# genetic analysis of binary and categorical traits part one

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GENETIC ANALYSIS OF BINARY and CATEGORICAL TRAITS PART ONE. TABLE 1. Twin Pair Concordances for Major Depression (Virginia Twin Study data, adapted from Neale and Cardon, 1992). 166+95+83 1180. 126+82+94 880. 2 x concordant affected pairs + discordant pairs 2 x Total Pairs. - PowerPoint PPT Presentation

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• GENETIC ANALYSIS OF

BINARY and CATEGORICAL TRAITS

PART ONE

• TABLE 1. Twin Pair Concordances for Major Depression

(Virginia Twin Study data, adapted from Neale and Cardon, 1992)

MZ FEMALE PAIRSDZ FEMALE PAIRSTwin BTwin BUnaffectedAffectedUnaffectedAffectedTwin A - Unaffected32983Twin A - Unaffected20194 - Affected9583 - Affected8263

• Prevalence=

e.g. for MZ pairs=

e.g. for DZ pairs=Prevalance = proportion of affected (alcoholic) twins in the general population.

2 x concordant affected pairs + discordant pairs2 x Total Pairs= 29.2%

= 34.3%

• Probandwise concordance rate=

e.g. for MZ pairs=

e.g. for DZ pairs=Probandwise concordance rate = probability that cotwin of a depressed twinwill also have a history of depression.Recurrence Risk-ratio2 x concordant affected pairs2 x concordant affected pairs + discordant pairs= 48.3%

= 41.7%

=

• Why do we have (2 x number of concordant affected pairs) in the numerator and denominator of the expression for the probandwise concordance rate? Consider a simple example where there are 4 affected individuals, who came from 3 twin pairs, ie,

1 01 01 1

There are 4 potential probands, so if we randomly select an affected individual, the probability that the cotwin of that individual is also affected will be 50%

• TABLE 1a. Twin Pair Concordances for Alcohol Dependence (DSM-IIIR)

(Virginia Twin Study data, from Kendler et al., 1992)

MZFemale PairsDZFemale Pairs

N pairs590440Population prevalence8.1%10.2%Probandwise concordance31.6%24.4%

• Number of concordant alcoholic pairs=N pairs x prevalence x probandwise concordanceMZ:15 pairsDZ:11 pairs

Number of discordant pairs=2 x N pairs x prevalence x (1 - probandwise concordance)MZ:65 pairsDZ:68 pairs

Number of concordant unaffected pairsMZ:510 pairsDZ:361 pairs

• Some investigators also report a PAIRWISE CONCORDANCE RATE - the proportion of pairs with at least one twin affected who are concordant.

The PAIRWISE concordance rate is redundant --PAIRWISE CONCORDANCE RATE =where CR is the probandwise concordance rateCR2-CR

• Alcoholism RiskAlcoholism RiskUNAFFECTEDAFFECTEDa) Normal Liability Threshold Modelb) Multiple-threshold ModelUNAFFECTEDMILDCASESSEVERECASESt200t1t1

• CUMULATIVE NORMAL FREQUENCY DISTRIBUTION

Threshold value(t)Prevalence(area under the standard normal curve)0.050%0.2540%0.5330%0.8420%1.0415%1.2810%1.645%1.952.5%2.331%3.080.1%-0.2560%

• Table 3. Population distribution of pairs of relatives with both alcoholic, neither alcoholic, or only one relative alcoholic, as a function of (i) lifetime prevalence of alcoholism, and (ii) liability correlation for alcoholism in relativesai.e. Probandwise concordance rate

PREVALENCERelative ARelative BLiabilitycorrelationBothaffectedDiscordantA affected B affectedBothunaffectedRisk to relativeof an alcoholicaRelatives Recurrence Risk Ratio(%)(%)(%)(%)(%)(%)30%30%0.617.312.712.757.357.61.90.312.817.217.252.842.71.40.1510.919.119.150.936.21.220%20%0.69.910.110.169.949.62.50.36.613.413.466.633.11.70.155.214.814.865.226.21.310%10%0.63.96.16.183.939.03.90.32.27.87.882.221.62.20.151.58.58.581.515.21.5

• EXAMPLE DATA-FILE FOR MX RAW ORDINAL DATA:MZF DEPRESSION DATA (depmzf.dat)00329018310951183

• EXAMPLE DATA-FILE (II):DERIVED FROM PUBLISHED SOURCESMZF ALCOHOL DEPENDENCE DATA (alcmzf.dat)003100132.51032.51115

• ! tetrachoric.mx! estimating tetrachoric correlations #define nvar 1#define maxthresf 1 ! number of thresholdsAnalysis of depression data: estimating tetrachorics & confidence intervals data NI=3 NG=4LAbels twina twinb countmzOrdinal fi=depmzf.rec! Count is a definition variable that we use to tell MX the frequency count ! for each element of the 2x2 table ! Definition_variables countmz / Begin matrices; W LO nvar nvar fr ! w*w' is the tetrachoric correlation Y LO nvar nvar fr ! y*y' is 1-tetrachoric correlation M FU maxthresf nvar fi S DI nvar nvar ! Matrix that will store weight variable end matrices; SP M 3 MATRIX M 1.5487 ! This tells MX to store the definition variable count in S SP S -1 mat w 0.7 mat y 0.7

• Begin algebra; R=W*W'; E=Y*Y'; V=R+E; end algebra; FREQ S; ! tells MX that S contains the weight (frequency) variable TH M|M; ! tells MX that row and column thresholds contained in M|M CO V|R_ R'|V; ! formula for correlation matrix! bo 0.001 1.0 y(1,1) bo 0.0001 0.999 w(1,1) bo -5.0 5.0 m(1,1) interval r(1,1) ! compute 95% confidence interval for correlation OPT func=1.E-12 OPT RS END

• Analysis of depression data: DZm data NI=3 LAbels twina twinb countdz OR fi=depdzf.rec Definition_variables countdz / Begin matrices; W LO nvar nvar fr ! w*w' is the tetrachoric correlation for DZ group Y LO nvar nvar fr ! y*y' is 1-tetrachoric correlation for DZ group N FU maxthresf nvar fr S DI nvar nvar ! Matrix that will store weight variable end matrices; SP N 6 MATRIX N 1.4487 SP S -1 mat w 0.6 mat y 0.8 Begin algebra; R=W*W'; E=Y*Y'; V=R+E; end algebra; FREQ S; TH N|N; CO V|R_R'|V; bo 0.001 1.0 y(1,1) bo 0.0001 0.999 w(1,1) bo -5.0 5.0 n(1,1) interval r(1,1) ! compute 95% confidence interval for correlation OPT RS END

• Constraint function - constrain variances to unity for MZ group CO NI=1 Begin matrices = group 1; U unit 1 nvar end matrices; CO \d2v(V) = u; end Constraint function - constrain variances to unity for DZ group CO NI=1 Begin matrices = group 2; U unit 1 nvar end matrices; CO \d2v(V) = u; end

• Summary of VL file data for group 1 COUNTMZ TWINA TWINB Code -1.0000E+00 1.0000E+00 2.0000E+00 Number 4.0000E+00 4.0000E+00 4.0000E+00 Mean 1.4750E+02 5.0000E-01 5.0000E-01 Variance 1.1005E+04 2.5000E-01 2.5000E-01 Minimum 8.3000E+01 0.0000E+00 0.0000E+00 Maximum 3.2900E+02 1.0000E+00 1.0000E+00 Summary of VL file data for group 2 COUNTDZ TWINA TWINB Code -1.0000 1.0000 2.0000 Number 4.0000 4.0000 4.0000 Mean 110.0000 0.5000 0.5000 Variance 2882.5000 0.2500 0.2500 Minimum 63.0000 0.0000 0.0000 Maximum 201.0000 1.0000 1.0000

• PARAMETER SPECIFICATIONS GROUP NUMBER: 1 Analysis of depression data: estimating tetrachorics & confidence intervals MATRIX E This is a computed FULL matrix of order 1 by 1 It has no free parameters specified MATRIX M This is a FULL matrix of order 1 by 1 1 1 3 MATRIX R This is a computed FULL matrix of order 1 by 1 It has no free parameters specified MATRIX S This is a DIAGONAL matrix of order 1 by 1 1 1 -1 MATRIX V This is a computed FULL matrix of order 1 by 1 It has no free parameters specified MATRIX W This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 1 MATRIX Y This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 2

• GROUP NUMBER: 2 Analysis of ordinal alcohol tolerance and dependence data: DZm MATRIX E This is a computed FULL matrix of order 1 by 1 It has no free parameters specified MATRIX N This is a FULL matrix of order 1 by 1 1 1 6 MATRIX R This is a computed FULL matrix of order 1 by 1 It has no free parameters specified MATRIX S This is a DIAGONAL matrix of order 1 by 1 1 1 -1 MATRIX V This is a computed FULL matrix of order 1 by 1 It has no free parameters specified MATRIX W This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 4 MATRIX Y This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 5

• MX PARAMETER ESTIMATES GROUP NUMBER: 1 Analysis of depression data: estimating tetrachorics & confidence intervals MATRIX E This is a computed FULL matrix of order 1 by 1 [=Y*Y'] 1 1 0.5660 MATRIX M This is a FULL matrix of order 1 by 1 1 1 0.5489 MATRIX R This is a computed FULL matrix of order 1 by 1 [=W*W'] 1 1 0.4340 MATRIX S This is a DIAGONAL matrix of order 1 by 1 1 1 83.0000 MATRIX V This is a computed FULL matrix of order 1 by 1 [=R+E] 1 1 1.0000

• MATRIX W This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 0.6588 MATRIX Y This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 0.7523 Matrix of EXPECTED thresholds TWINA TWINB Threshold 1 0.5489 0.5489 Threshold 2 1.0000 1.5487 (OBSERVED MATRIX is nonexistent for raw data) EXPECTED COVARIANCE MATRIX TWINA TWINB TWINA 1.0000 TWINB 0.4340 1.0000 Function value of this group: 1383.2565 Where the fit function is -2 * Log-likelihood of raw ordinal

• GROUP NUMBER: 2 Analysis of ordinal alcohol tolerance and dependence data: DZm MATRIX E This is a computed FULL matrix of order 1 by 1 [=Y*Y'] 1 1 0.8157 MATRIX N This is a FULL matrix of order 1 by 1 1 1 0.4038 MATRIX R This is a computed FULL matrix of order 1 by 1 [=W*W'] 1 1 0.1843 MATRIX S This is a DIAGONAL matrix of order 1 by 1 1 1 63.0000 MATRIX V This is a computed FULL matrix of order 1 by 1 [=R+E] 1 1 1.0000

• MATRIX W This is a LOWER TRIANGULAR matrix of order