Ficult to obtain c analytically. One obvious alternative would be the

It can be Ortunities and options of others. Our models are associated to other estimated by h(t) = 1 t -at a^ h(s)ds,a n^ T (t)U ^ B = n ^ C(t) + n^ C(t) + ntti n1^1 d( i Ni ) +i>n 1^2 d( i Ni )i>ni n^ i i 1 (X i )I (X i) +^ i i 2 (X i )I (X ii n^ i i 1 (X i )I (X it) +i>n^ i i 2 (X i )I (X iwhere i , i = 1, . . . , n, are independent variables that are also independent from the data. Furthermore, these variables have mean zero and variance converging to one as n . In the normal resampling approach mentioned above, the i 's are the standard normal variables. However, the standard normal variables often result fpsyg.2015.00360 in lower coverage probabilities in various simulation studies. Thus, with moderate sized samples, we need to make some adjustment. ^ Conditional on (X i , i , Z i ), i = 1, . . . , n, Wn is a sum of n independent variables at each time point. ^ In Appendix B of the Supplementary Material available at Biostatistics online, we show that Wn given ^ the data converges weakly to W . It follows that suptI |W /s| given the data converges in distribution to suptI |W /s |. Therefore, c can be estimated empirically from a large number of realizations of the ^ conditional distribution of suptI |W /s| given the data. Several choices of the weight s arise from recommendations in the literature for confidence bands of the survivor function and the cumulative hazard function in the one sample case. The choice s(t) = (t, t) results in equal precision bands (Nair, 1984), which differ from pointwise confidence intervals in ^ ^ that c replaces z /2 . The choice s(t) = 1 + (t, t) results in the Hall ellner type bands recommended by Bie and others (1987), which often have narrower widths in the middle of data range and wider widths ^ near the extremes of data range (Lin and others, 1994). One could also choose s(t) = h(t). This choice does not involve (t, t) and hence is pnas.1408988111 easier to implement.