A proposal of simple calculation (ERI calculator) to predict the early response to TNF-α blockers therapy in rheumatoid arthritis

Abstract

Increasing evidence has been accumulated for treating rheumatoid arthritis (RA) with TNF-α blocking agents. The formulation and definition of an early indicator of patient’s reactivity during therapy may be extremely simplified by a mathematical model of clinical response. We analyzed the most significant clinical and laboratory parameters of response of 35 homogeneous patients (30 women, 5 men mean age ± SD: 52.31 ± 12.30 years) treated with adalimumab 40 mg every 2 weeks associated with methotrexate (MTX) 10–15 mg/week and with a stable dosage of steroids for 30 weeks. The over time trend of the studied parameters showed a linear response, which has allowed the realization of a simple mathematical model. The formula derived from this mathematical model was then applied and therefore validated in a group of 121 patients previously treated with several anti-TNF-alpha agents for at least 6 months. We drafted a mathematical model (early response indicator, ERI) that, by using a simple calculation, allows us to identify a high percentage of responder patients after only 2 weeks of treatment. ERI identified a high percentage (88%) of patients responding after only 2 weeks, as was confirmed at weeks 30; the use of ERI calculation after 6 weeks increases the proportion of responding patients to 92% with a percentage of false negatives of only 12%. ERI could be a useful tool to early differentiate the responder from the non-responder patients.

Appendices

Appendix 1

Results are presented in Tables 10 and 11, recalling that the temporal scale is 1 week, and therefore, the values of B correspond to the typical factor by which the disease process is reduced (in responding patients) after each week of therapy.

Table 10 Average values of reduced indicators at every time (weeks) evaluated in responders (35 patients enroled in the first part of the study)

Table 11 Average values of variation ranges

Based on the above-mentioned analysis, we elaborated the ERI mathematical model considering that:

• 1. The average values of the reduced indicators at time t were really very close, and we could therefore replace individual indicators with their average, thus simplifying the model by considering exclusively the mean of relative change and taking into account normal values of the variables

• 2. The exponential fit of the average of indicators was optimized by the values AM = 0.29 and BM = 0.77. The values of RM(t) = AM + (1−AM)*BM(t) corresponding to these values and computed in 2-week intervals are reported in Table 12.

• 3. The values of variation ranges were basically constant in time and independent of the specific indicator. They could therefore be replaced by their general average, setting VM(t) = 0.25.

• 4. We can now define a function RM + 0.5 VM (Table 12), representing the value of the reduced indicator that a given patient must not exceed in order to be included among the responders.

• 5. The above procedure may be applied more than once, starting from a group of responders that have been selected after a very short time, but not very accurately, and improving the selection by a second check performed after a reasonable time (at least as long as the first reference interval).

• 6. In practice, our proposal was equal to accepting as responders all patients whose average entity of disease process, measured through the average of reduced indicators on a monthly basis, was smaller than 2/3 of its initial value 1 month after the beginning of therapy and smaller than half its initial value after 2 months. Tests may obviously be performed also at intermediate times, if desired.

Table 12 Exponential fit of the average of indicators, optimized by the values AM = 0.29 and BM = 0.77

Appendix 2: how to use ERI

$$ {\text{R}}\left[ {np} \right]\left( t \right) = {\frac{{I\_\left[ {np} \right]\left( t \right)-{\text{lN}}\left[ n \right]}}{{I\_\left\{ {np} \right\}\left( 0 \right)-{\text{IN}}\_\left\{ n \right\}}}} $$

If

$$ {\frac{{{\text{R}}\left[ {np} \right]\left( t \right)}}{\text{number of parameter}}} \le 0.84{\text{ the patient is responder}} $$

I_[np](t) = value of parameter after 2 weeks,

$$ {\text{lN}}\left[ n \right] = {\text{normal value}} $$

$$ I\_\left\{ {np} \right\}\left( 0 \right) = {\text{value of parameter at time }}0 $$

Example

	T0 = 0	T1 = 2 week	T6 = 30 week	Normal range
TJ	27	14	6
SWJ	16	22	16
ESR	62	73	75	0–30 mm/h
CRP	57.2	10.8	6	0–5 mg/dl
VAS patients	82	60	52
VAS physician	78	64	55
Illness activity	80	60	42