There is a well-known statisticians’ joke: with one foot in a bucket of boiling water and one in a bucket of ice water, you are, on average, comfortable. Looking at averages when comparing groups in a clinical trial — for example, average depression scores for a placebo versus treatment group — is firmly rooted in statistical theory and a meaningful thing to do. The question nevertheless arises whether group averages are sufficient to fully grasp a treatment’s effectiveness; as implied by the aforementioned joke, averages are summary measures that sometimes mix together quite different things. As such, comparing group averages might not unravel the full story.

Quantile regression analysis provides an alternative statistical framework that allows for comparing groups along the entire distribution of outcome scores – that is, it compares their low scores, middle scores, and high scores. Quantile regression thereby shows whether two groups differ in a simple and consistent way or whether there is a more nuanced story to tell. The best-known quantile is the median, which specifies the score that lies in the middle of a distribution: half of the sample has scores smaller than or equal to the median. Other quantiles are, for example, the 0.1 quantile, which specifies the score that is larger than or equal to 10% of scores; and the 0.8 quantile, which specifies the score that is larger than or equal to 80% of scores within the distribution. Comparing a low quantile (like the 0.1 quantile) in two groups allows for comparisons of the groups’ low scores. Comparing the groups’ high quantiles (like the 0.8 quantile) permits their high scores to be compared. Comparing quantiles in small intervals (e.g. the 0.05, 0.10, 0.15, etc., up to the 0.95 quantile) shows how groups differ along the entire range of outcome scores.


Applying the quantile regression framework, we (Foster & Mohler-Kuo, 2018) recently performed a secondary analysis of data from the Treatment for Adolescents with Depression Study (TADS, March et al., 2004), a cornerstone clinical trial in the United States that was funded by the National Institute of Mental Health (NIMH). TADS examined 439 adolescents suffering from major depression. Four treatment arms – a pill placebo; cognitive-behavioral therapy; fluoxetine (a drug within the class of selective serotonin reuptake inhibitors, SSRIs); and combined therapy (cognitive-behavioral therapy combined with fluoxetine) – were compared. Indicators of major depression were measured at baseline and again after 12 weeks of treatment. Analyzing response levels – i.e. the proportional change in depression scores from baseline to 12 weeks of treatment – with quantile regression models allowed us to examine the treatments’ impacts on low versus middle versus high response levels, relative to placebo.

Consistent with the original TADS analysis (March et al., 2004), analyzing response level quantiles revealed that, overall, fluoxetine and the combined treatment outperformed placebo treatment, whereas cognitive-behavioral therapy did not. However, the quantile treatment effects of fluoxetine alone and the combined therapy tended to follow the shape of a reversed U across response levels: treatments outperformed placebo in the middle range of response levels, but not at low and high response levels. Thus, there tended to be two groups of adolescents for which treatments were no more effective than placebo: those who did not improve much during the 12 weeks of treatment and those who improved a lot.

At this point, an important advantage of combined therapy surfaced: its superiority over placebo extended further into the low- and high-response levels. In particular, combined therapy retained some effectiveness at the low end of the response level distribution. Thus, one would rather be a low responder with combined therapy than a low responder in the other treatment arms, because low response levels for the combined therapy were higher than low response levels for the remaining treatments. For example, considering each treatment group’s 0.1 quantile, adolescents’ initial depression scores improved by no more than roughly 4 to 7% in the placebo, cognitive-behavioral therapy, and fluoxetine alone groups, but by roughly 18% in the combined-therapy group. Statistical testing (which accounted further for initial depression scores, the study site where the adolescent was treated, and adolescents’ expectations regarding treatment effectiveness) confirmed that there was no statistical evidence supporting differences between fluoxetine and placebo or between cognitive-behavioral therapy and placebo, but that combined therapy outperformed placebo.


The observation that combined therapy extended further into low-responding adolescents has an important implication: apparently, this treatment was more robust against factors that hampered recovery. It is well appreciated that clinical treatment is characterized by various factors that influence the clinical course of depression in positive and negative ways. Some factors might alter a treatment’s effectiveness (so-called effect modifiers), while others might impact the course of depression above and beyond any treatment. The set of factors that characterizes each patient places an upper limit upon what can be achieved with a particular treatment. Whereas our analysis does not reveal which factors were at play in the TADS sample, it suggests that combined therapy was a more robust treatment and was better able to withstand or overcome the influences of such factors.

As with any analysis, ours is not without caveats. Two are of particular importance. To start with, it is not yet clear to what extent our results can be generalized because scientific literature is not yet conclusive. On one hand, the limited effectiveness of cognitive-behavioral therapy was unexpected and contradicts the results of other studies (Weersing, Jeffreys, Do, Schwartz, & Bolano, 2017). On the other hand, both fluoxetine alone (Cipriani et al., 2016) and combined therapy (Dubicka et al., 2010) were found to be effective inconsistently across studies. A second word of warning concerns the treatments’ harm-benefit ratio. Particularly, treatment with SSRIs alone might be associated with the risk of harm, especially suicidality, which may outweigh potential treatment benefits. Although this downside seemed to be reduced by combined therapy in TADS (March et al., 2007), more research is needed.



Data used in the preparation of the above text were obtained by Simon Foster through a limited access data certificate from the National Institute of Mental Health (NIMH)-supported National Database for Clinical Trials (NDCT, of the United States of America (USA). NDCT is a collaborative informatics system created by the NIMH to provide a national resource to support and accelerate discovery related to clinical trial research in mental health. The above text reflects the views of the authors and may not reflect the opinions or views of those submitting original data to the NDCT or of the NIMH. Dataset identifier: Clinical Trials #2145.

These findings are described in the article entitled Treating a broader range of depressed adolescents with combined therapy, recently published in the Journal of Affective Disorders.


  1. Cipriani, A., Zhou, X., Del Giovane, C., Hetrick, S. E., Qin, B., Whittington, C., . . . Xie, P. (2016). Comparative efficacy and tolerability of antidepressants for major depressive disorder in children and adolescents: a network meta-analysis. Lancet, 388(10047), 881-890. doi:10.1016/s0140-6736(16)30385-3
  2. Dubicka, B., Elvins, R., Roberts, C., Chick, G., Wilkinson, P., & Goodyer, I. M. (2010). Combined treatment with cognitive-behavioural therapy in adolescent depression: meta-analysis. Br J Psychiatry, 197(6), 433-440. doi:10.1192/bjp.bp.109.075853
  3. Foster, S., & Mohler-Kuo, M. (2018). Treating a broader range of depressed adolescents with combined therapy. J Affect Disord, 241, 417-424. doi:10.1016/j.jad.2018.08.027
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  5. March, J. S., Silva, S., Petrycki, S., Curry, J., Wells, K., Fairbank, J., . . . Severe, J. (2007). The Treatment for Adolescents With Depression Study (TADS): long-term effectiveness and safety outcomes. Arch Gen Psychiatry, 64(10), 1132-1143. doi:64/10/1132 [pii] 10.1001/archpsyc.64.10.1132 [doi]
  6. Weersing, V. R., Jeffreys, M., Do, M. T., Schwartz, K. T., & Bolano, C. (2017). Evidence base update of psychosocial treatments for child and adolescent depression. J Clin Child Adolesc Psychol, 46(1), 11-43. doi:10.1080/15374416.2016.1220310

About The Author

Simon Foster is a scientific researcher at the University of Zurich.

Meichun Mohler-Kuo is a professor at the University of Applied Sciences and Arts Western Switzerland.