Objective

Perform real world data analysis using BifurcatoR tools to check bimodality

Table 1

Table 1. UK Twins Characteristics (N= 295)
Variable Concordant, N = 981 Discordant_A, N = 451 Discordant_B, N = 831 Intermediate, N = 691
Age 61.6 (7.9) 57.8 (11.5) 61.7 (8.7) 59.1 (6.2)
Sex
    F 98 (100%) 45 (100%) 83 (100%) 69 (100%)
Ethnicity
    Mixed 0 (0%) 0 (0%) 0 (0%) 0 (0%)
    White 97 (99%) 45 (100%) 83 (100%) 69 (100%)
    Other 1 (1.0%) 0 (0%) 0 (0%) 0 (0%)
Zygosity
    Dizygotic 0 (0%) 0 (0%) 0 (0%) 0 (0%)
    Monozygotic 98 (100%) 45 (100%) 83 (100%) 69 (100%)
BMI 26.2 (4.2) 24.8 (3.0) 26.6 (5.2) 27.9 (5.2)
Height 161.3 (5.9) 159.5 (6.0) 161.5 (5.3) 160.3 (7.2)
Weight 68.1 (11.5) 63.3 (8.6) 69.5 (14.1) 71.9 (16.1)
Obesity
    normal 81 (83%) 43 (96%) 64 (77%) 47 (68%)
    obese 13 (13%) 2 (4.4%) 13 (16%) 15 (22%)
    severe_obese 4 (4.1%) 0 (0%) 6 (7.2%) 7 (10%)
Lean_mass 38.9 (4.9) 37.3 (4.5) 39.5 (4.7) 40.5 (7.0)
Fat_mass 27.8 (7.5) 24.3 (5.6) 28.4 (10.2) 30.0 (9.7)
Lean Mass Index 14.9 (1.6) 14.7 (1.4) 15.2 (1.7) 15.7 (2.0)
Fat Mass Index 10.7 (2.9) 9.5 (2.2) 10.9 (3.9) 11.7 (3.5)
PGA3 0.2 (0.9) 0.0 (0.9) -0.1 (1.0) 0.1 (1.2)
HDAC_signature 0.2 (0.7) -0.2 (0.9) -0.1 (1.2) 0.3 (1.0)
IGN1_exp 0.0 (1.0) 0.3 (0.9) 0.1 (0.9) -0.2 (1.1)
NNAT_adipo_exp 2.2 (0.1) 2.2 (0.1) 2.2 (0.1) 2.2 (0.1)
Insulin 3.9 (0.6) 3.6 (0.6) 3.7 (0.6) 4.0 (0.9)
    (Missing) 5 4 2 3
1 Mean (SD); n (%)

NNAT (All Samples)

NNAT (Density Plot by Clusters)

Mclust

Ameijeiras-Alonso et al. Excess Mass Fit

## [1] "Bimodality P-value of NNAT using Ameijeiras-Alonso et al. Excess Mass Fit is: 0.351"

Bimodality Coefficient

##      sub_twins_MZ$NNAT_adipo_exp
## [1,]                       FALSE
## [1] "Bimodality Coefficient of NNAT is: 0.33, which is less than 0.555, so no bimodality detected."

Cheng and Hall Excess Mass

## [1] "Bimodality P-value of NNAT using Cheng and Hall Excess Mass is: 0.429"

Fisher and Marron Carmer-von Mises

## [1] "Bimodality P-value of NNAT using Fisher and Marron Carmer-von Mises is: 0.936"

Hall and York Bandwidth test

## [1] "Bimodality P-value of NNAT using Hall and York Bandwidth test is: 0.864"

Hartigans’ dip test

## [1] "Bimodality P-value of NNAT using Hartigans' dip test is: 0.917"

Sliverman Bandwidth

## [1] "Bimodality P-value of NNAT using Sliverman Bandwidth is: 0.969"

mixR

## [1] "Bimodality P-value of NNAT using mixR(normal) is: 0.83"
## [1] "Bimodality P-value of NNAT using mixR(weibull) is: 0"

HDAC (All Samples)

HDAC (Density Plot by Clusters)

Mclust

Ameijeiras-Alonso et al. Excess Mass Fit

## [1] "Bimodality P-value of HDAC using Ameijeiras-Alonso et al. Excess Mass Fit is: 0.086"

Bimodality Coefficient

##      sub_twins_MZ$HDAC_signature
## [1,]                       FALSE
## [1] "Bimodality Coefficient of HDAC is: 0.3, which is less than 0.555, so no bimodality detected."

Cheng and Hall Excess Mass

## [1] "Bimodality P-value of HDAC using Cheng and Hall Excess Mass is: 0.123"

Fisher and Marron Carmer-von Mises

## [1] "Bimodality P-value of HDAC using Fisher and Marron Carmer-von Mises is: 0.637"

Hall and York Bandwidth test

## [1] "Bimodality P-value of HDAC using Hall and York Bandwidth test is: 0.401"

Hartigans’ dip test

## [1] "Bimodality P-value of HDAC using Hartigans' dip test is: 0.729"

Sliverman Bandwidth

## [1] "Bimodality P-value of HDAC using Sliverman Bandwidth is: 0.741"

mixR

## [1] "Bimodality P-value of HDAC using mixR(normal) is: 0.26"

IGN1 (All Samples)

IGN1 (Density Plot by Clusters)

Mclust

Ameijeiras-Alonso et al. Excess Mass Fit

## [1] "Bimodality P-value of IGN1 using Ameijeiras-Alonso et al. Excess Mass Fit is: 0.15"

Bimodality Coefficient

##      sub_twins_MZ$IGN1_exp
## [1,]                 FALSE
## [1] "Bimodality Coefficient of IGN1 is: 0.36, which is less than 0.555, so no bimodality detected."

Cheng and Hall Excess Mass

## [1] "Bimodality P-value of IGN1 using Cheng and Hall Excess Mass is: 0.134"

Fisher and Marron Carmer-von Mises

## [1] "Bimodality P-value of IGN1 using Fisher and Marron Carmer-von Mises is: 0.036"

Hall and York Bandwidth test

## [1] "Bimodality P-value of IGN1 using Hall and York Bandwidth test is: 0.012"

Hartigans’ dip test

## [1] "Bimodality P-value of IGN1 using Hartigans' dip test is: 0.651"

Sliverman Bandwidth

## [1] "Bimodality P-value of IGN1 using Sliverman Bandwidth is: 0.106"

mixR

## [1] "Bimodality P-value of IGN1 using mixR is: 0.33"

PGA3 (All Samples)

PGA3 (Density Plot by Clusters)

Mclust

Mclust clusters vs. original clusters
##               
##                Mclust_Cluster_1 Mcluster_Cluster_2 Sum
##   Concordant                 11                 87  98
##   Discordant_A                9                 36  45
##   Discordant_B               18                 65  83
##   Intermediate               12                 57  69
##   Sum                        50                245 295
## 
##  Pearson's Chi-squared test
## 
## data:  pga_co_cl$COTWIN_clusters and fit$classification
## X-squared = 3.9121, df = 3, p-value = 0.2711

Ameijeiras-Alonso et al. Excess Mass Fit

## [1] "Bimodality P-value of PGA3 using Ameijeiras-Alonso et al. Excess Mass Fit is: 0.389"

Bimodality Coefficient

##      sub_twins_MZ$PGA3
## [1,]             FALSE
## [1] "Bimodality Coefficient of PGA3 is: 0.4, which is less than 0.555, so no bimodality detected."

Cheng and Hall Excess Mass

## [1] "Bimodality P-value of PGA3 using Cheng and Hall Excess Mass is: 0.313"

Fisher and Marron Carmer-von Mises

## [1] "Bimodality P-value of PGA3 using Fisher and Marron Carmer-von Mises is: 0.246"

Hall and York Bandwidth test

## [1] "Bimodality P-value of PGA3 using Hall and York Bandwidth test is: 0.203"
Hartigans’ dip test
## [1] "Bimodality P-value of PGA3 using Hartigans' dip test is: 0.876"

Sliverman Bandwidth

## [1] "Bimodality P-value of PGA3 using Sliverman Bandwidth is: 0.416"

mixR

## [1] "Bimodality P-value of PGA3 using mixR is: 0"

Use KS test to assess pairwise clusters in PGA3

## [1] "P-value for ks test between concordant and discordant_A is: 0.38"
## [1] "P-value for ks test between concordant and discordant_B is: 0.08"
## [1] "P-value for ks test between concordant and intermediate is: 0.51"
## [1] "P-value for ks test between discordant_A and discordant_B is: 0.3"
## [1] "P-value for ks test between discordant_A and intermediate is: 0.63"
## [1] "P-value for ks test between discordant_B and intermediate is: 0.4"

Use CVM test to assess pairwise clusters in PGA3

## [1] "P-value for cvm test between concordant and discordant_A is: 0.44"
## [1] "P-value for cvm test between concordant and discordant_B is: 0.03"
## [1] "P-value for cvm test between concordant and intermediate is: 0.41"
## [1] "P-value for cvm test between discordant_A and discordant_B is: 0.47"
## [1] "P-value for cvm test between discordant_A and intermediate is: 0.57"
## [1] "P-value for cvm test between discordant_B and intermediate is: 0.42"

Use DTS test to assess pairwise clusters in PGA3

## [1] "P-value for DTS test between concordant and discordant_A is: 0.35"
## [1] "P-value for DTS test between concordant and discordant_B is: 0.03"
## [1] "P-value for DTS test between concordant and intermediate is: 0.14"
## [1] "P-value for DTS test between discordant_A and discordant_B is: 0.4"
## [1] "P-value for DTS test between discordant_A and intermediate is: 0.27"
## [1] "P-value for DTS test between discordant_B and intermediate is: 0.23"

Use AD test to assess pairwise clusters in PGA3

## [1] "P-value for AD test between concordant and discordant_A is: 0.31"
## [1] "P-value for AD test between concordant and discordant_B is: 0.03"
## [1] "P-value for AD test between concordant and intermediate is: 0.36"
## [1] "P-value for AD test between discordant_A and discordant_B is: 0.52"
## [1] "P-value for AD test between discordant_A and intermediate is: 0.4"
## [1] "P-value for AD test between discordant_B and intermediate is: 0.44"