Lab480373021
Sarah
03/04/2020
#ANZ Transplant Data Analysis
##Introduction End stage renal disease(ESRD) is the total and permanent failure of an individual’s kidney/s. Individuals with end stage renal disease have a very high risk of mortality [1]. ERSD carries a high risk of mortality and affects a large population (Incidence rate 363 per million per year)[1]. ERSD is treated by either dialysis or kidney transplant. ERSD presents high mortality and morbidity, as such it is important that data regarding treatment is regularly assessed to determine prognostic factors which determine treatment success. The Australia and New Zealand Dialysis and Transplant Registry (ANZDATA) collects and compiles data relating to the treatment and outcome of end stage renal failure, patient and clinical demographics such as: age, gender, age at transplant, creatinine levels, and the levels of certain antibodies are also collected. ANZDATA collects data from all renal units across Australia and New Zealand [2]. It was the purpose of this report to analyse the ANZDATA relating to patient and transplant factors exploring variables that effect transplant success. Specifically this report analysed: 1. The relationship between patient cancer history and transplant success 2. Whether kmeans clustering of continous variables associated with transplant can reveal patient sub-structures (clusters) 3. The relationship between graft number, transplant success, and their impact on time on dialysis 4. The relationship between age at time of transplant and graft survival time
##Results
#Read in packages
library(plyr)
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## x dplyr::summarize() masks plyr::summarize()library(naniar)## Warning: package 'naniar' was built under R version 3.6.3library(tidyr)
library(ggplot2)
library(RColorBrewer)
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## some#Read in data
Patientdata = read.csv("AnzdataPatients.csv")
Transplantdata = read.csv("AnzdataTransplants.csv")
dim(Patientdata)## [1] 999 23vis_miss(Patientdata)
dim(Transplantdata)## [1] 1000 38vis_miss(Transplantdata)
#Initial full set HLA mismatch to graft success not possible HLAmismatchesDQ = 74% missingness. Could simply exclude it or find another grafting variable to compare to
colSums(is.na(Transplantdata))## id graftno
## 0 0
## transplantdate transplantcentrestate
## 0 0
## recipientantibodycmvcode recipientantibodyebvcode
## 0 0
## donorsourcecode donorsourceother
## 0 0
## donorage donorgendercode
## 13 0
## ischaemia imediatefunctioncode
## 59 0
## firstprovendate diseaseingraftcode
## 0 0
## graftfailurecausecode graftfailurecauseother
## 0 0
## graftfailuredate countrycode
## 0 0
## endtransplantcode endtransplantdate
## 0 0
## lastknownstatus lastfollowupdate
## 0 0
## ageattransplant transplantstatus
## 0 0
## transplantperiod alivestatus
## 0 0
## aliveperiod hlamismatchesa
## 0 38
## hlamismatchesb hlamismatchesdr
## 38 41
## hlamismatchesdq maxcytotoxicantibodies
## 741 75
## currentcytotoxicantibodies timeondialysis
## 53 0
## lasttreatmentcodepretransplant lasttreatmentdatepretransplant
## 0 0
## lasttreatmentpretransplant gfailcat
## 0 01. Is there evidence that there is a significant relationship between patient cancer history and transplant status (transplant success or failure)
#Is transplant status (success or failure) associated with a patient history of cancer?
TransplantStat = data.table(Transplantdata$id, Transplantdata$transplantstatus)
colnames(TransplantStat)= c("ID", "Transplant Status")
TransplantStat = na.omit(TransplantStat)
Cancer = data.table(Patientdata$id, Patientdata$cancerever)
colnames(Cancer) = c("ID", "Cancer ever")
Joint2 = full_join(TransplantStat, Cancer, by = "ID")
#Chi-square test for independence
#H0 = there is no association between patient cancer history and transplant status (graft success) , Ha = there is an association between patient cancer history and transplant status
TAB = table(Joint2$`Cancer ever`, Joint2$`Transplant Status`)
TAB##
## 0 1
## No 643 222
## Yes 105 30test = chisq.test(TAB)
test$expected >= 5 ##
## 0 1
## No TRUE TRUE
## Yes TRUE TRUEchisq.test(TAB)##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: TAB
## X-squared = 0.5629, df = 1, p-value = 0.4531odds.ratio(TAB)## $res
## odds ratio p-value
## 0.8275418 0.3920659
##
## $ci
## [1] 0.5364489 1.2765903- Check assumptions - the expected value of all the cells is greater than 5, assumptions are met, therefore, a Chi square test of independence can be calculated
- The Chi square test for independence indicates that there is no statistically significant association between patient cancer history and transplant status as P < 0.05 (P = 0.4531)
- As such the null hypothesis is retained
- The odds ratio < 1 implying that a history of cancer decreases a patient’s risk of transplant failure, the Chi square test performed indicated the two variables were independent, the odds ratio is very close to 1 and P > 0.05 indicating supporting this interpretation
- There is no association between cancer history and transplant status
2. Can Kmeans clustering of continous variables associated with transplant data reveal patient sub-structures (clusters)
#Perform K means clustering on the Transplant dataset, select patient ID and Transplant status (this variable will be used to determine shape within the kmeans cluster plot) and the numeric continuous variables (Transplant period, Time on dialysis, Transplant status, Donor age, Age at Transplant)
data = data.table(Transplantdata$id, Transplantdata$transplantperiod,Transplantdata$timeondialysis, Transplantdata$transplantstatus, Transplantdata$donorage, Transplantdata$ageattransplant)
colnames(data) = c("ID", "Transplant period", "Time on Dialysis", "Transplant Status", "Donor Age", "Age at Transplant")
data = na.omit(data)
Vector = data %>%
select(-ID) %>%
select(-`Transplant Status`)
datanumeric = as.data.frame(sapply(data, as.numeric))
datascaled <- datanumeric%>%
scale()
set.seed(50000)
kM <- kmeans(datascaled, 2)
clustered <- data.frame(data, cluster = factor(kM$cluster))
clustered$Transplant.Status = as.factor(clustered$Transplant.Status)
cbPalette <- c("#ff9f88", "#fdc344", "#fdf6eb", "#d5c5a7", "#413d46", "#0072B2", "#D55E00", "#CC79A7")
graph <- ggplot(clustered, aes(x=`Age.at.Transplant`, y=`Time.on.Dialysis`, colour = cluster, shape = `Transplant.Status`)) + geom_point()
graph <- graph + ggtitle("Kmeans clustering: Dialysis, Age at Transplant & Transplant Status") + labs(y="Time on Dialysis", x="Age at Transplant (Yrs)", caption = "Figure1. Kmeans clustering of numeric continuous variables in the ANZ Transplant dataset (Transplant period, Time on dialysis, Transplant status, Donor age, Age at Transplant) plotted with the variables Time on Dialysis and Age at Transplant, with shapes determined by Transplant Status, and clusters by colour") + theme(plot.title = element_text(hjust=0.5)) + theme(plot.caption = element_text(hjust = 0)) + scale_shape_discrete(name = "Transplant Status", labels = c("Functional", "Failed")) + scale_colour_manual(values=cbPalette)
graph
- The kmeans clustering observed does not indicate any obvious patterns - This may be due to a sub-optimal level of clusters and an absence of PCA - Generally, the pink cluster have a greater spread in terms of time on dialysis and have a smaller age at transplant spread than cluster 2. The yellow cluster have a smaller spread across time on dialysis and a greater spread across age at transplant
- This model indicates Kmeans clustering could potentially reveal patient sub-groups (clusters) relating to transplant data such as: transplant period, age at transplant, and time on dialysis, however, the model generated above is not very useful at this
3. Do the variables patient graft number, time on dialysis, and transplant success have any interaction?
#Two way ANOVA
#
Part1 = data.table(Transplantdata$id, Transplantdata$graftno, Transplantdata$timeondialysis, Transplantdata$transplantstatus)
colnames(Part1) = c("ID", "Graft Number", "Time on Dialysis", "Transplant Status")
Dataframe1 = na.omit(Part1)
Dataframe1$`Transplant Status` = as.factor(Dataframe1$`Transplant Status`)
#Does Transplant status interact with Age at Transplant
#boxplot(`Time on Dialysis`~`Graft Number`, Joint3)
#Does cancer ever have an effect on
#boxplot(`Time on Dialysis`~`Sex`, Joint3)
#Generate an interaction plot to visualise and determine if sex and graft number have an interactive or additive effect on time on dialysis
graph2 <- ggplot(Dataframe1, aes(x=as.factor(`Graft Number`), y=`Time on Dialysis`, colour = `Transplant Status`)) + stat_summary(fun.y=mean, geom = "line", aes(group=`Transplant Status`), size=2) +theme_classic()
graph2 <- graph2 + ggtitle("Interaction Plot: Transplant Status & Graft Number on Time on Dialysis") + labs(y="Time on Dialysis", x="Graft Number", caption = "Figure2. Interaction Plot of Transplant Status and Graft Number on Time on Dialysis") + theme(plot.title = element_text(hjust=0.5)) + theme(plot.caption = element_text(hjust = 0)) +scale_colour_manual(values=cbPalette)
graph2
#H01 = there is no difference in the means for Graft number, Ha1 = there is a difference in the means for Graft number; H02 = there is no difference in the means for Transplant Status, Ha2 = there is a difference in means for Transplant Status; H03 = there is no interaction between Graft Number and Transplant Status, Ha3 = there is an interaction between Graft Number and Transplant Status
a1 = aov(`Time on Dialysis`~`Graft Number`*`Transplant Status`, Dataframe1)
summary(a1)## Df Sum Sq Mean Sq F value Pr(>F)
## `Graft Number` 1 13489 13489 1316.179 < 2e-16 ***
## `Transplant Status` 1 35 35 3.434 0.0642 .
## `Graft Number`:`Transplant Status` 1 259 259 25.260 5.94e-07 ***
## Residuals 996 10208 10
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(a1)## Analysis of Variance Table
##
## Response: Time on Dialysis
## Df Sum Sq Mean Sq F value Pr(>F)
## `Graft Number` 1 13489.5 13489.5 1316.1791 < 2.2e-16 ***
## `Transplant Status` 1 35.2 35.2 3.4341 0.06416 .
## `Graft Number`:`Transplant Status` 1 258.9 258.9 25.2595 5.939e-07 ***
## Residuals 996 10208.0 10.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Equality of variance
Dataframe1$`Graft Number` = as.factor(Dataframe1$`Graft Number`)
Dataframe1$`Transplant Status` = as.factor(Dataframe1$`Transplant Status`)
leveneTest(`Time on Dialysis`~`Graft Number`*`Transplant Status`, Dataframe1)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 39.406 < 2.2e-16 ***
## 993
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1plot(a1, 1)
#Normality
plot(a1, 2)
a1residuals = residuals(object = a1)
shapiro.test(x = a1residuals)##
## Shapiro-Wilk normality test
##
## data: a1residuals
## W = 0.88019, p-value < 2.2e-16- The plot suggests an interaction model as the lines are non-parallel. This is confirmed by the interactive analysis of variance model (a1), the interaction between Graft number and Transplant Status is statistically significant P = 5.94e-07 (p<0.05). As such, the null hypothesis (H03) is rejected in favour of Ha3. This confirms that an interaction model is apporpriate.
- The effect of Graft number on Time on Dialysis is statistically significant P < 0.05 (P < 2e-16), patients who are recieving a higher graft number (ie. their 3rd or 4th graft) spend longer on dialysis pre-transplant
- The effect of Transplant Status on Time on Dialysis is not statistically significant P < 0.05 (P = 0.0642)
- There is a significant interaction between Transplant Status and Graft number, and while Graft number has a significant effect on Time on Dialysis Transplant Status does not
- As such, the amount of time a patient spent on dialysis pre-transplant does not effect the success of their transplant. However, there is an effect between the time spent on dialysis pre-transplant and the graft number this was for the patient. In addition, there is an interaction between what graft number this was for the patient and the success of the transplant
- Assumptions:
- Normality: As within the normality plot of the residuals the points roughly fall along the reference line of the normal Q-Q plot normality may be assumed. However, this is not held by the Shapiro-Wilk test where a statistically significant value P < 0.05 (P < 2.2e-16) was obtained. This is likely due to the manner in which the observations are grouped in the variable graft number (ie. its more categorical (1,2,3,4 grafts) than a continous numerical variable)
- Equality of variance: a Levene test was performed, this revealed a statistically significant result P < 0.05 (P < 2.2e-16) which indicates there is evidence to suggest variance across groups is statistically significant. Therefore, we cannot assume homogenity of variances in the different groups this is confirmed by the residual vs fitted value plot
- However, it should be noted that the residual plot appears as such because of the grouping and values of the observations under the variable Graft number
4. What is the relationship between age at time of transplant and graft survivial time, and is there any association with transplant status (transplant success) with this?
#Is there a relationships between Transplant period (Graft survival time) and Age at Transplant
#Regression model
data = data.table(Transplantdata$id, Transplantdata$transplantperiod, Transplantdata$transplantstatus, Transplantdata$ageattransplant)
colnames(data) = c("ID", "Transplant period", "Transplant Status", "Age at Transplant")
data = na.omit(data)
data$`Transplant Status` = as.factor(data$`Transplant Status`)
graph3 <- ggplot(data, aes(x=`Age at Transplant`, y = `Transplant period`, colour =`Transplant Status`)) + geom_point() + theme_bw() + geom_smooth(method = 'lm', col = "black")
graph3 <- graph3 + labs(y="Graft survival time", x="Age at Transplant (Yrs)", caption = "Figure3. Regression model of Graft survival time against patient age at transplant, with colours determined by transplant status") + theme(plot.title = element_text(hjust=0.5)) + theme(plot.caption = element_text(hjust = 0)) + scale_color_manual(values=cbPalette) + labs(fill="Transplant Status") + scale_fill_discrete(name = "Transplant Status", labels = c("Graft failed", "Functioning"))
graph3
#Assess assumptions
fit = lm(`Age at Transplant`~`Transplant period`, data)
summary(fit)##
## Call:
## lm(formula = `Age at Transplant` ~ `Transplant period`, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -46.165 -9.926 2.938 11.402 31.598
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 48.4823916 0.7948715 60.99 < 2e-16 ***
## `Transplant period` -0.0013512 0.0002851 -4.74 2.45e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.24 on 998 degrees of freedom
## Multiple R-squared: 0.02202, Adjusted R-squared: 0.02104
## F-statistic: 22.47 on 1 and 998 DF, p-value: 2.449e-06plot(fit)
- The above model indicates a negative linear association between Graft survival time and Age at Transplant. The model indicates that generally graft survival time decreases with increasing age at time of transplant. This indicates that younger invidividuals have generally higher graft survival time, whereas the grafts in older individuals do not last as long. From the model nothing can be confidently concluded about transplant status. - Assumptions - Homogenity of variance: It can be assumed there is homogenity of variance as there is no clear relationship between the residuals and fitted values in the residual versus fits plot - Normality: It can be assumed the data is normal as within the Normal Q-Q plot of the residuals the points roughly fall along the reference line normality may be assumed - Homoscedasticity: the fitted line in the Scale-location plot indicates the residuals have uniform variance across the range, the data is homoscedastic - Outliers: there do not appear to be any points beyond the Cook’s distance, therefore, there are no evident influential outliers which should be assessed. - As such this model can be retained
##Conclusion The analyses performed within the ANZDATA patient and transplant datasets indicates that cancer history is not predicitive of transplant success or failure. Kmeans clustering of transplant data was not able to elucidate underlying patient sub-groups, however, this was identified to be due to the absence of principal component analysis clustering and a sub-optimal level of cluster numbers. As such, Kmeans clustering should not be excluded as a powerful way to utilise patient and transplant data to reveal important patient population sub-structures. Further this report concluded that there is no significant relationship between time on dialysis pre-transplant and transplant success, however, there is a signficant relationship between time on dialysis pre-transplant and the graft number this was for the patient, in addition there was a statistically significant interaction between graft number and transplant success. This reveals that graft number could be a clinically indicative measure for likely transplant success. This study also generated a linear regression model which demonstrates the negative linear relationship between graft survival time and age at transplant, this indicates that younger patients grafts survive longer whereas older patients grafts do not survive as long. This could be clinically significant and may indicate a need for a shorter time between transplant and followup to assess function in older patients, in addition it may indicate that older patients need more intensive post-transplant care as oppossed to younger patients.
##Bibliography 1 Kidney Disease Statistics for the United States. (2016, December 1). Retrieved April 2020, from https://www.niddk.nih.gov/health-information/health-statistics/kidney-disease 2 Australia and New Zealand Dialysis and Transplant Registry. (n.d.). Retrieved March 20, 2020, from https://www.anzdata.org.au/anzdata/