Description Usage Arguments Details Value Author(s) Examples
View source: R/ynegbinompowersim.R
This will calculate the power for the negative binomial distribution for the 2-sample case under different follow-up scenarios: 1: fixed follow-up, 2: fixed follow-up with drop-out, 3: variable follow-up with a minimum fu and a maximum fu, 4: variable follow-up with a minimum fu and a maximum fu and drop-out.
1 2 3 4 |
nsize |
total number of subjects in two groups |
r0 |
event rate for the control |
r1 |
event rate for the treatment |
shape0 |
dispersion parameter for the control |
shape1 |
dispersion parameter for the treatment |
pi1 |
allocation prob for the treatment |
alpha |
type-1 error |
twosided |
1: two-side, others: one-sided |
fixedfu |
fixed follow-up time for each patient |
type |
follow-up time type, type=1: fixed fu with fu time |
u |
recruitment rate |
ut |
recruitment interval, must have the same length as |
tfix |
fixed study duration, often equals to recruitment time plus minimum follow-up |
maxfu |
maximum follow-up time, should not be greater than |
tchange |
a strictly increasing sequence of time points starting from zero at which the drop-out rate changes. The first element of tchange must be zero. The above rates and |
ratec1 |
piecewise constant drop-out rate for the treatment |
ratec0 |
piecewise constant drop-out rate for the control |
rn |
Number of repetitions |
Let τ_{min} and τ_{max} correspond to the minimum follow-up time fixedfu
and the maximum follow-up time maxfu
. Let T_f, C, E and R be the follow-up time, the drop-out time, the study entry time and the total recruitment period(R is the last element of ut
). For type 1 follow-up, T_f=τ_{min}. For type 2 follow-up T_f=min(C,τ_{min}). For type 3 follow-up, T_f=min(R+τ_{min}-E,τ_{max}). For type 4 follow-up, T_f=min(R+τ_{min}-E,τ_{max},C). Let f be the density of T_f.
Suppose that Y_i is the number of event obsevred in follow-up time t_i for patient i with treatment assignment Z_i, i=1,…,n. Suppose that Y_i follows a negative binomial distribution such that
P(Y_i=y\mid Z_i=j)=\frac{Γ(y+1/k_j)}{Γ(y+1)Γ(1/k_j)}\Bigg(\frac{k_ju_i}{1+k_ju_i}\Bigg)^y\Bigg(\frac{1}{1+k_ju_i}\Bigg)^{1/k_j},
where k_j, j=0,1 are the dispersion parameters for control j=0 and treatment j=1 and
\log(u_i)=\log(t_i)+β_0+β_1 Z_i.
The data will be gnerated according to the above model. Note that the piecewise exponential distribution and the piecewise uniform distribution are genrated using R package PWEALL functions "rpwe" and "rpwu", respectively.
The parameters in the model are estimated by MLE using the R package MASS function "glm.nb".
power |
simulation power (in percentage) |
Xiaodong Luo
1 2 3 4 5 6 7 8 |
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