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The effect of diet type and nutrients on blood glucose levels using - - PowerPoint PPT Presentation

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The effect of diet type and nutrients on blood glucose levels using Fosr models Nihan Acar-Denizli 1 Pedro Delicado 2 Belchin Adriyanov Kostov 1 2 az-Rizzolo 3 Diana A. D o 4 Ramon Gomis 3 Antoni Sis 1 Mimar Sinan G uzel Sanatlar

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SLIDE 1

The effect of diet type and nutrients on blood glucose levels using Fosr models

Nihan Acar-Denizli 1 Pedro Delicado 2 Belchin Adriyanov Kostov 1 2 Diana A. D´ ıaz-Rizzolo 3 Antoni Sis´

  • 4

Ramon Gomis 3

1Mimar Sinan G¨

uzel Sanatlar ¨ Universitesi Istanbul, Turkey

2Universitat Polit`

ecnica de Catalunya Barcelona,Spain

3IDIBAPS

Barcelona, Spain

4CAPSBE

Barcelona, Spain

24 May 2019

24 May 2019 1 / 46

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SLIDE 2

MOTIVATION

24 May 2019 2 / 46

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SLIDE 3

AIMS

The main objective of this study is to analyze the effect of quinoa consumption and the products made from it for the prevention of type 2 diabetes mellitus. To provide a functional data framework in order to model the effect of diet type, patient and nutrient intake on monitored blood glucose levels.

24 May 2019 3 / 46

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SLIDE 4

Design of the Study

Subjects followed a diet based on the decided nutrients (first 14 days a regular diet and then a quinoa based diet).

24 May 2019 4 / 46

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SLIDE 5

Design of the Study

During that time their blood glucose levels have been monitored by using a sensor repeatedly each 15 minutes.

24 May 2019 5 / 46

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SLIDE 6

Design of the Study

24 May 2019 6 / 46

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SLIDE 7

Data

9 patients with prediabetes have been followed up. 14 days with a regular diet, 14 days a diet based on quinoa products. Totally 222 curves with measurements at discrete time points. For each day the amount of intaken nutrients are recorded. There are totally 142 different type of nutrients related to each day.

24 May 2019 7 / 46

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SLIDE 8

Data

Consider the glucose curve g(t), measuring the glucose concentration as a function of time (in minutes) corresponding to breakfast. We use the concentration values half an hour before, and 2 hours after the meal: t ∈ [−30, 120]. t = 0 indicates the beginning of breakfast. Breakfast glucose curves are considered as functional response.

24 May 2019 8 / 46

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SLIDE 9

Original glucose measurements of patients for regular diet

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100 50 150

1st patient regular diet

Time Glucose

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100 50 150

2nd patient regular diet

Time Glucose

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100 50 150

3th patient regular diet

Time Glucose

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100 50 150

4th patient regular diet

Time Glucose

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5th patient regular diet

Time Glucose

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100 50 150

6th patient regular diet

Time Glucose

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7th patient regular diet

Time Glucose

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8th patient regular diet

Time Glucose

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100 50 150

9th patient regular diet

Time Glucose

  • 24 May 2019

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SLIDE 10

Original glucose measurements of patients for quinoa diet

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100 50 150

1st patient quinoa diet

Time Glucose

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100 50 150

2nd patient quinoa diet

Time Glucose

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100 50 150

3th patient quinoa diet

Time Glucose

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100 50 150

4th patient quinoa diet

Time Glucose

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100 50 150

5th patient quinoa diet

Time Glucose

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100 50 150

6th patient quinoa diet

Time Glucose

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100 50 150

7th patient quinoa diet

Time Glucose

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100 50 150

8th patient quinoa diet

Time Glucose

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100 50 150

9th patient quinoa diet

Time Glucose

  • 24 May 2019

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SLIDE 11

Functional Data Analysis The Steps of Functional Data Analysis:

1

Interpolation in the interval [−30, 120].

24 May 2019 11 / 46

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SLIDE 12

Interpolated glucose curves of patients for regular diet

50 100 100 200

patient 1 regular diet

Time Glucose 50 100 100 200

patient 2 regular diet

Time Glucose 50 100 100 200

patient 3 regular diet

Time Glucose 50 100 100 200

patient 4 regular diet

Time Glucose 50 100 100 200

patient 5 regular diet

Time Glucose 50 100 100 200

patient 6 regular diet

Time Glucose 50 100 100 200

patient 7 regular diet

Time Glucose 50 100 100 200

patient 8 regular diet

Time Glucose 50 100 100 200

patient 9 regular diet

Time Glucose

24 May 2019 12 / 46

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SLIDE 13

Interpolated glucose curves of patients for quinoa diet

50 100 100 200

patient 1 quinoa diet

Time Glucose 50 100 100 200

patient 2 quinoa diet

Time Glucose 50 100 100 200

patient 3 quinoa diet

Time Glucose 50 100 100 200

patient 4 quinoa diet

Time Glucose 50 100 100 200

patient 5 quinoa diet

Time Glucose 50 100 100 200

patient 6 quinoa diet

Time Glucose 50 100 100 200

patient 7 quinoa diet

Time Glucose 50 100 100 200

patient 8 quinoa diet

Time Glucose 50 100 100 200

patient 9 quinoa diet

Time Glucose

24 May 2019 13 / 46

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SLIDE 14

Functional Data Analysis The Steps of Functional Data Analysis:

1

Interpolation in the interval [−30, 120].

2

Registration of the curves by using warping functions ("fdapace").

24 May 2019 14 / 46

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SLIDE 15

Raw and aligned patient curves by using warping function indicated by diet factor

50 100 100 160

Raw 1 th patient

x Y 50 100 100 160

Aligned 1 th patient

x Y 50 100 80 120 180

Raw 2 th patient

x Y 50 100 80 120

Aligned 2 th patient

x Y 50 100 80 120 180

Raw 3 th patient

x Y 50 100 80 120 180

Aligned 3 th patient

x Y 50 100 50 150

Raw 4 th patient

x Y 50 100 50 150

Aligned 4 th patient

x Y 50 100 80 140 200

Raw 5 th patient

x Y 50 100 80 140 200

Aligned 5 th patient

x Y 50 100 80 120

Raw 6 th patient

x Y 50 100 80 120

Aligned 6 th patient

x Y 50 100 100 200

Raw 7 th patient

x Y 50 100 100 200

Aligned 7 th patient

x Y 50 100 50 150

Raw 8 th patient

x Y 50 100 50 150

Aligned 8 th patient

x Y 50 100 100 200

Raw 9 th patient

x Y 50 100 100 200

Aligned 9 th patient

x Y

24 May 2019 15 / 46

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SLIDE 16

Raw versus Aligned Functional Data

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Raw total curves

Time Glucose 50 100 50 100 150 200

Aligned total curves

Time Glucose 24 May 2019 16 / 46

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SLIDE 17

Functional Data Analysis The Steps of Functional Data Analysis:

1

Interpolation in the interval [−30, 120].

2

Registration of the curves by using warping functions ("fdapace").

3

Smoothing of the curves by using B-spline functions.

24 May 2019 17 / 46

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SLIDE 18

Raw versus Smoothed Functional Data

50 100 50 100 150 200

Glucose Curves

Time Glucose 50 100 50 100 150 200

Smoothed Glucose Curves

Time Glucose 24 May 2019 18 / 46

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SLIDE 19

Functional Data Analysis The Steps of Functional Data Analysis:

1

Interpolation in the interval [−30, 120].

2

Registration of the curves by using warping functions ("fdapace").

3

Smoothing of the curves by using B-spline functions.

4

Univariate function on scalar regression (fosr) to examine how the diet type, patient and nutrients affect the breakfast glucose curves.

24 May 2019 19 / 46

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SLIDE 20

Functional regression model for breakfast glucose curves We study how the following explanatory variables affect the glucose curves: Diet indicator (Regular diet / Quinoa diet). Patient indicator (1 to 9). Breakfast contents in different nutrients (K scalar explanatory variables). We use the function on scalar regression (fosr) model: gij(t) = β0(t) + αi(t) +

K

  • k=1

xij

k βk(t) + Ij RβR(t) + Ij QβQ(t) + εij(t),

where i = 1, . . . , n indicates the patient (n = 9), j = 1, . . . , J indicates the day of

  • bservation (J = 28), xij

k , k = 1, . . . , K, is the content of nutrient k in the breakfast

that patient i takes in the day j, Ij

R takes value 1 for regular diet, and 0 for Quinoa diet,

Ij

Q = 1 − Ij R is the indicator of Quinoa diet, and εij(t) is a random noise function with

expected value 0 for all t, and independent from noise function corresponding to other days or patients. The overall shape of glucose curves is described by the functional coefficient β0(t). The diet effect is summarized by the functions βR(t) and βQ(t) that, by construction, verify that βR(t) = −βQ(t). Functions αi(t) measure the individual effects. βk(t) function shows the effect of nutrient k.

24 May 2019 20 / 46

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SLIDE 21

Functional regression model using only the diet factor gij(t) = β0(t) + Ij

RβR(t) + Ij QβQ(t) + εij(t),

50 100 100 110 120 130 140 150 Coefficient function 50 100 −5 5 Coefficient function 50 100 −5 5 Coefficient function

24 May 2019 21 / 46

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SLIDE 22

Functional regression model using only the patient factor gij(t) = β0(t) + αi(t) + εij(t),

50 100 100 130 Coefficient function 50 100 −40 20 Coefficient function 50 100 −40 20 Coefficient function 50 100 −40 20 Coefficient function 50 100 −40 20 Coefficient function 50 100 −40 20 Coefficient function 50 100 −40 20 Coefficient function 50 100 −40 20 Coefficient function 50 100 −40 20 Coefficient function 50 100 −40 20 Coefficient function

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SLIDE 23

Functional regression model using both the diet and the patient factor gij(t) = β0(t) + Ij

RβR(t) + Ij QβQ(t) + αi(t) + εij(t),

50 100 100 130 Coefficient function 50 100 −6 4 Coefficient function 50 100 −6 4 Coefficient function 50 100 −40 20 Coefficient function 50 100 −40 20 Coefficient function 50 100 −40 20 Coefficient function 50 100 −40 20 Coefficient function 50 100 −40 20 Coefficient function 50 100 −40 20 Coefficient function 50 100 −40 20 Coefficient function 50 100 −40 20 Coefficient function 50 100 −40 20 Coefficient function

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SLIDE 24

Fosr model with Fructosa as explanatory variable gij(t) = β0(t) + xij

k βk(t) + εij(t), k ≡ Fructosa

50 100 100 110 120 130 140

Intercept

Coefficient function 50 100 −1 1 2 3 4 5

Fructosa

Coefficient function

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SLIDE 25

Statistics related to Fosr models with one nutrient as explanatory variable gij(t) = β0(t) + xij

k βk(t) + εij(t), k ≡ Fructosa

50 100 −1 1 2 3 4 5

Fructosa

time Coefficient function prop.sign 50 100 1 2 3 4

Cumulated t−value

time t−value(time)

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SLIDE 26

Significant variables using permutation tests gij(t) = β0(t) + xij

k βk(t) + εij(t), k = 1, . . . , K.

  • 0.0

0.2 0.4 0.6 0.8 1.0 50 100 150 prop.sign cum.t.val

Energía Proteínas Hidratos.Carbono Fibra.vegetal Lípidos Colesterol AGS AGM AGP Calcio Hierro Sodio Vit..A Vit..B1 Vit..B2 Ac.Fólico Vit..C Alcohol Almidón Azúcares.sencillos Glucosa Fructosa Galactosa Sacarosa Maltosa Lactosa Fibra.soluble Fibra.insoluble Agua C14.0 C16.0 C18.0 C16.1 C18.1 C18.2 C18.3 C20.4 Niacina Niacina.preformada Vit..B6 Ac.Fólico.añadido Folatos.alimentarios Vit..B12 Retinol Carotenos Carotenoides.totales a.Caroteno B.Caroteno B.Criptoxantina Luteína Zeaxantina Vit..D Vit.E Tocoferoles.totales a.Tocoferol B.Tocoferol G.Tocoferol D.Tocoferol Yodo Zinc Magnesio Potasio Manganeso Cobalto Cobre Níquel Cromo Aluminio Fósforo Cloro Flúor Selenio Bromo Cistina Histidina Isoleucina Leucina Lisina Metionina Fenilalanina Serina Treonina Triptófano Tirosina Valina Arginina Ac.Glutámico C20.5 C22.5 C22.6 Vit..K Ac.Pantoténico Biotina Fosfatidilcolina Licopeno Fitosteroles Azufre Ac.Grasos.cis Ac.Grasos.trans AGM.cis AGP.cis AGP.w6 AGP.w3 AGM.trans AGP.trans Celulosa Polisacáridos.solubl Polisacáridos.insolu Lignina Ac.Fítico Purinas Adenina Guanina Ac.Org.Disp. Ac.Málico Ac.Cítrico Ac.Oxálico Ac.Acético Ac.Láctico Cafeína Teobromina B.Sitosterol Campesterol Estigmasterol Alanina Ac.Aspártico Glicina Prolina Hidroxiprolina I.glicémico CG Colina ORAC FRAP TRAP TEAC N1 N2 X.EProteínas X.ELípidos X.EHC X.EAlcohol Y

24 May 2019 26 / 46

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SLIDE 27

Nutrient Variables sorted by prop.sign

No Nutriente prop.sign No Nutriente prop.sign No Nutriente prop.sign No Nutriente prop.sign No Nutriente prop.sign 1 X.EProteínas 1 45 I.glicémico 0.581 84 Licopeno 0.194 99 Energía 143 Oligosacáridos NA 2 X.EHC 1 46 Maltosa 0.548 85 TEAC 0.194 100 Fibra.vegetal 144 Almidón.res. NA 3 Hidratos.Carbono 0.968 47 Glicina 0.548 86 Vit..D 0.129 101 Lípidos 145 Ac.Tartárico NA 4 Bromo 0.903 48 a.Tocoferol 0.516 87 G.Tocoferol 0.129 102 Colesterol 146 Estigmasterol.D7 NA 5 Polisacáridos.solubl 0.903 49 Azufre 0.516 88 AGP.cis 0.129 103 AGM 147 Brásica.esterol NA 6 Lignina 0.903 50 Almidón 0.484 89 C16.0 0.097 104 AGP 148 Avenaesterol.D5 NA 7 Fibra.soluble 0.871 51 Sacarosa 0.484 90 Yodo 0.097 105 Hierro 149 Avenaesterol.D7 NA 8 Fibra.insoluble 0.871 52 Tocoferoles.totales 0.484 91 Triptófano 0.097 106 Vit..B1 150 Otros.fitosteroles NA 9 Ac.Glutámico 0.871 53 Celulosa 0.484 92 AGP.w6 0.097 107 Vit..B2 151 Quercetina NA 10 Ac.Láctico 0.871 54 Lactosa 0.452 93 C18.2 0.065 108 Alcohol 152 N3 NA 11 Manganeso 0.839 55 Metionina 0.452 94 C22.6 0.065 109 Galactosa 153 N4 NA 12 AGP.trans 0.839 56 Proteínas 0.419 95 C18.0 0.032 110 C18.1 154 N5 NA 13 Biotina 0.806 57 Agua 0.419 96 Cobalto 0.032 111 C18.3 155 N6 NA 14 AGM.trans 0.806 58 Cistina 0.419 97 Serina 0.032 112 C20.4 156 N7 NA 15 Teobromina 0.774 59 Ac.Cítrico 0.419 98 Ac.Grasos.cis 0.032 113 Ac.Fólico.añadido 157 N8 NA 16 Carotenos 0.742 60 Ac.Pantoténico 0.387 114 Vit..B12 158 N9 NA 17 a.Caroteno 0.742 61 AGS 0.355 115 B.Tocoferol 159 N10 NA 18 Ac.Acético 0.742 62 Vit..C 0.355 116 D.Tocoferol 160 COSTE NA 19 ORAC 0.742 63 C14.0 0.355 117 Zinc 20 Sodio 0.71 64 Carotenoides.totales 0.355 118 Potasio 21 Azúcares.sencillos 0.71 65 Luteína 0.355 119 Cobre 22 B.Caroteno 0.71 66 Zeaxantina 0.355 120 Níquel 23 Histidina 0.677 67 Ac.Fólico 0.323 121 Cromo 24 Lisina 0.677 68 B.Criptoxantina 0.323 122 Aluminio 25 Tirosina 0.677 69 Ac.Org.Disp. 0.323 123 Cloro 26 Estigmasterol 0.677 70 Retinol 0.29 124 Flúor 27 Alanina 0.677 71 Vit.E 0.29 125 C20.5 28 Prolina 0.677 72 Fenilalanina 0.29 126 C22.5 29 CG 0.677 73 Calcio 0.258 127 Vit..K 30 Fructosa 0.645 74 Vit..B6 0.258 128 Fosfatidilcolina 31 Isoleucina 0.645 75 Folatos.alimentarios 0.258 129 AGM.cis 32 Leucina 0.645 76 Magnesio 0.258 130 AGP.w3 33 Treonina 0.645 77 Arginina 0.258 131 Polisacáridos.insolu 34 Valina 0.645 78 TRAP 0.258 132 Ac.Fítico 35 Fitosteroles 0.645 79 Selenio 0.226 133 Purinas 36 Cafeína 0.645 80 Ac.Grasos.trans 0.226 134 Adenina 37 Campesterol 0.645 81 Vit..A 0.194 135 Guanina 38 Ac.Aspártico 0.645 82 Niacina 0.194 136 Ac.Oxálico 39 X.ELípidos 0.645 83 Niacina.preformada 0.194 137 Hidroxiprolina 40 Glucosa 0.613 138 Colina 41 C16.1 0.613 139 FRAP 42 Fósforo 0.613 140 N1 43 B.Sitosterol 0.613 141 N2 44 Ac.Málico 0.581 142 X.EAlcohol

24 May 2019 27 / 46

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SLIDE 28

Function on scalar regression with significant variables I gij(t) = β0(t) + xij

k βk(t) + εij(t), k = 1, . . . , 83.

50 100 −2.5 −1.0 0.0

X.EProteínas

time values 50 100 0.2 0.6 1.0

X.EHC

time values 50 100 0.0 0.4 0.8

Hidratos.Carbono

time values 50 100 −0.12 −0.04

Bromo

time values 50 100 5 10

Polisacáridos.solubl

time values 50 100 20 40

Lignina

time values 50 100 5 15

Fibra.soluble

time values 50 100 4 8

Fibra.insoluble

time values 50 100 −0.008 −0.002

Ac.Glutámico

time values 50 100 −50 −20

Ac.Láctico

time values 50 100 5 15

Manganeso

time values 50 100 −50 50 150

AGP.trans

time values 50 100 −0.5 1.0 2.5

Biotina

time values 50 100 50 100

AGM.trans

time values 50 100 −0.5 1.0 2.0

Teobromina

time values

24 May 2019 28 / 46

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SLIDE 29

Function on scalar regression with significant variables II gij(t) = β0(t) + xij

k βk(t) + εij(t), k = 1, . . . , 83.

50 100 0.00 0.10

Carotenos

time values 50 100 −0.1 0.2 0.4

a.Caroteno

time values 50 100 −2000 4000

Ac.Acético

time values 50 100 −0.002 0.006

ORAC

time values 50 100 −0.04 −0.01

Sodio

time values 50 100 0.0 1.0

Azúcares.sencillos

time values 50 100 0.00 0.10

B.Caroteno

time values 50 100 −0.06 −0.02

Histidina

time values 50 100 −0.020 0.000

Lisina

time values 50 100 −0.04 −0.01

Tirosina

time values 50 100 −5 5 15

Estigmasterol

time values 50 100 −0.04 −0.01

Alanina

time values 50 100 −0.020 −0.005

Prolina

time values 50 100 0.0 1.0

CG

time values 50 100 −1 1 3 5

Fructosa

time values

24 May 2019 29 / 46

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SLIDE 30

Function on scalar regression with significant variables III gij(t) = β0(t) + xij

k βk(t) + εij(t), k = 1, . . . , 83.

50 100 −0.03 −0.01

Isoleucina

time values 50 100 −0.015 0.000

Leucina

time values 50 100 −0.04 −0.01

Treonina

time values 50 100 −0.025 −0.005

Valina

time values 50 100 −1 1 2

Fitosteroles

time values 50 100 −0.8 −0.2

Cafeína

time values 50 100 −10 5 15

Campesterol

time values 50 100 −0.015 0.000

Ac.Aspártico

time values 50 100 −0.8 −0.2

X.ELípidos

time values 50 100 2 4 6

Glucosa

time values 50 100 −40 −10 10

C16.1

time values 50 100 −0.05 −0.01

Fósforo

time values 50 100 −1 1 3

B.Sitosterol

time values 50 100 −40 40

Ac.Málico

time values 50 100 −0.2 0.1 0.3

I.glicémico

time values

24 May 2019 30 / 46

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SLIDE 31

Function on scalar regression with significant variables IV gij(t) = β0(t) + xij

k βk(t) + εij(t), k = 1, . . . , 83.

50 100 −10 20 40

Maltosa

time values 50 100 −0.04 −0.01

Glicina

time values 50 100 5 15

a.Tocoferol

time values 50 100 −250 −50

Azufre

time values 50 100 −0.2 0.4 1.0

Almidón

time values 50 100 −1 1 3

Sacarosa

time values 50 100 5 10

Tocoferoles.totales

time values 50 100 5 15

Celulosa

time values 50 100 −1.5 0.0 1.5

Lactosa

time values 50 100 −0.05 −0.01

Metionina

time values 50 100 −1.0 −0.4 0.2

Proteínas

time values 50 100 −0.05 0.05

Agua

time values 50 100 −0.01 0.02

Cistina

time values 50 100 −5 5 15

Ac.Cítrico

time values 50 100 −5 5 15

Ac.Pantoténico

time values

24 May 2019 31 / 46

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SLIDE 32

Function on scalar regression with significant variables V gij(t) = β0(t) + xij

k βk(t) + εij(t), k = 1, . . . , 83.

50 100 −2.0 −0.5 0.5

AGS

time values 50 100 −0.1 0.1 0.3

Vit..C

time values 50 100 −10 5

C14.0

time values 50 100 −0.02 0.04

Carotenoides.totales

time values 50 100 0.0 0.2

Luteína

time values 50 100 −0.1 0.1 0.3

Zeaxantina

time values 50 100 −0.05 0.15 0.30

Ac.Fólico

time values 50 100 −0.01 0.03

B.Criptoxantina

time values 50 100 −5 5 10

Ac.Org.Disp.

time values 50 100 −0.08 0.00

Retinol

time values 50 100 −2 2 4 6

Vit.E

time values 50 100 −0.03 −0.01

Fenilalanina

time values 50 100 −0.04 0.00

Calcio

time values 50 100 −20 10 40

Vit..B6

time values 50 100 0.0 0.2

Folatos.alimentarios

time values

24 May 2019 32 / 46

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SLIDE 33

Function on scalar regression with significant variables VI gij(t) = β0(t) + xij

k βk(t) + εij(t), k = 1, . . . , 83.

50 100 −0.20 0.00

Magnesio

time values 50 100 −0.030 −0.005

Arginina

time values 50 100 −0.6 −0.2

TRAP

time values 50 100 −0.4 0.0 0.4

Selenio

time values 50 100 −20 20

Ac.Grasos.trans

time values 50 100 −0.08 −0.02

Vit..A

time values 50 100 −2.0 −0.5 1.0

Niacina

time values 50 100 −2 1 2

Niacina.preformada

time values

24 May 2019 33 / 46

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SLIDE 34

Clustering of 83 nutrient functions

X.EProteínas Bromo Fósforo C14.0 Vit..A Azufre Retinol TRAP Magnesio AGS Fenilalanina Metionina Proteínas Ac.Aspártico Leucina Valina C16.1 Isoleucina Treonina Glicina Sodio X.ELípidos Cafeína Ac.Láctico Tirosina Prolina Ac.Glutámico Histidina Lisina Alanina X.EHC Hidratos.Carbono CG Fibra.insoluble Fibra.soluble Manganeso Polisacáridos.solubl Lignina AGP.trans AGM.trans Carotenos B.Caroteno a.Tocoferol Tocoferoles.totales Campesterol Fitosteroles B.Sitosterol Ac.Acético Estigmasterol Ac.Málico Sacarosa Biotina Teobromina a.Caroteno ORAC Azúcares.sencillos Fructosa Glucosa Luteína Zeaxantina Vit..B6 Ac.Fólico Folatos.alimentarios Carotenoides.totales Vit..C Celulosa B.Criptoxantina Agua Ac.Pantoténico Ac.Cítrico Ac.Org.Disp. Ac.Grasos.trans Lactosa Calcio Selenio Niacina Niacina.preformada Almidón Cistina Maltosa Vit.E I.glicémico Licopeno 200 400 600 800

Cluster Dendrogram

hclust (*, "ward.D") as.dist(d) Height

24 May 2019 34 / 46

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SLIDE 35

Clustering of 83 nutrient functions

5 10 15 20 25 30 −15 −10 −5 5 10

Gruop Means of 83 Coefficient Functions

t X(t)

24 May 2019 35 / 46

slide-36
SLIDE 36

Significant variables using permutation tests including diet and patient levels gij(t) = β0(t) + αi(t) + xij

k βk(t) + Ij RβR(t) + Ij QβQ(t) + εij(t), k = 1, . . . , K.

  • 0.0

0.2 0.4 0.6 0.8 1.0 20 40 60 80 100 120 prop.sign.f cum.t.val.f

Energía Proteínas Hidratos.Carbono Fibra.vegetal Lípidos Colesterol AGS AGM AGP Calcio Hierro Sodio Vit..A Vit..B1 Vit..B2 Ac.Fólico Vit..C Alcohol Almidón Azúcares.sencillos Glucosa Fructosa Galactosa Sacarosa Maltosa Lactosa Fibra.soluble Fibra.insoluble Agua C14.0 C16.0 C18.0 C16.1 C18.1 C18.2 C18.3 C20.4 Niacina Niacina.preformada Vit..B6 Ac.Fólico.añadido Folatos.alimentarios Vit..B12 Retinol Carotenos Carotenoides.totales a.Caroteno B.Caroteno B.Criptoxantina Luteína Zeaxantina Vit..D Vit.E Tocoferoles.totales a.Tocoferol B.Tocoferol G.Tocoferol D.Tocoferol Yodo Zinc Magnesio Potasio Manganeso Cobalto Cobre Níquel Cromo Aluminio Fósforo Cloro Flúor Selenio Bromo Cistina Histidina Isoleucina Leucina Lisina Metionina Fenilalanina Serina Treonina Triptófano Tirosina Valina Arginina Ac.Glutámico C20.5 C22.5 C22.6 Vit..K Ac.Pantoténico Biotina Fosfatidilcolina Licopeno Fitosteroles Azufre Ac.Grasos.cis Ac.Grasos.trans AGM.cis AGP.cis AGP.w6 AGP.w3 AGM.trans AGP.trans Celulosa Polisacáridos.solubl Polisacáridos.insolu Lignina Ac.Fítico Purinas Adenina Guanina Ac.Org.Disp. Ac.Málico Ac.Cítrico Ac.Oxálico Ac.Acético Ac.Láctico Cafeína Teobromina B.Sitosterol Campesterol Estigmasterol Alanina Ac.Aspártico Glicina Prolina Hidroxiprolina I.glicémico CG Colina ORAC FRAP TRAP TEAC N1 N2 X.EProteínas X.ELípidos X.EHC X.EAlcohol

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slide-37
SLIDE 37

Nutrient Variables sorted by prop.sign including diet and patient levels

No Nutriente prop.sign No Nutriente prop.sign No Nutriente prop.sign No Nutriente prop.sign No Nutriente prop.sign 1 Polisacáridos.solubl 1,000 34 Azúcares.sencillos 0,194 60 Proteínas 102 Lisina 143 Oligosacáridos NA 2 B.Criptoxantina 0,968 35 Colina 0,194 61 Fibra.vegetal 103 Metionina 144 Almidón.res. NA 3 Zeaxantina 0,968 36 Hidratos.Carbono 0,161 62 Lípidos 104 Fenilalanina 145 Ac.Tartárico NA 4 Lignina 0,968 37 Vit..B1 0,161 63 AGS 105 Serina 146 Estigmasterol.D7 NA 5 Fibra.soluble 0,935 38 Cloro 0,161 64 Hierro 106 Treonina 147 Brásica.esterol NA 6 Celulosa 0,935 39 Ac.Acético 0,161 65 Sodio 107 Triptófano 148 Avenaesterol.D5 NA 7 Luteína 0,839 40 Ac.Láctico 0,161 66 Vit..B2 108 Tirosina 149 Avenaesterol.D7 NA 8 Carotenoides.totales 0,806 41 Teobromina 0,161 67 Alcohol 109 Valina 150 Otros.fitosteroles NA 9 Vit..C 0,774 42 CG 0,129 68 Almidón 110 Arginina 151 Quercetina NA 10 Fibra.insoluble 0,774 43 AGM 0,097 69 Galactosa 111 Ac.Glutámico 152 N3 NA 11 a.Tocoferol 0,774 44 Calcio 0,097 70 Maltosa 112 C20.5 153 N4 NA 12 I.glicémico 0,742 45 C18.1 0,097 71 C14.0 113 C22.5 154 N5 NA 13 Ac.Cítrico 0,710 46 Retinol 0,097 72 C16.0 114 C22.6 155 N6 NA 14 X.EProteínas 0,710 47 Ac.Pantoténico 0,097 73 C18.0 115 Vit..K 156 N7 NA 15 Ac.Org.Disp. 0,613 48 B.Sitosterol 0,097 74 C16.1 116 Biotina 157 N8 NA 16 Cafeína 0,613 49 Estigmasterol 0,097 75 C18.3 117 Fosfatidilcolina 158 N9 NA 17 Glucosa 0,581 50 Energía 0,065 76 C20.4 118 Azufre 159 N10 NA 18 Lactosa 0,581 51 Colesterol 0,065 77 Niacina 119 Ac.Grasos.cis 160 COSTE NA 19 Carotenos 0,581 52 AGP 0,065 78 iacina.preformad 120 Ac.Grasos.trans 20 B.Caroteno 0,581 53 C18.2 0,065 79 Vit..B6 121 AGM.cis 21 Tocoferoles.totales 0,548 54 Fósforo 0,065 80 Ac.Fólico.añadido 122 AGP.cis 22 Fructosa 0,516 55 AGP.w6 0,065 81 Vit..B12 123 AGP.w3 23 ORAC 0,516 56 X.ELípidos 0,065 82 Vit..D 124 AGM.trans 24 Sacarosa 0,484 57 Vit..A 0,032 83 B.Tocoferol 125 AGP.trans 25 X.EHC 0,452 58 Fitosteroles 0,032 84 D.Tocoferol 126 Polisacáridos.insolu 26 Folatos.alimentarios 0,419 59 Guanina 0,032 85 Yodo 127 Ac.Fítico 27 G.Tocoferol 0,419 86 Zinc 128 Purinas 28 Ac.Málico 0,419 87 Magnesio 129 Adenina 29 Ac.Fólico 0,323 88 Potasio 130 Ac.Oxálico 30 Licopeno 0,323 89 Manganeso 131 Campesterol 31 a.Caroteno 0,290 90 Cobalto 132 Alanina 32 Vit.E 0,290 91 Cobre 133 Ac.Aspártico 33 Agua 0,258 92 Níquel 134 Glicina 93 Cromo 135 Prolina 94 Aluminio 136 Hidroxiprolina 95 Flúor 137 FRAP 96 Selenio 138 TRAP 97 Bromo 139 TEAC 98 Cistina 140 N1 99 Histidina 141 N2 100 Isoleucina 142 X.EAlcohol 101 Leucina

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slide-38
SLIDE 38

Function on scalar regression with significant nutrients including diet and patient levels I gij(t) = β0(t) + αi(t) + xij

k βk(t) + Ij RβR(t) + Ij QβQ(t) + εij(t), k = 1, . . . , 33.

50 100 5 15

Polisacáridos.solubl

time values 50 100 0.00 0.04 0.08

B.Criptoxantina

time values 50 100 0.0 0.3

Zeaxantina

time values 50 100 20 40

Lignina

time values 50 100 10 20

Fibra.soluble

time values 50 100 5 15

Celulosa

time values 50 100 0.0 0.2 0.4

Luteína

time values 50 100 −0.02 0.04 0.10

Carotenoides.totales

time values 50 100 −0.1 0.2 0.5

Vit..C

time values 50 100 4 8

Fibra.insoluble

time values 50 100 10 20

a.Tocoferol

time values 50 100 −0.4 0.2 0.6

I.glicémico

time values 50 100 −5 5 15

Ac.Cítrico

time values 50 100 −1.5 −0.5 0.5

X.EProteínas

time values 50 100 −5 5 15

Ac.Org.Disp.

time values

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slide-39
SLIDE 39

Function on scalar regression with significant nutrients including diet and patient levels II gij(t) = β0(t) + αi(t) + xij

k βk(t) + Ij RβR(t) + Ij QβQ(t) + εij(t), k = 1, . . . , 33.

50 100 −0.2 0.2 0.6

Cafeína

time values 50 100 −2 2 4 6

Glucosa

time values 50 100 −3 −1 1

Lactosa

time values 50 100 0.00 0.10

Carotenos

time values 50 100 0.00 0.10

B.Caroteno

time values 50 100 5 10

Tocoferoles.totales

time values 50 100 −1 1 3 5

Fructosa

time values 50 100 −0.002 0.006

ORAC

time values 50 100 −2 2 4

Sacarosa

time values 50 100 −0.2 0.2 0.6

X.EHC

time values 50 100 −0.1 0.1 0.3

Folatos.alimentarios

time values 50 100 −60 40

G.Tocoferol

time values 50 100 −20 20

Ac.Málico

time values 50 100 0.0 0.2

Ac.Fólico

time values 50 100 −0.010 0.010

Licopeno

time values

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slide-40
SLIDE 40

Function on scalar regression with significant nutrients including diet and patient levels III gij(t) = β0(t) + αi(t) + xij

k βk(t) + Ij RβR(t) + Ij QβQ(t) + εij(t), k = 1, . . . , 33.

50 100 −0.2 0.0 0.2

a.Caroteno

time values 50 100 −2 2 4 6

Vit.E

time values 50 100 −0.05 0.05

Agua

time values

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slide-41
SLIDE 41

Clustering of 33 nutrient functions

Glucosa Vit.E B.Criptoxantina Zeaxantina Luteína Fibra.insoluble Ac.Cítrico Vit..C Lactosa Lignina a.Tocoferol Celulosa Carotenoides.totales Ac.Fólico Polisacáridos.solubl B.Caroteno a.Caroteno I.glicémico X.EProteínas Fibra.soluble Cafeína Tocoferoles.totales X.EHC Fructosa G.Tocoferol Carotenos Sacarosa Licopeno ORAC Agua Folatos.alimentarios Ac.Org.Disp. Ac.Málico 10000 30000 50000

Cluster Dendrogram

as.dist(d2) Height

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slide-42
SLIDE 42

Clustering of 33 nutrient functions

5 10 15 20 25 30 −1000 1000 2000 3000 4000 5000

Group Means of 33 Coefficient Functions

t X(t)

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slide-43
SLIDE 43

CONCLUSIONS Fosr model with only diet factor shows that diet type is related to glucose and quinoa diet reduces the glucose level. Each patient has a different effect on glucose. Univariate fosr model with nutrients found 83 significant variables. Fosr model including diet, patient effect and one nutrient results 33 significant

  • variables. 31 of them are common with the previous model with different proportion
  • f significance.

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slide-44
SLIDE 44

LIMITATIONS / FUTURE WORK Small sample size Multivariate functional regression model with chosen nutrient variables Which nutrients? Functional data analysis on lunch and dinner or on whole interval How to deal with ”midmorning snack (media manana)” and ”afternoon snack (merienda)”?

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slide-45
SLIDE 45

LIMITATIONS / FUTURE WORK Small sample size Multivariate functional regression model with chosen nutrient variables Which nutrients? Functional data analysis on lunch and dinner or on whole interval How to deal with ”midmorning snack (media manana)” and ”afternoon snack (merienda)”?

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slide-46
SLIDE 46

LIMITATIONS / FUTURE WORK Small sample size Multivariate functional regression model with chosen nutrient variables Which nutrients? Functional data analysis on lunch and dinner or on whole interval How to deal with ”midmorning snack (media manana)” and ”afternoon snack (merienda)”?

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slide-47
SLIDE 47

LIMITATIONS / FUTURE WORK Small sample size Multivariate functional regression model with chosen nutrient variables Which nutrients? Functional data analysis on lunch and dinner or on whole interval How to deal with ”midmorning snack (media manana)” and ”afternoon snack (merienda)”?

24 May 2019 44 / 46

slide-48
SLIDE 48

LIMITATIONS / FUTURE WORK Small sample size Multivariate functional regression model with chosen nutrient variables Which nutrients? Functional data analysis on lunch and dinner or on whole interval How to deal with ”midmorning snack (media manana)” and ”afternoon snack (merienda)”?

24 May 2019 44 / 46

slide-49
SLIDE 49

REFERENCES Febrero-Bande, M., and M. Oviedo De La Fuente (2012). "fda. usc: Functional Data Analysis and Utilities for Statistical Computing (fda.usc). R package version 1.5.0. Goldsmith, J., Scheipl, F., Huang, L., Wrobel, J. et al. (2018). "refund: Regression with Functional Data". R package version 0.1-17. Dai, X., Hadjipantelis, P. Z., Ji, H., Mueller, H. G. and Wang, J. L. (2017). "fdapace: Functional data analysis and empirical dynamics (fdapace). R package version 0.4.0.

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slide-50
SLIDE 50

THANK YOU FOR YOUR ATTENDANCE...

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