# Sib-pair Command: sml

 Class Global Utility Name sml Arguments

Calculates recurrence risks and segregation ratios under a specified diallelic generalized single major locus model.

The results include the input penetrances, the resulting trait prevalence, the population attributable risk fraction ("Pop AR"):

AR = (Prev-min(fAA,fAB,fBB))/Prev ;

the additive and dominance variances following James [1971], the expected recurrence risks, relative risks, odds ratios and population risk ratios for four classes of relative pair (MZ twins, full siblings, parent-offspring pairs, second degree relatives):

Rec Riski = Pr(Ego affected | relative of ith class affected)
Rel Riski = Pr(Ego affected | relative of ith class affected) / Pr(Ego affected | relative of ith class unaffected)
Odds Ratioi = Odds(Ego affected | relative of ith class affected) / Odds(Ego affected | relative of ith class unaffected)
PRRi = Pr(Ego affected | relative of ith class affected) / Prevalence ;

the expected identity-by-descent sharing for those four types of pair at the trait locus for concordantly affected and discordant pairs; the allele and genotype frequencies in affected and unaffected individuals; the risk to offspring by mating type (zero, one or both parents affected).

Example:

```>> sml 0.17 0.21 0.08 0.03

------------------------------------------------
Single Major Locus Recurrence Risk Calculation
------------------------------------------------

Frequency(A): 0.170000; Pen(AA): 0.210; Pen(AB): 0.080; Pen(BB): 0.030
Trait Prev  : 0.049312; Pop AR:  39.2%; Var(Add): 0.001141; Var(Dom): 0.000127

Measure      MZ Twin       Sib-Sib        Par-Off      Second
----------   ----------    ----------     ---------    ----------
Rec risk         0.075         0.062         0.061         0.055
Rel risk         1.564         1.264         1.250         1.124
Odds rat         1.610         1.281         1.266         1.131
PRR              1.522         1.248         1.235         1.117
ibd|A-A          1.000         0.552         0.500         0.276
ibd|A-U          1.000         0.497         0.500         0.248

Freq of A if Affected: 0.351983 (0.123,0.458,0.419)
Freq of A if Unaffctd: 0.160561 (0.024,0.273,0.703)

Mating       Proportion    Risk to offspring
----------   -----------   ------------------
UnA x UnA         0.904         0.048
Aff x UnA         0.094         0.060
Aff x Aff         0.002         0.075

```

 grr recurrence risks

# Sib-pair Command: sml

 Class Global Utility Name sml Arguments [ []].

Calculates mean, variance components and parent-offspring regression results under a specified diallelic generalized single major locus model.

Example:

```>> sml 0.05 5 0 -5 1

------------------------------------------------
Quantitative Trait SML Expectations
------------------------------------------------

A allele frequency       = 0.050
Genotypes                =      A/A         A/B          B/B
Genotype frequencies     =     0.003        0.095        0.902
Genotypic means          =     5.000000     0.000000    -5.000000
Genotypic SDs            =     1.000000     1.000000     1.000000

Expected trait mean (SD) =    -4.500000 (    1.837117)
Variances (A, D, E)      =     2.375000     0.000000     1.000000

Midparent    E(Child)        Expected IQR
----------- ------------ -------------------------
-10.0114      -8.3784     -10.0911      -6.6656
-8.1742      -7.0856      -8.7983      -5.3728
-6.3371      -5.7928      -7.5056      -4.0800
-4.5000      -4.5000      -6.2128      -2.7872
-2.6629      -3.2072      -4.9200      -1.4944
-0.8258      -1.9144      -3.6272      -0.2017
1.0114      -0.6216      -2.3344       1.0911

```

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