Tablas de contingencia y GLMs

Instrucciones

Con los datos que se importan a continuación, concluir si es el tipo tratamiento médico (T: A,B), o la clínica (Clinic: uno,dos) lo que explica el pronóstico (positivo, negativo).

packages

if(!require(googlesheets4)){install.packages("googlesheets4")}
if(!require(googledrive)){install.packages("googledrive")}
if(!require(ggplot2)){install.packages("ggplot2")}
if(!require(DescTools)){install.packages("DescTools")}
if(!require(MASS)){install.packages("MASS")}
if(!require(binom)){install.packages("binom")}
if(!require(scales)){install.packages("scales")}
##
library(googlesheets4)
library(googledrive)
library(ggplot2)
library(DescTools)
library(MASS)
library(binom)
library(scales)

Table Treatment & Clinics

ss= "https://docs.google.com/spreadsheets/d/1RFCYi7rjRPcbzcB01Nq3jgtc_o21LaDU8yFU41gjQKs/edit?usp=sharing"
hoja= "clinicTrat"
rango = "B4:E8"
#
gs4_deauth()
trat <- read_sheet(ss,
                   sheet=hoja,
                   range=rango,
                   col_names=TRUE
                   )

✔ Reading from ClinicaxTratamiento.
✔ Range ''clinicTrat'!B4:E8'.

trat$Clinic <- as.factor(trat$Clinic)
trat$T <- as.factor(trat$T) 
#
trat$pr.exito <- trat$Posit / 
  (trat$Posit+trat$Negat)           # Proporción de éxito (resultado positivo al tratamiento)
trat

ggplot

ggplot( aes( x= T, y= pr.exito, fill = T), data= trat) + 
  geom_bar(stat="identity", position= "dodge")

ggplot( aes( x= Clinic, y= pr.exito), data= trat) + 
  geom_bar(stat="identity", position= "dodge")

p <- ggplot( aes( x= Clinic, y= pr.exito, fill = T), data= trat) + 
  geom_bar(stat="identity", position= "dodge")
p

obs <-  cbind(Pronóstico_Positivo =trat$Posit, Pronóstico_Negativo= trat$Negat)
obs

     Pronóstico_Positivo Pronóstico_Negativo
[1,]                   4                  16
[2,]                  22                  32
[3,]                   8                  32
[4,]                  12                   8

mosaicplot(obs, main = , xlab = , ylab = )

Odds

trat$Odds.exito <- trat$Posit / trat$Negat
trat

glm

```r
# Variable respuesta es binaria (dos columnas)
Y.trat <- cbind(trat$Posit, trat$Negat)
Y.trat

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 [,1] [,2]

[1,] 4 16 [2,] 22 32 [3,] 8 32 [4,] 12 8

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#### Modelo comparando clínicas

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```r
```r
glm.clinic <- glm( Y.trat ~ trat$Clinic, family=binomial)
summary(glm.clinic)

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Call: glm(formula = Y.trat ~ trat$Clinic, family = binomial)

Deviance Residuals: 1 2 3 4
-1.4844 0.8536 -1.8696 2.4359

Coefficients: Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.61310 0.24351 -2.518 0.0118 * trat$Clinicuno -0.08004 0.36646 -0.218 0.8271
— Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 12.409  on 3  degrees of freedom

Residual deviance: 12.361 on 2 degrees of freedom AIC: 30.97

Number of Fisher Scoring iterations: 4

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#### Modelo comparando tratamientos médicos

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```r
```r
glm.trat <- glm( Y.trat ~ trat$T, family=binomial)
summary(glm.trat)

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Call: glm(formula = Y.trat ~ trat$T, family = binomial)

Deviance Residuals: 1 2 3 4
0.0000 -0.7704 0.0000 1.2599

Coefficients: Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.3863 0.3227 -4.295 1.74e-05 * trat$TB 1.2238 0.3982 3.073 0.00212 — Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 12.409  on 3  degrees of freedom

Residual deviance: 2.181 on 2 degrees of freedom AIC: 20.79

Number of Fisher Scoring iterations: 3

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#### Modelo en busca de interacción: Clinic * T

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```r
```r
glm <- glm( Y.trat ~ trat$T * trat$Clinic, family=binomial)
summary(glm)

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Call: glm(formula = Y.trat ~ trat\(T * trat\)Clinic, family = binomial)

Deviance Residuals: [1] 0 0 0 0

Coefficients: Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.386e+00 5.590e-01 -2.480 0.0131 * trat\(TB 1.012e+00 6.239e-01 1.622 0.1049 trat\)Clinicuno -5.861e-13 6.847e-01 0.000 1.0000
trat\(TB:trat\)Clinicuno 7.802e-01 8.682e-01 0.899 0.3689
— Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 1.2409e+01  on 3  degrees of freedom

Residual deviance: 8.8818e-15 on 0 degrees of freedom AIC: 22.609

Number of Fisher Scoring iterations: 3

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#### Modelo aditivo: Clinic + T

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Call: glm(formula = Y.trat ~ trat\(T + trat\)Clinic, family = binomial)

Deviance Residuals: 1 2 3 4
0.6023 -0.2762 -0.3845 0.4521

Coefficients: Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.7352 0.4507 -3.850 0.000118 *** trat\(TB 1.4369 0.4458 3.223 0.001268 ** trat\)Clinicuno 0.4987 0.4277 1.166 0.243581
— Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 12.40871  on 3  degrees of freedom

Residual deviance: 0.79129 on 1 degrees of freedom AIC: 21.4

Number of Fisher Scoring iterations: 4 ```

Refeencias

Agresti, A., & Coull, B. A. (1998). Approximate is better than “exact” for interval estimation of binomial proportions. The American Statistician, 52(2), 119–126.