Description Usage Arguments Details Value Note Author(s) See Also Examples

Interested parameters/linear combinations LB from more than one
independent populations can be aggregrate togeter by
appending mu vertically and Sigma/n diagonally

Consider Lb~N(MU,SIGMA) as the aggregrated estimates

Any comparison of interested parameters can be formulated by
multiplying a contrast matrix C on LB and set

H0: C*LB=d for any vector of value d to be tested

We then have

C*Lb~N(C*MU,C*SIGMA*C')

and

(C*Lb-d)'*inv(C*SIGMA*C')*(C*Lb-d)~chisq(q,lambda)

where degree of freedom q=rank(C*SIGMA*C'),

non-centrality parameter lambda=(C*LB-d)'*inv(C*SIGMA*C')*(C*LB-d)

Power of the test H0 is given by 1-beta=P(chisq(q,lambda)>qchisq(1-alpha,lambda))

Required sample size for desired power can be obtained by bisection method.

1 2 |

`thetas` |
list of theta (LB and VLb), can be different for each group |

`C` |
Contrast of Matrix |

`d` |
Value vector to be tested for all contrast |

`alpha` |
significant level |

`power` |
desired power for sample size calculation |

`n` |
sample size for power calculation / |

solved.power given sample size n, this gives the power for testing H0

solved.n given the desired power, this gives the sample size for H0

License: GPL-3

Marco Chak Yan YU

Maintainer: Marco Chak Yan YU <[email protected]>

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 | ```
#Example 1 (test fixed effect coefficient 2=0) with power of 80%
# for 1-level LME model, with covariates X, Z: (1,t), t=1,2,3
# for both fixed and random effects, with fixed effect coefficients B: (100,-0.5),
# random effect variance D: (2 1;1 2), residual variance R: 0.2
B <- matrix(c(100,-0.5),2,1)
D <- matrix(c(2,1,1,2),2,2)
R <- 0.2
X <- cbind(rep(1,3),1:3)
Z <- X
theta <- lme.Lb.dist.theta(B,D,R,X,Z)
pass.lme.CLb.test(list(theta),alpha=0.05,power=0.8)
pass.lme.CLb.test(list(theta),alpha=0.05,n=66)
#Example 2 (compare two fixed effect coefficient 2) with power of 80%
# Consider above model as a control group model,
# with an independent treatment group with model same as the control
# except a different fixed effect coefficient 2 for treatment
# = fixed effect coefficient 2 for control x 0.7
theta2 <- theta
theta2$mu <- theta$mu *0.7
C <- matrix(c(1,-1),1,2)
pass.lme.CLb.test(list(theta,theta2),C,alpha=0.05,power=0.8)
pass.lme.CLb.test(list(theta,theta2),C,alpha=0.05,n=1468)
#Example 3 (compare two fixed effect coefficient 2) with power of 80%
# with sample size ratio, control:treatment = 1:2
pass.lme.CLb.test(list(theta,theta2),C,alpha=0.05,power=0.8,n=c(1,2))
pass.lme.CLb.test(list(theta,theta2),C,alpha=0.05,n=c(1101,2202))
#Example 4 (repeated-measures ANOVA for comparing 3 group means) with power of 80%
# for 1-level LME model with mean for group 1, 2 and 3 are 100, 99, 102, respectively,
# each subject to be measured 2 times, with within-subject variance = 15, residual variance = 10
B <- 100
D <- 15
R <- 10
X <- matrix(1,2,1)
Z <- X
theta <- lme.Lb.dist.theta(B,D,R,X,Z)
theta2 <- theta
theta3 <- theta
theta2$mu <- 99
theta3$mu <- 102
C <- rbind(c(1,-1,0),c(1,0,-1))
pass.lme.CLb.test(list(theta,theta2,theta3),C,alpha=0.05,power=0.8)
pass.lme.CLb.test(list(theta,theta2,theta3),C,alpha=0.05,n=41)
``` |

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