A mathematical model for short-term vs. long-term survival in patients with glioma

Abstract

Gliomas, the most common primary brain tumors in adults, constitute clinically, histologically, and molecularly a most heterogeneous type of cancer. Owing to this, accurate clinical prognosis for short-term vs. long-term survival for patients with grade II or III glioma is currently nonexistent. A rigorous, multi-method bioinformatic approach was used to identify the top most differentially expressed genes as captured by mRNA sequencing of tumor tissue. Mathematical modeling was employed to develop the model, and three different and independent methods of validation were used to assess its performance. I present here a mathematical model that can identify with a high accuracy (sensitivity=92.9%, specificity=96.0%) those patients with glioma (grade II or III) who will experience short-term survival (≤ 1 year), as well as those with long-term survival (≥ 3 years), at the time of diagnosis and prior to surgery and adjuvant chemotherapy. The 5 gene input variables to the model are: FAM120AOS, PDLIM4, OCIAD2, PCDH15, and MXI1. MXI1, a transcriptional repressor, represents the top biomarker of survival and the most promising target for the development of a pharmacological treatment.

Keywords: Glioma; RNA-Sequencing; cancer genomics; computational biology; mathematical modeling; survival; systems biology.

Figure 1

Heat map of the expression of the 29 most significant tumor tissue genes of all 89 subjects. Heat map of the tumor tissue gene expression, generated from mRNA sequencing, of 75 LTS subjects (columns # 1-75) (x-axis) and 14 STS subjects (columns # 76-89) (x-axis) with respect to the 29 most significant genes (rows # 1-29) (y-axis). The order of those 29 genes is alphabetical (the same as the one in Table 1). All 29 gene variables were standardized (mean=0 and SD=1). The intensity scale of the standardized expression values represents, therefore, the z scores; and it ranges from -7.5 [blue: low expression (7.5 SD below the mean)] to +7.5 [red: high expression (7.5 SD above the mean)], with 0 [white (mean=0)] representing the reference intensity value (mean expression value of all 89 subjects). As can be seen, based on the expression of those 29 most significant genes, there is a distinct overall separation between the LTS and the STS subjects.

Figure 2

Filled-contour plot of the expression of the 29 most significant tumor tissue genes of all 89 subjects. Tumor tissue gene expression, generated from mRNA sequencing, of 75 LTS subjects (columns # 1-75) (x-axis) and 14 STS subjects (columns # 76-89) (x-axis) with respect to the 29 most significant genes (rows # 1-29) (y-axis). The order of those 29 genes is alphabetical (the same as the one in Table 1). All 29 gene variables were standardized (mean=0 and SD=1). The intensity scale of the standardized expression values represents, therefore, the z scores; and it ranges from -2 [dark blue: low expression (2 SD below the mean)] to +2 [dark red: high expression (2 SD above the mean)], with 0 [light green (mean=0)] representing the reference intensity value (mean expression value of all 89 subjects). As can be seen, based on the expression of those 29 most significant genes, there is a distinct overall separation between the LTS and the STS subjects.

Figure 3

Overall results of the F₁ function. The F₁ uses 5 of the 29 most significant genes as its input variables. Using the expression value of those 5 genes for a particular subject, the F₁ yields the F₁ score of that subject; and, based on the determined cut-off score of 25.165, the F₁ classifies that subject as a long-term survivor (LTS) if the F₁ score is < 25.165 or as a short-term survivor (STS) if the F₁ score is ≥ 25.165. The results of the overall performance of the F₁ were obtained by combining the results from the development and the validation phases. As can be seen by its overall performance in this dot plot & bar graph, the F₁ classified correctly all but one of the STS subjects [sensitivity=(13/14)=0.929] and all but three of the LTS subjects [specificity=(72/75)=0.960]. The mean F₁ score of the LTS subjects was 20.511 (top of the green bar) and their standard deviation (whiskers above or below the top of the green bar) was 2.790. Using bootstrapping with a sample size of 100,000, the 99.99% confidence interval of the mean F₁ score of the LTS subjects was: [19.150, 21.738]. The mean F₁ score of the STS subjects was 30.157 (top of the orange bar) and their standard deviation (whiskers above or below the top of the orange bar) was 4.068. Using bootstrapping with a sample size of 100,000, the 99.99% confidence interval of the mean F₁ score of the STS subjects was: [26.160, 34.108].The significance level was set at α=0.001 (two-tailed), and the probability of significance for the F₁ was P=4.05 × 10^-18 (independent t-Test with T-value=-10.986). The F₁ is parametrically distributed with respect to both groups. The F₁ scores of all 89 subjects are shown in Table S7.

Figure 4

3D space position of all 89 subjects according to their F₁ scores. The F₁ scores of all 89 subjects [75 LTS (#1-75) and 14 STS (#76-89)] are plotted in the z-axis. The subject number (#1-89) is plotted in the x-axis and the y-axis. The order of the subjects is the same as the one that appears in Table S7. A plane parallel to the x-y plane that intersects the z-axis at the point 25.165, which is the cut-off score, represents the cut-off plane. Subjects that are classified as STS lie above the cut-off plane, whereas subjects that are classified as LTS lie below the cut-off plane.