Sib-pair Command: kendalltau

Class	Analysis and data manipulation command
Name	kendalltau
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. Bootstrap standard errors are calculated for each zygosity group, and a permutation test is performed comparing the MZ and DZ taus.

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 S_ij 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"
--------------------------------------------------------------

Zyg    Pairs   Conc   Disc  Tau    (BSE)        OR     Tau(n) (BSE)        OR(n)
----  ------   ----  -----  ---------------- --------  ----------------- --------
MZ        17     96     37  0.4338 ( 0.1566)     2.53  0.4436 ( 0.1733)     2.59

See also:

twin	classical twin analysis
kaplan-meier	univariate survivor function estimate