Introducción

La enfermedad de Alzheimer (EA) es un trastorno neurodegenerativo progresivo que afecta la memoria, el pensamiento y el comportamiento. Su diagnóstico temprano es crucial para implementar intervenciones que retrasen su progresión. En este estudio, se desarrolla un Modelo Lineal Generalizado (GLM) para predecir el diagnóstico de Alzheimer en función de variables demográficas, clínicas y cognitivas.

Objetivo

Identificar los factores más relevantes asociados al diagnóstico de Alzheimer mediante un modelo estadístico que permita predecir la probabilidad de ser diagnosticado. Para esto se estudiaran individualmenete las variables y luego se buscara la realcion entre estas y la variable respuesta diagnosisi (Diagnostico) para asi pbtener el mejor modelo

Variables del Conjunto de Datos

Este conjunto de datos proporciona un análisis detallado de los factores asociados con la enfermedad de Alzheimer, incluyendo variables demográficas, de estilo de vida, médicas, cognitivas y funcionales. Con un total de 2,149 registros de pacientes

Información del Paciente

Identificación del Paciente

Detalles Demográficos

Factores de Estilo de Vida

Historial Médico

Mediciones Clínicas

Evaluaciones Cognitivas y Funcionales

Síntomas

Información del Diagnóstico

Información Confidencial

Analisis descriptivo univariado

##       Age              Gender             Ethnicity         EducationLevel
##  Min.   :60.00   Masculino:1061   Caucásico    :1278   Ninguno     :446   
##  1st Qu.:67.00   Femenino :1088   Afroamericano: 454   Secundaria  :854   
##  Median :75.00                    Asiático     : 206   Licenciatura:636   
##  Mean   :74.91                    Otro         : 211   Superior    :213   
##  3rd Qu.:83.00                                                            
##  Max.   :90.00                                                            
##       BMI        Smoking   AlcoholConsumption  PhysicalActivity  
##  Min.   :15.01   No:1529   Min.   : 0.002003   Min.   :0.003616  
##  1st Qu.:21.61   Sí: 620   1st Qu.: 5.139810   1st Qu.:2.570626  
##  Median :27.82             Median : 9.934412   Median :4.766424  
##  Mean   :27.66             Mean   :10.039442   Mean   :4.920202  
##  3rd Qu.:33.87             3rd Qu.:15.157931   3rd Qu.:7.427899  
##  Max.   :39.99             Max.   :19.989293   Max.   :9.987429  
##   DietQuality        SleepQuality    FamilyHistoryAlzheimers
##  Min.   :0.009385   Min.   : 4.003   No:1607                
##  1st Qu.:2.458455   1st Qu.: 5.483   Sí: 542                
##  Median :5.076087   Median : 7.116                          
##  Mean   :4.993138   Mean   : 7.051                          
##  3rd Qu.:7.558625   3rd Qu.: 8.563                          
##  Max.   :9.998346   Max.   :10.000                          
##  CardiovascularDisease Diabetes  Depression HeadInjury Hypertension
##  No:1839               No:1825   No:1718    No:1950    No:1829     
##  Sí: 310               Sí: 324   Sí: 431    Sí: 199    Sí: 320     
##                                                                    
##                                                                    
##                                                                    
##                                                                    
##    SystolicBP     DiastolicBP     CholesterolTotal CholesterolLDL  
##  Min.   : 90.0   Min.   : 60.00   Min.   :150.1    Min.   : 50.23  
##  1st Qu.:112.0   1st Qu.: 74.00   1st Qu.:190.3    1st Qu.: 87.20  
##  Median :134.0   Median : 91.00   Median :225.1    Median :123.34  
##  Mean   :134.3   Mean   : 89.85   Mean   :225.2    Mean   :124.34  
##  3rd Qu.:157.0   3rd Qu.:105.00   3rd Qu.:262.0    3rd Qu.:161.73  
##  Max.   :179.0   Max.   :119.00   Max.   :300.0    Max.   :199.97  
##  CholesterolHDL  CholesterolTriglycerides      MMSE          
##  Min.   :20.00   Min.   : 50.41           Min.   : 0.005312  
##  1st Qu.:39.10   1st Qu.:137.58           1st Qu.: 7.167602  
##  Median :59.77   Median :230.30           Median :14.441660  
##  Mean   :59.46   Mean   :228.28           Mean   :14.755132  
##  3rd Qu.:78.94   3rd Qu.:314.84           3rd Qu.:22.161028  
##  Max.   :99.98   Max.   :399.94           Max.   :29.991381  
##  FunctionalAssessment MemoryComplaints BehavioralProblems      ADL           
##  Min.   :0.00046      No:1702          No:1812            Min.   : 0.001288  
##  1st Qu.:2.56628      Sí: 447          Sí: 337            1st Qu.: 2.342836  
##  Median :5.09444                                          Median : 5.038973  
##  Mean   :5.08005                                          Mean   : 4.982958  
##  3rd Qu.:7.54698                                          3rd Qu.: 7.581490  
##  Max.   :9.99647                                          Max.   : 9.999747  
##  Confusion Disorientation PersonalityChanges DifficultyCompletingTasks
##  No:1708   No:1809        No:1825            No:1808                  
##  Sí: 441   Sí: 340        Sí: 324            Sí: 341                  
##                                                                       
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##                                                                       
##  Forgetfulness Diagnosis
##  No:1501       No:1389  
##  Sí: 648       Sí: 760  
##                         
##                         
##                         
##

Diagnosis (Diagnoticado o no)

Se tiene un registro total de 1389 personas sin diagnóstico de Alzheimer y 760 personas con diagnóstico positivo.

Analisis descriptivo Bivariado

Age - Diagnosis

Distribución Edad según diagnóstico
Diagnóstico n Proporción Media Mediana Desv. Estándar
No 1389 64.6% 74.9 75.0 8.9
Sí 760 35.4% 74.8 75.0 9.1

Gender (Genero)

Tabla de Contingencia
No Sí Sum
Masculino 675 386 1061
Femenino 714 374 1088
Sum 1389 760 2149
Note:
Prueba: Chi-cuadrado, p-valor = 0.354

Se evaluó si existe una asociación significativa entre el género (masculino/femenino) y el diagnóstico de Alzheimer (Sí/No) en una muestra de 2,149 individuos. La prueba de Chi-cuadrado se aplicó bajo la siguiente hipótesis:

  • \(H_0\): No existe asociación entre el género y el diagnóstico de Alzheimer (las variables son independientes).

Los resultados mostraron que la distribución de diagnósticos (Sí/No) fue similar entre hombres (36.4% Sí) y mujeres (34.4% Sí). El p-valor obtenido (p = 0.354) supera el nivel de significancia convencional (\(\alpha\) = 0.05), por lo que no se rechaza la hipótesis nula. Esto indica que, no hay evidencia estadística suficiente para afirmar que el género influye en la presencia de Alzheimer.

Ethnicity (Etnia)

Tabla de Contingencia
No Sí Sum
Caucásico 815 463 1278
Afroamericano 308 146 454
Asiático 122 84 206
Otro 144 67 211
Sum 1389 760 2149
Note:
Prueba: Chi-cuadrado, p-valor = 0.098

Se evaluó si existe una asociación significativa entre la etnia (Caucásico/Afroamericano/Asiático/Otro) y el diagnóstico de Alzheimer (Sí/No), esta prueba de Chi-cuadrado se aplicó bajo la siguiente hipótesis:

  • \(H_0\): No existe asociación entre la etnia y el diagnóstico de Alzheimer (las variables son independientes).

El p-valor obtenido (p = 0.098) supera el nivel de significancia convencional (\(\alpha\) = 0.05), por lo que no se rechaza la hipótesis nula. Esto indica que no hay evidencia estadística suficiente para afirmar que la etnia influye en la presencia de Alzheimer.

EducationLevel (Nivel de Educacion)

Tabla de Contingencia
No Sí Sum
Ninguno 272 174 446
Secundaria 552 302 854
Licenciatura 419 217 636
Superior 146 67 213
Sum 1389 760 2149
Note:
Prueba: Chi-cuadrado, p-valor = 0.217

Se evaluó si existe una asociación significativa entre el nivel educativo (Ninguno/Secundaria/Licenciatura/Superior) y el diagnóstico de Alzheimer (Sí/No), esta prueba de Chi-cuadrado se aplicó bajo la siguiente hipótesis:

  • \(H_0\): No existe asociación entre el nivel educativo y el diagnóstico de Alzheimer (las variables son independientes).

El p-valor obtenido (p = 0.217) supera el nivel de significancia convencional (\(\alpha\) = 0.05), por lo que no se rechaza la hipótesis nula. Esto indica que no hay evidencia estadística suficiente para afirmar que el nivel educativo influye en la presencia de Alzheimer.

BMI (Indice de masa corporal)

Distribución BMI según diagnóstico
Diagnóstico n Proporción Media Mediana Desv. Estándar
No 1389 64.6% 27.5 27.6 7.2
Sí 760 35.4% 27.9 28.0 7.3

Smoking (Fuma)

Tabla de Contingencia
No Sí Sum
No 986 543 1529
Sí 403 217 620
Sum 1389 760 2149
Note:
Prueba: Chi-cuadrado, p-valor = 0.860

Se evaluó si existe una asociación significativa entre el historial de tabaquismo (No/Sí) y el diagnóstico de Alzheimer (Sí/No), esta prueba de Chi-cuadrado se aplicó bajo la siguiente hipótesis:

  • \(H_0\): No existe asociación entre el tabaquismo y el diagnóstico de Alzheimer (las variables son independientes).

El p-valor obtenido (p = 0.860) supera ampliamente el nivel de significancia convencional (\(\alpha\) = 0.05), por lo que no se rechaza la hipótesis nula. Esto indica que no hay evidencia estadística que sugiera que el tabaquismo influye en la presencia de Alzheimer.

AlcoholConsumption (consumo de alcohol)

Distribución Consumo Alcohol según diagnóstico
Diagnóstico n Proporción Media Mediana Desv. Estándar
No 1389 64.6% 10.1 10.0 5.8
Sí 760 35.4% 10.0 9.9 5.8

PhysicalActivity (Actividad Fisica)

Distribución Actividad Fisica según diagnóstico
Diagnóstico n Proporción Media Mediana Desv. Estándar
No 1389 64.6% 74.9 75.0 8.9
Sí 760 35.4% 74.8 75.0 9.1

DietQuality (Calidad de la Dieta)

Distribución Calidad del Sueño según diagnóstico
Diagnóstico n Proporción Media Mediana Desv. Estándar
No 1389 64.6% 5.0 5.1 2.9
Sí 760 35.4% 5.0 5.1 2.9

SleepQuality (Calidad del Sueño)

Estadísticos de SleepQuality por Diagnóstico
Diagnóstico n Proporción Media Mediana Desv. Estándar
No 1389 64.6% 7.1 7.2 1.8
Sí 760 35.4% 6.9 6.9 1.8

FamilyHistoryAlzheimers (familiares con alzheimer)

Tabla de Contingencia
No Sí Sum
No 1024 583 1607
Sí 365 177 542
Sum 1389 760 2149
Note:
Prueba: Chi-cuadrado, p-valor = 0.141

Se evaluó si existe una asociación significativa entre el antecedente familiar de Alzheimer (No/Sí) y el diagnóstico de Alzheimer (Sí/No). La prueba de Chi-cuadrado se aplicó bajo la siguiente hipótesis:

  • \(H_0\): No existe asociación entre los antecedentes familiares de Alzheimer y el diagnóstico de Alzheimer en el paciente (las variables son independientes).

El p-valor obtenido (p = 0.141) supera el nivel de significancia convencional (\(\alpha\) = 0.05), por lo que no se rechaza la hipótesis nula. Aunque se observa una diferencia porcentual, esta no es estadísticamente significativa. Por lo tanto, no podemos afirmar que los antecedentes familiares influyan significativamente en el diagnóstico de Alzheimer.

CardiovascularDisease

Tabla de Contingencia
No Sí Sum
No 1200 639 1839
Sí 189 121 310
Sum 1389 760 2149
Note:
Prueba: Chi-cuadrado, p-valor = 0.163

Se evaluó la posible asociación entre la presencia de enfermedad cardiovascular (No/Sí) y el diagnóstico de Alzheimer (Sí/No) en una muestra de 2,149 individuos. La prueba de Chi-cuadrado se aplicó bajo la siguiente hipótesis:

  • \(H_0\): No existe asociación entre enfermedad cardiovascular y diagnóstico de Alzheimer (las variables son independientes).

El p-valor obtenido (p = 0.163) supera el umbral de significancia (α = 0.05), por lo que no se rechaza la hipótesis nula. Aunque se observa una diferencia de 4.2 puntos porcentuales, esta no alcanza significancia estadística. Por lo tanto, no hay evidencia suficiente para afirmar que la enfermedad cardiovascular influya en el diagnóstico de Alzheimer.

Diabetes

Tabla de Contingencia
No Sí Sum
No 1168 657 1825
Sí 221 103 324
Sum 1389 760 2149
Note:
Prueba: Chi-cuadrado, p-valor = 0.162

Se examinó la relación entre diabetes (No/Sí) y diagnóstico de Alzheimer (Sí/No) en una cohorte de 2,149 pacientes. El análisis mediante prueba de Chi-cuadrado evaluó:

  • Hipótesis nula (\(H_0\)): No existe asociación entre diabetes y Alzheime

El p-valor obtenido (p = 0.162) supera el umbral de significancia (α = 0.05), por lo que no se rechaza la hipótesis nula. Por lo tanto, no hay evidencia suficiente para afirmar que la diabetes influya en el diagnóstico de Alzheimer.

Depression

Tabla de Contingencia
No Sí Sum
No 1108 610 1718
Sí 281 150 431
Sum 1389 760 2149
Note:
Prueba: Chi-cuadrado, p-valor = 0.828

Se evaluó si existe una asociación significativa entre la depresión (No/Sí) y el diagnóstico de Alzheimer (Sí/No). La prueba de Chi-cuadrado se aplicó bajo la siguiente hipótesis:

  • **Hipótesis nula (\(H_0\)):* No existe asociación entre la depresión y el diagnóstico de Alzheimer (las variables son independientes).

Los resultados mostraron que la distribución de diagnósticos (Sí/No) fue similar entre quienes no tenían depresión (35.5% Sí) y quienes sí la tenían (34.8% Sí). El p-valor obtenido (p = 0.828) supera ampliamente el nivel de significancia convencional (\(\alpha\) = 0.05), por lo que no se rechaza la hipótesis nula. Esto indica que no hay evidencia estadística suficiente para afirmar que la depresión influye en la presencia de Alzheimer.

HeadInjury

Tabla de Contingencia
No Sí Sum
No 1254 696 1950
Sí 135 64 199
Sum 1389 760 2149
Note:
Prueba: Chi-cuadrado, p-valor = 0.360

Se evaluó si existe una asociación significativa entre los antecedentes de trauma craneoencefálico (No/Sí) y el diagnóstico de Alzheimer (Sí/No) en una muestra de 2,149 individuos. La prueba de Chi-cuadrado se aplicó bajo la siguiente hipótesis:

  • Hipótesis nula (\(H_=0\)): No existe asociación entre el trauma craneoencefálico y el diagnóstico de Alzheimer (las variables son independientes).

Los resultados mostraron que la distribución de diagnósticos (Sí/No) fue similar entre quienes no tenían antecedentes de trauma (35.7% Sí) y quienes sí los tenían (32.2% Sí). El p-valor obtenido (p = 0.360) supera el nivel de significancia convencional (\(\alpha\) = 0.05), por lo que no se rechaza la hipótesis nula. Esto indica que no hay evidencia estadística suficiente para afirmar que los traumas craneoencefálicos influyen en la presencia de Alzheimer.

Hypertension (Hipertención)

Tabla de Contingencia
No Sí Sum
No 1195 634 1829
Sí 194 126 320
Sum 1389 760 2149
Note:
Prueba: Chi-cuadrado, p-valor = 0.118

Se aplicó una prueba de independencia chi-cuadrado con el objetivo de evaluar si existe una relación significativa entre la presencia de hipertensión (sí o no) y la presencia de diagnóstico (sí o no).

  • Hipótesis nula (\(H_0\)): No existe asociación entre la hipertensión y la presencia del diagnóstico

El resultado de la prueba arrojó un valor p de 0.118, el cual es mayor al nivel de significancia comúnmente utilizado (\(\alpha = 0.05\)). En consecuencia, no se rechaza la hipótesis nula, lo que indica que no hay evidencia estadísticamente significativa de una relación entre la hipertensión y la presencia del diagnóstico.

Por lo tanto, la hipertensión no está asociada de manera significativa con la presencia del diagnóstico.

SystolicBP (Presión arterial sistólica)

Distribución Presión Arterial sistolica según diagnóstico
Diagnóstico n Proporción Media Mediana Desv. Estándar
No 1389 64.6% 134.6 135.0 25.9
Sí 760 35.4% 133.7 133.0 26.0

DiastolicBP (Presión arterial diastólica)

Distribución Presión Arterial Distolica según diagnóstico
Diagnóstico n Proporción Media Mediana Desv. Estándar
No 1389 64.6% 89.8 90.0 17.7
Sí 760 35.4% 90.0 91.0 17.5

CholesterolTotal (Colesterorl Total)

Distribución Colesterol Total según diagnóstico
Diagnóstico n Proporción Media Mediana Desv. Estándar
No 1389 64.6% 225.0 224.5 42.2
Sí 760 35.4% 225.6 226.4 43.2

CholesterolLDL (Colesterol LDL)

Distribución Colesterol LDL según diagnóstico
Diagnóstico n Proporción Media Mediana Desv. Estándar
No 1389 64.6% 125.4 124.8 43.4
Sí 760 35.4% 122.5 121.8 43.2

CholesterolHDL (Colesterol HDL)

Distribución Colesterol HDL según diagnóstico
Diagnóstico n Proporción Media Mediana Desv. Estándar
No 1389 64.6% 58.7 58.3 23.1
Sí 760 35.4% 60.8 61.8 23.2

CholesterolTriglycerides (Niveles Triglicéridos)

Distribución Niveles Trigligerios según diagnóstico
Diagnóstico n Proporción Media Mediana Desv. Estándar
No 1389 64.6% 226.6 226.1 101.9
Sí 760 35.4% 231.4 239.6 102.1

MMSE (Miniexamen del estado mental)

Distribución MiniExamen Estado Mental según diagnóstico
Diagnóstico n Proporción Media Mediana Desv. Estándar
No 1389 64.6% 16.3 17.1 8.9
Sí 760 35.4% 12.0 11.6 7.2

FunctionalAssessment (Evaluación Funcional)

Distribución Evaluación Funcional según diagnóstico
Diagnóstico n Proporción Media Mediana Desv. Estándar
No 1389 64.6% 5.9 6.2 2.8
Sí 760 35.4% 3.7 3.3 2.6

MemoryComplaints (Perdida de Memoria)

Tabla de Contingencia
No Sí Sum
No 1228 474 1702
Sí 161 286 447
Sum 1389 760 2149
Note:
Prueba: Chi-cuadrado, p-valor = 0.000

Se aplicó una prueba de independencia chi-cuadrado con el objetivo de evaluar si existe una relación significativa entre perdidas de memoria (sí o no) y la presencia de diagnóstico (sí o no).

  • Hipótesis nula (\(H_0\)): No existe asociación entre perdidas de memoria y la presencia del diagnóstico

El resultado de la prueba arrojo un p valor menor al nivel de significancia comúnmente utilizado (\(\alpha = 0.05\)). En consecuencia, se rechaza la hipótesis nula, lo que indica que hay evidencia estadísticamente significativa de una relación entre las perdidas de memoria y la presencia del diagnóstico.

BehavioralProblems (Problemas de Comportamiento)

Tabla de Contingencia
No Sí Sum
No 1255 557 1812
Sí 134 203 337
Sum 1389 760 2149
Note:
Prueba: Chi-cuadrado, p-valor = 0.000

Se aplicó una prueba de independencia chi-cuadrado con el objetivo de evaluar si existe una relación significativa entre los problemas de comportamiento (sí o no) y la presencia de diagnóstico (sí o no).

  • Hipótesis nula (\(H_0\)): No existe asociación entre los problemas de comportamiento y la presencia del diagnóstico.

El resultado de la prueba arrojó un valor p menor al nivel de significancia comúnmente utilizado (\(\alpha = 0.05\)). En consecuencia, se rechaza la hipótesis nula, lo que indica que hay evidencia estadísticamente significativa de una relación entre los problemas de comportamiento y la presencia del diagnóstico.

ADL (Actividades de la Vida Diaria)

Distribución Actividades Vida Diaria según diagnóstico
Diagnóstico n Proporción Media Mediana Desv. Estándar
No 1389 64.6% 5.7 6.1 2.8
Sí 760 35.4% 3.7 3.2 2.7

Confusion

Tabla de Contingencia
No Sí Sum
No 1096 612 1708
Sí 293 148 441
Sum 1389 760 2149
Note:
Prueba: Chi-cuadrado, p-valor = 0.405

Se aplicó una prueba de independencia chi-cuadrado con el objetivo de evaluar si existe una relación significativa entre la confusión (sí o no) y la presencia de diagnóstico (sí o no).

  • Hipótesis nula (\(H_0\)): No existe asociación entre la confusión y la presencia del diagnóstico.

El resultado de la prueba arrojó un valor p de 0.405, el cual es mayor al nivel de significancia comúnmente utilizado (\(\alpha = 0.05\)). En consecuencia, no se rechaza la hipótesis nula, lo que indica que no hay evidencia estadísticamente significativa de una relación entre la confusión y la presencia del diagnóstico.

Disorientation

Tabla de Contingencia
No Sí Sum
No 1160 649 1809
Sí 229 111 340
Sum 1389 760 2149
Note:
Prueba: Chi-cuadrado, p-valor = 0.280

Se aplicó una prueba de independencia chi-cuadrado con el objetivo de evaluar si existe una relación significativa entre la desorientación (sí o no) y la presencia de diagnóstico (sí o no).

  • Hipótesis nula (\(H_0\)): No existe asociación entre la desorientación y la presencia del diagnóstico.

El resultado de la prueba arrojó un valor p de 0.280, el cual es mayor al nivel de significancia comúnmente utilizado (\(\alpha = 0.05\)). En consecuencia, no se rechaza la hipótesis nula, lo que indica que no hay evidencia estadísticamente significativa de una relación entre la desorientación y la presencia del diagnóstico.

PersonalityChanges

Tabla de Contingencia
No Sí Sum
No 1172 653 1825
Sí 217 107 324
Sum 1389 760 2149
Note:
Prueba: Chi-cuadrado, p-valor = 0.372

Se aplicó una prueba de independencia chi-cuadrado con el objetivo de evaluar si existe una relación significativa entre los cambios de personalidad (sí o no) y la presencia de diagnóstico (sí o no).

  • Hipótesis nula (\(H_0\)): No existe asociación entre los cambios de personalidad y la presencia del diagnóstico.

El resultado de la prueba arrojó un valor p de 0.372, el cual es mayor al nivel de significancia comúnmente utilizado (\(\alpha = 0.05\)). En consecuencia, no se rechaza la hipótesis nula, lo que indica que no hay evidencia estadísticamente significativa de una relación entre los cambios de personalidad y la presencia del diagnóstico.

DifficultyCompletingTasks (Dificutades para Completar Tareas)

Tabla de Contingencia
No Sí Sum
No 1172 636 1808
Sí 217 124 341
Sum 1389 760 2149
Note:
Prueba: Chi-cuadrado, p-valor = 0.720

Se aplicó una prueba de independencia chi-cuadrado con el objetivo de evaluar si existe una relación significativa entre las dificultades para completar tareas (sí o no) y la presencia de diagnóstico (sí o no).

  • Hipótesis nula (\(H_0\)): No existe asociación entre las dificultades para completar tareas y la presencia del diagnóstico.

El resultado de la prueba arrojó un valor p de 0.720, el cual es mayor al nivel de significancia comúnmente utilizado (\(\alpha = 0.05\)). En consecuencia, no se rechaza la hipótesis nula, lo que indica que no hay evidencia estadísticamente significativa de una relación entre las dificultades para completar tareas y la presencia del diagnóstico.

Forgetfulness (Presenta Olvidos)

Tabla de Contingencia
No Sí Sum
No 970 531 1501
Sí 419 229 648
Sum 1389 760 2149
Note:
Prueba: Chi-cuadrado, p-valor = 1.000

Se aplicó una prueba de independencia chi-cuadrado con el objetivo de evaluar si existe una relación significativa entre la presencia de olvidos (sí o no) y la presencia de diagnóstico (sí o no).

  • Hipótesis nula (\(H_0\)): No existe asociación entre los olvidos y la presencia del diagnóstico.

El resultado de la prueba arrojó un valor p de 1.000, el cual es significativamente mayor al nivel de significancia comúnmente utilizado (\(\alpha = 0.05\)). En consecuencia, no se rechaza la hipótesis nula, lo que indica que no hay evidencia estadísticamente significativa de una relación entre los olvidos y el diagnostico diagnóstico.

Asociacion variables

## [1] "Variables significativas (p < 0.05):"
##                                  Variable  Association
## FunctionalAssessment FunctionalAssessment 8.991514e-65
## ADL                                   ADL 6.050180e-53
## MemoryComplaints         MemoryComplaints 1.526605e-45
## MMSE                                 MMSE 6.621144e-28
## BehavioralProblems     BehavioralProblems 4.731447e-25
## SleepQuality                 SleepQuality 9.359779e-03
## CholesterolHDL             CholesterolHDL 4.864476e-02

Creacion modelo lineal Generalizado

Se crea el modelo con las diferentes funciones de enlace

## 
## Call:
## glm(formula = Diagnosis ~ ., family = binomial(link = "logit"), 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.7343  -0.5536  -0.2042   0.4856   3.8784  
## 
## Coefficients:
##                               Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                  5.4278533  0.9771756   5.555 2.78e-08 ***
## Age                         -0.0105082  0.0070752  -1.485   0.1375    
## GenderFemenino              -0.0549320  0.1279495  -0.429   0.6677    
## EthnicityAfroamericano      -0.2211344  0.1655276  -1.336   0.1816    
## EthnicityAsiático            0.2298599  0.2231986   1.030   0.3031    
## EthnicityOtro               -0.2555481  0.2275640  -1.123   0.2614    
## EducationLevelSecundaria    -0.2424893  0.1723839  -1.407   0.1595    
## EducationLevelLicenciatura  -0.1394103  0.1844665  -0.756   0.4498    
## EducationLevelSuperior      -0.3963829  0.2471226  -1.604   0.1087    
## BMI                         -0.0044044  0.0088921  -0.495   0.6204    
## SmokingSí                   -0.2041624  0.1425496  -1.432   0.1521    
## AlcoholConsumption          -0.0092070  0.0109928  -0.838   0.4023    
## PhysicalActivity            -0.0067143  0.0220515  -0.304   0.7608    
## DietQuality                  0.0112428  0.0222094   0.506   0.6127    
## SleepQuality                -0.0583832  0.0364452  -1.602   0.1092    
## FamilyHistoryAlzheimersSí   -0.0981272  0.1488527  -0.659   0.5098    
## CardiovascularDiseaseSí      0.1548321  0.1761933   0.879   0.3795    
## DiabetesSí                   0.0233487  0.1837190   0.127   0.8989    
## DepressionSí                 0.0727888  0.1566490   0.465   0.6422    
## HeadInjurySí                -0.3548529  0.2228865  -1.592   0.1114    
## HypertensionSí               0.2115128  0.1777708   1.190   0.2341    
## SystolicBP                  -0.0008700  0.0024629  -0.353   0.7239    
## DiastolicBP                  0.0019086  0.0036070   0.529   0.5967    
## CholesterolTotal             0.0002876  0.0014906   0.193   0.8470    
## CholesterolLDL              -0.0029533  0.0015020  -1.966   0.0493 *  
## CholesterolHDL               0.0049236  0.0027678   1.779   0.0753 .  
## CholesterolTriglycerides     0.0007797  0.0006282   1.241   0.2145    
## MMSE                        -0.1077221  0.0082257 -13.096  < 2e-16 ***
## FunctionalAssessment        -0.4521595  0.0266631 -16.958  < 2e-16 ***
## MemoryComplaintsSí           2.5886387  0.1671286  15.489  < 2e-16 ***
## BehavioralProblemsSí         2.5065363  0.1855537  13.508  < 2e-16 ***
## ADL                         -0.4206530  0.0260357 -16.157  < 2e-16 ***
## ConfusionSí                 -0.1679901  0.1602357  -1.048   0.2945    
## DisorientationSí            -0.1018618  0.1763523  -0.578   0.5635    
## PersonalityChangesSí        -0.1050889  0.1835794  -0.572   0.5670    
## DifficultyCompletingTasksSí  0.0993529  0.1747529   0.569   0.5697    
## ForgetfulnessSí              0.0053150  0.1392772   0.038   0.9696    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2792.3  on 2148  degrees of freedom
## Residual deviance: 1576.1  on 2112  degrees of freedom
## AIC: 1650.1
## 
## Number of Fisher Scoring iterations: 6
## 
## Call:
## glm(formula = Diagnosis ~ ., family = binomial(link = "probit"), 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.7585  -0.6062  -0.1970   0.5301   4.5047  
## 
## Coefficients:
##                               Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                  2.989e+00  5.403e-01   5.532 3.17e-08 ***
## Age                         -5.736e-03  3.940e-03  -1.456   0.1455    
## GenderFemenino              -4.409e-02  7.105e-02  -0.620   0.5349    
## EthnicityAfroamericano      -1.104e-01  9.156e-02  -1.206   0.2279    
## EthnicityAsiático            1.350e-01  1.230e-01   1.097   0.2725    
## EthnicityOtro               -1.367e-01  1.262e-01  -1.084   0.2785    
## EducationLevelSecundaria    -1.445e-01  9.601e-02  -1.505   0.1323    
## EducationLevelLicenciatura  -1.007e-01  1.022e-01  -0.985   0.3246    
## EducationLevelSuperior      -2.095e-01  1.369e-01  -1.530   0.1260    
## BMI                         -4.271e-03  4.945e-03  -0.864   0.3877    
## SmokingSí                   -1.371e-01  7.932e-02  -1.728   0.0840 .  
## AlcoholConsumption          -4.768e-03  6.116e-03  -0.780   0.4356    
## PhysicalActivity            -5.542e-03  1.229e-02  -0.451   0.6520    
## DietQuality                  6.192e-03  1.231e-02   0.503   0.6149    
## SleepQuality                -3.502e-02  2.019e-02  -1.734   0.0829 .  
## FamilyHistoryAlzheimersSí   -6.861e-02  8.247e-02  -0.832   0.4055    
## CardiovascularDiseaseSí      1.003e-01  9.866e-02   1.016   0.3096    
## DiabetesSí                   6.432e-03  1.014e-01   0.063   0.9494    
## DepressionSí                 2.641e-02  8.789e-02   0.300   0.7638    
## HeadInjurySí                -2.170e-01  1.249e-01  -1.738   0.0823 .  
## HypertensionSí               1.382e-01  9.948e-02   1.389   0.1648    
## SystolicBP                  -8.301e-05  1.369e-03  -0.061   0.9517    
## DiastolicBP                  1.036e-03  2.008e-03   0.516   0.6058    
## CholesterolTotal             5.795e-05  8.285e-04   0.070   0.9442    
## CholesterolLDL              -1.599e-03  8.304e-04  -1.925   0.0542 .  
## CholesterolHDL               2.629e-03  1.536e-03   1.712   0.0870 .  
## CholesterolTriglycerides     3.747e-04  3.495e-04   1.072   0.2836    
## MMSE                        -5.722e-02  4.403e-03 -12.995  < 2e-16 ***
## FunctionalAssessment        -2.423e-01  1.388e-02 -17.459  < 2e-16 ***
## MemoryComplaintsSí           1.413e+00  8.943e-02  15.800  < 2e-16 ***
## BehavioralProblemsSí         1.346e+00  9.975e-02  13.497  < 2e-16 ***
## ADL                         -2.214e-01  1.351e-02 -16.394  < 2e-16 ***
## ConfusionSí                 -1.048e-01  8.896e-02  -1.178   0.2387    
## DisorientationSí            -8.458e-02  9.852e-02  -0.859   0.3906    
## PersonalityChangesSí        -2.471e-02  1.012e-01  -0.244   0.8072    
## DifficultyCompletingTasksSí  3.277e-02  9.695e-02   0.338   0.7354    
## ForgetfulnessSí             -6.714e-03  7.743e-02  -0.087   0.9309    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2792.3  on 2148  degrees of freedom
## Residual deviance: 1606.6  on 2112  degrees of freedom
## AIC: 1680.6
## 
## Number of Fisher Scoring iterations: 6
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
## 
## Call:
## glm(formula = Diagnosis ~ ., family = binomial(link = "cloglog"), 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.6501  -0.5860  -0.2905   0.4269   3.4368  
## 
## Coefficients:
##                               Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                  3.173e+00  6.565e-01   4.833 1.34e-06 ***
## Age                         -1.037e-03  4.790e-03  -0.217   0.8286    
## GenderFemenino              -9.519e-02  8.795e-02  -1.082   0.2791    
## EthnicityAfroamericano      -1.392e-01  1.147e-01  -1.213   0.2250    
## EthnicityAsiático            1.834e-01  1.489e-01   1.232   0.2179    
## EthnicityOtro               -1.392e-01  1.567e-01  -0.888   0.3745    
## EducationLevelSecundaria    -1.800e-01  1.160e-01  -1.552   0.1207    
## EducationLevelLicenciatura  -1.969e-01  1.243e-01  -1.584   0.1132    
## EducationLevelSuperior      -2.727e-01  1.682e-01  -1.622   0.1049    
## BMI                         -6.871e-03  6.019e-03  -1.141   0.2537    
## SmokingSí                   -1.125e-01  9.784e-02  -1.150   0.2503    
## AlcoholConsumption          -1.050e-02  7.484e-03  -1.402   0.1608    
## PhysicalActivity            -4.829e-05  1.513e-02  -0.003   0.9975    
## DietQuality                  7.689e-03  1.510e-02   0.509   0.6105    
## SleepQuality                -4.161e-02  2.482e-02  -1.676   0.0937 .  
## FamilyHistoryAlzheimersSí   -1.574e-02  1.017e-01  -0.155   0.8770    
## CardiovascularDiseaseSí      1.574e-01  1.197e-01   1.314   0.1887    
## DiabetesSí                   1.499e-02  1.273e-01   0.118   0.9063    
## DepressionSí                 9.500e-02  1.082e-01   0.878   0.3799    
## HeadInjurySí                -1.737e-01  1.542e-01  -1.126   0.2600    
## HypertensionSí               1.404e-01  1.203e-01   1.167   0.2431    
## SystolicBP                  -1.412e-03  1.696e-03  -0.833   0.4049    
## DiastolicBP                  2.128e-03  2.485e-03   0.856   0.3919    
## CholesterolTotal            -2.904e-04  1.018e-03  -0.285   0.7755    
## CholesterolLDL              -2.584e-03  1.023e-03  -2.525   0.0116 *  
## CholesterolHDL               3.982e-03  1.920e-03   2.074   0.0381 *  
## CholesterolTriglycerides     5.007e-04  4.267e-04   1.173   0.2407    
## MMSE                        -8.200e-02  5.655e-03 -14.500  < 2e-16 ***
## FunctionalAssessment        -3.130e-01  1.782e-02 -17.559  < 2e-16 ***
## MemoryComplaintsSí           1.713e+00  1.058e-01  16.191  < 2e-16 ***
## BehavioralProblemsSí         1.682e+00  1.204e-01  13.969  < 2e-16 ***
## ADL                         -2.881e-01  1.720e-02 -16.750  < 2e-16 ***
## ConfusionSí                 -6.203e-02  1.089e-01  -0.569   0.5691    
## DisorientationSí            -8.650e-02  1.232e-01  -0.702   0.4827    
## PersonalityChangesSí        -6.009e-02  1.252e-01  -0.480   0.6313    
## DifficultyCompletingTasksSí  5.412e-02  1.195e-01   0.453   0.6507    
## ForgetfulnessSí              8.710e-02  9.479e-02   0.919   0.3581    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2792.3  on 2148  degrees of freedom
## Residual deviance: 1587.4  on 2112  degrees of freedom
## AIC: 1661.4
## 
## Number of Fisher Scoring iterations: 10

Buscamos el mejor IAC

## [1] 1650.118
## [1] 1680.636
## [1] 1661.356

Miramos el diviance de cada modelo

## [1] 1576.118
## [1] 1606.636
## [1] 1587.356

Aunque el mejor modelo obtenido utiliza una función de enlace logit, para alinearse con los objetivos de este trabajo, se optará por la función de enlace probit. A continuación, se procederá a seleccionar el modelo más adecuado, identificando qué variables predictoras tienen mayor significancia estadística en la explicación del diagnóstico.

Este análisis se basa en pruebas de Wald, donde en cada iteración se incorpora una nueva variable predictora para evaluar si aporta una mejora significativa en la capacidad predictiva del modelo. De esta manera, se determinará cuáles factores influyen de manera más relevante en el diagnóstico.

## 
##   Wald test 
## 
## Model 1 :  Diagnosis ~ 1 
## Model 2 :  Diagnosis ~ Age 
## Model 3 :  Diagnosis ~ Age + Gender 
## Model 4 :  Diagnosis ~ Age + Gender + Ethnicity 
## Model 5 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel 
## Model 6 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI 
## Model 7 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking 
## Model 8 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption 
## Model 9 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity 
## Model 10 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality 
## Model 11 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality 
## Model 12 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers 
## Model 13 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease 
## Model 14 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes 
## Model 15 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression 
## Model 16 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury 
## Model 17 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension 
## Model 18 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP 
## Model 19 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP 
## Model 20 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal 
## Model 21 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL 
## Model 22 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL 
## Model 23 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + CholesterolTriglycerides 
## Model 24 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + CholesterolTriglycerides + MMSE 
## Model 25 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + CholesterolTriglycerides + MMSE + FunctionalAssessment 
## Model 26 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + CholesterolTriglycerides + MMSE + FunctionalAssessment + MemoryComplaints 
## Model 27 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + CholesterolTriglycerides + MMSE + FunctionalAssessment + MemoryComplaints + BehavioralProblems 
## Model 28 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + CholesterolTriglycerides + MMSE + FunctionalAssessment + MemoryComplaints + BehavioralProblems + ADL 
## Model 29 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + CholesterolTriglycerides + MMSE + FunctionalAssessment + MemoryComplaints + BehavioralProblems + ADL + Confusion 
## Model 30 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + CholesterolTriglycerides + MMSE + FunctionalAssessment + MemoryComplaints + BehavioralProblems + ADL + Confusion + Disorientation 
## Model 31 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + CholesterolTriglycerides + MMSE + FunctionalAssessment + MemoryComplaints + BehavioralProblems + ADL + Confusion + Disorientation + PersonalityChanges 
## Model 32 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + CholesterolTriglycerides + MMSE + FunctionalAssessment + MemoryComplaints + BehavioralProblems + ADL + Confusion + Disorientation + PersonalityChanges + DifficultyCompletingTasks 
## Model 33 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + CholesterolTriglycerides + MMSE + FunctionalAssessment + MemoryComplaints + BehavioralProblems + ADL + Confusion + Disorientation + PersonalityChanges + DifficultyCompletingTasks + Forgetfulness 
## 
##               Chi    df  Pr(Chisq>)    
## 1 vs 2   6.4300e-02   1    0.799824    
## 2 vs 3   9.3379e-01   1    0.333881    
## 3 vs 4   6.4177e+00   3    0.092966 .  
## 4 vs 5   4.5838e+00   3    0.204937    
## 5 vs 6   1.5015e+00   1    0.220441    
## 6 vs 7   3.1956e-02   1    0.858125    
## 7 vs 8   1.6397e-01   1    0.685529    
## 8 vs 9   7.4360e-02   1    0.785091    
## 9 vs 10  1.5931e-01   1    0.689790    
## 10 vs 11 6.7209e+00   1    0.009529 ** 
## 11 vs 12 1.8176e+00   1    0.177599    
## 12 vs 13 2.1558e+00   1    0.142035    
## 13 vs 14 2.2127e+00   1    0.136879    
## 14 vs 15 6.4443e-02   1    0.799606    
## 15 vs 16 1.4044e+00   1    0.235992    
## 16 vs 17 3.1623e+00   1    0.075359 .  
## 17 vs 18 8.6013e-01   1    0.353703    
## 18 vs 19 1.9067e-01   1    0.662357    
## 19 vs 20 1.0234e-01   1    0.749034    
## 20 vs 21 2.2627e+00   1    0.132524    
## 21 vs 22 3.8408e+00   1    0.050021 .  
## 22 vs 23 9.3137e-01   1    0.334507    
## 23 vs 24 1.2584e+02   1   < 2.2e-16 ***
## 24 vs 25 2.7238e+02   1   < 2.2e-16 ***
## 25 vs 26 2.3003e+02   1   < 2.2e-16 ***
## 26 vs 27 1.4513e+02   1   < 2.2e-16 ***
## 27 vs 28 2.6901e+02   1   < 2.2e-16 ***
## 28 vs 29 1.4682e+00   1    0.225631    
## 29 vs 30 7.3396e-01   1    0.391602    
## 30 vs 31 5.3197e-02   1    0.817592    
## 31 vs 32 1.1400e-01   1    0.735635    
## 32 vs 33 7.5184e-03   1    0.930903    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Para identificar el modelo más optimo, definimos el conjunto de modelos basados en los resultados preliminares que mostraron mejor significancia estadística

## 
## Call:
## glm(formula = Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + 
##     BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + 
##     SleepQuality, family = binomial(link = "probit"), data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.1926  -0.9473  -0.8697   1.3777   1.7230  
## 
## Coefficients:
##                              Estimate Std. Error z value Pr(>|z|)   
## (Intercept)                -0.0341022  0.2983030  -0.114  0.90898   
## Age                        -0.0007094  0.0031131  -0.228  0.81974   
## GenderFemenino             -0.0569578  0.0557553  -1.022  0.30699   
## EthnicityAfroamericano     -0.1052002  0.0711511  -1.479  0.13926   
## EthnicityAsiático           0.1406555  0.0957205   1.469  0.14171   
## EthnicityOtro              -0.1194105  0.0974132  -1.226  0.22027   
## EducationLevelSecundaria   -0.0926328  0.0750095  -1.235  0.21685   
## EducationLevelLicenciatura -0.1270200  0.0795623  -1.596  0.11038   
## EducationLevelSuperior     -0.1990580  0.1084202  -1.836  0.06636 . 
## BMI                         0.0046380  0.0038631   1.201  0.22991   
## SmokingSí                  -0.0112650  0.0616307  -0.183  0.85497   
## AlcoholConsumption         -0.0021155  0.0048447  -0.437  0.66235   
## PhysicalActivity            0.0024501  0.0097585   0.251  0.80175   
## DietQuality                 0.0052235  0.0096102   0.544  0.58676   
## SleepQuality               -0.0410658  0.0158404  -2.592  0.00953 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2792.3  on 2148  degrees of freedom
## Residual deviance: 2771.7  on 2134  degrees of freedom
## AIC: 2801.7
## 
## Number of Fisher Scoring iterations: 4
## 
## Call:
## glm(formula = Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + 
##     BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + 
##     SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + 
##     Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + 
##     DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + 
##     CholesterolTriglycerides + MMSE, family = binomial(link = "probit"), 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.4881  -0.9409  -0.6861   1.2187   2.1154  
## 
## Coefficients:
##                              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                 0.4966221  0.4264145   1.165  0.24416    
## Age                        -0.0008168  0.0031920  -0.256  0.79804    
## GenderFemenino             -0.0459291  0.0572064  -0.803  0.42205    
## EthnicityAfroamericano     -0.1220589  0.0730955  -1.670  0.09495 .  
## EthnicityAsiático           0.1385621  0.0982113   1.411  0.15829    
## EthnicityOtro              -0.1424059  0.0999676  -1.425  0.15430    
## EducationLevelSecundaria   -0.0851513  0.0769761  -1.106  0.26864    
## EducationLevelLicenciatura -0.0903530  0.0815335  -1.108  0.26779    
## EducationLevelSuperior     -0.1822583  0.1115061  -1.635  0.10215    
## BMI                         0.0044086  0.0039593   1.113  0.26550    
## SmokingSí                  -0.0185804  0.0634272  -0.293  0.76957    
## AlcoholConsumption         -0.0030477  0.0049708  -0.613  0.53980    
## PhysicalActivity            0.0007955  0.0100143   0.079  0.93668    
## DietQuality                 0.0085160  0.0098613   0.864  0.38782    
## SleepQuality               -0.0418800  0.0162516  -2.577  0.00997 ** 
## FamilyHistoryAlzheimersSí  -0.0874654  0.0663890  -1.317  0.18768    
## CardiovascularDiseaseSí     0.1534581  0.0807564   1.900  0.05740 .  
## DiabetesSí                 -0.1271866  0.0810028  -1.570  0.11638    
## DepressionSí               -0.0143068  0.0715446  -0.200  0.84150    
## HeadInjurySí               -0.1141019  0.1000804  -1.140  0.25424    
## HypertensionSí              0.1636529  0.0797092   2.053  0.04006 *  
## SystolicBP                 -0.0011055  0.0011006  -1.004  0.31516    
## DiastolicBP                 0.0002276  0.0016312   0.140  0.88903    
## CholesterolTotal            0.0001577  0.0006725   0.234  0.81463    
## CholesterolLDL             -0.0007584  0.0006611  -1.147  0.25135    
## CholesterolHDL              0.0024812  0.0012378   2.004  0.04502 *  
## CholesterolTriglycerides    0.0002634  0.0002813   0.936  0.34903    
## MMSE                       -0.0379861  0.0033862 -11.218  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2792.3  on 2148  degrees of freedom
## Residual deviance: 2626.0  on 2121  degrees of freedom
## AIC: 2682
## 
## Number of Fisher Scoring iterations: 4
## 
## Call:
## glm(formula = Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + 
##     BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + 
##     SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + 
##     Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + 
##     DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + 
##     CholesterolTriglycerides + MMSE + FunctionalAssessment, family = binomial(link = "probit"), 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.0114  -0.8527  -0.5180   0.9668   2.7802  
## 
## Coefficients:
##                              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                 1.3403318  0.4512274   2.970  0.00297 ** 
## Age                        -0.0008469  0.0033457  -0.253  0.80016    
## GenderFemenino             -0.0097464  0.0601418  -0.162  0.87126    
## EthnicityAfroamericano     -0.1585841  0.0772328  -2.053  0.04004 *  
## EthnicityAsiático           0.1746044  0.1030167   1.695  0.09009 .  
## EthnicityOtro              -0.1943052  0.1055023  -1.842  0.06552 .  
## EducationLevelSecundaria   -0.1197598  0.0811225  -1.476  0.13987    
## EducationLevelLicenciatura -0.0684850  0.0858702  -0.798  0.42514    
## EducationLevelSuperior     -0.1889216  0.1173104  -1.610  0.10730    
## BMI                         0.0027962  0.0041634   0.672  0.50182    
## SmokingSí                  -0.0609531  0.0667228  -0.914  0.36096    
## AlcoholConsumption         -0.0050668  0.0052215  -0.970  0.33186    
## PhysicalActivity            0.0009883  0.0104756   0.094  0.92484    
## DietQuality                 0.0054623  0.0103755   0.526  0.59857    
## SleepQuality               -0.0382445  0.0171463  -2.230  0.02572 *  
## FamilyHistoryAlzheimersSí  -0.1018110  0.0696811  -1.461  0.14399    
## CardiovascularDiseaseSí     0.1071115  0.0843533   1.270  0.20416    
## DiabetesSí                 -0.0853435  0.0855643  -0.997  0.31856    
## DepressionSí                0.0082888  0.0753334   0.110  0.91239    
## HeadInjurySí               -0.0718865  0.1053316  -0.682  0.49494    
## HypertensionSí              0.1436023  0.0838954   1.712  0.08696 .  
## SystolicBP                 -0.0008377  0.0011571  -0.724  0.46909    
## DiastolicBP                 0.0012920  0.0017156   0.753  0.45141    
## CholesterolTotal            0.0001987  0.0007063   0.281  0.77848    
## CholesterolLDL             -0.0009885  0.0006934  -1.426  0.15400    
## CholesterolHDL              0.0027725  0.0013011   2.131  0.03309 *  
## CholesterolTriglycerides    0.0002219  0.0002960   0.750  0.45343    
## MMSE                       -0.0398020  0.0035735 -11.138  < 2e-16 ***
## FunctionalAssessment       -0.1809752  0.0109656 -16.504  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2792.3  on 2148  degrees of freedom
## Residual deviance: 2327.3  on 2120  degrees of freedom
## AIC: 2385.3
## 
## Number of Fisher Scoring iterations: 4
## 
## Call:
## glm(formula = Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + 
##     BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + 
##     SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + 
##     Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + 
##     DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + 
##     CholesterolTriglycerides + MMSE + FunctionalAssessment + 
##     MemoryComplaints, family = binomial(link = "probit"), data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.1422  -0.7751  -0.4021   0.8342   3.0997  
## 
## Coefficients:
##                              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                 1.374e+00  4.726e-01   2.907  0.00365 ** 
## Age                        -1.503e-03  3.520e-03  -0.427  0.66936    
## GenderFemenino             -1.130e-02  6.333e-02  -0.178  0.85834    
## EthnicityAfroamericano     -1.605e-01  8.114e-02  -1.979  0.04787 *  
## EthnicityAsiático           1.360e-01  1.088e-01   1.250  0.21138    
## EthnicityOtro              -2.107e-01  1.118e-01  -1.885  0.05949 .  
## EducationLevelSecundaria   -1.279e-01  8.527e-02  -1.500  0.13352    
## EducationLevelLicenciatura -7.461e-02  9.040e-02  -0.825  0.40917    
## EducationLevelSuperior     -1.966e-01  1.235e-01  -1.592  0.11133    
## BMI                         8.476e-04  4.384e-03   0.193  0.84669    
## SmokingSí                  -9.095e-02  7.061e-02  -1.288  0.19773    
## AlcoholConsumption         -3.439e-03  5.501e-03  -0.625  0.53182    
## PhysicalActivity           -2.486e-03  1.097e-02  -0.227  0.82067    
## DietQuality                 4.843e-03  1.098e-02   0.441  0.65915    
## SleepQuality               -3.871e-02  1.809e-02  -2.140  0.03235 *  
## FamilyHistoryAlzheimersSí  -8.844e-02  7.315e-02  -1.209  0.22669    
## CardiovascularDiseaseSí     7.325e-02  8.834e-02   0.829  0.40699    
## DiabetesSí                 -6.908e-02  9.061e-02  -0.762  0.44586    
## DepressionSí                3.847e-02  7.881e-02   0.488  0.62545    
## HeadInjurySí               -4.444e-02  1.112e-01  -0.400  0.68951    
## HypertensionSí              1.890e-01  8.881e-02   2.128  0.03336 *  
## SystolicBP                 -6.761e-04  1.222e-03  -0.553  0.58010    
## DiastolicBP                 1.497e-03  1.808e-03   0.828  0.40787    
## CholesterolTotal            3.384e-05  7.432e-04   0.046  0.96369    
## CholesterolLDL             -1.055e-03  7.317e-04  -1.441  0.14950    
## CholesterolHDL              2.483e-03  1.371e-03   1.811  0.07013 .  
## CholesterolTriglycerides    2.851e-04  3.115e-04   0.915  0.36008    
## MMSE                       -4.457e-02  3.798e-03 -11.734  < 2e-16 ***
## FunctionalAssessment       -2.053e-01  1.181e-02 -17.387  < 2e-16 ***
## MemoryComplaintsSí          1.188e+00  7.830e-02  15.167  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2792.3  on 2148  degrees of freedom
## Residual deviance: 2080.3  on 2119  degrees of freedom
## AIC: 2140.3
## 
## Number of Fisher Scoring iterations: 5
## 
## Call:
## glm(formula = Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + 
##     BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + 
##     SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + 
##     Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + 
##     DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + 
##     CholesterolTriglycerides + MMSE + FunctionalAssessment + 
##     MemoryComplaints + BehavioralProblems, family = binomial(link = "probit"), 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.5465  -0.7168  -0.3278   0.7284   3.3992  
## 
## Coefficients:
##                              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                 1.608e+00  4.915e-01   3.272  0.00107 ** 
## Age                        -3.431e-03  3.647e-03  -0.941  0.34688    
## GenderFemenino             -1.436e-02  6.573e-02  -0.219  0.82702    
## EthnicityAfroamericano     -1.452e-01  8.399e-02  -1.729  0.08378 .  
## EthnicityAsiático           1.719e-01  1.135e-01   1.515  0.12969    
## EthnicityOtro              -1.765e-01  1.163e-01  -1.517  0.12932    
## EducationLevelSecundaria   -1.493e-01  8.857e-02  -1.686  0.09186 .  
## EducationLevelLicenciatura -1.361e-01  9.363e-02  -1.454  0.14596    
## EducationLevelSuperior     -2.079e-01  1.282e-01  -1.622  0.10471    
## BMI                        -2.216e-03  4.545e-03  -0.488  0.62578    
## SmokingSí                  -8.385e-02  7.304e-02  -1.148  0.25100    
## AlcoholConsumption         -4.741e-03  5.691e-03  -0.833  0.40482    
## PhysicalActivity           -1.717e-03  1.136e-02  -0.151  0.87983    
## DietQuality                 6.256e-03  1.139e-02   0.549  0.58294    
## SleepQuality               -3.646e-02  1.871e-02  -1.948  0.05139 .  
## FamilyHistoryAlzheimersSí  -7.254e-02  7.600e-02  -0.954  0.33985    
## CardiovascularDiseaseSí     1.112e-01  9.168e-02   1.213  0.22528    
## DiabetesSí                 -5.210e-02  9.442e-02  -0.552  0.58109    
## DepressionSí                3.145e-02  8.182e-02   0.384  0.70065    
## HeadInjurySí               -1.233e-01  1.154e-01  -1.068  0.28532    
## HypertensionSí              1.539e-01  9.244e-02   1.665  0.09596 .  
## SystolicBP                 -4.431e-04  1.269e-03  -0.349  0.72691    
## DiastolicBP                 9.708e-04  1.869e-03   0.519  0.60349    
## CholesterolTotal            3.315e-05  7.677e-04   0.043  0.96556    
## CholesterolLDL             -1.136e-03  7.631e-04  -1.489  0.13662    
## CholesterolHDL              2.108e-03  1.422e-03   1.483  0.13810    
## CholesterolTriglycerides    2.299e-04  3.233e-04   0.711  0.47700    
## MMSE                       -4.965e-02  4.006e-03 -12.396  < 2e-16 ***
## FunctionalAssessment       -2.223e-01  1.252e-02 -17.756  < 2e-16 ***
## MemoryComplaintsSí          1.286e+00  8.164e-02  15.751  < 2e-16 ***
## BehavioralProblemsSí        1.080e+00  8.964e-02  12.047  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2792.3  on 2148  degrees of freedom
## Residual deviance: 1927.5  on 2118  degrees of freedom
## AIC: 1989.5
## 
## Number of Fisher Scoring iterations: 5
## 
## Call:
## glm(formula = Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + 
##     BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + 
##     SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + 
##     Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + 
##     DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + 
##     CholesterolTriglycerides + MMSE + FunctionalAssessment + 
##     MemoryComplaints + BehavioralProblems + ADL, family = binomial(link = "probit"), 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.7344  -0.6066  -0.2015   0.5355   4.5397  
## 
## Coefficients:
##                              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                 2.957e+00  5.375e-01   5.501 3.78e-08 ***
## Age                        -5.825e-03  3.932e-03  -1.481   0.1385    
## GenderFemenino             -4.247e-02  7.085e-02  -0.599   0.5489    
## EthnicityAfroamericano     -1.120e-01  9.131e-02  -1.226   0.2200    
## EthnicityAsiático           1.338e-01  1.226e-01   1.092   0.2749    
## EthnicityOtro              -1.289e-01  1.258e-01  -1.024   0.3058    
## EducationLevelSecundaria   -1.381e-01  9.564e-02  -1.444   0.1487    
## EducationLevelLicenciatura -9.298e-02  1.019e-01  -0.912   0.3617    
## EducationLevelSuperior     -2.052e-01  1.364e-01  -1.504   0.1326    
## BMI                        -3.946e-03  4.915e-03  -0.803   0.4221    
## SmokingSí                  -1.361e-01  7.915e-02  -1.720   0.0855 .  
## AlcoholConsumption         -4.759e-03  6.106e-03  -0.779   0.4357    
## PhysicalActivity           -4.997e-03  1.226e-02  -0.407   0.6837    
## DietQuality                 6.241e-03  1.227e-02   0.509   0.6110    
## SleepQuality               -3.516e-02  2.014e-02  -1.745   0.0809 .  
## FamilyHistoryAlzheimersSí  -7.240e-02  8.234e-02  -0.879   0.3792    
## CardiovascularDiseaseSí     9.647e-02  9.826e-02   0.982   0.3262    
## DiabetesSí                  5.014e-03  1.012e-01   0.050   0.9605    
## DepressionSí                2.304e-02  8.769e-02   0.263   0.7928    
## HeadInjurySí               -2.169e-01  1.244e-01  -1.743   0.0813 .  
## HypertensionSí              1.341e-01  9.925e-02   1.351   0.1766    
## SystolicBP                 -1.167e-04  1.366e-03  -0.085   0.9319    
## DiastolicBP                 1.076e-03  2.005e-03   0.537   0.5915    
## CholesterolTotal            2.763e-05  8.266e-04   0.033   0.9733    
## CholesterolLDL             -1.655e-03  8.283e-04  -1.998   0.0458 *  
## CholesterolHDL              2.566e-03  1.531e-03   1.676   0.0937 .  
## CholesterolTriglycerides    3.893e-04  3.482e-04   1.118   0.2636    
## MMSE                       -5.728e-02  4.391e-03 -13.045  < 2e-16 ***
## FunctionalAssessment       -2.412e-01  1.382e-02 -17.456  < 2e-16 ***
## MemoryComplaintsSí          1.413e+00  8.928e-02  15.827  < 2e-16 ***
## BehavioralProblemsSí        1.347e+00  9.945e-02  13.543  < 2e-16 ***
## ADL                        -2.213e-01  1.349e-02 -16.401  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2792.3  on 2148  degrees of freedom
## Residual deviance: 1609.0  on 2117  degrees of freedom
## AIC: 1673
## 
## Number of Fisher Scoring iterations: 6

{, echo=FALSEr} anova2(modelo11,modelo24,test = "lr")

Se aplicó una prueba de razón de verosimilitud para comparar dos modelos logísticos. La hipótesis nula (\(H_0\)) de esta prueba establece que las variables adicionales incluidas en el modelo 2 no mejoran significativamente el ajuste del modelo en comparación con el modelo 1. El resultado de la prueba arrojó un estadístico Chi-cuadrado de 145.65 con 13 grados de libertad y un valor p de < 2.2e-16, el cual es considerablemente menor al nivel de significancia comúnmente utilizado (α = 0.05). En consecuencia, se rechaza la hipótesis nula.

Por lo tanto, se concluye que la inclusión de las variables adicionales en el modelo 2 mejora significativamente el ajuste del modelo para predecir el diagnóstico.

## 
##   Likelihood-ratio test 
## 
## Model 1 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + CholesterolTriglycerides + MMSE 
## Model 2 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + CholesterolTriglycerides + MMSE + FunctionalAssessment 
## 
##         Chi    df  Pr(Chisq>)    
## 1 vs 2 298.68   1   < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Se aplicó una prueba de razón de verosimilitud para comparar dos modelos logísticos. La hipótesis nula (\(H_0\)) de esta prueba establece que la inclusión de la variable FunctionalAssessment no mejora significativamente el ajuste del modelo en comparación con el modelo sin dicha variable. El resultado de la prueba arrojó un estadístico Chi-cuadrado de 298.68 con 1 grado de libertad y un valor p de < 2.2e-16, el cual es considerablemente menor al nivel de significancia comúnmente utilizado (α = 0.05). En consecuencia, se rechaza la hipótesis nula. Por lo tanto, se concluye que la variable FunctionalAssessment mejora significativamente la capacidad predictiva del modelo para el diagnóstico.

## 
##   Likelihood-ratio test 
## 
## Model 1 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + CholesterolTriglycerides + MMSE + FunctionalAssessment 
## Model 2 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + CholesterolTriglycerides + MMSE + FunctionalAssessment + MemoryComplaints 
## 
##         Chi    df  Pr(Chisq>)    
## 1 vs 2 247.08   1   < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Se aplicó una prueba de razón de verosimilitud para comparar dos modelos logísticos. La hipótesis nula (\(H_0\)) establece que la adición de la variable MemoryComplaints no mejora significativamente el ajuste del modelo, que ya incluye variables sociodemográficas, clínicas, funcionales y cognitivas. El estadístico de la prueba fue de 247.08 con 1 grado de libertad, y el valor p asociado fue < 2.2e-16, lo cual es significativamente menor que el nivel de significancia comúnmente usado (α = 0.05). En consecuencia, se rechaza la hipótesis nula. Por lo tanto, se concluye que la variable MemoryComplaints aporta información adicional valiosa y mejora significativamente la capacidad del modelo para predecir el diagnóstico.

## 
##   Likelihood-ratio test 
## 
## Model 1 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + CholesterolTriglycerides + MMSE + FunctionalAssessment + MemoryComplaints + BehavioralProblems 
## Model 2 :  Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + CholesterolTriglycerides + MMSE + FunctionalAssessment + MemoryComplaints + BehavioralProblems + ADL 
## 
##         Chi    df  Pr(Chisq>)    
## 1 vs 2 318.52   1   < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Se aplicó una prueba de razón de verosimilitud para comparar dos modelos logísticos. La hipótesis nula (\(H_0\)) plantea que la inclusión de la variable ADL (Actividades de la Vida Diaria) no mejora significativamente el ajuste del modelo, que ya incorpora variables sociodemográficas, clínicas, cognitivas, funcionales y de comportamiento. El resultado de la prueba arrojó un estadístico Chi-cuadrado de 318.52 con 1 grado de libertad y un valor p de < 2.2e-16, considerablemente menor que el nivel de significancia (α = 0.05). En consecuencia, se rechaza la hipótesis nula. Por lo tanto, se concluye que la inclusión de ADL mejora significativamente la capacidad predictiva del modelo para el diagnóstico.

De acuerdo con los resultados anteriores, cada nueva variable (o conjunto de variables) contribuyó de manera significativa al ajuste del modelo, lo que se evidencia por los valores p < 0.05 en cada comparación. En particular, el último modelo evaluado el cual es el siguiente

## 
## Call:
## glm(formula = Diagnosis ~ Age + Gender + Ethnicity + EducationLevel + 
##     BMI + Smoking + AlcoholConsumption + PhysicalActivity + DietQuality + 
##     SleepQuality + FamilyHistoryAlzheimers + CardiovascularDisease + 
##     Diabetes + Depression + HeadInjury + Hypertension + SystolicBP + 
##     DiastolicBP + CholesterolTotal + CholesterolLDL + CholesterolHDL + 
##     CholesterolTriglycerides + MMSE + FunctionalAssessment + 
##     MemoryComplaints + BehavioralProblems + ADL, family = binomial(link = "probit"), 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.7344  -0.6066  -0.2015   0.5355   4.5397  
## 
## Coefficients:
##                              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                 2.957e+00  5.375e-01   5.501 3.78e-08 ***
## Age                        -5.825e-03  3.932e-03  -1.481   0.1385    
## GenderFemenino             -4.247e-02  7.085e-02  -0.599   0.5489    
## EthnicityAfroamericano     -1.120e-01  9.131e-02  -1.226   0.2200    
## EthnicityAsiático           1.338e-01  1.226e-01   1.092   0.2749    
## EthnicityOtro              -1.289e-01  1.258e-01  -1.024   0.3058    
## EducationLevelSecundaria   -1.381e-01  9.564e-02  -1.444   0.1487    
## EducationLevelLicenciatura -9.298e-02  1.019e-01  -0.912   0.3617    
## EducationLevelSuperior     -2.052e-01  1.364e-01  -1.504   0.1326    
## BMI                        -3.946e-03  4.915e-03  -0.803   0.4221    
## SmokingSí                  -1.361e-01  7.915e-02  -1.720   0.0855 .  
## AlcoholConsumption         -4.759e-03  6.106e-03  -0.779   0.4357    
## PhysicalActivity           -4.997e-03  1.226e-02  -0.407   0.6837    
## DietQuality                 6.241e-03  1.227e-02   0.509   0.6110    
## SleepQuality               -3.516e-02  2.014e-02  -1.745   0.0809 .  
## FamilyHistoryAlzheimersSí  -7.240e-02  8.234e-02  -0.879   0.3792    
## CardiovascularDiseaseSí     9.647e-02  9.826e-02   0.982   0.3262    
## DiabetesSí                  5.014e-03  1.012e-01   0.050   0.9605    
## DepressionSí                2.304e-02  8.769e-02   0.263   0.7928    
## HeadInjurySí               -2.169e-01  1.244e-01  -1.743   0.0813 .  
## HypertensionSí              1.341e-01  9.925e-02   1.351   0.1766    
## SystolicBP                 -1.167e-04  1.366e-03  -0.085   0.9319    
## DiastolicBP                 1.076e-03  2.005e-03   0.537   0.5915    
## CholesterolTotal            2.763e-05  8.266e-04   0.033   0.9733    
## CholesterolLDL             -1.655e-03  8.283e-04  -1.998   0.0458 *  
## CholesterolHDL              2.566e-03  1.531e-03   1.676   0.0937 .  
## CholesterolTriglycerides    3.893e-04  3.482e-04   1.118   0.2636    
## MMSE                       -5.728e-02  4.391e-03 -13.045  < 2e-16 ***
## FunctionalAssessment       -2.412e-01  1.382e-02 -17.456  < 2e-16 ***
## MemoryComplaintsSí          1.413e+00  8.928e-02  15.827  < 2e-16 ***
## BehavioralProblemsSí        1.347e+00  9.945e-02  13.543  < 2e-16 ***
## ADL                        -2.213e-01  1.349e-02 -16.401  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2792.3  on 2148  degrees of freedom
## Residual deviance: 1609.0  on 2117  degrees of freedom
## AIC: 1673
## 
## Number of Fisher Scoring iterations: 6

##                 [,1]
##    [1,] -0.550217901
##    [2,] -0.417393949
##    [3,] -0.310555739
##    [4,] -0.575086762
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##   [18,]  1.460865805
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## [2059,]  0.767706897
## [2060,] -0.974930341
## [2061,]  0.275802343
## [2062,]  2.581149021
## [2063,] -0.106169827
## [2064,]  2.698515486
## [2065,]  1.747820098
## [2066,]  2.353075818
## [2067,]  1.954702189
## [2068,] -0.702448843
## [2069,] -0.412770943
## [2070,] -1.916203775
## [2071,] -1.221569106
## [2072,] -0.728470649
## [2073,] -0.592574031
## [2074,]  2.952445482
## [2075,]  2.495267449
## [2076,] -0.202060135
## [2077,]  0.308299865
## [2078,]  1.998651602
## [2079,] -0.345246401
## [2080,]  3.362869171
## [2081,]  1.664147159
## [2082,] -0.403994128
## [2083,] -2.412250904
## [2084,] -0.231650364
## [2085,]  1.326487325
## [2086,]  0.660259737
## [2087,] -1.389299373
## [2088,]  1.477748614
## [2089,]  1.693909128
## [2090,]  1.583792554
## [2091,] -0.108383131
## [2092,] -1.102272543
## [2093,]  0.362192361
## [2094,] -0.580085051
## [2095,] -0.445597227
## [2096,] -0.202717916
## [2097,]  3.100990029
## [2098,] -2.541254283
## [2099,]  0.884727645
## [2100,] -1.081553202
## [2101,]  3.207582587
## [2102,]  0.885132672
## [2103,]  3.164575753
## [2104,] -0.614751802
## [2105,]  0.443238031
## [2106,] -1.015105627
## [2107,]  2.020975191
## [2108,] -0.862329722
## [2109,] -1.431312380
## [2110,] -1.321617530
## [2111,] -1.079774766
## [2112,]  0.835019126
## [2113,] -0.246676256
## [2114,]  1.590329723
## [2115,]  4.539751076
## [2116,] -1.236469504
## [2117,] -0.567156150
## [2118,] -1.470719149
## [2119,] -0.696025062
## [2120,] -0.303067423
## [2121,]  3.058374165
## [2122,]  1.749098890
## [2123,] -0.676046661
## [2124,] -0.083836598
## [2125,]  2.486184146
## [2126,]  0.956789201
## [2127,]  0.540129228
## [2128,] -2.039213489
## [2129,] -1.336223274
## [2130,] -0.262672847
## [2131,]  0.876216065
## [2132,]  4.005924610
## [2133,]  0.702227808
## [2134,]  0.079110373
## [2135,] -1.855607571
## [2136,]  0.786226655
## [2137,]  0.290120079
## [2138,] -0.440656084
## [2139,]  2.278478516
## [2140,] -0.070386777
## [2141,] -0.977229135
## [2142,] -0.033910811
## [2143,]  3.082216401
## [2144,]  0.877907867
## [2145,]  0.529004847
## [2146,]  1.816179459
## [2147,]  1.361323953
## [2148,]  1.312048566
## [2149,] -0.869553779
## 
##  Shapiro-Wilk normality test
## 
## data:  rsd
## W = 0.96965, p-value < 2.2e-16
## 
  |       
  | |   0%
  |       
  |+| 100%

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