This is the first investigation in which predictions for 5 types of dynamics of CD4+ lymphocyte counts are conducted based on the absolute leukocyte count for the cases with counts > 500, between 200 to 500 and < 200 cells/µL3 as well as for the counts that present fluctuations of values between 200 to 500 and > 500 and < 200 cells/µL3 in 250 HIV-infected individuals in the context of probability theory, achieving a mathematical physical simplification of the phenomenon with a predictive precision of 99% with values of sensitivity and specificity of 99%.
With this methodology, mathematical relationships are established between the absolute leukocyte count and the CD4 + count along time in ranges of clinical interest. Since the values of probability were always above 0.96 and three of the types of dynamics have probabilities of 1, this suggest that the phenomenon itself presents a strong underlying deterministic order and that the method is highly accurate to predict the counts. Given these considerations, this methodology could be useful for clinicians to perform following ups of patients in time and to evaluate the effectivity of antiretroviral regimens, especially in low-income countries [13, 14], since only a complete blood count is required to establish measurements, which could also improve the medical assistance provided as well as patients’ survival.
In other predictive research [7], the use of absolute leukocyte count has been proposed as a surrogate to establish the quantity of CD4 + cells, predicting counts < 200 cells/µL3 with sensitivity and specificity values between 20.2% and 61%. Other predictive approximations have been conducted achieving more precise values [6, 15, 16] considering other markers such as the CD4+/CD8 + ratio [17] or the CD4 + percentage [18]. More recently, data mining algorithms such as Random Forest [19] have been developed to predict values of CD4 + < 100 cells/µL3, obtaining a precision close to 100%. This algorithm implements rules that involucrate variables such as liver function, age, marital status, employment, education status, residence condition, functional status, WHO clinical stage, baseline and current antiretroviral regimen as well as time with treatment, baseline CD4/CD8 ratio, religion, weight, among others. In contrast, the developed methodology in this research offers a simplification of all these variables because it only requires a variable to predict CD4 + counts. Furthermore, this method distinguishes between ranges of clinical interest.
The mathematical thinking seeks to establish patterns, [20] this why when addressing a phenomenon as the one in this research, the efforts must be focused in establishing the right questions since they will allow to decide which is the relevant data from the one that is not, and in the case of medicine, this confers great utility. According to Frenkel: “my experience is that only about 10–15% of the information that the doctors collected was ever used when they made the diagnosis or treatment recommendations” [21] and “Yakov Isaevich used to say that doctors’ thinking was well adapted to analyzing particular patients and making decisions on a case-by-case basis. But this also made it sometimes difficult for them to focus on the big picture and try to find general patterns and principles” which highlights the necessity of the mathematical thinking to find patterns that provide orders in the phenomena studied.
In this sense, the acausal impact of physics and mathematics is evidenced in the search of objective patterns that adequately describe distinct phenomena of nature. Following the line of thinking [12] different predictive methodologies have been developed that have addressed the problem of obtaining values of CD4 + lymphocyte counts from other variables. As an example of this, set theory has allowed to organize triplets of total leukocytes, lymphocytes and CD4 + counts to predict the counts of the last cellular line, with a precision up to 100% in specific ranges of leukocytes [22].