TH BIO CARRO VINICKI
2024-12-10
Carga de librerías. Deben estar previamente instaladas
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library(tableone)
options(scipen = 999, digits = 3, encoding = 'UTF-8') Carga del dataset. También se puede realizar mediante File, Import dataset, from excel.
Framingham_1_ <- read_excel("C:/Users/Administrador/Downloads/Framingham (1).xlsx")- Calculen la tasa de mortalidad global DEATH de la población total. Previamenteponemos en minúscula para agilizar la escritura. Luego pasamos a factor las variables CHR
mortalidad_global <- (sum(Framingham_1_$DEATH, na.rm = TRUE) / nrow(Framingham_1_)) * 100
mortalidad_global## [1] 35Framingham_1_ <- Framingham_1_ %>% mutate(across(c(CURSMOKE, SEX, DIABETES, PREVCHD, PREVSTRK,PREVHYP, DEATH, ANGINA, HOSPMI, ANYCHD, STROKE), as.factor))
names (Framingham_1_)<- tolower (names (Framingham_1_))
#La mortalidad global fue del 35%2.Armen una Tabla 1 para las variables SEX, AGE, SYSBP, CURSMOKE, CIGPDAY, BMI, DIABETES, PREVCHD, PREVSTRK, PREVHYP agrupando por DEATH Si – No. Para ello evaluen la distribución de las variables continuas con testeos y gráficos para definir qué medida de resumen le corresponde a cada una.
#La tabla 1 (como tabla de presentación) se adjunta en el archivo THBIO CARRO VINICKI.DOCX
#variable edad: la distribución se considera normal (ver entrega en word) y también su distribución en cada estrato de DEATH
hist(Framingham_1_$age)
qqnorm(Framingham_1_$age)
qqline(Framingham_1_$age)
describe(Framingham_1_$age)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 4434 49.9 8.68 49 49.7 10.4 32 70 38 0.19 -1.03 0.13shapiro.test(Framingham_1_$age)##
## Shapiro-Wilk normality test
##
## data: Framingham_1_$age
## W = 1, p-value <0.0000000000000002#age por grupo death/nodeath
hist(Framingham_1_$age[Framingham_1_$death==0])
hist(Framingham_1_$age[Framingham_1_$death==1])
describeBy(Framingham_1_$age,Framingham_1_$death)##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 2884 47.2 7.67 46 46.8 8.9 32 69 37 0.43 -0.72 0.14
## ------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1550 54.9 8.22 56 55.4 8.9 34 70 36 -0.39 -0.83 0.21shapiro.test(Framingham_1_$age [Framingham_1_$death==0])##
## Shapiro-Wilk normality test
##
## data: Framingham_1_$age[Framingham_1_$death == 0]
## W = 1, p-value <0.0000000000000002shapiro.test(Framingham_1_$age [Framingham_1_$death==1])##
## Shapiro-Wilk normality test
##
## data: Framingham_1_$age[Framingham_1_$death == 1]
## W = 1, p-value <0.0000000000000002#variable presion sistolica: la distribución se considera normal(ver entrega en word)
hist(Framingham_1_$sysbp)
qqnorm(Framingham_1_$sysbp)
qqline(Framingham_1_$sysbp)
describe(Framingham_1_$sysbp)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 4434 133 22.4 129 131 19.3 83.5 295 212 1.15 2.08 0.34shapiro.test(Framingham_1_$sysbp)##
## Shapiro-Wilk normality test
##
## data: Framingham_1_$sysbp
## W = 0.9, p-value <0.0000000000000002#sysbp por grupo death/nodeath
hist(Framingham_1_$sysbp[Framingham_1_$death==0])
hist(Framingham_1_$sysbp[Framingham_1_$death==1])
describeBy(Framingham_1_$sysbp,Framingham_1_$death)##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 2884 128 18.5 125 126 16.3 85 243 158 1.02 1.75 0.35
## ------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1550 142 25.8 138 140 23.7 83.5 295 212 0.89 1.17 0.66shapiro.test(Framingham_1_$sysbp[Framingham_1_$death==0])##
## Shapiro-Wilk normality test
##
## data: Framingham_1_$sysbp[Framingham_1_$death == 0]
## W = 0.9, p-value <0.0000000000000002shapiro.test(Framingham_1_$sysbp[Framingham_1_$death==1])##
## Shapiro-Wilk normality test
##
## data: Framingham_1_$sysbp[Framingham_1_$death == 1]
## W = 1, p-value <0.0000000000000002#variable numero de cigarrillos dia: la distribución se considera no normal(ver entrega en word)
hist(Framingham_1_$cigpday)
qqnorm(Framingham_1_$cigpday)
qqline(Framingham_1_$cigpday)
describe(Framingham_1_$cigpday)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 4402 8.97 11.9 0 6.84 0 0 70 70 1.26 1.07 0.18shapiro.test(Framingham_1_$cigpday)##
## Shapiro-Wilk normality test
##
## data: Framingham_1_$cigpday
## W = 0.8, p-value <0.0000000000000002#cigpday por grupo death/nodeath
hist(Framingham_1_$cigpday[Framingham_1_$death==0])
hist(Framingham_1_$cigpday[Framingham_1_$death==1])
describeBy(Framingham_1_$cigpday,Framingham_1_$death)##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 2862 8.44 11.4 0 6.42 0 0 70 70 1.3 1.25 0.21
## ------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1540 9.95 12.8 1 7.79 1.48 0 60 60 1.16 0.7 0.33shapiro.test(Framingham_1_$cigpday[Framingham_1_$death==0])##
## Shapiro-Wilk normality test
##
## data: Framingham_1_$cigpday[Framingham_1_$death == 0]
## W = 0.8, p-value <0.0000000000000002shapiro.test(Framingham_1_$cigpday[Framingham_1_$death==1])##
## Shapiro-Wilk normality test
##
## data: Framingham_1_$cigpday[Framingham_1_$death == 1]
## W = 0.8, p-value <0.0000000000000002#variable indice de masa corporal: la distribución se considera normal(ver entrega en word)
hist(Framingham_1_$bmi)
qqnorm(Framingham_1_$bmi)
qqline(Framingham_1_$bmi)
describe(Framingham_1_$bmi)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 4415 25.9 4.1 25.4 25.6 3.68 15.5 56.8 41.3 0.98 2.6 0.06shapiro.test(Framingham_1_$bmi)##
## Shapiro-Wilk normality test
##
## data: Framingham_1_$bmi
## W = 1, p-value <0.0000000000000002#bmi por grupo death/nodeath
describeBy(Framingham_1_$bmi,Framingham_1_$death)##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 2878 25.5 3.91 25.1 25.3 3.53 16.6 56.8 40.2 1.04 3.1 0.07
## ------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1537 26.4 4.38 26.1 26.1 3.83 15.5 51.3 35.7 0.84 1.89 0.11hist(Framingham_1_$bmi[Framingham_1_$death==0])
hist(Framingham_1_$bmi[Framingham_1_$death==1])
shapiro.test(Framingham_1_$bmi[Framingham_1_$death==0])##
## Shapiro-Wilk normality test
##
## data: Framingham_1_$bmi[Framingham_1_$death == 0]
## W = 1, p-value <0.0000000000000002shapiro.test(Framingham_1_$bmi[Framingham_1_$death==1])##
## Shapiro-Wilk normality test
##
## data: Framingham_1_$bmi[Framingham_1_$death == 1]
## W = 1, p-value <0.0000000000000002#tabla 1
table1(~ sex + age + sysbp + cursmoke + cigpday + bmi+ diabetes+ prevchd + prevstrk + prevhyp|death,data=Framingham_1_)| 0 (N=2884) |
1 (N=1550) |
Overall (N=4434) |
|
|---|---|---|---|
| sex | |||
| 0 | 1783 (61.8%) | 707 (45.6%) | 2490 (56.2%) |
| 1 | 1101 (38.2%) | 843 (54.4%) | 1944 (43.8%) |
| age | |||
| Mean (SD) | 47.2 (7.67) | 54.9 (8.22) | 49.9 (8.68) |
| Median [Min, Max] | 46.0 [32.0, 69.0] | 56.0 [34.0, 70.0] | 49.0 [32.0, 70.0] |
| sysbp | |||
| Mean (SD) | 128 (18.5) | 142 (25.8) | 133 (22.4) |
| Median [Min, Max] | 125 [85.0, 243] | 138 [83.5, 295] | 129 [83.5, 295] |
| cursmoke | |||
| 0 | 1491 (51.7%) | 762 (49.2%) | 2253 (50.8%) |
| 1 | 1393 (48.3%) | 788 (50.8%) | 2181 (49.2%) |
| cigpday | |||
| Mean (SD) | 8.44 (11.4) | 9.95 (12.8) | 8.97 (11.9) |
| Median [Min, Max] | 0 [0, 70.0] | 1.00 [0, 60.0] | 0 [0, 70.0] |
| Missing | 22 (0.8%) | 10 (0.6%) | 32 (0.7%) |
| bmi | |||
| Mean (SD) | 25.5 (3.91) | 26.4 (4.38) | 25.8 (4.10) |
| Median [Min, Max] | 25.1 [16.6, 56.8] | 26.1 [15.5, 51.3] | 25.5 [15.5, 56.8] |
| Missing | 6 (0.2%) | 13 (0.8%) | 19 (0.4%) |
| diabetes | |||
| 0 | 2857 (99.1%) | 1456 (93.9%) | 4313 (97.3%) |
| 1 | 27 (0.9%) | 94 (6.1%) | 121 (2.7%) |
| prevchd | |||
| 0 | 2834 (98.3%) | 1406 (90.7%) | 4240 (95.6%) |
| 1 | 50 (1.7%) | 144 (9.3%) | 194 (4.4%) |
| prevstrk | |||
| 0 | 2877 (99.8%) | 1525 (98.4%) | 4402 (99.3%) |
| 1 | 7 (0.2%) | 25 (1.6%) | 32 (0.7%) |
| prevhyp | |||
| 0 | 2212 (76.7%) | 792 (51.1%) | 3004 (67.7%) |
| 1 | 672 (23.3%) | 758 (48.9%) | 1430 (32.3%) |
3.Analicen la relación entre presión arterial sistólica, como variable continua, y DEATH. Interpreten sus resultados.
Pista: Piensen que tipo de variables tienen para elegir el test correspondiente
#analisis de la variable presion sistolica en los grupos de muerte (si/no) para evaluar utilizacion de t test o wilcoxon((remitirse al archivo THBIO CARRO VINICKI.DOCX)). La hipótesis nula indica que la presión sistólica entre ambos grupos es similar. La hipótesis alternativa indica que la presión sistólica en ambos grupos es diferente
hist(Framingham_1_$sysbp[Framingham_1_$death==1])
hist(Framingham_1_$sysbp[Framingham_1_$death==0])
qqnorm(Framingham_1_$sysbp[Framingham_1_$death==1])
qqnorm(Framingham_1_$sysbp[Framingham_1_$death==0])
qqline(Framingham_1_$sysbp[Framingham_1_$death==1])
qqline(Framingham_1_$sysbp[Framingham_1_$death==0])
describeBy(Framingham_1_$sysbp, Framingham_1_$death)##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 2884 128 18.5 125 126 16.3 85 243 158 1.02 1.75 0.35
## ------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1550 142 25.8 138 140 23.7 83.5 295 212 0.89 1.17 0.66shapiro.test(Framingham_1_$sysbp[Framingham_1_$death==0])##
## Shapiro-Wilk normality test
##
## data: Framingham_1_$sysbp[Framingham_1_$death == 0]
## W = 0.9, p-value <0.0000000000000002shapiro.test(Framingham_1_$sysbp[Framingham_1_$death==1])##
## Shapiro-Wilk normality test
##
## data: Framingham_1_$sysbp[Framingham_1_$death == 1]
## W = 1, p-value <0.0000000000000002#en base a la distribución normal de la variable en ambos estratos, se decide utilizar t test
bartlett.test(Framingham_1_$sysbp,Framingham_1_$death)##
## Bartlett test of homogeneity of variances
##
## data: Framingham_1_$sysbp and Framingham_1_$death
## Bartlett's K-squared = 233, df = 1, p-value <0.0000000000000002#Hipótesis nula: Las varianzas son iguales. Hipótesis alternativa: las varianzas no son iguales. El resultado descarta la hipótesis nula, por lo cual se puede usar el comando de ttest sin aclarar VAR=true.
t.test(Framingham_1_$sysbp~Framingham_1_$death)##
## Welch Two Sample t-test
##
## data: Framingham_1_$sysbp by Framingham_1_$death
## t = -19, df = 2426, p-value <0.0000000000000002
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## -15.7 -12.8
## sample estimates:
## mean in group 0 mean in group 1
## 128 142#Se halla una diferencia estadísticamente significativa entre la presión sistólica de pacientes que fallecieron y de los que no fallecieron (ver entrega en word)- Dicotomicen la variable presión arterial sistólica (variable SYSBP) en menores de 140 (normotensos) y mayores o iguales 140 mm hg (hipertensos), llámenla CATHYP. Vuelvan a analizar la relación entre hipertensión arterial ahora como variable dicotómica y el evento DEATH. Reporten e interpreten la magnitud de la asociación (con intervalos de confianza) en caso de que exista una asociación entre estas dos variables.
Pista: Piensen si DEATH es incidencia o prevalencia…
#DEATH es incidencia dado que es una cohorte
#creamos la variable cathyp
Framingham_1_ <- Framingham_1_ %>% mutate(cathyp = factor(case_when(
sysbp < 140 ~ "normotensos",
sysbp >= 140 ~ "hipertensos",
)))
#cambiamos el orden de los niveles para mejorar la vision en la tabla y la interpretacion del OR
levels(Framingham_1_$cathyp)## [1] "hipertensos" "normotensos"levels(Framingham_1_$death)## [1] "0" "1"Framingham_1_ <- Framingham_1_ %>% mutate(death = factor(death, levels = c("1", "0")))
Framingham_1_ <- Framingham_1_ %>% mutate(cathyp = factor(cathyp, levels = c("hipertensos", "normotensos")))
levels(Framingham_1_$cathyp)## [1] "hipertensos" "normotensos"levels(Framingham_1_$death)## [1] "1" "0"tabla_cruzada <- table(Framingham_1_$cathyp,Framingham_1_$death)
tabla_cruzada##
## 1 0
## hipertensos 731 650
## normotensos 819 2234#aplicamos chi2 y fisher para relacionar las variables. Hipótesis nula: No existe relación entre la presencia de hipertensión arterial y la muerte. Según los resultados, las mismas presentan una asociación estadísticamente significativa. El estadístico utilizado fue CHI2
tabla2x2 <- crosstab(Framingham_1_$cathyp,Framingham_1_$death, prop.r = TRUE, prop.c = TRUE, chisq = TRUE, fisher = TRUE, expected = TRUE)
tabla2x2## Cell Contents
## |-------------------------|
## | Count |
## | Expected Values |
## | Row Percent |
## | Column Percent |
## |-------------------------|
##
## =============================================
## Framingham_1_$death
## Framingham_1_$cathyp 1 0 Total
## ---------------------------------------------
## hipertensos 731 650 1381
## 483 898
## 52.9% 47.1% 31.1%
## 47.2% 22.5%
## ---------------------------------------------
## normotensos 819 2234 3053
## 1067 1986
## 26.8% 73.2% 68.9%
## 52.8% 77.5%
## ---------------------------------------------
## Total 1550 2884 4434
## 35% 65%
## =============================================
##
## Statistics for All Table Factors
##
## Pearson's Chi-squared test
## ------------------------------------------------------------
## Chi^2 = 285 d.f. = 1 p <0.0000000000000002
##
## Pearson's Chi-squared test with Yates' continuity correction
## ------------------------------------------------------------
## Chi^2 = 284 d.f. = 1 p <0.0000000000000002
##
##
## Fisher's Exact Test for Count Data
## ------------------------------------------------------------
## Sample estimate odds ratio: 3.07
##
## Alternative hypothesis: true odds ratio is not equal to 1
## p <0.0000000000000002
## 95% confidence interval: 2.68 3.51
##
## Alternative hypothesis: true odds ratio is less than 1
## p = 1
## 95%s confidence interval: % 0 3.44
##
## Alternative hypothesis: true odds ratio is greater than 1
## p <0.0000000000000002
## 95%s confidence interval: % 2.74 Inf
##
## Minimum expected frequency: 483#Se calcula el Riesgo relativo para obtener la medida de asociación
epi.2by2(table(Framingham_1_$cathyp,Framingham_1_$death)[c("hipertensos","normotensos"),c("1","0")], method = "cohort.count", conf.level = 0.95, outcome = "as.columns")## Outcome + Outcome - Total Inc risk *
## Exposed + 731 650 1381 52.93 (50.26 to 55.59)
## Exposed - 819 2234 3053 26.83 (25.26 to 28.44)
## Total 1550 2884 4434 34.96 (33.55 to 36.38)
##
## Point estimates and 95% CIs:
## -------------------------------------------------------------------
## Inc risk ratio 1.97 (1.83, 2.13)
## Inc odds ratio 3.07 (2.69, 3.50)
## Attrib risk in the exposed * 26.11 (23.04, 29.17)
## Attrib fraction in the exposed (%) 49.32 (45.27, 53.07)
## Attrib risk in the population * 8.13 (6.02, 10.24)
## Attrib fraction in the population (%) 23.26 (20.32, 26.10)
## -------------------------------------------------------------------
## Uncorrected chi2 test that OR = 1: chi2(1) = 285.029 Pr>chi2 = <0.001
## Fisher exact test that OR = 1: Pr>chi2 = <0.001
## Wald confidence limits
## CI: confidence interval
## * Outcomes per 100 population units#el riesgo de morir para personas hipertensas es de 1.97 veces (1.83, 2.13) que para personas normotensas con una certeza del 95%5.Evalúen si la variable que consigna CURSMOKE se comporta como confundidor y/o modificador de efecto en la relación entre hipertensión arterial como variable dicotómica CATHYP (variable que dicotomizaron en el punto 3, ojo, no es PREVHYP) y DEATH. Justifiquen su respuesta.
Pista: Si estamos agregando una segunda variable para explicar la relación entre un factor de riesgo y un evento ¿qué test podemos usar?
#Para evaluar si es confundidor, se debe explorar la relación cursmoke vs cathyp y cursmoke vs death con el objetivo de ver si se relaciona con la exposicion y el evento
#ordenamos los niveles de la variable cursmoke
Framingham_1_ <- Framingham_1_ %>% mutate(cursmoke = factor(cursmoke, levels = c("1", "0")))
#Relación cathyp vs death. Se realiza el estadístico Chi2, con la hipótesis nula de que no hay asociación entre hipertensión y muerte. Al realizar el test, se encuentra asociación entre ambas variables, por lo cual se descarta la hipótesis nula.
crosstab(Framingham_1_$cathyp,Framingham_1_$death,prop.r = TRUE, prop.c = TRUE, chisq = TRUE, fisher = TRUE, expected = TRUE)
## Cell Contents
## |-------------------------|
## | Count |
## | Expected Values |
## | Row Percent |
## | Column Percent |
## |-------------------------|
##
## =============================================
## Framingham_1_$death
## Framingham_1_$cathyp 1 0 Total
## ---------------------------------------------
## hipertensos 731 650 1381
## 483 898
## 52.9% 47.1% 31.1%
## 47.2% 22.5%
## ---------------------------------------------
## normotensos 819 2234 3053
## 1067 1986
## 26.8% 73.2% 68.9%
## 52.8% 77.5%
## ---------------------------------------------
## Total 1550 2884 4434
## 35% 65%
## =============================================
##
## Statistics for All Table Factors
##
## Pearson's Chi-squared test
## ------------------------------------------------------------
## Chi^2 = 285 d.f. = 1 p <0.0000000000000002
##
## Pearson's Chi-squared test with Yates' continuity correction
## ------------------------------------------------------------
## Chi^2 = 284 d.f. = 1 p <0.0000000000000002
##
##
## Fisher's Exact Test for Count Data
## ------------------------------------------------------------
## Sample estimate odds ratio: 3.07
##
## Alternative hypothesis: true odds ratio is not equal to 1
## p <0.0000000000000002
## 95% confidence interval: 2.68 3.51
##
## Alternative hypothesis: true odds ratio is less than 1
## p = 1
## 95%s confidence interval: % 0 3.44
##
## Alternative hypothesis: true odds ratio is greater than 1
## p <0.0000000000000002
## 95%s confidence interval: % 2.74 Inf
##
## Minimum expected frequency: 483#se obtiene la magnitud de la asociación a través del cálculo del RR
epi.2by2(table(Framingham_1_$cathyp,Framingham_1_$death)[c("hipertensos","normotensos"),c("1","0")], method = "cohort.count", conf.level = 0.95, outcome = "as.columns")## Outcome + Outcome - Total Inc risk *
## Exposed + 731 650 1381 52.93 (50.26 to 55.59)
## Exposed - 819 2234 3053 26.83 (25.26 to 28.44)
## Total 1550 2884 4434 34.96 (33.55 to 36.38)
##
## Point estimates and 95% CIs:
## -------------------------------------------------------------------
## Inc risk ratio 1.97 (1.83, 2.13)
## Inc odds ratio 3.07 (2.69, 3.50)
## Attrib risk in the exposed * 26.11 (23.04, 29.17)
## Attrib fraction in the exposed (%) 49.32 (45.27, 53.07)
## Attrib risk in the population * 8.13 (6.02, 10.24)
## Attrib fraction in the population (%) 23.26 (20.32, 26.10)
## -------------------------------------------------------------------
## Uncorrected chi2 test that OR = 1: chi2(1) = 285.029 Pr>chi2 = <0.001
## Fisher exact test that OR = 1: Pr>chi2 = <0.001
## Wald confidence limits
## CI: confidence interval
## * Outcomes per 100 population units#Relación cursmoke vs cathyp (se encuentra asociación mediante el test chi2)
crosstab(Framingham_1_$cursmoke,Framingham_1_$cathyp,prop.r = TRUE, prop.c = TRUE, chisq = TRUE, fisher = TRUE, expected = TRUE)
## Cell Contents
## |-------------------------|
## | Count |
## | Expected Values |
## | Row Percent |
## | Column Percent |
## |-------------------------|
##
## ===========================================================
## Framingham_1_$cathyp
## Framingham_1_$cursmoke hipertensos normotensos Total
## -----------------------------------------------------------
## 1 558 1623 2181
## 679 1502
## 25.6% 74.4% 49.2%
## 40.4% 53.2%
## -----------------------------------------------------------
## 0 823 1430 2253
## 702 1551
## 36.5% 63.5% 50.8%
## 59.6% 46.8%
## -----------------------------------------------------------
## Total 1381 3053 4434
## 31.1% 68.9%
## ===========================================================
##
## Statistics for All Table Factors
##
## Pearson's Chi-squared test
## ------------------------------------------------------------
## Chi^2 = 61.9 d.f. = 1 p = 0.00000000000000362
##
## Pearson's Chi-squared test with Yates' continuity correction
## ------------------------------------------------------------
## Chi^2 = 61.4 d.f. = 1 p = 0.00000000000000468
##
##
## Fisher's Exact Test for Count Data
## ------------------------------------------------------------
## Sample estimate odds ratio: 0.597
##
## Alternative hypothesis: true odds ratio is not equal to 1
## p = 0.00000000000000373
## 95% confidence interval: 0.524 0.681
##
## Alternative hypothesis: true odds ratio is less than 1
## p = 0.00000000000000201
## 95%s confidence interval: % 0 0.667
##
## Alternative hypothesis: true odds ratio is greater than 1
## p = 1
## 95%s confidence interval: % 0.535 Inf
##
## Minimum expected frequency: 679epi.2by2(table(Framingham_1_$cursmoke,Framingham_1_$cathyp)[c("1","0"),c("hipertensos","normotensos")], method = "cohort.count", conf.level = 0.95, outcome = "as.columns")## Outcome + Outcome - Total Inc risk *
## Exposed + 558 1623 2181 25.58 (23.76 to 27.47)
## Exposed - 823 1430 2253 36.53 (34.54 to 38.56)
## Total 1381 3053 4434 31.15 (29.78 to 32.53)
##
## Point estimates and 95% CIs:
## -------------------------------------------------------------------
## Inc risk ratio 0.70 (0.64, 0.77)
## Inc odds ratio 0.60 (0.53, 0.68)
## Attrib risk in the exposed * -10.94 (-13.65, -8.24)
## Attrib fraction in the exposed (%) -42.78 (-56.21, -30.50)
## Attrib risk in the population * -5.38 (-7.79, -2.97)
## Attrib fraction in the population (%) -17.28 (-21.67, -13.06)
## -------------------------------------------------------------------
## Uncorrected chi2 test that OR = 1: chi2(1) = 61.899 Pr>chi2 = <0.001
## Fisher exact test that OR = 1: Pr>chi2 = <0.001
## Wald confidence limits
## CI: confidence interval
## * Outcomes per 100 population units#Relación cursmoke vs death(a pesar de que el IC toca el 1, el límite inferior es de 0.99, podría considerarse que hay asociación)
crosstab(Framingham_1_$cursmoke,Framingham_1_$death, prop.r = TRUE, prop.c = TRUE, chisq = TRUE, fisher = TRUE, expected = TRUE)
## Cell Contents
## |-------------------------|
## | Count |
## | Expected Values |
## | Row Percent |
## | Column Percent |
## |-------------------------|
##
## ===============================================
## Framingham_1_$death
## Framingham_1_$cursmoke 1 0 Total
## -----------------------------------------------
## 1 788 1393 2181
## 762 1419
## 36.1% 63.9% 49.2%
## 50.8% 48.3%
## -----------------------------------------------
## 0 762 1491 2253
## 788 1465
## 33.8% 66.2% 50.8%
## 49.2% 51.7%
## -----------------------------------------------
## Total 1550 2884 4434
## 35% 65%
## ===============================================
##
## Statistics for All Table Factors
##
## Pearson's Chi-squared test
## ------------------------------------------------------------
## Chi^2 = 2.6 d.f. = 1 p = 0.107
##
## Pearson's Chi-squared test with Yates' continuity correction
## ------------------------------------------------------------
## Chi^2 = 2.5 d.f. = 1 p = 0.114
##
##
## Fisher's Exact Test for Count Data
## ------------------------------------------------------------
## Sample estimate odds ratio: 1.11
##
## Alternative hypothesis: true odds ratio is not equal to 1
## p = 0.108
## 95% confidence interval: 0.976 1.25
##
## Alternative hypothesis: true odds ratio is less than 1
## p = 0.95
## 95%s confidence interval: % 0 1.23
##
## Alternative hypothesis: true odds ratio is greater than 1
## p = 0.057
## 95%s confidence interval: % 0.996 Inf
##
## Minimum expected frequency: 762epi.2by2(table(Framingham_1_$cursmoke,Framingham_1_$death)[c("1","0"),c("1","0")], method = "cohort.count", conf.level = 0.95, outcome = "as.columns")## Outcome + Outcome - Total Inc risk *
## Exposed + 788 1393 2181 36.13 (34.11 to 38.19)
## Exposed - 762 1491 2253 33.82 (31.87 to 35.82)
## Total 1550 2884 4434 34.96 (33.55 to 36.38)
##
## Point estimates and 95% CIs:
## -------------------------------------------------------------------
## Inc risk ratio 1.07 (0.99, 1.16)
## Inc odds ratio 1.11 (0.98, 1.25)
## Attrib risk in the exposed * 2.31 (-0.50, 5.12)
## Attrib fraction in the exposed (%) 6.39 (-1.44, 13.61)
## Attrib risk in the population * 1.14 (-1.27, 3.54)
## Attrib fraction in the population (%) 3.25 (-0.78, 7.12)
## -------------------------------------------------------------------
## Uncorrected chi2 test that OR = 1: chi2(1) = 2.598 Pr>chi2 = 0.107
## Fisher exact test that OR = 1: Pr>chi2 = 0.108
## Wald confidence limits
## CI: confidence interval
## * Outcomes per 100 population units#Finalmente se realiza el test de Mantel Haenszel para evaluar si ser fumador (cursmoke) es confundidor. El porcentaje en que se modifica el Riesgo crudo del ajustado (2.5%) indica que cursmoke no es confundidor en la relación hipertensión y muerte (ver archivo word)
epi.2by2(table(Framingham_1_$cathyp,Framingham_1_$death,Framingham_1_$cursmoke)[c("hipertensos","normotensos"),c("1","0"),c("1","0")], method = "cohort.count", conf.level = 0.95, outcome = "as.columns")## Outcome + Outcome - Total Inc risk *
## Exposed + 731 650 1381 52.93 (50.26 to 55.59)
## Exposed - 819 2234 3053 26.83 (25.26 to 28.44)
## Total 1550 2884 4434 34.96 (33.55 to 36.38)
##
##
## Point estimates and 95% CIs:
## -------------------------------------------------------------------
## Inc risk ratio (crude) 1.97 (1.83, 2.13)
## Inc risk ratio (M-H) 2.02 (1.86, 2.18)
## Inc risk ratio (crude:M-H) 0.98
## Inc odds ratio (crude) 3.07 (2.69, 3.50)
## Inc odds ratio (M-H) 3.18 (2.78, 3.64)
## Inc odds ratio (crude:M-H) 0.96
## Attrib risk in the exposed (crude) * 26.11 (23.04, 29.17)
## Attrib risk in the exposed (M-H) * 26.77 (21.67, 31.88)
## Attrib risk (crude:M-H) 0.98
## -------------------------------------------------------------------
## M-H test of homogeneity of IRRs: chi2(1) = 1.834 Pr>chi2 = 0.176
## M-H test of homogeneity of ORs: chi2(1) = 0.280 Pr>chi2 = 0.597
## Test that M-H adjusted OR = 1: chi2(1) = 296.106 Pr>chi2 = <0.001
## Wald confidence limits
## M-H: Mantel-Haenszel; CI: confidence interval
## * Outcomes per 100 population units#Para evaluar si es Modificador de efecto, se debe analizar la relación Hipertensión arterial(cathyp) y muerte (death) en los estratos de Fumador (cursmoke)
#Relación entre hipertensión y muerte Estrato fumador (cursmoke=1):
epi.2by2(table(Framingham_1_$cathyp[Framingham_1_$cursmoke==1],Framingham_1_$death[Framingham_1_$cursmoke==1])[c("hipertensos","normotensos"),c("1","0")], method = "cohort.count", conf.level = 0.95, outcome = "as.columns") ## Outcome + Outcome - Total Inc risk *
## Exposed + 312 246 558 55.91 (51.68 to 60.08)
## Exposed - 476 1147 1623 29.33 (27.12 to 31.61)
## Total 788 1393 2181 36.13 (34.11 to 38.19)
##
## Point estimates and 95% CIs:
## -------------------------------------------------------------------
## Inc risk ratio 1.91 (1.72, 2.12)
## Inc odds ratio 3.06 (2.51, 3.73)
## Attrib risk in the exposed * 26.59 (21.91, 31.26)
## Attrib fraction in the exposed (%) 47.55 (41.71, 52.80)
## Attrib risk in the population * 6.80 (3.81, 9.80)
## Attrib fraction in the population (%) 18.83 (15.18, 22.31)
## -------------------------------------------------------------------
## Uncorrected chi2 test that OR = 1: chi2(1) = 127.181 Pr>chi2 = <0.001
## Fisher exact test that OR = 1: Pr>chi2 = <0.001
## Wald confidence limits
## CI: confidence interval
## * Outcomes per 100 population units#Relación entre hipertensión y muerte Estrato No fumador (cursmoke=0):
epi.2by2(table(Framingham_1_$cathyp[Framingham_1_$cursmoke==0],Framingham_1_$death[Framingham_1_$cursmoke==0])[c("hipertensos","normotensos"),c("1","0")], method = "cohort.count", conf.level = 0.95, outcome = "as.columns") ## Outcome + Outcome - Total Inc risk *
## Exposed + 419 404 823 50.91 (47.44 to 54.38)
## Exposed - 343 1087 1430 23.99 (21.79 to 26.29)
## Total 762 1491 2253 33.82 (31.87 to 35.82)
##
## Point estimates and 95% CIs:
## -------------------------------------------------------------------
## Inc risk ratio 2.12 (1.89, 2.38)
## Inc odds ratio 3.29 (2.74, 3.95)
## Attrib risk in the exposed * 26.93 (22.86, 31.00)
## Attrib fraction in the exposed (%) 52.89 (47.19, 57.97)
## Attrib risk in the population * 9.84 (6.88, 12.79)
## Attrib fraction in the population (%) 29.08 (24.34, 33.52)
## -------------------------------------------------------------------
## Uncorrected chi2 test that OR = 1: chi2(1) = 169.194 Pr>chi2 = <0.001
## Fisher exact test that OR = 1: Pr>chi2 = <0.001
## Wald confidence limits
## CI: confidence interval
## * Outcomes per 100 population units#El riesgo relativo en ambos estratos (fumador y no fumador) es similar (1.91 y 2.1), por lo que no se considera modificador de efecto6.Analicen la relación entre presencia de DIABETES y DEATH. Interpreten sus resultados. Reporten e interpreten la magnitud de la asociación (con intervalos de confianza) en caso de que exista una asociación entre estas dos variables.
#Se ordenan los niveles de la variable diabetes
levels(Framingham_1_$diabetes)## [1] "0" "1"Framingham_1_ <- Framingham_1_ %>% mutate(diabetes = factor(diabetes, levels = c("1", "0")))
levels(Framingham_1_$diabetes)## [1] "1" "0"#se utiliza test de chi2 para evaluar asociación
tabla2x2chi2fisher <- crosstab(Framingham_1_$diabetes,Framingham_1_$death, prop.r = TRUE, prop.c = TRUE, chisq = TRUE, fisher = TRUE, expected =TRUE)
tabla2x2chi2fisher## Cell Contents
## |-------------------------|
## | Count |
## | Expected Values |
## | Row Percent |
## | Column Percent |
## |-------------------------|
##
## =================================================
## Framingham_1_$death
## Framingham_1_$diabetes 1 0 Total
## -------------------------------------------------
## 1 94 27 121
## 42.3 78.7
## 77.7% 22.3% 2.7%
## 6.1% 0.9%
## -------------------------------------------------
## 0 1456 2857 4313
## 1507.7 2805.3
## 33.8% 66.2% 97.3%
## 93.9% 99.1%
## -------------------------------------------------
## Total 1550 2884 4434
## 35% 65%
## =================================================
##
## Statistics for All Table Factors
##
## Pearson's Chi-squared test
## ------------------------------------------------------------
## Chi^2 = 99.9 d.f. = 1 p <0.0000000000000002
##
## Pearson's Chi-squared test with Yates' continuity correction
## ------------------------------------------------------------
## Chi^2 = 98 d.f. = 1 p <0.0000000000000002
##
##
## Fisher's Exact Test for Count Data
## ------------------------------------------------------------
## Sample estimate odds ratio: 6.83
##
## Alternative hypothesis: true odds ratio is not equal to 1
## p <0.0000000000000002
## 95% confidence interval: 4.39 11
##
## Alternative hypothesis: true odds ratio is less than 1
## p = 1
## 95%s confidence interval: % 0 10.2
##
## Alternative hypothesis: true odds ratio is greater than 1
## p <0.0000000000000002
## 95%s confidence interval: % 4.68 Inf
##
## Minimum expected frequency: 42.3epi.2by2(table(Framingham_1_$diabetes,Framingham_1_$death)[c("1","0"),c("1","0")], method = "cohort.count", conf.level = 0.95, outcome = "as.columns")## Outcome + Outcome - Total Inc risk *
## Exposed + 94 27 121 77.69 (69.22 to 84.75)
## Exposed - 1456 2857 4313 33.76 (32.35 to 35.19)
## Total 1550 2884 4434 34.96 (33.55 to 36.38)
##
## Point estimates and 95% CIs:
## -------------------------------------------------------------------
## Inc risk ratio 2.30 (2.07, 2.55)
## Inc odds ratio 6.83 (4.43, 10.53)
## Attrib risk in the exposed * 43.93 (36.38, 51.48)
## Attrib fraction in the exposed (%) 56.55 (51.77, 60.85)
## Attrib risk in the population * 1.20 (-0.79, 3.19)
## Attrib fraction in the population (%) 3.43 (2.58, 4.27)
## -------------------------------------------------------------------
## Uncorrected chi2 test that OR = 1: chi2(1) = 99.887 Pr>chi2 = <0.001
## Fisher exact test that OR = 1: Pr>chi2 = <0.001
## Wald confidence limits
## CI: confidence interval
## * Outcomes per 100 population units#Existe una relación estadísticamente significativa entre diabetes y muerte. Los pacientes con diabetes presentan un riesgo 2.3 veces mayor de muerte que los no diabéticos. Ver word adjunto7.¿Consideran que el sexo (SEX) se comporta como un confundidor y/o modificador de efecto en la relación entre DIABETES y DEATH? Justifiquen su respuesta.
#Para evaluar si SEX es confundidor se debe evaluar si se encuentra relacionada a la exposición y al evento, es decir con diabetes y con muerte (death) y luego aplicar Mantel Haenszel. Para determinar si existe modificación de efecto se analiza la relación entre diabetes y muerte en los estratos de sexo (femenino y masculino).
#Primero ordenamos los niveles de sex
Framingham_1_ <- Framingham_1_ %>% mutate(sex = factor(sex, levels = c("1", "0")))
#Relación entre SEX y DIABETES (Sexo y Diabetes). Hipótesis nula: El sexo no se encuentra asociado a la muerte. Hipótesis alternativa: existe asociación entre sexo y muerte. En el análisis realizado no se encuentra relación entre sexo y diabetes por lo cual no se descarta la hipótesis nula. No impresiona ser confundidor, dado que éste debería asociarse a exposición y evento. Sin embargo, se prosigue con el resto de las pruebas
crosstab(Framingham_1_$sex,Framingham_1_$diabetes, prop.r = TRUE, prop.c = TRUE, chisq = TRUE, fisher = TRUE, expected = TRUE)
## Cell Contents
## |-------------------------|
## | Count |
## | Expected Values |
## | Row Percent |
## | Column Percent |
## |-------------------------|
##
## ===========================================
## Framingham_1_$diabetes
## Framingham_1_$sex 1 0 Total
## -------------------------------------------
## 1 59 1885 1944
## 53.1 1890.9
## 3.0% 97.0% 43.8%
## 48.8% 43.7%
## -------------------------------------------
## 0 62 2428 2490
## 67.9 2422.1
## 2.5% 97.5% 56.2%
## 51.2% 56.3%
## -------------------------------------------
## Total 121 4313 4434
## 2.7% 97.3%
## ===========================================
##
## Statistics for All Table Factors
##
## Pearson's Chi-squared test
## ------------------------------------------------------------
## Chi^2 = 1.22 d.f. = 1 p = 0.269
##
## Pearson's Chi-squared test with Yates' continuity correction
## ------------------------------------------------------------
## Chi^2 = 1.02 d.f. = 1 p = 0.311
##
##
## Fisher's Exact Test for Count Data
## ------------------------------------------------------------
## Sample estimate odds ratio: 1.23
##
## Alternative hypothesis: true odds ratio is not equal to 1
## p = 0.307
## 95% confidence interval: 0.839 1.79
##
## Alternative hypothesis: true odds ratio is less than 1
## p = 0.884
## 95%s confidence interval: % 0 1.69
##
## Alternative hypothesis: true odds ratio is greater than 1
## p = 0.156
## 95%s confidence interval: % 0.889 Inf
##
## Minimum expected frequency: 53.1epi.2by2(table(Framingham_1_$sex,Framingham_1_$diabetes)[c("1","0"),c("1","0")], method = "cohort.count", conf.level = 0.95, outcome = "as.columns")## Outcome + Outcome - Total Inc risk *
## Exposed + 59 1885 1944 3.03 (2.32 to 3.90)
## Exposed - 62 2428 2490 2.49 (1.91 to 3.18)
## Total 121 4313 4434 2.73 (2.27 to 3.25)
##
## Point estimates and 95% CIs:
## -------------------------------------------------------------------
## Inc risk ratio 1.22 (0.86, 1.73)
## Inc odds ratio 1.23 (0.85, 1.76)
## Attrib risk in the exposed * 0.55 (-0.43, 1.52)
## Attrib fraction in the exposed (%) 17.96 (-16.60, 42.27)
## Attrib risk in the population * 0.24 (-0.54, 1.02)
## Attrib fraction in the population (%) 8.76 (-8.30, 23.13)
## -------------------------------------------------------------------
## Uncorrected chi2 test that OR = 1: chi2(1) = 1.222 Pr>chi2 = 0.269
## Fisher exact test that OR = 1: Pr>chi2 = 0.307
## Wald confidence limits
## CI: confidence interval
## * Outcomes per 100 population units#Relación entre SEX y DEATH (Sexo y Muerte). El sexo masculino presenta una probabilidad de muerte 1.53 veces mayor que el sexo femenino y esta relación es estadísticamente significativa.Existe asociación con el evento.
crosstab(Framingham_1_$sex,Framingham_1_$death, prop.r = TRUE, prop.c = TRUE, chisq = TRUE, fisher = TRUE, expected = TRUE)
## Cell Contents
## |-------------------------|
## | Count |
## | Expected Values |
## | Row Percent |
## | Column Percent |
## |-------------------------|
##
## ==========================================
## Framingham_1_$death
## Framingham_1_$sex 1 0 Total
## ------------------------------------------
## 1 843 1101 1944
## 680 1264
## 43.4% 56.6% 43.8%
## 54.4% 38.2%
## ------------------------------------------
## 0 707 1783 2490
## 870 1620
## 28.4% 71.6% 56.2%
## 45.6% 61.8%
## ------------------------------------------
## Total 1550 2884 4434
## 35% 65%
## ==========================================
##
## Statistics for All Table Factors
##
## Pearson's Chi-squared test
## ------------------------------------------------------------
## Chi^2 = 108 d.f. = 1 p <0.0000000000000002
##
## Pearson's Chi-squared test with Yates' continuity correction
## ------------------------------------------------------------
## Chi^2 = 107 d.f. = 1 p <0.0000000000000002
##
##
## Fisher's Exact Test for Count Data
## ------------------------------------------------------------
## Sample estimate odds ratio: 1.93
##
## Alternative hypothesis: true odds ratio is not equal to 1
## p <0.0000000000000002
## 95% confidence interval: 1.7 2.19
##
## Alternative hypothesis: true odds ratio is less than 1
## p = 1
## 95%s confidence interval: % 0 2.15
##
## Alternative hypothesis: true odds ratio is greater than 1
## p <0.0000000000000002
## 95%s confidence interval: % 1.74 Inf
##
## Minimum expected frequency: 680epi.2by2(table(Framingham_1_$sex,Framingham_1_$death)[c("1","0"),c("1","0")], method = "cohort.count", conf.level = 0.95, outcome = "as.columns")## Outcome + Outcome - Total Inc risk *
## Exposed + 843 1101 1944 43.36 (41.15 to 45.60)
## Exposed - 707 1783 2490 28.39 (26.63 to 30.21)
## Total 1550 2884 4434 34.96 (33.55 to 36.38)
##
## Point estimates and 95% CIs:
## -------------------------------------------------------------------
## Inc risk ratio 1.53 (1.41, 1.66)
## Inc odds ratio 1.93 (1.70, 2.19)
## Attrib risk in the exposed * 14.97 (12.14, 17.80)
## Attrib fraction in the exposed (%) 34.52 (29.04, 39.58)
## Attrib risk in the population * 6.56 (4.30, 8.82)
## Attrib fraction in the population (%) 18.78 (15.11, 22.29)
## -------------------------------------------------------------------
## Uncorrected chi2 test that OR = 1: chi2(1) = 107.608 Pr>chi2 = <0.001
## Fisher exact test that OR = 1: Pr>chi2 = <0.001
## Wald confidence limits
## CI: confidence interval
## * Outcomes per 100 population units#Se realiza Mantel Haenszel para evaluar si el sexo (sex) es confundidor en la relación Diabetes y muerte. El sexo no es confundidor en dicha relación dado que la diferencia entre el riesgo crudo y el ajustado es de 1% (menor al 10% que se requiere para que se considere confundidor)
epi.2by2(table(Framingham_1_$diabetes,Framingham_1_$death,Framingham_1_$sex)[c("1","0"),c("1","0"),c("1","0")], method = "cohort.count", conf.level = 0.95, outcome = "as.columns")## Outcome + Outcome - Total Inc risk *
## Exposed + 94 27 121 77.69 (69.22 to 84.75)
## Exposed - 1456 2857 4313 33.76 (32.35 to 35.19)
## Total 1550 2884 4434 34.96 (33.55 to 36.38)
##
##
## Point estimates and 95% CIs:
## -------------------------------------------------------------------
## Inc risk ratio (crude) 2.30 (2.07, 2.55)
## Inc risk ratio (M-H) 2.25 (2.03, 2.49)
## Inc risk ratio (crude:M-H) 1.02
## Inc odds ratio (crude) 6.83 (4.43, 10.53)
## Inc odds ratio (M-H) 6.81 (4.39, 10.56)
## Inc odds ratio (crude:M-H) 1.00
## Attrib risk in the exposed (crude) * 43.93 (36.38, 51.48)
## Attrib risk in the exposed (M-H) * 43.18 (-33.42, 119.79)
## Attrib risk (crude:M-H) 1.02
## -------------------------------------------------------------------
## M-H test of homogeneity of IRRs: chi2(1) = 10.547 Pr>chi2 = 0.001
## M-H test of homogeneity of ORs: chi2(1) = 0.360 Pr>chi2 = 0.548
## Test that M-H adjusted OR = 1: chi2(1) = 97.964 Pr>chi2 = <0.001
## Wald confidence limits
## M-H: Mantel-Haenszel; CI: confidence interval
## * Outcomes per 100 population units#para evaluar si existe modificacion de efecto, se debe evaluar la relación diabetes y muerte (death) en los diferentes estratos de sexo (sex)
epi.2by2(table(Framingham_1_$diabetes[Framingham_1_$sex==1],Framingham_1_$death[Framingham_1_$sex==1])[c("1","0"),c("1","0")], method = "cohort.count", conf.level = 0.95, outcome = "as.columns") ## Outcome + Outcome - Total Inc risk *
## Exposed + 48 11 59 81.36 (69.09 to 90.31)
## Exposed - 795 1090 1885 42.18 (39.93 to 44.44)
## Total 843 1101 1944 43.36 (41.15 to 45.60)
##
## Point estimates and 95% CIs:
## -------------------------------------------------------------------
## Inc risk ratio 1.93 (1.69, 2.20)
## Inc odds ratio 5.98 (3.09, 11.59)
## Attrib risk in the exposed * 39.18 (29.00, 49.37)
## Attrib fraction in the exposed (%) 48.16 (40.78, 54.62)
## Attrib risk in the population * 1.19 (-1.95, 4.32)
## Attrib fraction in the population (%) 2.74 (1.74, 3.73)
## -------------------------------------------------------------------
## Uncorrected chi2 test that OR = 1: chi2(1) = 35.760 Pr>chi2 = <0.001
## Fisher exact test that OR = 1: Pr>chi2 = <0.001
## Wald confidence limits
## CI: confidence interval
## * Outcomes per 100 population units#Relación entre diabetes y muerte en estrato mujeres
epi.2by2(table(Framingham_1_$diabetes[Framingham_1_$sex==0],Framingham_1_$death[Framingham_1_$sex==0])[c("1","0"),c("1","0")], method = "cohort.count", conf.level = 0.95, outcome = "as.columns") ## Outcome + Outcome - Total Inc risk *
## Exposed + 46 16 62 74.19 (61.50 to 84.47)
## Exposed - 661 1767 2428 27.22 (25.46 to 29.04)
## Total 707 1783 2490 28.39 (26.63 to 30.21)
##
## Point estimates and 95% CIs:
## -------------------------------------------------------------------
## Inc risk ratio 2.73 (2.32, 3.20)
## Inc odds ratio 7.69 (4.32, 13.67)
## Attrib risk in the exposed * 46.97 (35.93, 58.00)
## Attrib fraction in the exposed (%) 63.31 (56.92, 68.75)
## Attrib risk in the population * 1.17 (-1.33, 3.67)
## Attrib fraction in the population (%) 4.12 (2.71, 5.50)
## -------------------------------------------------------------------
## Uncorrected chi2 test that OR = 1: chi2(1) = 65.600 Pr>chi2 = <0.001
## Fisher exact test that OR = 1: Pr>chi2 = <0.001
## Wald confidence limits
## CI: confidence interval
## * Outcomes per 100 population units#Relación entre diabetes y muerte en estrato hombres. En este caso, en hombres el riesgo relativo de morir es de 1.93 y en mujeres de 2.73, con lo cual se considera que el sexo es un modificador de efecto en la relación diabetes y muerte8.Generen la variable OBESE como categorías de BMI: normopeso BMI<= 25; sobrepeso BMI >25 y <=30; y obesidad BMI > 30. Pista: Usen case_when para crear los niveles
Framingham_1_ <- Framingham_1_ %>% mutate(obese=as.factor(case_when(bmi>30 ~"obesidad",
bmi>25 & bmi<=30 ~ "sobrepeso",
bmi<=25 ~ "normopeso")))
Framingham_1_ <- Framingham_1_ %>% mutate(obese = factor(obese, levels = c("normopeso", "sobrepeso","obesidad")))
levels(Framingham_1_$obese)## [1] "normopeso" "sobrepeso" "obesidad"9.Comparen la SYSBP (variable continua) de los pacientes en las diferentes categorías de OBESE (usted en el punto 8 genero las variables de obesidad). Por favor explique que test/tests eligió y fundamente el por qué. Asimismo, exprese cual fue la media de tensión arterial sistólica (variable continua) en cada grupo de OBESE, y entre qué grupos ha habido diferencia significativa en relación con dichas medias.
#Evaluación de la normalidad la variable sysbp por estratos
hist(Framingham_1_$sysbp[Framingham_1_$obese=="normopeso"])
hist(Framingham_1_$sysbp[Framingham_1_$obese=="sobrepeso"])
hist(Framingham_1_$sysbp[Framingham_1_$obese=="obesidad"])
qqnorm(Framingham_1_$sysbp[Framingham_1_$obese=="normopeso"])
qqline(Framingham_1_$sysbp[Framingham_1_$obese=="normopeso"])
qqnorm(Framingham_1_$sysbp[Framingham_1_$obese=="sobrepeso"])
qqline(Framingham_1_$sysbp[Framingham_1_$obese=="sobrepeso"])
qqnorm(Framingham_1_$sysbp[Framingham_1_$obese=="obesidad"])
qqline(Framingham_1_$sysbp[Framingham_1_$obese=="obesidad"])
describeBy(Framingham_1_$sysbp,Framingham_1_$obese)##
## Descriptive statistics by group
## group: normopeso
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1993 127 20.4 123 124 16.3 83.5 244 160 1.4 3.15 0.46
## ------------------------------------------------------------
## group: sobrepeso
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1848 136 21.5 132 134 19.3 83.5 243 160 0.98 1.11 0.5
## ------------------------------------------------------------
## group: obesidad
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 574 145 24.6 141 143 21.1 93 295 202 1.09 2.67 1.03shapiro.test(Framingham_1_$sysbp[Framingham_1_$obese=="normopeso"])##
## Shapiro-Wilk normality test
##
## data: Framingham_1_$sysbp[Framingham_1_$obese == "normopeso"]
## W = 0.9, p-value <0.0000000000000002shapiro.test(Framingham_1_$sysbp[Framingham_1_$obese=="sobrepeso"])##
## Shapiro-Wilk normality test
##
## data: Framingham_1_$sysbp[Framingham_1_$obese == "sobrepeso"]
## W = 0.9, p-value <0.0000000000000002shapiro.test(Framingham_1_$sysbp[Framingham_1_$obese=="obesidad"])##
## Shapiro-Wilk normality test
##
## data: Framingham_1_$sysbp[Framingham_1_$obese == "obesidad"]
## W = 0.9, p-value = 0.0000000000001#Se realiza Bartlett test para igualdad de varianzas
bartlett.test(Framingham_1_$sysbp,Framingham_1_$obese) ##
## Bartlett test of homogeneity of variances
##
## data: Framingham_1_$sysbp and Framingham_1_$obese
## Bartlett's K-squared = 34, df = 2, p-value = 0.00000004#Si bien la distribución de la variable impresiona normal en cada estrato, no se cumple el principio de homocedasticidad que es una condición necesaria para utilizar ANOVA. Se debe utilizar, entonces, kruskal wallis para la comparación entre más de 2 grupos.Hipótesis nula: la media de presión arterial es similar en las personas con normopeso, sobrepeso y obesos. Hipótesis alternativa: La media de presión arterial es diferente en las personas con normopeso, sobrepeso y obesos. Aplicando Kruskal Wallis, se encuentra que existe una diferencia estadísticamente significativa entre los grupos.Las medias de presión sistólica son 127 mmhg para el grupo normopeso, 136 mmgh para el grupo sobrepeso y 145 mmhg para el grupo obesidad. Se descarta la hipótesis nula
kruskal.test(Framingham_1_$sysbp~Framingham_1_$obese)##
## Kruskal-Wallis rank sum test
##
## data: Framingham_1_$sysbp by Framingham_1_$obese
## Kruskal-Wallis chi-squared = 418, df = 2, p-value <0.0000000000000002# CORRECCIÓN POR BONFERRONI para ver las diferencias entre los grupos.Todos los grupos presentan diferencias en el valor de presión sistólica entre sí, siendo esta diferencia estadísticamente significativa.
pairwise.wilcox.test(Framingham_1_$sysbp,Framingham_1_$obese,"bonferroni")##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: Framingham_1_$sysbp and Framingham_1_$obese
##
## normopeso sobrepeso
## sobrepeso <0.0000000000000002 -
## obesidad <0.0000000000000002 <0.0000000000000002
##
## P value adjustment method: bonferroni10.Elaboren sus Tablas de Resultados con los testeos que realizaron, incluyan cuando corresponda, medida de asociación, intervalo de confianza y/o valor de p. Si encontraron algún modificador de efecto pueden reportar por separado los estratos.
#Se realiza una tabla donde se describen todas las características y su distribución según Fallecidos y no fallecidos. Se indica que la variable cigpday tiene distribución no normal. En esta tabla se indica si existe diferencia estadísticamente significativa entre las diferentes variables en grupos de pacientes fallecidos y no fallecidos
catvars = c( "sex","obese","cathyp","cursmoke", "death","diabetes","prevstrk", "prevhyp","prevchd")
vars = c("sex","obese","cathyp","cursmoke", "diabetes","sysbp","cigpday","bmi","age","prevstrk", "prevhyp","prevchd")
tabla_1 <- CreateTableOne(vars = vars, strata = "death", factorVars = catvars, data = Framingham_1_)
print(tabla_1, nonnormal = c("cigpday"))# wilcoxon para continuas no normales## Stratified by death
## 1 0 p
## n 1550 2884
## sex = 0 (%) 707 (45.6) 1783 (61.8) <0.001
## obese (%) <0.001
## normopeso 589 (38.3) 1404 (48.8)
## sobrepeso 691 (45.0) 1157 (40.2)
## obesidad 257 (16.7) 317 (11.0)
## cathyp = normotensos (%) 819 (52.8) 2234 (77.5) <0.001
## cursmoke = 0 (%) 762 (49.2) 1491 (51.7) 0.114
## diabetes = 0 (%) 1456 (93.9) 2857 (99.1) <0.001
## sysbp (mean (SD)) 142.18 (25.82) 127.92 (18.54) <0.001
## cigpday (median [IQR]) 1.00 [0.00, 20.00] 0.00 [0.00, 20.00] 0.003
## bmi (mean (SD)) 26.41 (4.38) 25.54 (3.91) <0.001
## age (mean (SD)) 54.92 (8.22) 47.24 (7.67) <0.001
## prevstrk = 1 (%) 25 ( 1.6) 7 ( 0.2) <0.001
## prevhyp = 1 (%) 758 (48.9) 672 (23.3) <0.001
## prevchd = 1 (%) 144 ( 9.3) 50 ( 1.7) <0.001
## Stratified by death
## test
## n
## sex = 0 (%)
## obese (%)
## normopeso
## sobrepeso
## obesidad
## cathyp = normotensos (%)
## cursmoke = 0 (%)
## diabetes = 0 (%)
## sysbp (mean (SD))
## cigpday (median [IQR]) nonnorm
## bmi (mean (SD))
## age (mean (SD))
## prevstrk = 1 (%)
## prevhyp = 1 (%)
## prevchd = 1 (%)kableone(tabla_1)| 1 | 0 | p | test | |
|---|---|---|---|---|
| n | 1550 | 2884 | ||
| sex = 0 (%) | 707 (45.6) | 1783 (61.8) | <0.001 | |
| obese (%) | <0.001 | |||
| normopeso | 589 (38.3) | 1404 (48.8) | ||
| sobrepeso | 691 (45.0) | 1157 (40.2) | ||
| obesidad | 257 (16.7) | 317 (11.0) | ||
| cathyp = normotensos (%) | 819 (52.8) | 2234 (77.5) | <0.001 | |
| cursmoke = 0 (%) | 762 (49.2) | 1491 (51.7) | 0.114 | |
| diabetes = 0 (%) | 1456 (93.9) | 2857 (99.1) | <0.001 | |
| sysbp (mean (SD)) | 142.18 (25.82) | 127.92 (18.54) | <0.001 | |
| cigpday (mean (SD)) | 9.95 (12.77) | 8.44 (11.42) | <0.001 | |
| bmi (mean (SD)) | 26.41 (4.38) | 25.54 (3.91) | <0.001 | |
| age (mean (SD)) | 54.92 (8.22) | 47.24 (7.67) | <0.001 | |
| prevstrk = 1 (%) | 25 ( 1.6) | 7 ( 0.2) | <0.001 | |
| prevhyp = 1 (%) | 758 (48.9) | 672 (23.3) | <0.001 | |
| prevchd = 1 (%) | 144 ( 9.3) | 50 ( 1.7) | <0.001 |
11.Grafiquen por separado la distribución de las variables SEX, SYSBP, CURSMOKE, BMI, DIABETES y las nuevas variables CATHYP y OBESE, en función de la variable DEATH. Relacionen lo que observan en los gráficos con sus resultados previos.
#grafico de presión sistólica en funcion de muerte: El gráfico muestra que los pacientes fallecidos presentan una mediana de SYSBP más elevada que los no fallecidos. Además, el grupo de fallecidos tiene mayor dispersión y presencia de valores extremos hacia valores más altos, lo que indica una variabilidad mayor en las presiones sistólicas de este grupo.
Framingham_1_ <- Framingham_1_ %>% mutate(Mortalidad=as.factor(case_when(death=="1" ~"Fallecido", death=="0" ~ "No fallecido"
)))
ggplot(Framingham_1_, aes(x = Mortalidad, y = sysbp, fill = Mortalidad)) + geom_boxplot(alpha = 0.5) + labs(title = "Presion sistolica en fallecidos y no fallecidos", x = "Mortalidad", y = "Presion sistolica") + theme_minimal()
#grafico de indice de masa corporal segun muerte: El gráfico muestra que los valores de BMI (índice de masa corporal) están distribuidos de manera similar entre los pacientes fallecidos (DEATH = 1) y no fallecidos (DEATH = 0). Sin embargo, la mediana del indice de masa corporal es ligeramente mayor en el grupo de pacientes fallecidos (diferencia estadísticamente significativa).
ggplot(Framingham_1_, aes(x = Mortalidad, y = bmi, fill = Mortalidad)) + geom_boxplot(alpha = 0.5) + labs(title = "Indice de masa corporal según muerte", x = "Mortalidad", y = "Indice de masa corporal") + theme_minimal()## Warning: Removed 19 rows containing non-finite outside the scale range
## (`stat_boxplot()`).
#grafico de barras de sexo en función de mortalidad
Framingham_1_ <- Framingham_1_ %>% mutate(Sexo=as.factor(case_when(sex=="1" ~"Hombre",sex=="0" ~ "Mujer")))
ggplot(Framingham_1_, aes(x = factor(Mortalidad), fill = factor (Sexo))) +
geom_bar(position = "fill") +
scale_x_discrete(labels = c("Fallecido", "No Fallecido")) +
labs(
title = "Distribucion Sexo según Mortalidad",
x = "Mortalidad",
y = "Numero de Personas",
fill = "Sexo"
) +
theme_minimal()
#grafico de barras fumador en funcion de muerte: El gráfico muestra que las proporciones son similares entre los fumadores y no fumadores en ambos grupos según la mortalidad.
Framingham_1_ <- Framingham_1_ %>% mutate(Tabaquismo=as.factor(case_when(cursmoke=="1" ~"Fumador",cursmoke=="0" ~ "No fumador")))
ggplot(Framingham_1_, aes(x = factor(Mortalidad), fill = factor(Tabaquismo))) +
geom_bar(position = "fill") +
scale_x_discrete(labels = c("Fallecido", "No Fallecido")) +
labs(
title = "Distribución de personas fumadoras y no fumadoras segun Mortalidad",
x = "Mortalidad",
y = "Número de Personas",
fill = "Tabaquismo"
) +
theme_minimal()
#grafico de barras diabetes en funcion de muerte
# El gráfico muestra que, entre los pacientes con diabetes (DIABETES = 1), la proporción de fallecidos (DEATH = 1) es mayor en comparación con los pacientes sin diabetes (DIABETES = 0).
Framingham_1_ <- Framingham_1_ %>% mutate(Diabegraf=as.factor(case_when(diabetes=="1" ~"Diabetes si",diabetes=="0" ~ "Diabetes no")))
ggplot(Framingham_1_, aes(x = Mortalidad, fill = as.factor(Diabegraf))) +
geom_bar(position = "fill") +
labs(
title = "Distribución de Diabetes en función de Mortalidad",
x = "Mortalidad",
y = "Proporción",
fill = "Diabetes"
) +
scale_fill_manual(values = c("#FF9999", "#66B2FF")) +
theme_minimal()
#grafico de barras Hipertension en funcion de muerte: El gráfico muestra que los fallecidos tienen una mayor proporción de hipertensos en comparación con los no fallecidos
ggplot(Framingham_1_, aes(x = Mortalidad, fill = as.factor(cathyp))) +
geom_bar(position = "fill") +
labs(
title = "Distribución de Hipertensión en función de Mortalidad",
x = "Mortalidad",
y = "Proporción",
fill = "Hipertension"
) +
scale_fill_manual(values = c("#FF9999", "#66B2FF")) +
theme_minimal()
#grafico de barras Obesidad en funcion de muerte: El gráfico evidencia una mayor proporción de obesos en el grupo de fallecidos en comparación con los normopesos.
Framingham_1_clean <- Framingham_1_ %>%
filter(!is.na(obese))
ggplot(Framingham_1_clean, aes(x = Mortalidad, fill = obese)) +
geom_bar(position = "fill") +
labs(
title = "Estado nutricional según Mortalidad",
x = "Mortalidad",
y = "Frecuencia",
fill = "Estado nutricional"
) + scale_fill_manual(values = c("pink","skyblue", "blue"))+
theme_minimal()
Escriban una breve conclusión sobre factores de riesgo de muerte
asociada a Hipertensión Arterial, Diabetes y Obesidad.
La hipertensión arterial es un factor de riesgo para la muerte dado que, tanto la presencia de hipertensión arterial como el antecedente de padecerla se asocian a una mayor mortalidad. En el caso de hipertensión sistólica, la media presión en pacientes fallecidos fue de 142 y en no fallecidos fue de 128, siendo esta diferencia estadísticamente significativa (p<0.001). La presencia de diabetes también se encontró asociada a la muerte. Padecer diabetes aumentó el riesgo de muerte en 2.3 veces (RR 2.3 (2.07-2.55)). Dicho riesgo fue mayor en mujeres con diabetes (RR 2.7 (2.32-3.20)) que en hombres con diabetes (RR 1.9 (1.69-2.20)). La presencia de obesidad y sobrepeso también se encontró asociada a la muerte, con mayor prevalencia de pacientes obesos entre los pacientes fallecidos (16.7%) que entre los no fallecidos (11%), p<0.001 Muchas gracias Tomás y Ceci por todo lo que aprendimos.