The application Diabetes prediction prototype is an experimental software intended as a method of prediction for type II diabetes. Examples for this program are related to glycemic values. Note that these glycemic values are not binding. Other numeric values (integers originating from any type of biochemical data) can also be used in different contexts. However, this application converts a sequence of numbers into a sequence of two states (strings like ABABBBBABBBBABBA). The sequence of states is then converted into a transition matrix. Transition probabilities are calculated for each element of the transition matrix based on the sequence of states. The transition matrix is further used for a prediction in a Markov chain.
The program includes the following sections/panels/frames:
a) Patient blood sugar for a period of time (days) Info: the main input of the program.
b) Processes k steps Info: the period of time for which the prediction is made. If the series of blood glucose levels from the input is composed of blood glucose values measured once a day, then the predictions are made on days. If, for instance, the input consists of blood glucose values measured once a week, then the predictions are made on weeks.
c) Step by step Info: this section aims to present the calculations and the current state (L or H) for each day as an animation shown at different speeds. The purpose of this section is the slow motion observation of the prediction process.
d) Probability values of the last vector Info: is a graph showing the probabilities for low or high blood sugar in the distant future. The graph shows these probabilities as bars (low in blue and high in red). The y axis represents the probability of these low or high events and the x axis shows the number of states (bars).
e) Prediction of behavior Info: is a graph showing the day-by-day probabilities for low or high blood sugar. The y axis represents the probability of low or high glycemic events and the x axis shows the number of days for which the prediction is made.
f) Vector components - probability plot Info: Both axis represent probability values. The x coordinate of a circle from the graph is represented by the low probability value and the y coordinate of a circle is represented by the high probability value.
a) a series of blood glucose levels (data sets) from the same patient are inserted in the input text box. Preferably the measurements should be made at fixed time intervals. For instance, this set of measurements from below belongs to a single patient. The set of measurements is composed of glycemic values taken each morning for a period of 31 days. Other data sets (for specific experiments) may contain two measurements per day (or more). Another approach would be the use of data sets consisting of blood glucose measurements taken each week in an experiment of, for instance, tens of weeks.
b) a threshold is inserted. This threshold represents the expected blood sugar level for a normal individual. In this case, 108 mg/dL has been chosen as the expected blood sugar level for a normal individual. Different situations in clinical practice (or a particular experimental setup) may require a variation of this threshold value.
c) The “Analyze” button is pressed.
.png)
(A) Manually set an upper limit (Lu) value and a down limit (Ld) value to establish the range from which the two states are calculated. Optionally this range can be set/extracted based on the maximum and minimum values present in the sequence of glycemic values. But how are the states calculated in this option? There is the upper limit (Lu) and the down limit (Ld). What the implementation needs is an automated threshold value. To compute the threshold value, the down limit is subtracted from the upper limit (Lu - Ld), and the result is further divided by the number of states (n = 2, as there are only two states, thus ((Lu - Ld)/n). This last result is added to the down limit value in order to obtain the threshold value in between the two limits(threshold = Ld + ((Lu - Ld)/n)). This method is explicitly described for n states in the book entitled Markov chains: from theory to implementation and experimentation (see references).
(B and C) Set a threshold where all values bigger than the threshold will be considered in one state and all values below the threshold will be considered in the other state.
(D) The sequence of glycemic values separated by a comma delimiter.
(E) The button that executes the computational procedure.
.png)
(F) Lu means upper limit, whereas Ld means down limit.
The main results are presented in various forms. However, those results of major interest are shown in the middle of the window and in the lower right:
The following sequence of blood glucose levels was analyzed for illustration:
137,154,126,120,115,102,113,107,107,108,111,109,118,124,114,111,103,117,108,114,104,112,115,109,114,118,118,120,130,126,104
For the above sequence of blood glucose levels the software shows the results in an explicit manner, such as: The threshold glucose level was set at 108 mg/dL (representing the normal level of blood sugar). Elevated levels or low levels of blood sugar are considered according to this threshold (108 mg/dL). Therefore, in the future the patient will have a LOW blood sugar (under 108 mg/dL) about 27.63% of the time, and a HIGH blood sugar (above 108 mg/dL) about 72.37% of the time. Patient's glycemic events indicate the following observations: if the patient has a high blood sugar it returns to a high blood sugar 72.73% of the time, and if it has a low blood sugar it returns to a low blood sugar level 28.57% of the time. If the patient has a HIGH blood sugar it moves to a LOW blood sugar level 27.27% of the time, and if it has a LOW blood sugar it moves to a HIGH blood sugar level 71.43% of the time. Nevertheless, in the first instance the application shows a series of numbers as follows:
H[1] = [0.272727272727 - 0.727272727273]
H[2] = [0.27626918536 - 0.72373081464]
H[3] = [0.276315184225 - 0.723684815775]
H[4] = [0.276315781613 - 0.723684218387]
H[5] = [0.276315789372 - 0.723684210628]
H[6] = [0.276315789472 - 0.723684210528]
H[7] = [0.276315789474 - 0.723684210526]
H[8] = [0.276315789474 - 0.723684210526]
H[9] = [0.276315789474 - 0.723684210526]
Steady state vector at [9] !
Note that the "-" character is just a delimiter between the two probability values, and not the minus sign.
These numbers represent predictions (in this case) of the blood sugar level each day in the future. Day 1 is the next day after the last measurement was taken. The steady state vector represents the probability for low or high blood sugar in the distant future (all times).
The significance of the colors on the above prediction meter is as follows: red indicates diabetes in the near future, orange indicates prediabetes in the near future, yellow indicates normal blood sugar in the near future, and light or dark green color indicates hypoglycemia in the near future.
- Paul A. Gagniuc. Markov chains: from theory to implementation and experimentation. Hoboken, NJ, John Wiley & Sons, USA, 2017, ISBN: 978-1-119-38755-8.