Sib-pair Command: kendalltau


ClassAnalysis and data manipulation command
Namekendalltau
Arguments <age-at-onset> <censor> [<zygosity_score> even | odd | (>|>=|<|<=|==|^= <threshold>)]

For all pairs of twins or siblings from each twin zygosity group, calculate Oakes's version of Kendall's tau for right censored data.

If a gamma frailty model fits the data, the estimator is unbiased in the presence of censoring [Oakes 2008], and,

tau = (OR-1)/(OR+1) ,

where OR is the continuation odds ratio,

OR = S11S00 / (S10S01)

with Sij is (d/dt)i (d/dt)j S(t1,t2), and S(t1, t2) the bivariate survivor function. In the Clayton-Cuzick bivariate survival model, OR is constant at all (pairs of) ages.

Example:

>> #
>> # Cable insulation failure data used as an example by Oakes 1986
>> # S is the time to inception of the fault, and T the subsequent
>> # time to failure
>> # Oakes, D. A model for bivariate survival data. 
>> # In Moolgavkar, S.H. and Prentice, R.L. (Eds.)
>> #   Modern Statistical Methods in Chronic Disease 
>> #   Epidemiology, Wiley, New York, pp. 151-166, 1986
>> #
>> set loc zyg qua
>> set loc type qua
>> set loc time qua
>> read pedigree inline
>> 1  S 1 2 x 1 0 228
>> 1  T 1 2 x 1 1 30
>> 2  S 1 2 x 1 0 106
>> 2  T 1 2 x 1 1 8
>> 3  S 1 2 x 1 0 246
>> 3  T 1 2 x 1 1 66
>> 4  S 1 2 x 1 0 700
>> 4  T 1 2 x 1 1 72
>> 5  S 1 2 x 1 0 473
>> 5  T 1 2 x 1 1 25
>> 6  S 1 2 x 1 0 155
>> 6  T 1 2 x 1 1 7
>> 7  S 1 2 x 1 0 414
>> 7  T 1 2 x 1 1 30
>> 8  S 1 2 x 1 0 1374
>> 8  T 1 2 x 1 1 90
>> 9  S 1 2 x 1 0 1227
>> 9  T 1 2 x 1 1 39
>> 10 S 1 2 x 1 0 254
>> 10 T 1 2 x 1 1 46
>> 11 S 1 2 x 1 0 435
>> 11 T 1 2 x 1 1 85
>> 12 S 1 2 x 1 0 1155
>> 12 T 1 2 x 1 1 85
>> 13 S 1 2 x 1 0 195
>> 13 T 1 2 x 1 1 27
>> 14 S 1 2 x 1 0 117
>> 14 T 1 2 x 1 1 27
>> 15 S 1 2 x 1 0 724
>> 15 T 1 2 x 1 1 21
>> 16 S 1 2 x 1 0 300
>> 16 T 1 2 x 1 1 96
>> 17 S 1 2 x 1 0 128
>> 17 T 1 2 x 1 1 4
>> ;;;;
>> run
>> set loc dummy aff
>> dummy = y
>> set twi zyg
>> ken time dummy

--------------------------------------------------------------
Twin survival analysis of "time" for outcome "dummy"
--------------------------------------------------------------

Zygosity group    Pairs   Conc   Disc  Tau       OR     Tau(n)   OR(n)
---------------  ------   ----  -----  ------ --------  ------ --------
MZ twins             17     96     37  0.4338     2.53  0.4436     2.59
DZ twins              0      0      0  0.0000     1.00  0.0000     1.00
Sibs (non-MZ)         0      0      0  0.0000     1.00  0.0000     1.00

See also:

twin classical twin analysis
kaplan-meier univariate survivor function estimate


<< (twin)Up to index>> (varcomp)