Quantitative Model Analysis

As established in the Introduction, different modelling types are available depending on the end goal. For large networks, Boolean models are usually employed, as the simplified logic allows for a lower computational demand, whilst mathematically precise models are typically used for smaller-scale networks. One persistent limitation of Boolean models is that the discrete states (1, 0, NaN) allow for only a limited capturing of the overall state of a node. There is a continuing drive to develop algorithms that allow for a more quantitative analysis to be performed on Boolean models. One such algorithm is the STSFA, which superimposes ChIP-seq and/or microarray data onto a model to analyse it quantitatively (Isik et al., 2012).

4.6.1 Model Validation by STSFA Analysis

The same twelve microarray datasets described in Table ‎4.4.3 (Page 168) were used to analyse the model via the STSFA and the same six comparisons were used to evaluate the prediction accuracy of STSFA. Individual comparison results are shown in Appendix Table 7 - Appendix Table 12 (Page 223-238).

A summary of the correct/small error/large error percentages for each comparison is provided in Table ‎4.6.1. Comparisons 1-6 are the same comparisons performed previously (Table ‎4.4.3, Page 168)

Table ‎4.6.1: Summary of prediction rates from all STSFA comparison scenarios.

Comparison Correct (%) Small Error (%) Large Error (%)

1 82.6 17.4 0.0

2 83.0 17.0 0.0

3 87.2 12.8 0.0

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5 74.5 23.4 2.1

6 80.9 17.0 2.1

AVERAGE 80.1 18.9 1.0

Examination of Table ‎4.6.1 shows high correct prediction rates obtained via STSFA analysis. With a correct prediction range from approximately 72% to 87% and large errors occurring at 2.1% in three simulations (0% in the other three), the increased accuracy provided by the semi-quantitative approach of the STSFA provides a more robust analysis.

4.6.2 Comparison of LSSA and STSFA

It is expected that quantitative (even semi-quantitative) analysis would yield better prediction outcomes than static Boolean analysis, and indeed this has been shown previously (Hussain et al., 2014). The correct prediction rates of LSSA and STSFA with cell-based microarray data (Table ‎4.4.4, Page 169 for LSSA and Table ‎4.6.1, Page 172 for STSFA) were compared as shown in Figure ‎4.6.1:

Figure ‎4.6.1: LSSA vs STSFA.

Data represents the average correct predictions across the six comparisons detailed in Table ‎4.4.3 (Page

174 As shown above, the use of the STSFA lead to a significantly higher level of correct predictions obtained when compared to LSSA. Although both were improved over a random model, STSFA still remains higher than LSSA likely due to its semi- quantitative nature.

4.6.3 Preliminary Clinical Validation of GEB052 Model (STSFA)

To assess the predictive power of the model under STSFA analysis at the clinical level, microarray data from thirteen leukaemia patients (taken before patients were treated) were used.

Table ‎4.6.2: Patient microarray data used for STSFA analysis.

Patient data obtained from Schmidt et al. (2006). Microarray data obtained from the GEO database after its deposit from the original study (Schmidt et al., 2006).

Patient Number Gender Age (Years) Clustering Status at Risk Assessment? GEO ID 2 M 8.5 T-ALL Alive GSM51712 13 M 5.9 Not assigned Alive GSM51679 17 F 14.7 Hyperploidy Deceased GSM51682 20 M 5 T-ALL Alive GSM51706 24 M 2.6 Not assigned Alive GSM51676 25 F 10.3 T-ALL Alive GSM51709 31 F 17.2 Hyperploidy Alive GSM51685 32 F 3.7 TEL-AML Alive GSM51688 33 M 2.5 Hyperploidy Alive GSM51691 37 F 15.1 Not assigned Alive GSM51694 38 M 3.2 TEL-AML Alive GSM51697 40 M 17.3 Not Alive GSM51700

175 assigned

43 F 1.6 TEL-AML Alive GSM51703

The microarray data shown above were each in turn superimposed onto the model and analysed via the STSFA. The edge weights for all edges to cell death were totalled (for each patient individually) and patients were grouped as shown in Figure ‎4.6.2:

Figure ‎4.6.2: Preliminary clinical validation of GEB052 model (STSFA, alive/deceased status).

Patient groups (Died Before Risk Assessment, n=1, Alive at Risk Assessment, n=12) are shown on the x- axis, whilst the y-axis shows the average for each group of the total edge weights targeting cell death +/- SEM.

As shown above, the model under STSFA analysis predicted that the patient who died before risk assessment would have a lower (more negative) total edge weight for edges that affect cell death than those who were alive at risk assessment. What this translates to‎is‎that‎cell‎death‎is‎“more‎inhibited”‎in‎that‎patient‎than‎those who were alive at risk assessment, at least according to the model predictions. Given that cell death in this context equates to the death of the cancer cells, the fact that this patient died before risk assessment (i.e. before other patients) is consistent with the model prediction. However, the sample size and unequal groupings make the above data insufficient to draw full conclusions, though it is a promising and interesting indication nonetheless.

176 To complement the above analysis, patients were also grouped by age:

Figure ‎4.6.3: Preliminary clinical validation of GEB052 model (STSFA, age groupings).

Patient groups (<15 years old, n=10, >15 years old, n=3) are shown on the x-axis whilst the y-axis shows the average for each group of the total edge weights targeting cell death +/- SEM.

According to Cancer Research UK, ALL patients aged fourteen or younger have a five- year survival rate of approximately 90%, whilst patients aged between fifteen and twenty-four have a five-year survival rate of approximately 70% (CRUK, 2015c). Therefore, if this difference in survival rate was seen through the GEB052 model predictions as shown in Figure ‎4.6.3, then the first group (less than fifteen years old) would have a higher (less negative) total edge weight to cell death. However, this is not the case. Although the difference between the two groups was statistically insignificant (p>0.05), the trend shown in Figure ‎4.6.3 is that patients who were less than fifteen years old have cell death as more negatively regulated (in turn, meaning less death of the cancer cells and arguably reduced survival). Thus, although the alive/deceased status shown in Figure ‎4.6.2 appears to correlate with clinical outcomes, this does not appear to be the case for Figure ‎4.6.3, which indicates some shortcomings of the model and required improvements.

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