Modeling the antidepressant treatment response to transcranial … – Nature.com

Modeling treatment response to TMS in a clinical sample

The NLME model demonstrated that the TMS treatment response was well modeled with the exponential decay function, yielding significant estimates for model parameters A, B, and C (all p<0.0001). Each individual contributed 2 to 9 (median=6) longitudinal measurements of depressive symptoms for a total of 562 observations. The exponential model captured a wide range of individual treatment response trajectories, as illustrated in Fig.2. The magnitude of total response (A) was estimated to be a clinically meaningful 5.8-point drop in PHQ-9 scores with a time constant (B) of 1.2weeks or 6 TMS treatments. When compared to a corresponding LME, the exponential decay model displayed lower AIC and BIC values and a significant likelihood ratio (LRT=63.2, p<0.0001), suggesting that the NLME model based on the exponential decay function is a better fit.

Individual estimates of TMS treatment response from the nonlinear mixed-effects model. These panels illustrate representative longitudinal depression ratings from the Patient Health Questionnaire 9 (PHQ-9) during TMS treatment (open circles) from nine individuals as well as the nonlinear mixed-effects model fit (line).

In subsets containing complete longitudinal data from this naturalistic sample, k-fold and leave-one-out cross-validation approaches yielded consistent estimates of the time constant B (fivefold: mean 1.218weeks, sd 0.079; tenfold: mean 1.217weeks, sd 0.080; LOOCV: mean 1.213weeks, sd 0.023). By rearranging Eq.(1) as shown in Eq.(2), we calculated predicted values of C for the left-out samples using the time constant estimate (B) and symptom scores at baseline and after one week (n=90) or two weeks (n=82) of treatment. Predicted C values were constrained to 0 to 27, inclusive, corresponding with the range of possible PHQ-9 scores.

$$begin{array}{c}frac{Dleft(tright)-Dleft(0right){times e}^{left(frac{-t}{B}right)}}{1-{e}^{left(frac{-t}{B}right)}}=C.end{array}$$

(2)

Predicted C values from each cross-validation approach were highly correlated (r>0.999) and yielded significant correlations with PHQ-9 scores at the end of treatment, accounting for 38% to 58% of the variance in final scores, using PHQ-9 scores at baseline and after one week (adjusted R2=0.379 to 0.383, p<0.0001) or two weeks (adjusted R2=0.576 to 0.580, p<0.0001) of daily TMS sessions.

Predicted categorical treatment response, defined by a 50% reduction in PHQ-9 scores at the end of treatment, was assigned using the C values in Eq.(2) (i.e. C0.50 D(0)). These assignments did not differ across cross-validation methods. Using week 1 predictions, treatment response was assigned with 78% accuracy, 68% sensitivity, 82% specificity, 85% negative predictive value (NPV), and 63% positive predictive value (PPV). Assigning categorical treatment response using week 2 estimates, yielded 80% accuracy, 73% sensitivity, 84% specificity, 87% NPV and 68% PPV.

The NLME model was extended to group-level data from three published studies comparing multiple TMS modalities for treatment-resistant depression9,26,27, including left-sided high-frequency (10Hz) repetitive TMS, standard and accelerated TBS, and right-sided, low-frequency (1Hz) stimulation. These NLME models using the exponential decay function yielded significant estimates for all model parameters (all p<0.005).

In a randomized noninferiority study comparing TBS to 10Hz stimulation, the THREE-D study26, the NLME model estimated the magnitude of total response (A) to be a drop of 12.2 points on the HAM-D with a time constant of 2.3weeks. When compared to the corresponding LME model, the NLME model yielded a significant likelihood ratio (LRT=18.1, p<0.0001) and lower AIC (49 vs 65) and BIC values (53 vs 69), demonstrating the NLME model is a better fit.

Similarly, when this exponential decay model was applied to a randomized controlled trial comparing left-sided 10Hz stimulation and right-sided 1Hz stimulation27, estimates of the treatment response (A) demonstrated an average 13.6 point drop on the HAM-D with a time constant B of 1.2weeks. This NLME model demonstrated a significant likelihood ratio (LRT=22.7, p<00001) and lower AIC (81 vs. 102) and BIC (88 vs. 108) values compared to the corresponding LME model, indicating the nonlinear model is a better fit.

Finally, when applied to a randomized controlled trial comparing accelerated bilateral TBS above (120%) and below (80%) MT to standard left-sided 10Hz stimulation9, the NLME model yielded estimates of a total 6.0 point drop on the QIDS-C29 with a time constant of 0.7weeks. When compared to the corresponding LME model, the NLME model yielded a significant likelihood ratio (LRT=44.1, p<0.0001) and lower AIC (30 vs 72) and BIC (35 vs 76) values, suggesting the exponential decay model was a superior fit.

The exponential decay model was also fit at the individual group level using nonlinear least squares for each group in the above studies9,26,27, an unblinded accelerated, high dose TBS study7 and our naturalistic clinical sample. Although these individual group fits did not always yield significant estimates for all model parameters based on limited degrees of freedom, when the AIC and BIC values from these nonlinear fits were compared to corresponding linear models of the same group-level data, exponential decay models consistently yielded lower AIC and BIC values for all TMS samples studied (Fig.3).

Modeling group-level symptom response to transcranial magnetic stimulation (TMS): the exponential decay model was applied to group-level depression ratings from our clinical sample (n=97) as well as group-level data four published clinical trials7,9,26,27 utilizing a variety of TMS protocols including left-sided repetitive 10Hz TMS, standard and accelerated theta-burst stimulation, and right-sided, low-frequency (1Hz) TMS. In each case, the exponential decay models (solid line) yielded better fits when compared to corresponding linear models (dotted line) as illustrated by lower Akaike Information Criterion (AIC) values (lower right).

When the exponential decay model was applied to the unique group-level symptom trajectories identified in the secondary analysis of the THREE-D study10, the NLME model was able to describe each group trajectory in terms of parameters A, B, and C, (Eq.1, Fig.4). The three groups of responders demonstrated similar estimates of the magnitude of treatment response (parameter A), with reductions of 13.0, 13.9 and 14.5 points on the HAM-D for Lower baseline symptoms, linear response, Higher baseline symptoms, linear response, and Rapid response groups, respectively. However, these groups differed more markedly in their group estimates of the time constant B, with Rapid response at 1.1weeks, followed by Lower baseline symptoms, linear response at 2.4weeks, and Higher baseline symptoms, linear response at 3.8weeks. These differences correspond to the speed at which these groups approach their minimum depressive symptom rating scores during TMS treatment. In contrast, the Nonresponse group was associated with a minimal estimate of total treatment response (parameter A) of a 2.7-point reduction on the HAM-D and a long estimate for the time constant B of 7.5weeks. This NLME model was associated with a significant likelihood ratio (LRT=30.7, p<0.0001) and lower AIC (121 vs. 143) and BIC (134 vs. 151) values compared to a corresponding LME model, indicating that these trajectories were better modeled with the nonlinear exponential decay function.

Modeling unique treatment response trajectories to transcranial magnetic stimulation (TMS): A nonlinear mixed-effects model (solid lines) was constructed to model the four treatment trajectories identified by Kaster et al. (N=388)10. Each of these response trajectories could be described using the three parameters of the exponential decay function (Eq.1). This nonlinear mixed-effects model demonstrated a superior fit when compared to a corresponding linear mixed-effects model (dotted lines).

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