# bcmixed

The bcmixed package provides two categories of important functions: bcmarg and bcmmrm. The bcmarg function provides inferences on the marginal model of the mixed effect model with the Box-Cox transformation and the bcmmrm function provides inferences on the model median differences between treatment groups for longitudinal randomized clinical trials. These statistical methods are proposed by Maruo et al. (2017).

## Installation

You can install the released version of bcmixed from CRAN with:

``````install.packages("bcmixed")
``````

And the development version from GitHub with:

``````# install.packages("devtools")
devtools::install_github("kzkzmr/bcmixed")
``````

## Example

This is a basic example which shows you how to solve a common problem:

``````library(bcmixed)
data(aidscd4)
# Marginal model of mixed model with the Box-Cox transformation
res1 <- bcmarg(cd4 ~ as.factor(treatment) * as.factor(weekc) + age,
data = aidscd4, time = weekc, id = id)
summary(res1)
#> Box-Cox transformed mixed model analysis
#>   Formula: cd4 ~ as.factor(treatment) * as.factor(weekc) + age
#>   Time: weekc
#>   ID: id
#>   Covariance structure: "UN"
#>   Data: aidscd4
#>   Log-likelihood: -13623.31
#>   Estimated transformation parameter:  0.183
#>
#> Coefficients on the transformed scale:
#>                                            Value Std.Error t-value p-value
#> (Intercept)                               3.1483   0.25917  12.147   0.000
#> as.factor(treatment)2                     0.2967   0.16995   1.746   0.081
#> as.factor(treatment)3                     0.4716   0.16946   2.783   0.005
#> as.factor(treatment)4                     0.7614   0.16763   4.542   0.000
#> as.factor(weekc)16                       -0.2254   0.09248  -2.437   0.015
#> as.factor(weekc)24                       -0.4863   0.09781  -4.972   0.000
#> as.factor(weekc)32                       -0.7246   0.10834  -6.688   0.000
#> age                                       0.0207   0.00612   3.384   0.001
#> as.factor(treatment)2:as.factor(weekc)16 -0.1386   0.12994  -1.067   0.286
#> as.factor(treatment)3:as.factor(weekc)16 -0.0500   0.12943  -0.387   0.699
#> as.factor(treatment)4:as.factor(weekc)16  0.0682   0.12896   0.529   0.597
#> as.factor(treatment)2:as.factor(weekc)24 -0.2078   0.13763  -1.510   0.131
#> as.factor(treatment)3:as.factor(weekc)24 -0.0235   0.13758  -0.171   0.864
#> as.factor(treatment)4:as.factor(weekc)24  0.0821   0.13754   0.597   0.551
#> as.factor(treatment)2:as.factor(weekc)32 -0.1034   0.15508  -0.667   0.505
#> as.factor(treatment)3:as.factor(weekc)32 -0.1018   0.15353  -0.663   0.507
#> as.factor(treatment)4:as.factor(weekc)32  0.1436   0.15162   0.947   0.344
#>
#> Covariance parameters on the transformed scale:
#> UN(1,1) UN(1,2) UN(1,3) UN(1,4) UN(2,2) UN(2,3) UN(2,4) UN(3,3) UN(3,4) UN(4,4)
#>    3.72    2.76    2.61    2.34    3.47    2.67    2.56    3.24    2.68    3.27
#>
#> Correlations on the transformed scale:
#>        8    16    24    32
#> 8  1.000 0.767 0.751 0.670
#> 16 0.767 1.000 0.797 0.761
#> 24 0.751 0.797 1.000 0.821
#> 32 0.670 0.761 0.821 1.000

# Box-Cox transformation for the baseline
lmd.bl <- bcmarg(cd4.bl ~ 1, data = aidscd4[aidscd4\$weekc == 8, ])\$lambda
aidscd4\$cd4.bl.tr <- bct(aidscd4\$cd4.bl, lmd.bl)

# Inference on model median differences between groups at each time point
res2 <- bcmmrm(outcome = cd4, group = treatment, data = aidscd4, time = weekc,
id = id, covv = c("cd4.bl.tr", "sex"), cfactor = c(0, 1),
glabel = c("Zid/Did", "Zid+Zal", "Zid+Did", "Zid+Did+Nev"))

# Summarize
print(res2)
#> Model median estimation based on MMRM with Box-Cox transformation
#>   Outcome: cd4
#>   Group: treatment
#>   Time: weekc
#>   ID: id
#>   Covariate(s): c("cd4.bl.tr", "sex")
#>   Covariance structure: "UN"
#>   Data: aidscd4
#>   Estimated transformation parameter:  0.154
#>   Log-likelihood: -13322.36
#>
#> Model median estimates (row: group, col: time):
#>   treatment | weekc    8   16   24   32
#> 1           Zid/Did 18.9 16.5 14.1 12.1
#> 2           Zid+Zal 22.0 17.9 14.6 13.5
#> 3           Zid+Did 24.5 20.9 18.2 15.1
#> 4       Zid+Did+Nev 30.1 27.8 24.2 21.8

summary(res2)
#> Model median inference based on MMRM with Box-Cox transformation
#>
#> Data and variable information:
#>   Outcome: cd4
#>   Group: treatment
#>   Time: weekc
#>   ID: id
#>   Covariate(s): c("cd4.bl.tr", "sex")
#>   Data: aidscd4
#>
#> Analysis information:
#>   Covariance structure: "UN"
#>   Robust inference: TRUE
#>   Empirical small sample adjustment: TRUE
#>   Confidence level: 0.95
#>
#> Analysis results:
#>   Estimated transformation parameter:  0.154
#>
#>
#> Model median inferences for weekc = 8
#>
#>     treatment median    SE lower.CL upper.CL
#> 1     Zid/Did   18.9 0.862     17.2     20.6
#> 2     Zid+Zal   22.0 1.124     19.8     24.2
#> 3     Zid+Did   24.5 1.465     21.6     27.4
#> 4 Zid+Did+Nev   30.1 1.597     27.0     33.3
#>
#>
#> Model median inferences for weekc = 16
#>
#>     treatment median    SE lower.CL upper.CL
#> 1     Zid/Did   16.5 0.799     15.0     18.1
#> 2     Zid+Zal   17.9 0.932     16.1     19.8
#> 3     Zid+Did   20.9 1.207     18.5     23.2
#> 4 Zid+Did+Nev   27.8 1.596     24.6     30.9
#>
#>
#> Model median inferences for weekc = 24
#>
#>     treatment median    SE lower.CL upper.CL
#> 1     Zid/Did   14.1 0.716     12.7     15.5
#> 2     Zid+Zal   14.6 0.864     12.9     16.3
#> 3     Zid+Did   18.2 1.175     15.9     20.5
#> 4 Zid+Did+Nev   24.2 1.510     21.3     27.2
#>
#>
#> Model median inferences for weekc = 32
#>
#>     treatment median    SE lower.CL upper.CL
#> 1     Zid/Did   12.1 0.662     10.8     13.4
#> 2     Zid+Zal   13.5 0.813     11.9     15.1
#> 3     Zid+Did   15.1 1.019     13.1     17.1
#> 4 Zid+Did+Nev   21.8 1.376     19.1     24.5
#>
#>
#> Inferences of model median difference between groups ( treatment 1 - treatment 0 ) for weekc = 8
#>
#>   treatment 1 treatment 0 delta   SE lower.CL upper.CL t.value p.value
#> 1     Zid+Zal     Zid/Did  3.12 1.40    0.363     5.87    2.22   0.027
#> 2     Zid+Did     Zid/Did  5.64 1.69    2.325     8.96    3.34   0.001
#> 3 Zid+Did+Nev     Zid/Did 11.25 1.80    7.711    14.80    6.24   0.000
#> 4     Zid+Did     Zid+Zal  2.53 1.83   -1.059     6.12    1.39   0.167
#> 5 Zid+Did+Nev     Zid+Zal  8.14 1.93    4.349    11.93    4.22   0.000
#> 6 Zid+Did+Nev     Zid+Did  5.61 2.16    1.372     9.85    2.60   0.010
#>
#>
#> Inferences of model median difference between groups ( treatment 1 - treatment 0 ) for weekc = 16
#>
#>   treatment 1 treatment 0 delta   SE lower.CL upper.CL t.value p.value
#> 1     Zid+Zal     Zid/Did  1.38 1.21  -1.0015     3.75    1.14   0.256
#> 2     Zid+Did     Zid/Did  4.31 1.43   1.4940     7.12    3.01   0.003
#> 3 Zid+Did+Nev     Zid/Did 11.22 1.78   7.7118    14.73    6.29   0.000
#> 4     Zid+Did     Zid+Zal  2.93 1.50  -0.0162     5.88    1.95   0.051
#> 5 Zid+Did+Nev     Zid+Zal  9.84 1.84   6.2318    13.46    5.36   0.000
#> 6 Zid+Did+Nev     Zid+Did  6.91 2.00   2.9767    10.84    3.45   0.001
#>
#>
#> Inferences of model median difference between groups ( treatment 1 - treatment 0 ) for weekc = 24
#>
#>   treatment 1 treatment 0  delta   SE lower.CL upper.CL t.value p.value
#> 1     Zid+Zal     Zid/Did  0.534 1.12   -1.660     2.73   0.479   0.632
#> 2     Zid+Did     Zid/Did  4.139 1.36    1.459     6.82   3.035   0.003
#> 3 Zid+Did+Nev     Zid/Did 10.135 1.66    6.874    13.40   6.108   0.000
#> 4     Zid+Did     Zid+Zal  3.605 1.44    0.768     6.44   2.498   0.013
#> 5 Zid+Did+Nev     Zid+Zal  9.601 1.73    6.204    13.00   5.554   0.000
#> 6 Zid+Did+Nev     Zid+Did  5.996 1.89    2.291     9.70   3.180   0.002
#>
#>
#> Inferences of model median difference between groups ( treatment 1 - treatment 0 ) for weekc = 32
#>
#>   treatment 1 treatment 0 delta   SE lower.CL upper.CL t.value p.value
#> 1     Zid+Zal     Zid/Did  1.35 1.04   -0.692     3.40    1.30   0.194
#> 2     Zid+Did     Zid/Did  3.00 1.20    0.633     5.37    2.49   0.013
#> 3 Zid+Did+Nev     Zid/Did  9.70 1.52    6.705    12.69    6.37   0.000
#> 4     Zid+Did     Zid+Zal  1.65 1.30   -0.907     4.20    1.27   0.206
#> 5 Zid+Did+Nev     Zid+Zal  8.34 1.60    5.206    11.48    5.23   0.000
#> 6 Zid+Did+Nev     Zid+Did  6.70 1.71    3.338    10.06    3.92   0.000

plot(res2, ylab = "CD4+1", xlab = "Week", verbose = TRUE)
``````

``````#> Analysis information:
#>   Covariance structure: "UN"
#>   Robust inference: TRUE
#>   Empirical small sample adjustment: TRUE
#>
#> Error bar: 95% confidence interval
``````

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bcmixed documentation built on March 31, 2020, 5:22 p.m.