Kinetics versus Statistics in the Analysis of Therapeutic Effects of Mometasone and Calcipotriol for the Treatment of Alopecia Areata.

Sir,

A recent article published by Alam et al. examines the therapeutic efficacy of potential drugs for alopecia areata.[1] Based on their statistical analysis, the authors concluded that the application of calcipotriol ointment with mometasone cream (Group A) had higher efficacy than that of mometasone alone (Group B) in the treatment of alopecia areata.[1] While their research suggests cooperative or additive effects of both drugs, our kinetic analysis of their data indicates that calcipotriol ointment has no additional beneficial effects in the treatment. In this letter, we show our kinetic analysis of the results.

The process of treatment can be represented as a chemical reaction:

Disease → Treated      (1)

“Disease” can be expressed by the Severity of Alopecia Tool (SALT) score.[1] We propose that the rate of treatment can be expressed as a first-order chemical process in the following way:[2]

S / S0 = exp(- kt)      (2)

Where S is the SALT score at time t, S0 is the SALT score at time 0 (baseline SALT score), and k is the rate constant of the curing process. S/S0 represents a normalized SALT score. Figure 1 shows the plot of equation (2) for both Group A and Group B. From the regression analysis, one can obtain the value of k, which quantitatively represents the efficacy of each treatment.

Figure 1

Kinetics of the treatment of alopecia areata by two different regimens. Nonlinear regression was performed using SigmaPlot (Systat Software, San Jose, CA, USA)

According to our regression analysis, the mean value ± standard error of k for Group A was 0.0394 ± 0.0026/week and 0.0372 ± 0.0035/week for Group B. A t-test of those values indicates that there is no statistically significant difference between those values (P = 0.632). Our kinetic analysis clearly suggests that there is no statistical difference in the efficacy of both treatment regimens. The discrepancy between the original article and our analysis is attributed to the statistically statistical difference in the mean SALT score of both the groups at baseline (P = 0.145).[1] Although the P value is much larger than the α level used in the original article (α = 0.05), the power of the performed test (0.172) is significantly less than the desired power of 0.8 according to our own analysis.[3] The small value of the power may cause a Type 2 error, the failure of retaining the false null hypothesis.[3] Furthermore, our argument is in line with the growing concern for ambiguity associated with P value in assessing statistical significance.[4]

Our kinetic analysis can be extended to the thermodynamics of the treatment. According to the transition-state theory, the molar-free energy of activation (△Ga°) at temperature T can be calculated using k:

Where R, h, and kB are the ideal gas constant, the Planck's constant, and the Boltzmann constant, respectively.[2] Using Equation (3), we found that △Ga° for Group A and Group B was 118.7 kJ/mol and 118.9 kJ/mol, respectively. These values are comparable to △Ga° for the proliferation of matrix cells of human scalp hair, 106.6 kJ/mol, which was calculated using the duration of their total cell cycle of 38.8 h.[5] This thermodynamic feature strongly suggests that mometasone-based treatment involves cell proliferation.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.