Projects:2016s1-120 Attacking Cancer with Signal Processing - Revision history

A1658794: /* Kolmogorov–Smirnov Test */

2016-10-26T05:20:34Z

‎Kolmogorov–Smirnov Test

2016-10-26T05:18:25Z

‎Monte-Carlo Analysis

2016-10-26T05:17:20Z

‎Monte-Carlo Analysis

2016-10-26T05:16:04Z

‎Monte-Carlo Analysis

2016-10-26T05:15:26Z

‎Kolmogorov–Smirnov Test

2016-10-26T05:14:39Z

‎References

2016-10-26T05:12:31Z

‎Testing of Dr. Madondo's Data

2016-10-26T04:58:31Z

‎Monte-Carlo Analysis

2016-10-26T04:58:01Z

‎Sine Wave Fitting

2016-10-26T04:56:13Z

‎Kolmogorov–Smirnov Test

@@ Line 34: / Line 34: @@
 Kolmogorov–Smirnov test can compare a sample with a reference probability distribution. Figure 2 shows the Kolmogorov–Smirnov test of the raw CRP data. The CRP data are formed in log scale，and follow the Gaussian distribution. Therefore, we can generate Gaussian random pseudo-data by creating Gaussian random variables based on the log scale CRP data.
-                                                           pseudo_data=(random×σ)+μ
+                                                                pseudo_data=(random×σ)+μ
 [[File:KS_plot_CRP.jpg|350px|thumb|centre|Figure 2. Kolmogorov–Smirnov Test of CRP Data]]

@@ Line 87: / Line 87: @@
 The p-value is formed below:
-                                                             p(false-positive)=∑(P_REAL<P_VIRUAL)/N
+                                                           p(false-positive)=∑(P_REAL<P_VIRUAL)/N
 Where P_REAL is the peak of real CRP data ,P_VIRTUAL is the peak of Gaussian random pseudo-data and N is the times of simulation.

@@ Line 87: / Line 87: @@
 The p-value is formed below:
-                                                    p(false-positive)=∑(P_REAL<P_VIRUAL)/N
+                                                             p(false-positive)=∑(P_REAL<P_VIRUAL)/N
 Where P_REAL is the peak of real CRP data ,P_VIRTUAL is the peak of Gaussian random pseudo-data and N is the times of simulation.

@@ Line 87: / Line 87: @@
 The p-value is formed below:
-                                            p(false-positive)=∑(P_REAL<P_VIRUAL)/N
+                                                    p(false-positive)=∑(P_REAL<P_VIRUAL)/N
 Where P_REAL is the peak of real CRP data ,P_VIRTUAL is the peak of Gaussian random pseudo-data and N is the times of simulation.

@@ Line 34: / Line 34: @@
 Kolmogorov–Smirnov test can compare a sample with a reference probability distribution. Figure 2 shows the Kolmogorov–Smirnov test of the raw CRP data. The CRP data are formed in log scale，and follow the Gaussian distribution. Therefore, we can generate Gaussian random pseudo-data by creating Gaussian random variables based on the log scale CRP data.
-                                                       pseudo_data=(random×σ)+μ
+                                                           pseudo_data=(random×σ)+μ
 [[File:KS_plot_CRP.jpg|350px|thumb|centre|Figure 2. Kolmogorov–Smirnov Test of CRP Data]]

@@ Line 115: / Line 115: @@
 ==References==
-Bracewell, R.N., 1984. The fast Hartley transform. Proceedings of the IEEE, 72(8), pp.1010-1018.
+Bracewell, R.N., 1984. The fast Hartley transform. Proceedings of the IEEE, vol.72, pp.1010-1018.
 Brendon, J.C., Martin , LA & Michael AQ ,2009 ’CRP identifies homeostatic immune oscillations in cancer patients: a potential treatment targeting tool?’, Journal of Translational Medicine vol.7,pp.1-8.

@@ Line 104: / Line 104: @@
 ===Testing of Dr. Madondo's Data===
-Dr. Madondo's raw data include two groups, IRS and BLV. Performing same signal processing method, we found the data of some MP have high-reliability peak ,which inconsistent to Dr. Madondo's conclusion, the CRP level does not appear to be periodic.
+Dr. Madondo's raw data include two groups, IRS and BLV. Performing same signal processing method, we found the data of some MP have high-reliability peak ,which inconsistent to Dr. Madondo's conclusion, the CRP level does not appear to be periodic. As shown on Figure 8 and Figure 9, the probability of false positive is kind of high in BLV patient (0.4624), and the period on the IRS patient is 3.5 days. However, periodic behaviour is still detected and cannot be neglected.
-[[File:BLV_3.jpg|350px|thumb|centre|Figure 8. Patient BLV, MP 3]]
+Madondo, M.T., Tuyaerts, S &Turnbull ,BB ,2014 ’Variability in CRP, regulatory T cells and effector T cells over time in gynecological cancer patients: a study of potential oscillatory behaviour and correlations’ ,Translational Medicine. vol. 12, no. 1, pp.1-9.
-[[File:IRS_3.jpg|350px|thumb|centre|Figure 9. Patient IRS, MP 3]]
+Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P., 1996. Numerical recipes in C (Vol. 2). Cambridge: Cambridge university press.

@@ Line 62: / Line 62: @@
 The equation of fitting cure is:
-y_i=Acos(ωt )+Bsin(ωt )+C
+                                                          y_i=Acos(ωt )+Bsin(ωt )+C
 The coefficient A, coefficient B , constant offset C ,ω and initial parameters are the unknown value will be obtained by using the least square method. The frequency of peak will be used to create the initial parameters. According to the fundamental theorem of algebra, each monitoring periodic should contain at least 5 data for sine-wave fitting.
@@ Line 70: / Line 70: @@
 The minimum is at
-ωt+θ=2Nπ-2π
+                                                                ωt+θ=2Nπ-2π
 To estimate the next minimum time,
-N= ceil((ωt_Last+θ+π/2)/2π)
+                                                          N= ceil((ωt_Last+θ+π/2)/2π)
 The next minimum time:
-t_min=(N∙2π-π/2-θ)/ω
+                                                               t_min=(N∙2π-π/2-θ)/ω
 ===Monte-Carlo Analysis===