorphic markers and quantitative traits in pedigrees. Genet Epidemiol; 4: George VT, Elston RC. [1989]: "Biostatistical methods for the familial study of cancer", in Genetic Epidemiology of Cancer (Chapter 2): edited by Lynch and Hirayama, CRC Press, Inc. Haseman JK, Elston RC. [1972]: The investigation of linkage between a quantitative trait and a marker locus. Behav Genet; 2:3-19. Kaplan, EB, Elston, RC. [1972]: A subroutine package for maximum likelihood estimation (MAXLIK). Institute of Statistics Mimeo Series No. 823, University of North Carolina at Chapel Hill. Karlin S, Cameron EC, Williams PT. [1981]: Sibling and parent-offspring correlation estimation with variable family size. Proc Nat Acad Sc, Vol. 78, No. 5, pp Keats BJB, Elston RC. [1986]: Determination of the order of loci on the short arm of chromosome 11 using two and three locus linkage analyses of pedigree and sib pair data. Genet Epidemiol Supp; 1: Lalouel JM. [1979]: GEMINI - a computer program for optimization of general nonlinear functions. Technical Report No. 14, Population Genetics Laboratory, University of Hawaii, Honolulu. Rao DC, Morton NE, Lindsten J, Hultén M, Yee S. [1977]: A mapping function for man. Hum Hered; 27: Risch N. [1990]: Linkage Strategies for Genetically Complex Traits. I. Multilocus models. Am J Hum Genet; 46: Risch N. [1990]: Linkage Strategies for Genetically Complex Traits. II. The power of affected relative pairs. Am J Hum Genet; 46:

20 INTRODUCTION Sorant AJM, Bonney GE. [1997]: Sample data for segregation analysis (SEG format): Part of the S.A.G.E. documentation. Zlotnik LH, Elston RC, Namboodiri KK. [1983]: Pedigree discriminant analysis: a method to identify monogenic segregation. Am J Med Genet; 15: