Medical Data Analytics Using R
27/07/17 Information Technology Reference this
Disclaimer: This work has been submitted by a student. This is not an example of the work produced by our Essay Writing Service. You can view samples of our professional work here.
Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of UK Essays.
1.) R for Recency => months since last donation, 2.) F for Frequency => total number of donation, 3.) M for Monetary => total amount of blood donated in c.c., 4.) T for Time => months since first donation and 5.) Binary variable => 1 > donated blood, 0> didn’t donate blood.
The main idea behind this dataset is the concept of relationship management CRM. Based on three metrics: Recency, Frequency and Monetary (RFM) which are 3 out of the 5 attributes of the dataset, we would be able to predict whether a customer is likely to donate blood again based to a marketing campaign. For example, customers who have donated or visited more currently (Recency), more frequently (Frequency) or made higher monetary values (Monetary) are more likely to respond to a marketing effort. Customers with less RFM score are less likely to react. It is also known in customer behavior, that the time of the first positive interaction (donation, purchase) is not significant. However, the Recency of the last donation is very important.
In the traditional RFM implementation each customer is ranked based on his RFM value parameters against all the other customers and that develops a score for every customer. Customers with bigger scores are more likely to react in a positive way for example (visit again or donate). The model constructs the formula which could predict the following problem.
 Keep in repository only customers that are more likely to continue donating in the future and remove those who are less likely to donate, given a certain period of time. The previous statement also determines the problem which will be trained and tested in this project.
Firstly, I created a .csv file and generated 748 unique random numbers in Excel in the domain [1,748] in the first column, which corresponds to the customers or users ID. Then I transferred the whole data from the .txt file (transfusion.data) to the .csv file in excel by using the delimited (‘,’) option. Then I randomly split it in a train file and a test file. The train file contains the 530 instances and the test file has the 218 instances. Afterwards, I read both the training dataset and the test dataset.
From the previous results, we can see that we have no missing or invalid values. Data ranges and units seem reasonable.
Figure 1 above depicts boxplots of all the attributes and for both train and test datasets. By examining the figure, we notice that both datasets have similar distributions and there are some outliers (Monetary > 2,500) that are visible. The volume of blood variable has a high correlation with frequency. Because the volume of blood that is donated each time is fixed, the Monetary value is proportional to the Frequency (number of donations) each person gave. For example, if the amount of blood drawn in each person was 250 ml/bag (Taiwan Blood Services Foundation 2007) March then Monetary = 250*Frequency. This is also why in the predictive model we will not consider the Monetary attribute in the implementation. So, it is reasonable to expect that customers with higher frequency will have a lot higher Monetary value. This can be verified also visually by examining the Monetary outliers for the train set. We retrieve back 83 instances.
In order, to understand better the statistical dispersion of the whole dataset (748 instances) we will look at the standard deviation (SD) between the Recency and the variable ‘whether customer has donated blood’ (Binary variable) and the SD between the Frequency and the Binary variable.The distribution of scores around the mean is small, which means the data is concentrated. This can also be noticed from the plots.

Another observation is that the various Recency numbers are not factors of 3. This goes to opposition with what the description said about the data being collected every 3 months. Additionally, there is always a maximum number of times you can donate blood per certain period (e.g. 1 time per month), but the data shows that.
36 customers donated blood more than once and 6 customers had donated 3 or more times in the same month.
The features that will be used to calculate the prediction of whether a customer is likely to donate again are 2, the Recency and the Frequency (RF). The Monetary feature will be dropped. The number of categories for R and F attributes will be 3. The highest RF score will be 33 equivalent to 6 when added together and the lowest will be 11 equivalent to 2 when added together. The threshold for the added score to determine whether a customer is more likely to donate blood again or not, will be set to 4 which is the median value. The users will be assigned to categories by sorting on RF attributes as well as their scores. The file with the donators will be sorted on Recency first (in ascending order) because we want to see which customers have donated blood more recently. Then it will be sorted on frequency (in descending order this time because we want to see which customers have donated more times) in each Recency category. Apart from sorting, we will need to apply some business rules that have occurred after multiple tests:
 For Recency (Business rule 1):
 If the Recency in months is less than 15 months, then these customers will be assigned to category 3.
 If the Recency in months is equal or greater than 15 months and less than 26 months, then these customers will be assigned to category 2.
 Otherwise, if the Recency in months is equal or greater than 26 months, then these customers will be assigned to category 1
 And for Frequency (Business rule 2):
 If the Frequency is equal or greater than 25 times, then these customers will be assigned to category 3.
 If the Frequency is less than 25 times or greater than 15 months, then these customers will be assigned to category 2.
 If the Frequency is equal or less than 15 times, then these customers will be assigned to category 1
RESULTS
The output of the program are two smaller files that have resulted from the train file and the other one from the test file, that have excluded several customers that should not be considered future targets and kept those that are likely to respond. Some statistics about the precision, recall and the balanced Fscore of the train and test file have been calculated and printed. Furthermore, we compute the absolute difference between the results retrieved from the train and test file to get the offset error between these statistics. By doing this and verifying that the error numbers are negligible, we validate the consistency of the model implemented. Moreover, we depict two confusion matrices one for the test and one for the training by calculating the true positives, false negatives, false positives and true negatives. In our case, true positives correspond to the customers (who donated on March 2007) and were classified as future possible donators. False negatives correspond to the customers (who donated on March 2007) but were not classified as future possible targets for marketing campaigns. False positives correlate to customers (who did not donate on March 2007) and were incorrectly classified as possible future targets. Lastly, true negatives which are customers (who did not donate on March 2007) and were correctly classified as not plausible future donators and therefore removed from the data file. By classification we mean the application of the threshold (4) to separate those customers who are more likely and less likely to donate again in a certain future period.
Lastly, we calculate 2 more single value metrics for both train and test files the Kappa Statistic (general statistic used for classification systems) and Matthews Correlation Coefficient or cost/reward measure. Both are normalized statistics for classification systems, its values never exceed 1, so the same statistic can be used even as the number of observations grows. The error for both measures are MCC error: 0.002577Â and Kappa error:Â 0.002808, which is very small (negligible), similarly with all the previous measures.
REFERENCES
 UCI Machine Learning Repository (2008) UCI machine learning repository: Blood transfusion service center data set. Available at: http://archive.ics.uci.edu/ml/datasets/Blood+Transfusion+Service+Center (Accessed: 30 January 2017).
 Fundation, T.B.S. (2015) Operation department. Available at: http://www.blood.org.tw/Internet/english/docDetail.aspx?uid=7741&pid=7681&docid=37144 (Accessed: 31 January 2017).
The Appendix with the code starts below. However the whole code has been uploaded on my Git Hub profile and this is the link where it can be accessed.
https://github.com/it21208/RassignmentDataAnalysis/blob/master/RassignmentDataAnalysis.R
 library(ggplot2)
 library(car)
Â # read training and testing datasets
 traindata ïƒŸÂ read.csv(‘C:/Users/Alexandros/Dropbox/MSc/2nd Semester/Data analysis/Assignment/transfusion.csv’)
 testdata ïƒŸÂ read.csv(‘C:/Users/Alexandros/Dropbox/MSc/2nd Semester/Data analysis/Assignment/test.csv’)
# assigning the datasets to dataframes
 dftrain ïƒŸ data.frame(traindata)
 dftest ïƒŸ data.frame(testdata)
 sapply(dftrain, typeof)
# give better names to columns
 names(dftrain)[1] ïƒŸ “ID”
 names(dftrain)[2] ïƒŸ “recency”
 names(dftrain)[3]ïƒŸ”frequency”
 names(dftrain)[4]ïƒŸ”cc”
 names(dftrain)[5]ïƒŸ”time”
 names(dftrain)[6]ïƒŸ”donated”
#——————————————————
 names(dftest)[1]ïƒŸ”ID”
 names(dftest)[2]ïƒŸ”recency”
 names(dftest)[3]ïƒŸ”frequency”
 names(dftest)[4]ïƒŸ”cc”
 names(dftest)[5]ïƒŸ”time”
 names(dftest)[6]ïƒŸ”donated”
# drop time column from both files
 dftrain$time ïƒŸ NULL
 dftest$time ïƒŸ NULL
#Â sort (train) dataframe on Recency in ascending order
 sorted_dftrain ïƒŸ dftrain[ order( dftrain[,2] ), ]
#Â add column in (train) dataframe Â hold score (rank) of Recency for each customer
 sorted_dftrain[ , “Rrank”] ïƒŸ 0
#Â convert train file from dataframe format to matrix
 matrix_train ïƒŸ as.matrix(sapply(sorted_dftrain, as.numeric))
#Â sort (test) dataframe on Recency in ascending order
 sorted_dftest ïƒŸ dftest[ order( dftest[,2] ), ]
#Â add column in (test) dataframe hold score (rank) of Recency for each customer
 sorted_dftest[ , “Rrank”] ïƒŸ 0
#Â convert train file from dataframe format to matrix
 matrix_test ïƒŸ as.matrix(sapply(sorted_dftest, as.numeric))
# categorize matrix_train and add scores for Recency – apply business rule
 for(i in 1:nrow(matrix_train)) {
if (matrix_train [i,2] < 15) {
Â Â Â Â matrix_train [i,6] ïƒŸ 3
} else if ((matrix_train [i,2] < 26) & (matrix_train [i,2] >= 15)) {
Â Â Â Â matrix_train [i,6] ïƒŸ 2
} else {Â matrix_train [i,6] ïƒŸ 1Â }
Â Â Â Â Â }
# categorize matrix_test and add scores for Recency – apply business rule
 for(i in 1:nrow(matrix_test)) {
if (matrix_test [i,2] < 15) {
Â Â Â Â matrix_test [i,6] ïƒŸ 3
} else if ((matrix_test [i,2] < 26) & (matrix_test [i,2] >= 15)) {
Â Â Â Â matrix_test [i,6] ïƒŸ 2
} else {Â matrix_test [i,6] ïƒŸ 1 }
Â Â Â Â Â }
# convert matrix_train back to dataframe
 sorted_dftrain ïƒŸ data.frame(matrix_train)
# sort dataframe 1rst by Recency Rank (desc.) then by Frequency (desc.)
 sorted_dftrain_2ïƒŸ sorted_dftrain[order(sorted_dftrain[,6], sorted_dftrain[,3] ), ]
# add column in train dataframe hold Frequency score (rank) for each customer
 sorted_dftrain_2[ , “Frank”] ïƒŸ 0
# convert dataframe to matrix
 matrix_train ïƒŸ as.matrix(sapply(sorted_dftrain_2, as.numeric))
# convert matrix_test back to dataframe
 sorted_dftest ïƒŸ data.frame(matrix_test)
# sort dataframe 1rst by Recency Rank (desc.) then by Frequency (desc.)
 sorted_dftest2 ïƒŸ sorted_dftest[ order( sorted_dftest[,6], sorted_dftest[,3] ), ]
# add column in test dataframe hold Frequency score (rank) for each customer
 sorted_dftest2[ , “Frank”] ïƒŸ 0
# convert dataframe to matrix
 matrix_test ïƒŸ as.matrix(sapply(sorted_dftest2, as.numeric))
#categorize matrix_train, add scores for Frequency
 for(i in 1:nrow(matrix_train)){
Â if (matrix_train[i,3] >= 25) {
Â Â Â matrix_train[i,7] ïƒŸ 3
Â } else if ((matrix_train[i,3] > 15) & (matrix_train[i,3] < 25)) {
Â Â Â matrix_train[i,7] ïƒŸ 2
Â } else {Â matrix_train[i,7] ïƒŸ 1Â }
Â Â Â Â Â Â Â Â }
#categorize matrix_test, add scores for Frequency
 for(i in 1:nrow(matrix_test)){
Â if (matrix_test[i,3] >= 25) {
Â Â Â matrix_test[i,7] ïƒŸ 3
Â } else if ((matrix_test[i,3] > 15) & (matrix_test[i,3] < 25)) {
Â Â Â matrix_test[i,7] ïƒŸ 2
Â } else {Â Â matrix_test[i,7] ïƒŸ 1Â }
}
#Â convert matrix test back to dataframe
 sorted_dftrain ïƒŸ data.frame(matrix_train)
# sort (train) dataframe 1rst on Recency rank (desc.) & 2^{nd }Frequency rank (desc.)
 sorted_dftrain_2 ïƒŸ sorted_dftrain[ order( sorted_dftrain[,6], sorted_dftrain[,7] ), ]
# add another column for the Sum of Recency rank and Frequency rank
 sorted_dftrain_2[ , “SumRankRAndF”] ïƒŸ 0
# convert dataframe to matrix
 matrix_train ïƒŸ as.matrix(sapply(sorted_dftrain_2, as.numeric))
#Â convert matrix test back to dataframe
 sorted_dftest ïƒŸ data.frame(matrix_test)
# sort (train) dataframe 1rst on Recency rank (desc.) & 2^{nd }Frequency rank (desc.)
 sorted_dftest2 ïƒŸ sorted_dftest[ order( sorted_dftest[,6],Â sorted_dftest[,7] ), ]
# add another column for the Sum of Recency rank and Frequency rank
 sorted_dftest2[ , “SumRankRAndF”] ïƒŸ 0
# convert dataframe to matrix
 matrix_test ïƒŸ as.matrix(sapply(sorted_dftest2, as.numeric))
# sum Recency rank and Frequency rank for train file
 for(i in 1:nrow(matrix_train))
{ matrix_train[i,8] ïƒŸ matrix_train[i,6] + matrix_train[i,7] }
# sum Recency rank and Frequency rank for test file
 for(i in 1:nrow(matrix_test))
{ matrix_test[i,8] ïƒŸ matrix_test[i,6] + matrix_test[i,7] }
# convert matrix_train back to dataframe
 sorted_dftrain ïƒŸ data.frame(matrix_train)
# sort train dataframe according to total rank in descending order
 sorted_dftrain_2 ïƒŸ sorted_dftrain[ order( sorted_dftrain[,8] ), ]
# convert sorted train dataframe
 matrix_train ïƒŸ as.matrix(sapply(sorted_dftrain_2, as.numeric))
# convert matrix_test back to dataframe
 sorted_dftest ïƒŸ data.frame(matrix_test)
# sort test dataframe according to total rank in descending order
 sorted_dftest2 ïƒŸ sorted_dftest[ order( sorted_dftest[,8] ), ]
# convert sorted test dataframe to matrix
 matrix_test ïƒŸ as.matrix(sapply(sorted_dftest2, as.numeric))
# apply business rule check & count customers whose score >= 4 and that Have Donated, train file
# check & count for all customers that have donated in the train dataset
 count_train_predicted_donations ïƒŸ 0
 counter_train ïƒŸ 0
 number_donation_instances_whole_train ïƒŸ 0
 false_positives_train_counter ïƒŸ 0
 for(i in 1:nrow(matrix_train)) {
Â if ((matrix_train[i,8] >= 4) & (matrix_train[i,5] == 1)) {
Â Â Â count_train_predicted_donations = count_train_predicted_donations + 1Â }
if ((matrix_train[i,8] >= 4) & (matrix_train[i,5] == 0)) {
Â Â Â false_positives_train_counter = false_positives_train_counter + 1}
Â if (matrix_train[i,8] >= 4) {
Â Â Â Â Â counter_train ïƒŸ counter_train + 1
Â Â Â }
Â if (matrix_train[i,5] == 1) {
Â Â Â number_donation_instances_whole_train ïƒŸ number_donation_instances_whole_train + 1
Â }
}
# apply business rule check & count customers whose score >= 4 and that Have Donated, test file
# check & count for all customers that have donated in the test dataset
 count_test_predicted_donations ïƒŸ 0
 counter_test ïƒŸ 0
 number_donation_instances_whole_test ïƒŸ 0
 false_positives_test_counter ïƒŸ 0
 for(i in 1:nrow(matrix_test)) {
Â if ((matrix_test[i,8] >= 4) & (matrix_test[i,5] == 1)) {
Â Â Â count_test_predicted_donations = count_test_predicted_donations + 1Â }
if ((matrix_test[i,8] >= 4) & (matrix_test[i,5] == 0)) {
Â Â Â false_positives_test_counter = false_positives_test_counter + 1}
Â if (matrix_test[i,8] >= 4) {
Â Â Â Â Â counter_test ïƒŸ counter_test + 1
Â Â Â }
Â if (matrix_test[i,5] == 1) {
Â Â Â Â number_donation_instances_whole_test ïƒŸ number_donation_instances_whole_test + 1
Â Â }
}
# convert matrix_train to dataframe
 dftrain ïƒŸ data.frame(matrix_train)
# remove the group of customers who are less likely to donate again in the future from train file
 dftrain_final ïƒŸ dftrain[c(1:counter_train),1:8]
# convert matrix_train to dataframe
 dftest ïƒŸ data.frame(matrix_test)
# remove the group of customers who are less likely to donate again in the future from test file
 dftest_final ïƒŸ dftest[c(1:counter_test),1:8]
# save final train dataframe as a CSV in the specified directory – reduced target future customers
 write.csv(dftrain_final, file = “C:\Users\Alexandros\Dropbox\MSc\2nd Semester\Data analysis\Assignment\train_output.csv”, row.names = FALSE)
#save final test dataframe as a CSV in the specified directory – reduced target future customers
 write.csv(dftest_final, file = “C:\Users\Alexandros\Dropbox\MSc\2nd Semester\Data analysis\Assignment\test_output.csv”, row.names = FALSE)
#train precision=number of relevant instances retrieved / number of retrieved instances collect.530
precision_train ïƒŸÂ count_train_predicted_donations / counter_train
# train recall = number of relevant instances retrieved / number of relevant instances in collect.530
recall_train ïƒŸ count_train_predicted_donations / number_donation_instances_whole_train
# measure combines Precision&Recall is harmonic mean of Precision&Recall balanced Fscore for # train file
f_balanced_score_train ïƒŸ 2*(precision_train*recall_train)/(precision_train+recall_train)
# test precision
precision_test ïƒŸ count_test_predicted_donations / counter_test
# test recall
recall_test ïƒŸ count_test_predicted_donations / number_donation_instances_whole_test
# the balanced Fscore for test file
f_balanced_score_test ïƒŸ 2*(precision_test*recall_test)/(precision_test+recall_test)
# error in precision
error_precision ïƒŸ abs(precision_trainprecision_test)
# error in recall
error_recall ïƒŸ abs(recall_trainrecall_test)
# error in fbalanced scores
error_f_balanced_scores ïƒŸ abs(f_balanced_score_trainf_balanced_score_test)
# Print Statistics for verification and validation
 cat(“Precision with training dataset: “, precision_train)
 cat(“Recall with training dataset: “, recall_train)
 cat(“Precision with testing dataset: “, precision_test)
 cat(“Recall with testing dataset: “, recall_test)
 cat(“The Fbalanced scores with training dataset: “, f_balanced_score_train)
 cat(“The Fbalanced scores with testing dataset:Â “, f_balanced_score_test)
 cat(“Error in precision: “, error_precision)
 cat(“Error in recall: “, error_recall)
 cat(“Error in Fbalanced scores: “, error_f_balanced_scores)
# confusion matrix (true positives, false positives, false negatives, true negatives)
# calculate true positives for train which is the variable ‘count_train_predicted_donations’
# calculate false positives for train which is the variable ‘false_positives_train_counter’
# calculate false negatives for train
 false_negatives_for_train ïƒŸ number_donation_instances_whole_train – count_train_predicted_donations
# calculate true negatives for train
 true_negatives_for_train ïƒŸ (nrow(matrix_train) – number_donation_instances_whole_train) – false_positives_train_counter
 collect_trainïƒŸc(false_positives_train_counter, true_negatives_for_train, count_train_predicted_donations, false_negatives_for_train)
# calculate true positives for test which is the variable ‘count_test_predicted_donations’
# calculate false positives for test which is the variable ‘false_positives_test_counter’
# calculate false negatives for test
 false_negatives_for_test ïƒŸ number_donation_instances_whole_test – count_test_predicted_donations
# calculate true negatives for test
 true_negatives_for_testïƒŸ(nrow(matrix_test)number_donation_instances_whole_test) false_positives_test_counter
 collect_test ïƒŸ c(false_positives_test_counter, true_negatives_for_test, count_test_predicted_donations, false_negatives_for_test)
 TrueCondition ïƒŸ factor(c(0, 0, 1, 1))
 PredictedCondition ïƒŸ factor(c(1, 0, 1, 0))
# print confusion matrix for train
 df_conf_mat_train ïƒŸ data.frame(TrueCondition,PredictedCondition,collect_train)
 ggplot(data = df_conf_mat_train, mapping = aes(x = PredictedCondition, y = TrueCondition)) +
Â geom_tile(aes(fill = collect_train), colour = “white”) +
Â geom_text(aes(label = sprintf(“%1.0f”, collect_train)), vjust = 1) +
Â scale_fill_gradient(low = “blue”, high = “red”) +
Â theme_bw() + theme(legend.position = “none”)
#Â print confusion matrix for test
 df_conf_mat_test ïƒŸ data.frame(TrueCondition,PredictedCondition,collect_test)
 ggplot(data =Â df_conf_mat_test, mapping = aes(x = PredictedCondition, y = TrueCondition)) +
Â geom_tile(aes(fill = collect_test), colour = “white”) +
Â geom_text(aes(label = sprintf(“%1.0f”, collect_test)), vjust = 1) +
Â scale_fill_gradient(low = “blue”, high = “red”) +
Â theme_bw() + theme(legend.position = “none”)
# MCC = (TP * TN – FP * FN)/sqrt((TP+FP) (TP+FN) (FP+TN) (TN+FN)) for train values
 mcc_train ïƒŸ ((count_train_predicted_donations * true_negatives_for_train) – (false_positives_train_counter * false_negatives_for_train))/sqrt((count_train_predicted_donations+false_positives_train_counter)*(count_train_predicted_donations+false_negatives_for_train)*(false_positives_train_counter+true_negatives_for_train)*(true_negatives_for_train+false_negatives_for_train))
# print MCC for train
 cat(“Matthews Correlation Coefficient for train: “,mcc_train)
# MCC = (TP * TN – FP * FN)/sqrt((TP+FP) (TP+FN) (FP+TN) (TN+FN)) for test values
 mcc_test ïƒŸ ((count_test_predicted_donations * true_negatives_for_test) – (false_positives_test_counter * false_negatives_for_test))/sqrt((count_test_predicted_donations+false_positives_test_counter)*(count_test_predicted_donations+false_negatives_for_test)*(false_positives_test_counter+true_negatives_for_test)*(true_negatives_for_test+false_negatives_for_test))
# print MCC for test
 cat(“Matthews Correlation Coefficient for test: “,mcc_test)
# print MCC err between train and err
 cat(“Matthews Correlation Coefficient error: “,abs(mcc_trainmcc_test))
# Total = TP + TN + FP + FN for train
 total_train ïƒŸ count_train_predicted_donations + true_negatives_for_train + false_positives_train_counter + false_negatives_for_train
# Total = TP + TN + FP + FN for test
 Â total_test ïƒŸ count_test_predicted_donations + true_negatives_for_test + false_positives_test_counter + false_negatives_for_test
# totalAccuracy = (TP + TN) / Total – for train values
 totalAccuracyTrain ïƒŸ (count_train_predicted_donations + true_negatives_for_train)/ total_train
# totalAccuracy = (TP + TN) / Total – for test values
 totalAccuracyTest ïƒŸ (count_test_predicted_donations + true_negatives_for_test)/ total_test
# randomAccuracy = ((TN+FP)*(TN+FN)+(FN+TP)*(FP+TP)) / (Total*Total)Â for train values
 randomAccuracyTrainïƒŸ((true_negatives_for_train+false_positives_train_counter)*(true_negatives_for_train+false_negatives_for_train)+(false_negatives_for_train+count_train_predicted_donations)*(false_positives_train_counter+count_train_predicted_donations))/(total_train*total_train)
# randomAccuracy = ((TN+FP)*(TN+FN)+(FN+TP)*(FP+TP)) / (Total*Total)Â for test values
 randomAccuracyTestïƒŸ((true_negatives_for_test+false_positives_test_counter)*(true_negatives_for_test+false_negatives_for_test)+(false_negatives_for_test+count_test_predicted_donations)*(false_positives_test_counter+count_test_predicted_donations))/(total_test*total_test)
# kappa = (totalAccuracy – randomAccuracy) / (1 – randomAccuracy) for train
 kappa_train ïƒŸ (totalAccuracyTrainrandomAccuracyTrain)/(1randomAccuracyTrain)
# kappa = (totalAccuracy – randomAccuracy) / (1 – randomAccuracy) for test
 kappa_test ïƒŸ (totalAccuracyTestrandomAccuracyTest)/(1randomAccuracyTest)
# print kappa error
 cat(“Kappa error: “,abs(kappa_trainkappa_test))
If you need assistance with writing your essay, our professional essay writing service is here to help!
Find out moreCite This Work
To export a reference to this article please select a referencing style below:
Related Services
View allDMCA / Removal Request
If you are the original writer of this essay and no longer wish to have the essay published on the UK Essays website then please: