Overview 

Part I (PREST)
==============

  PREST is a program, written in C, for detection of pedigree
  errors ("PREST" stands for Pedigree RElationship Statistical Test
  and it is also a Latin word meaning "ready").  The presence of 
  pedigree errors in a data set may result in either reduced power 
  or false positive evidence for linkage, so detection of such errors 
  is useful prior to linkage analysis.  This program performs
  statistical tests using genome-screen data to determine whether the
  pattern of allele sharing by each pair of relatives is consistent with
  the relationship indicated by the pedigree.  PREST computes the
  EIBD, AIBS, IBS and MLLR statistics developed by McPeek and Sun (2000)
  and performs the corresponding hypothesis tests for relationship
  misspecification.  All relative pairs of the following 10 types are
  checked: full-sib, half-sib, grandparent-grandchild, avuncular,
  first-cousin, unrelated, half-avuncular, half-first-cousin, 
  half-sib-plus-first-cousin and parent-offspring.  (A pair is called 
  half-sib-plus-first-cousin if they have the same mother and different 
  fathers and the two fathers are full-sib, or the same father and 
  different mothers who are sisters.)  Furthermore, MZ twins can be 
  checked using the companion program ALTERTEST.  To make the
  likelihood calculation meaningful for parent-offspring pairs 
  and MZ twins in the presence of genotyping error, we incorporate
  genotyping error in the model in the two cases.  The program currently 
  checks unrelated pairs only within a given pedigree; it does not
  check that individuals in different pedigrees are unrelated because
  of the enormous number of hypothesis tests that would be involved.  
  Note that the program could be forced to check that individuals in 
  different pedigrees are unrelated by combining pedigrees into one 
  large pedigree in the input.  In the current implementation, data on 
  sex chromosomes are not used.

  For each pair, PREST also estimates p = (p0, p1, p2), the probability 
  of sharing zero, one or two alleles IBD by the pair as proposed in 
  McPeek and Sun (2000).  Note that the estimation does not depend on
  the null hypothesis.  The estimate can be useful for suggesting
  plausible relationships for problematic pairs and it can be
  particularly helpful for identifying parent-offspring pairs and 
  MZ twins.
  
  The MLLR test has higher power than the tests based on the EIBD,
  AIBS and IBS statistics.  However, the EIBD, AIBS and IBS tests 
  can be quickly performed because significance is assessed using a
  normal approximation, whereas the MLLR test requires simulation for
  each pair to assess significance.  To achieve reliable empirical
  p-values, the number of replicates in the simulation needs to be
  large.  For each relative pair, the MLLR test algorithm using
  100,000 simulated realizations takes approximately 5 minutes on a
  Sun Ultra-2.  In contrast, for each relative pair, the EIBD, AIBS
  and IBS tests using the normal approximation take less than 80
  milliseconds on the same machine.  In our simulation studies, the
  power of the EIBD test is generally close to that of the MLRT.  The
  power of the AIBS test is higher than that of the IBS test in all
  cases considered.  Parent-offspring relationship is a special case
  for the EIBD, AIBS and IBS tests.  Our simulation shows that if the
  null hypothesis is the parent-offspring relationship, while the true
  relationship has the same or close kinship coefficient,
  e.g. full-sib relationship, both the AIBS and IBS tests (the EIBD
  test does not apply to relationships such as parent-offspring,
  unrelated and MZ twins) have low power.  If the null hypothesis is
  the relationship as described above, while the true relationship is
  parent-offspring, all the EIBD, AIBS and IBS tests have low power.  
  However our simulation (genome-screen data) also shows that the
  estimate of p = (p0, p1, p2) (independent of the null hypothesis) 
  can successfully distinguish parent-offspring relationship from the 
  other 10 relationships as mentioned before.  Therefore, PREST gives
  users TWO OPTIONS.

    1.  Perform the fast EIBD, AIBS and IBS tests only, using the
        normal approximation to assess significance for each test.
	List the pairs that are not parent-offspring relationship 
	but have the estimates of p1 > 0.75.

    2.  Use a two-stage screening procedure.  For non-parent-offspring
        pairs and non-unrelated pairs, do preliminary screening with 
        the EIBD and AIBS tests and with the results of the estimation 
        of p = (p0, p1, p2), then apply the MLLR test to only those 
        pairs for which the p-value < .2 for at least one of the EIBD 
	and AIBS tests (as proposed by McPeek and Sun 2000) or for
        which the estimates of p1 > 0.75.  For unrelated pairs, apply
        the MLLR test if the p-value < .2 for the IBS test (the EIBD
        and AIBS tests are not applicable to unrelated pairs).  For 
	parent-offspring pairs, apply the MLLR test only if the
        estimate of p1 < 0.9.  For the MLLR test, the alternative 
	set A include 11 relationships.  They are full-sib,
        half-sib, grandparent-grandchild, avuncular, first-cousin, 
	unrelated, half-avuncular, half-first-cousin, 
	half-sib-plus-first-cousin, parent-offspring and MZ twins.
        (excluding the null relationship).  

  If option 1 is chosen, PREST first identifies all relative pairs
  considered (full-sib, half-sib, grandparent-grandchild, avuncular,
  first-cousin, unrelated, half-avuncular, half-first-cousin, 
  half-sib-plus-first-cousin and parent-offspring) among typed 
  individuals of each pedigree.  For each pair, PREST calculates 
  the EIBD, AIBS and IBS statistics, the null means and the null
  variances.  Then, PREST uses the normal approximation to assess
  significance for each test.  For unrelated pairs, the EIBD and AIBS
  tests are not applicable, so only the IBS test is applied.  For
  parent-offspring, the EIBD test are not applicable, so only the AIBS
  and IBS tests are applied.   For each pair, PREST further estimates
  p = (p0, p1, p2), the probability of sharing zero, one or two
  alleles IBD by the pair.  Finally PREST identifies the pairs that
  are not parent-offspring relationship but have the estimates of 
  p1 > 0.75, and it also identifies the pairs that are
  parent-offspring relationship but have the estimates of p1 < 0.9. 

  If option 2 is chosen, PREST will do everything that is done in
  option 1, then proceed to apply the MLRT to the subset of relative
  pairs selected by the initial screening as described above.
  100,000 replicates (this default value can be changed by the user) 
  are used to calculate the empirical p-value for the MLLR test.  
  PREST also calculates the empirical p-values for the EIBD, AIBS and
  IBS tests so that they can be compared with the p-values obtained 
  using the normal approximation.


Part II (ALTERTEST)
===================

  ALTERTEST (ALTERnative TEST) is a program that performs the 
  EIBD, AIBS, IBS and MLLR tests on problematic relative pairs
  identified using PREST.  The purpose of ALTERTEST is to allow the user
  to choose the relationship to be used as the null hypothesis for the
  tests, and this relationship is allowed to be different from that given
  by the pedigree.  In contrast, PREST will automatically use the
  relationship specified by the pedigree as the null hypothesis for the
  tests.  ALTERTEST is a stand-alone program.  If one has a null
  hypothesis in mind that is different from what is in the pedigree for
  some specific relative pairs, one can run ALTERTEST alone.  In other
  cases, it is helpful to run PREST first, so one can identify the
  problematic pairs and propose some likely relationships for the
  pairs.  The proposed likely relationships can then be tested by
  ALTERTEST for fit to the data.

  In a hypothesis test, if the null relationship (according to the
  pedigree) is rejected, it is of interest to know what relationships
  are compatible with the observed genotype data of the pair.  The
  estimate of p = (p0, p1, p2), the probability of sharing zero, one
  or two alleles IBD by the pair, can be useful for suggesting some
  likely relationships for the pair.  For example, with genome-screen 
  data available, consider a case that the estimate of 
  p = (p0, p1, p2) for a putative full-sib pair is (.463, .512, .025).  
  The true value of p is (.25, .5, .25) for a full-sib pair and is 
  (.5, .5, 0) for a half-sib pair, so it might be reasonable to test 
  whether half-sib relationship is compatible with the genotype data
  of this putative full-sib pair.  Consider another case where the
  estimate of p = (p0, p1, p2) for a putative grandparent-grandchild
  pair is (.005, .953, .042).  The true value of p is (.5, .5, 0) for
  a grandparent-grandchild pair and is (0, 1, 0) for a
  parent-offspring pair.  So it might be reasonable to test whether
  parent-offspring relationship is compatible with the genotype data
  of this putative grandparent-grandchild pair.  
  
  In the current implementation of ALTERTEST, 11 possible relationship
  types are allowed as null hypotheses for all the four tests (EIBD,
  AIBS, IBS and MLLR). They are full-sib, half-sib,
  grandparent-grandchild, avuncular, first-cousin, unrelated,
  half-avuncular, half-first-cousin, half-sib+first-cousin,
  parent-offspring and MZ twins.  These relationships are also the
  elements of the alternative set A for the MLLR test.  ALTERTEST
  allows more than one null hypothesis to be specified for each pair.
  It also uses a default value of 100,000 replicates to calculate the
  empirical p-values for the EIBD, AIBS, IBS and MLLR tests.  Moreover
  ALTERTEST estimates p = (p0, p1, p2) for each pair.  Note that for
  unrelated pairs, only the IBS and MLLR tests are applicable; for
  parent-offspring pairs, only the AIBS, IBS and MLLR tests are
  applicable; for MZ twins, only the MLLR test is applicable.