This is the initial approach adopted in implementing this study. In the pre-study strategy, a retrospective review of clinical non-invasive Breast cancer risks that are likely to cause re-hospitalization of discharged breast cancer patients was identified through questionnaires designed on the Likert scale. These questionnaires were then administered to stakeholders who were the oncology experts, nurse oncologists, clinical oncologists, radiologists, and Breast cancer pathologists. Acquired non-invasive Breast cancer risk variables that were likely to predispose discharged Breast cancer patients to the deteriorating quality of health thus surging rates of mortality were processed to remove outliers and obvious errors in the data set.

The re-engineering of discharging Breast cancer processes in KNH was undertaken to provide a conceptual understanding of the causes of preventable breast cancer risk variables to inform safety design concepts aimed at preventing and minimizing them by detecting them upfront before harm occurs. Figure 2 below highlights fundamental causes of Breast cancer re-hospitalization according to Forster et al. (2003) which were adopted to guide the engineering processes of the Kenyatta National Hospital (KNH) discharging framework. Medical errors are an important concern at hospital discharge. Forster and his colleagues identified four areas for improvement before discharging such as assessment and communication of problems that remain unresolved at the time of discharge; patient education regarding medications and other therapies; monitoring of drug therapies after discharge; and monitoring of the overall condition after discharge. Many adverse effects occur during the discharge period which could

be prevented with relatively simple strategies. Consequently, the re-engineering of the discharging Breast Cancer framework in Kenyatta National Hospital (KNH) considered both active and latent risks occurring at the time of hospital discharge.

Active re-hospitalization risks include those occurring at the time of hospital discharge during knowledge-based decision-making performed at the point of care by Clinicians. Active re-hospitalization risks are hospital characteristics related as shown in the conceptual model (Figure 2) above. Latent risks are observed when there is a system failure. Latent conditions are also clinicians and patients related as shown similarly in the Breast cancer-associated risk in the discharging Model (Figure 2). An example of a latent risk clinician related is when nurses and students are responsible for the discharge process and the harried nature of their work, and competing interests for example new admissions requiring their attention while at the same time, discharging a patient thus may not be considered by them a high priority and can therefore lead to an incomplete or haphazardly discharging resulting to re-hospitalization [12]. Another example of latent risk, is patient-related, for example, their lifestyle and non-compliance to the discharging guidelines or regime for better healing.

Thus taxonomy of avoidable Breast Cancer risk at the point of discharge in Figure 2, demonstrates how latent and active risks inter-relate, and their importance in the rule-based decision-making that the proposed decision support model will action.

With the re-engineered breast cancer discharging processes based on the concept shown in Figure 2 above, tend to promise value-based discharging outcomes needed in value-based healthcare in Breast Cancer as hospital discharge is the main stage that most re-hospitalization risks, lapses, and the adverse event happens. Also to note is that at the point of discharge is when latent conditions (system failures) combine with active failures pointing to the fact that the patient may be discharged with a huge health burden thus guaranteeing re-hospitalization within 30 - 45 days of discharge. As such, Breast cancer discharging processes in Kenyatta National Hospital may be improved through Business Re-engineering Processes (BRP) followed by robust modeling of its best practice processes.

Figure 3 displays the Breast Cancer risk elements that pertain to the decision-making of a Breast Cancer patient’s readiness for an improved discharge [13]. An optimal decision support model to discharge Breast cancer was coined

around this decision-making structure that required that Breast Cancer risk variables evaluate to a boolean expression, for example, that re-hospitalization shall take place within 30 - 45 days of discharge and or otherwise based on sufficient medical risk evidence of the patients. The decision-making structures that evaluate Breast Cancer risk variables to a boolean expression outcome are the if… else statement, the if…else if…else Statement, and the nested if statements inbuilt in Python programming language.

A research proposal of the entire study was submitted to Kenyatta National Hospital and the University of Nairobi Ethical Research Committee (KNH/UON-ERC) for review, suggestions, and approval upon satisfaction. The approved proposed study thus authorized access to the data. The source of data for this study was obtained therefore via a pre-study that had to be approved by the KNH/UON-ERC. The prestudy that obtained the dataset was conducted through a retrospective review of clinical non-invasive Breast cancer data risks that are likely to cause re-hospitalization and mistrusted discharges. The prestudy designed questionnaires on the Likert scale. These questionnaires were then administered to stakeholders who were the oncology experts, nurse oncologists, clinical oncologists, radiologists, and Breast cancer pathologists. Acquired data were non-invasive that were likely to predispose discharged Breast cancer patients to a deteriorating quality of health and surging rates of mortality. These data sets were processed to remove outliers and obvious errors. Also, additional first-hand data were obtained from Breast Cancer Past Records which was structured and unstructured and available in files.

The identified data sets instances can comfortably be represented by attribute-value pairs. For example, in smoking (committed, sneaking, or no smoking), in isolation (psychological, physical, or no Isolation), and data attributes (alcoholism, abuse of drugs, promiscuous) that have discrete output values (yes/no) therefore befitting this clinical decision problem well [14].

As the study is largely exploratory, the following designs are used;

1) Survey of literature concern, 2) Experience or clinician survey.

The survey of relevant literature e.g. hypothesis specified by earlier researchers is vigorously reviewed and evaluated to form the ground for the design study. Experience survey involves surveying of clinicians on practical experience of problem been studied e.g. surveys of the experienced clinician(s) who are selected randomly. The selected clinicians are given Likert scale questionnaires to respond to on how the design study should be approached. They are also allowed to raise additional issues which the investigator might have not considered within the questionnaires.

The targeted population included all breast cancer patients re-hospitalized within a period of three months in the years 2007-2013. It’s worth noting also that 10,000 breast cancer patients were estimated to have been re-hospitalized upon discharge between these years which translates to 2000 patients yearly on average.

• A participant should be a patient who has been diagnosed with breast cancer and has experienced re-hospitalized within 30 - 45 days upon discharge.

• A participant may also be a person who survived Breast cancer incidence and experienced re-hospitalization within 30 - 45 days upon discharge.

• A participant should also be a person who met any of the above criteria and has also consented by filling out a consent form to participate in the study.

• For clinical oncologists, oncology experts, nurse oncologists, radiologists, and Breast cancer pathologists to participate in the study, they must have experience obtained through practice in oncology for not less than 1 year. In addition, a participant should have also consented by filling out a consent form to participate in the study.

Any clinical oncologist, oncology expert, nurse oncologist, radiologist, and Breast cancer pathologist who doesn’t meet the inclusion criteria above.

The disproportionate sampling design method is deployed in this study as the data strata differ not only in size but also in variability, for example, the three data strata from the patients, oncologists, and records differ in size and variability. A larger sample is taken from more strata and smaller samples from the less variable strata [15]. The formula for the above statements is as follows:

n 1 / N 1 σ 1 = n 2 / N 2 σ 2 = ⋯ = n k / N k σ k

where σ 1 , σ 2 , ⋯ and σ k denotes the standard deviations of the k strata, N 1 , N 2 , ⋯ , N k denotes the sizes of k strata. This is called “optimum allocation” in the context of disproportionate sampling. The allocation in such situations results in the following formula for determining the sample sizes of different strata:

n i = n ⋅ N 1 σ 1 / N 2 σ 2 + ⋯ + N k σ k

for i = 1 , 2 , ⋯ and k. For example, in this study, we had strata oncologist O, strata patient P, and Strata data Record R with Standards deviation O = 15, P = 18, and R = 5, projected in the population of:

O p = 5000 , P p = 2000     and     R P = 3000 .

Thus total sample size of the dataset was n = 49 or n ≅ 50, apportion differently to sample size strata as follows:

O p = 5000 , n O = n ⋅ N 1 σ 1 / N 2 σ 2 + ⋯ + N k σ k = 49 × 5000 × 15 / 5000 × 15 + 2000 × 18 + 3000 s = 29.16 ≅ 30

as the sample size of oncologists or pathologists to be included in the study.

O E = 2000 , n O = n ⋅ N 1 σ 1 / N 2 σ 2 + ⋯ + N k σ k = 49 × 2000 × 18 / 5000 × 15 + 2000 × 18 + 3000 s = 14

as the sample size of the data record to be included in the study.

O p = 3000 , n O = n ⋅ N 1 σ 1 / N 2 σ 2 + ⋯ + N k σ k = 49 × 3000 × 5 / 5000 × 15 + 2000 × 18 + 3000 s = 5.833 ≅ 6

as the sample size of patients to be included in the study.

The dataset in this research study was collected from surveyed questionnaires. The surveyed questionnaires were built from suitable questions that were modified from related studies. In the questionnaire design, the Likert scale technique was used to determine if the respondent agreed or disagreed with a statement. The clinician’s, and oncologists’ survey questionnaires comprised section A, of 12 questions; section B, of 9 questions; section C, of 11 questions; and section D, of 21 questions on their clinician’s perception regarding discharging and re-hospitalization of a breast cancer patient. Patient or Breast cancer survivor’s survey questionnaires were made of section A, of 9 questions, and section B, of 20 questions. The clinician’s survey questionnaire was distributed to the participating clinicians and oncologists in the department of Cancer Treatment and Oncology within KNH. Other questionnaires were distributed by pathologists who referred their colleagues from other breast cancer treatment and management centers in Kenya such as Aga Khan hospital. The principal investigator also interviewed the Breast cancer patient and Breast cancer survivor against their questionnaires but if the patient or Breast cancer survivor was in a position to write, then he or she was given a questionnaire to answer.

Irrelevant attributes in administered questionnaire such as a patient’s residential address, name, application ID, etc. are removed. Obvious outliers and typo errors, for instance, a patient’s father’s name is irrelevant in predicting future re-hospitalizations. Cleaned “Re-hospitalization” data attributes are then added to hold the predictability result, which can either be “readmitted”, “no readmission” or “both”. Finally, a sample of the dataset tabular (database) as shown in Table 1 below is constructed from a cleaned dataset obtained from answered clinician’s or oncologist’s questionnaires, patient interview questions, and past patient records.

Prediction of the re-hospitalization is obtained from summation threshold of risk variables which forms the basis upon which decision is made using the machine learning perceptron algorithm inbuilt in Rapid miner software. The concept of Breast cancer Risk variables thresholding is better conveyed by the perceptron algorithm shown in Figure 4(a) below. Supervised Classification here is done by perceptron algorithm.

The implementation Clinical Decision Support Classifier is divided into five stages. In the first stage, data attributes that cause re-hospitalization are collected and then uploaded into the Rapidminer software algorithm. In the third stage, data preprocessing and visualization in the rapid miner are executed. In the fourth stage, modeling and generation of predictive decision trees based on ID3 and C4.5 algorithms are actioned.

• Splitting Re-hospitalization dataset to train and validate generated Breast Cancer Re-hospitalization prediction Model upon discharge

The Rapidminer software has been designed by default to split the Re-hospitalization dataset attributes into training and validation sets. The hypothetical optimal decision tree that is generated from these datasets, learns the training dataset and gets validated using the validation dataset. The patient’s dataset is split in the ratio of 0.7 and 0.3 to train and validate generated Breast cancer Re-hospitalization prediction model respectively. The diagram in Figure 4(b) below shows how the dataset is split in the ratio of 0.7 and 0.3 to train and validate generated Breast cancer Re-hospitalization prediction model. In Figure 4(b), Breast cancer feature sets on re-hospitalization, capture the basic information about each input risk variable to classify it as re-hospitalization related or non-re-hospitalization related. Pairs of these feature sets and labels are fed into the machine learning algorithm i.e. rapid miner software to generate a re-hospitalization predictive model.

• Training of generated re-hospitalization decision tree classifier model

Rapidminer software algorithm is configured in such a way that it generates a decision tree model classifier when provided with suitable risk datasets. Generated decision tree classifier is then trained to learn the training dataset as shown in Figure 4(b). As a result, a more optimal decision tree classifier is generated which is superior in classifying new unseen breast cancer re-hospitalization risk attributes. The ID3 and C4.5 Algorithms which are instances of decision tree algorithms are at play as the same are inbuilt in the Rapid miner software. The ID3 decision tree classifying model that has been generated from these breast cancer re-hospitalization risk datasets is represented in Figure 5 below.

• The ID3 Classifier errors due to overfitting of the Breast Cancer re-hospitalization dataset

The unpruned clinical decision tree model i.e. ID3 algorithm has a high error rate as can be demonstrated by the aid of Lemma’s theorem illustrated in figure 6 below.

The overfitting of the Breast cancer re-hospitalization dataset takes place when a classifier function is too closely aligned to a limited set of data points. As a result, the model is useful in reference only to its initial training data set, and not to any other data sets. For example, let D be a set of Breast cancer data examples and let H be a hypothesis space. The hypothesis space h ∈ H is considered to overfit D if an h ′ ∈ H with the following property exists:

E r r ( h ′ , D ) < E r r ( h , D )     and     E r r * ( h ) > E r r * ( h ′ ) ,

where E r r * ( h ) denotes the true misclassification rate of h, while E r r ( h ′ , D ) denotes the error of h ′ on the example set D. Reasons for overfitting are rooted in the example data set D and are that D is noisy, D is biased, and hence non-representative. D is too small and hence pretends unrealistic data properties. Thus given a hypothesis universal space H, and hypothesis h (or unpruned decision tree classifier), then h ∈ H . h ∈ H is said to overfit the training

dataset if there exists in H, an alternative hypothesis h ′ ∈ H such that h ∈ H has a bigger error than an alternative hypothesis over the training examples as h ′ ∈ H which is an alternative has a smaller error than h ∈ H which is considered to be unpruned. We can therefore conclude that h ∈ H memorizes the training dataset and thus can be a less classifier beyond memorized training dataset than the h ′ ∈ H . This has been outlined by the curves in Figure 6.

• The C4.5 decision tree classifier is an optimal Breast Cancer rehospitalization prediction model improved from the ID3 classifier Algorithm due to pruning

The C4.5 algorithm is an improved version of the ID3 classifier algorithm with fewer decision nodes compared to the ID3 Algorithm as shown in Figure 7 below. By deployment of C4.5 Algorithm in this study, we ensure that pruning of the resulting decision tree from ID3 classifier algorithm has been done. The model in Figure 7 is the generated C4.5 decision tree classifier for the prediction of re-hospitalization of discharged Breast cancer patients obtained by pruning ID3 decision tree Breast cancer classifier model.

• Evaluation and Analysis via Confusion Matrix of Clinical Decision support Model (C4.5 Algorithms)

Considering classification problems using only two classes, each instance is mapped to one element of the set {p, n} of positive and negative class labels. A classification model (or classifier) is mapping from instances to predicted classes. The classification model may produce continuous output (e.g., an estimate of an instance I). Also, they may produce discrete class labels indicating only the predicted class of the instance.

In this analysis and evaluation, to distinguish between the actual class and the predicted class we use the labels {P1, N2}. The below Figure 8(a) shows a 78.57% measure of the accuracy of the Clinical Decision support Model when built on C4.5 Algorithm i.e. pruned ID3 Algorithm. We also obtained the detection of a True negative of 85.71% and a True positive of 71.43% indicating that clinical decisions modeled on C4.5 Algorithm have better performance outcomes as shown in Figure 8(a) below.

For precision measures, the Clinical Decision support Modelled on C4.5 Algorithms for the prediction of Breast Cancer re-hospitalization upon discharge recorded 75.00% in identifying True negative and 83.33% level of precision in detection of true positive as shown in the below Figure 8(b).

Recall metrics measure the quantification of the number of positive class predictions made out of all positive examples in the dataset. In this instance, the Clinical Decision support Model built on C4.5 Algorithm has been able to quantify correctly the prediction of Breast Cancer re-hospitalization upon discharge by 71.43% for True positive and true negative by 85.71% showing the strength of the Clinical Decision support Model when built on C4.5 Algorithm. Figure 8(c) demonstrates this accomplishment.

These metrics outcomes mentioned above from the Clinical Decision support Model built on C4.5 Algorithm are also realized through the confusion matrix computation as shown in Table 2 below.

The confusion matrix and common performance metrics were calculated from the model. These were noted as follows:

Precision for True negative = (TP)/(TP) + (FP) = 6/8 = 75%, also

Precision for true positive = (TN)/(TN) + (FN) = 5/6 = 83.33%

Recall = (TP)/(TP) + (FN) = 6/7 = 85.71% also similar to sensitivity.

Classifier Accuracy, or recognition rate: percentage of test set tuples that are correctly classified. Accuracy = (TP + TN)/All = 6 + 5/14 = 78.57%.

Error rate: 1 – accuracy, or Error rate = (FP + FN)/All = 2 + 1/14 = 0.2142857142857143.

Sensitivity: True Positive recognition rate (Recall positive),

Sensitivity = TP/P = 6/7 = 85.714%.

Specificity: True Negative recognition rate (Recall Negative), Specificity = 5/7 = 71.43%.

By convention, the performance of a classification model such as the Clinical Decision support Model (C4.5 Algorithms) for the prediction of Breast Cancer re-hospitalization is usually summarized by the following two quantities related to the two types of errors: true-positive rate and false-positive rate. In this context, the true-positive rate is the probability that a patient to be re-hospitalized is correctly classified as such and the false-positive rate is the probability that a patient who shall not be re-hospitalized is incorrectly classified as shall be re-hospitalized. (The true-positive rate is also called sensitivity or recall and one minus the false-Positive rate is also called specificity). For an ideal classification rule, the true-positive rate is one and the false-positive rate is zero. The magnitudes of acceptable false-positive rates and true-positive rates depend on the corresponding costs and perceived benefits for the problem in question. For instance above results outcome for the Clinical Decision support Model (C4.5 Algorithm) for the prediction of Breast Cancer re-hospitalization is fairly acceptable to reinforce experts discharging decisions.

On the flip side, a comparison of C4.5 Algorithms performance to unpruned Clinical Decision support Model (ID3 Algorithms) for the prediction of Breast Cancer re-hospitalization indicates that the latter is a fewer performer in terms of accuracy, precision, and recalling while predicting re-hospitalization for discharged Breast cancer patients.. For example, Figure 9(a) below presents an accuracy of 64.29% which is lesser when compared to 78.57% which was obtained by the Clinical Decision support Model modeled on C4.5 Algorithm.

Furthermore, the unpruned Clinical Decision support Modeled on the ID3 Algorithm, provides the precision of 60.00% for True negative and true positive at 75.00% as shown in Figure 9(b) below unlike its counterpart implemented on the C4.5 Algorithm that scored precision of 75.00% for True negative and true positive of 83.33%.

It’s worth also noting that recall of prediction by the Clinical Decision support Model fashioned on ID3 Algorithm stands at 85.71% for True positive and true negative at 42.86% as shown in the Figure 9(c) below which is away lower as compared Clinical Decision support Model produced on the C4.5 Algorithm.

• The receiver operating characteristic (ROC) evaluation and analysis of the Clinical Decision support Model (built on ID3 and C4.5 Algorithm) for the prediction of Breast Cancer rehospitalization

ROC graphs have long been used in signal detection theory to depict the tradeoff between hit rates and false alarm rates of a classifier [16]. The medical decision-making community has extensive literature on the use of ROC graphs for diagnostic testing (Zou, 2002). Recent years have seen an increase in the use of ROC graphs in the machine learning community, due in part to the realization that simple classification accuracy is often a poor metric for measuring performance [17], and that they have properties that make them especially useful for domains with skewed class distribution (test set) and unequal classification error costs. These characteristics have become increasingly important as research continues into the areas of cost-sensitive learning and learning in the presence of unbalanced classes (test set).

As seen above, ROC graphs are two-dimensional graphs in which the TP rate is plotted on the Y-axis and the FP rate is plotted on the X-axis. A ROC graph depicts relative tradeoffs between benefits (true positives) and costs (false positives). Figure 9(d) shows that each discrete classifier produces a (TP rate, FP rate) pair corresponding to a single point in the ROC space. Several points in the ROC space are important to note. The lower left point (0, 0) represents the strategy of never issuing a positive classification; such a classifier commits no false-positive errors but also gains no true positives. The opposite strategy, of unconditionally issuing positive classifications, is represented by the upper right point (1, 1). The point (0, 1) represents perfect classification. Informally, one point in ROC space is better than another if it is to the northwest (TP rate is higher, FP rate is lower) appearing on the left-hand side of a ROC graph, near the X-axis, may turn to correspond to one ROC point. Thus, a discrete classifier produces only a single point in the ROC space. The rationale for the optimal ROC curve is that: 1) One wants the highest true-positive rate for a given false-positive rate, and 2) One can specify a rule on the ROC line linking two (false-positive rate, true-positive rate) points by applying the rule for one point with some probability and the rule for the other point with one minus that probability. However, in practice, one would like one of the points on the optimal ROC curve to lie near the target false- and true-positive rates. For the reasons given above, interest is in the part of the ROC curve corresponding to a low false-positive rate when evaluating prediction. The area under (ROC) curve is known as AUC. This area, therefore, should be greater than 0.5 for a model to be acceptable; a model with an AUC of 0.5 or less is worthless. Understandably, this area is a measure of the predictive accuracy of the model. Based on this information, the area under the curve (ROC) for the C4.5 Algorithm is relatively bigger than for the ID3 Algorithm shown in the Figure 9(e) below implying that C.4.5 is a superior classifier.

Finally, the confusion matrix and common performance metrics based on the Clinical Decision support Model (ID3 Algorithm) for the prediction of Breast Cancer re-hospitalization have lower metrics performance unlike if the Clinical Decision support Model is modeled on the C4.5 Algorithm for the prediction of Breast Cancer re-hospitalization.

The predictive patterns generated from data risk variables linked to Breast cancer readmission are coded into class methods of if-else ladders in Python programming language as shown in appendix I. The class method is configured in such a way that they accept only the splitting risk attributes. The class methods return the final result of that particular risk evaluation, indicating whether that patient would be re-hospitalized or will not should he/she be discharged. This understanding is mapped onto a web-based platform to assess and evaluate Breast Cancer patients before being integrated into the general public as, “medicare advantaged patients experience fewer re-hospitalizations”, Jaimie Oh, (2012). Figure 10(a) and Figure 10(b)) seen below are the web-based application designed and mapped from this understanding. This web-based application is fashioned from Django-1.6.5 as explained in the succeeding section.

• Code Igniter-Django-1.6.5.

As illustrated above, a web application that is mapping Clinical Decision Support (built on the C4.5 Algorithm) model to predict the re-hospitalization of Breast cancer patients before discharging is developed through a Python framework named Django 1.6.5. The web application has provisions for multiple simultaneous clinician registrations and logins thus ensuring independent clinical evaluation. Figure 10(a) and Figure 10(b) below depicts the built Clinical

Decision Support on the C4.5 Algorithm. Figure 10(a) is the registration interface for this clinical decision application while Figure 10(b) is the login interface respectively.

• The web-based Python application Predicting to Re-hospitalization of Breast cancer patients before discharging

Once the web-based Python application for Prediction of Re-hospitalization to Breast cancer patients is mapped in class python methods, a web-based application is designed for clinicians to do entries and evaluations on the splitting risk values attribute of a patient as conveyed below in Figure 11(a) and Figure 11(b) respectively. Breast cancer Risk values for re-hospitalization are used to evaluate avoidable re-hospitalization of a patient as either “Re-hospitalization occurs”, or “no re-hospitalization”.