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# Biomarkers predicting treatment outcome in depression: what is clinically significant?

^{1}Institute of Psychiatry, King’s College London, 16 De Crespigny Park, SE5 8AF, London, UK

^{2}Brain Repair Centre, Dalhousie University, Halifax, NS, Canada Laboratory of Psychiatric

^{3}Pharmacogenomics, Department of Psychiatry, Massachusetts General Hospital & Harvard Medical School, Boston, MA, USA

## Abstract

### Aim

To extend to biomarker studies the consensus clinical significance criterion of a three-point difference in Hamilton Rating Scale for Depression.

### Materials & methods

We simulated datasets modeled on large clinical trials.

### Results

In a typical clinical trial comparing active treatment and placebo, a difference of three Hamilton Rating Scale for Depression (HRSD) points at the end of treatment corresponds to 6.3% of variance in outcome explained. To achieve a similar explanatory power, genotypes with minor allele frequencies of 5, 10, 20, 30 and 50% need to attain a per allele difference of 4.7, 3.6, 2.8, 2.4 and 2.2 HRSD points, respectively. A normally distributed continuous biomarker will need an effect size of 1.5 HRSD points per standard deviation. A number needed to assess of three suggests that with this effect size, a biomarker will significantly improve the prediction of outcome in one out of every three patients assessed.

### Conclusion

This report provides guidance on assessing clinical significance of biomarkers predictive of outcome in depression treatment.

**Keywords:**antidepressant medication, biomarkers, clinical significance, major depressive disorder, number needed to assess

Depression is one of the most common and disabling diseases worldwide. Although a number of pharmacological and psychosocial treatment options are available, no single treatment is universally effective and most individuals with depression undergo multiple treatments before achieving remission. The substantial individual variation of treatment outcomes has motivated investigation of biomarkers with the hope that these can help select a treatment that a given individual is more likely to benefit from. However, with a large enough sample, even weak predictive effects can be found to be statistically significant. While the utility of any particular test depends on the context in which it is applied, there is a need for a benchmark that could determine if a predictive biomarker is likely to be meaningful in clinical settings [1].

The distinction between statistical and clinical significance has been made in the context of controlled clinical trials assessing the difference of outcome between active treatment and control condition [2–5]. It has been proposed that for a treatment to be considered clinically significant, it has to improve outcome by a degree that is noticeable to the individual or close others and that makes a meaningful difference to the individual’s ability to function and participate in society [2]. NICE in the UK had defined clinically significant effect size in comparison of two treatments for depression as a difference of three points or more on the 17-item Hamilton Rating Scale for Depression (HRSD) at the end of treatment [5,6]. This definition has been widely adopted as a benchmark for comparisons of antidepressant treatment against placebo [3,7,8]. The aim of this article is to extend the use of this clinical significance criterion to the study of biomarkers and other predictors of outcome.

This extension is not entirely straightforward. Unlike the typically equal groups receiving active treatment and comparator in a clinical trial, biomarkers are often unequally distributed in the population. Therefore, in addition to the effect size of prediction per unit of biomarker, we need to take into account its distribution. This is especially relevant to the decision whether to carry out a test to measure a biomarker. For example, consider a genotype that is associated with an improvement of three HRSD points less than alternative genotypes. If this genotype is carried by 50% of patients, it may be worthwhile genotyping it to improve prediction of outcome. Conversely, if the same genotype is only carried by 1% of patients, genotyping will be noninformative for the vast majority of patients and it will not be worth testing 100 patients to inform the prediction of outcome in a single individual unless it indicates a high probability of an extreme and dangerous outcome. In the present study, we establish thresholds for clinical significance for treatment outcome prediction by biomarkers that are either genetic (genotype is typically a three-level categorical variable) or of the type of protein levels (continuous variable).

## Materials & methods

### Standard

We took as the starting point the consensus recommendation by NICE that a difference of three points or more on the HRSD from control condition be the criterion for a clinically significant effect of a treatment for major depressive disorder [5,6]. Although this criterion was proposed as a ‘rule of thumb’, it was subsequently adopted by influential meta-analyses and obtained a status of a recognized benchmark for discussions of the efficacy of antidepressant treatments [3,7,8]. It also corresponds to approximately half the difference between bands on the Clinical Global Impression Scale, meaning that a difference greater than this threshold means that subject becomes more likely to transit into a different band of clinical impression, (e.g., from moderate to mild depression) [9]. Therefore, we make the assumption that a biomarker that predicts a difference of at least three HRSD points, or its equivalent on other measures [10,11], at the end of treatment for a substantial proportion of individuals is likely to be clinically significant.

### Simulated datasets

We modeled simulated datasets on recent largescale trials, the STAR*D [12] and the GENDEP [13], conducted in the USA and Europe, respectively. The characteristics of recruited patients and outcomes of 12 weeks of treatment with antidepressants were similar in these two large studies. Accordingly, we simulated samples with a mean baseline HRSD of 23.0 (standard deviation [SD] = 5.0) censored at the minimum value of 14, corresponding to the usual eligibility threshold for studies of antidepressants, and a mean exit HRSD score of 11.5 (SD = 7.0) censored at the natural minimum value of 0, with a typical correlation of 0.4 (Pearson product– moment correlation) between baseline and end point values, corresponding to the mean of STAR*D and GENDEP values. We simulated a range of potential predictor variables including three-level genotypes with varying minor allele frequency distributed according to Hardy–Weinberg equilibrium and normally distributed continuous variables (these may represent a level of protein in the blood, an electrophysiological measure, a measure of cerebral blood flow, but also a continuous composite measure derived from multiple genetic or nongenetic markers). The predictors were unrelated to baseline values of depression severity, but the relationship between the predictors and outcome was systematically varied over simulation sets. For comparison, we have also simulated an active treatment to control comparison in a typical randomized controlled trial, where half the subjects are randomly allocated to receive the active treatment and the other half receive control condition (e.g., placebo). Measures of effect size are independent of sample size. However, to obtain stable estimates, we simulated relatively large clinical trials with 1000 subjects. Each data point is based on 10,000 independently simulated datasets and analyzed with a routine statistical approach. For continuous outcomes, linear regression was used with end-of-treatment HRSD score as the dependent variable and the biomarker (genotype or continuous) as the predictor of interest. Logistic regression was used for categorical outcomes.

### Measures of effect size

In comparisons of active treatment to control condition, clinical significance is defined by the ‘d family’ group of effect size measures, including measures of between group difference, such as Cohen’s d, odds ratio or risk ratio, which range from minus infinity to plus infinity and can be readily translated one to another [14]. By contrast, biomarkers aim to explain variation within a single group of patients who receive the same treatment and the effect size of such prediction is typically expressed with a measure from the ‘r family’, such as correlation coefficients and other measures of association, which range from minus one to plus one [14]. Translation between effect size measures from the d and r families requires a set of assumptions that vary from setting to setting. The aim of this report is to provide a criterion for clinical significance of genetic and other biomarkers that is relevant to the setting of a typical depression treatment study and corresponds to the criterion of clinical significance established for comparisons of active treatment and control conditions in clinical trials.

We started with an absolute difference expressed as a number of points on the HRSD by which equally sized groups receiving active treatment and comparator in a randomized controlled trial differed at the end of treatment. Assuming no between group differences at baseline, a standardized measure of effect size from the d family, such as Cohen’s d, is calculated as the absolute difference between active treatment and comparator divided by the pooled SD at the end of treatment (e.g., for a group difference of three HRSD points and pooled SD of seven: d = 3/7 = 0.43) [14].

To compare the overall affect of the active treatment in the randomized controlled trial with the predictive power of variously distributed biomarkers in the population of patients with depression, we next calculated the proportion of variance explained (also known as coefficient of determination) as r^{2} in a linear regression of outcome on treatment or other predictor variable. Proportion of variance explained allows comparison of population-based effect sizes across predictors with varying distribution. We use proportion of variance explained as the common metric to compare the predictive power of active treatment in a randomized controlled trial with the effect of genetic or continuous biomarkers with various degrees of relationship to outcome.

Finally, there is a group of effect size measures designed to facilitate communication with clinicians, including the number needed to treat (more accurately termed number needed to assess [NNA] for predictive measures) and area under the receiver operating characteristic curve (AuROC), which are mutually convertible [1,4,14]. These effect size measures were originally developed for the relationship between two binary variables (e.g., treatment and remission) and have been extended to the relationship between one binary and one continuous variable [4]. However, there is no direct method of calculating these measures for the relationship between two variables that are both continuous or have more than two levels. To approximate these measures, we also derived a categorical outcome of remission based on the standard definition of an HRSD score of seven or less at the end of treatment [15]. We calculated the AuROC for the relationship between predictors and this dichotomized outcome and we used McFadden’s pseudo r^{2} measure from a logistic regression to approximate the proportion of variance explained. We used previously published equations to convert AuROC to number needed to treat/NNA, number needed to treat = 1/(2 × AUC-1) [16].

## Results

### Treatment comparison in a randomized controlled trial

In a typical clinical trial comparing equally large groups of patients treated with active treatment and placebo, a difference of three HRSD points at the end of treatment corresponds to 6.3% of the variance in outcome explained by treatment allocation (Figure 1). We use this as a benchmark to be translated into predictions by genetic and continuous biomarkers.

### Prediction of treatment outcome by genotypes

For genetic predictors, the proportion of variance explained depends on the minor allele frequency and the difference in outcome per allele (Figure 2). To explain 6.3% of the variance in outcome, genotypes with minor allele frequencies of 50, 30, 20, 10 and 5% need to attain a per-allele difference of 2.2, 2.4, 2.8, 3.6 and 4.7 HRSD points, respectively, under an additive genetic model (Figure 2). For very low minor allele frequencies, the required absolute effect sizes increase dramatically. For genotypes with minor allele frequencies of 4, 3 and 2%, effects of 5.2, 6.1 and 7.3 HRSD points per allele are needed to explain 6.3% of the variance in outcome. A genotype with a minor allele frequency of 1% does not attain this explanatory power even with effects exceeding ten HRSD points per allele. With a difference held constant at three HRSD points per allele, a genotype with a minor allele frequency of 13% explains a proportion of variance in outcome corresponding to a clinically significant difference between placebo and active treatment.

### Prediction of treatment outcome by continuous biomarkers

For a normally distributed continuous predictor, the proportion of variance explained is exponentially related to the absolute effect size expressed in HRSD point difference per one SD of the predictor (Figure 3). To explain 6.3% of the variance in outcome, an effect size of 1.52 HRSD points per one SD of a continuously distributed predictor is needed (Figure 3).

### Continuous & categorical outcomes

The categorical outcome of remission (end point HRSD of seven or less) was constructed in the same set of simulated datasets with continuous biomarkers as predictors. There was a perfect linear relationship between the proportion of variance explained in the categorical outcome and proportion of variance explained in the continuous outcome (Figure 4). The effect size of the categorical outcome prediction, expressed as proportion of variance explained estimated as pseudo r^{2}, was 50.6% (95% CI: 50.3–51.0) of that for the linear outcome (Figure 4).

### Proportion of variance explained & NNA

The NNA (calculated from AuROC) was in a negative exponential relationship to the proportion of variance in remission explained in a logistic model estimated as pseudo r^{2} (Figure 5). Proportion of variance explained of 6.3% corresponded to a NNA of three.

## Discussion

Using simulations incorporating parameters from real-world studies, we have translated the consensus criterion for clinical significance from comparative clinical trials to predictive biomarker research using genetic or continuously distributed biomarkers. In practice, the clinical applicability of predictive biomarkers will depend not only on effect size, but also on the biomarker availability and the cost, burden, delays associated with testing and the specificity of prediction to one treatment over another [1,4,17,18]. However, the present results provide several approximate rules that allow the translation of clinical significance between different types of predictors.

At the level of the whole patient population, the predictive power of genotypes depends on genotype frequency and absolute difference in outcome per each allele. A genotype with a minor allele frequency of 50% reaches the clinically significant prediction level if it is associated with a 2.2 HRSD point difference in outcome per allele. A genotype with a minor allele frequency of 10% needs a difference of 3.6 HRSD points per allele to reach the clinical significance criterion equivalent to that established in clinical trials. A normally distributed continuous biomarker that predicts a 1.5 HRSD point difference in outcome per SD has an explanatory power corresponding to the clinically significant difference of three HRSD points between equally sized groups. The graphs provided in this article (and an online calculator [101]) can serve to translate smaller or larger effect sizes for genetic or continuous predictors and compare their predictive power with a placebo–drug difference in randomized controlled trials.

If the continuous outcome measured on a depression rating scale is dichotomized to a categorical outcome of remission defined by a final score below a clinical cutoff, the predictive power of biomarkers is approximately halved. This is in line with previous studies demonstrating that dichotomization of continuous variables leads to a substantial loss of information and of statistical power [19–22]. Dichotomous outcomes allow an approximate translation between the proportion of variance explained (estimated as pseudo r^{2} in logistic models) and the clinically meaningful effect size measure of number needed to assess. The proportion of variance explained corresponding to the previously established clinical significance criterion (6.3%) corresponds approximately to a NNA of three. This means that for every three patients assessed for a biomarker, one significantly more accurate prediction of outcome can be made.

The literature on the pharmacogenetics of antidepressants suggests that a single genetic marker is unlikely to achieve clinically significant prediction [23–25]. Therefore, polygenic scores summarizing information from multiple markers may replace single genotypes as predictors of outcome [26,27]. The normally distributed continuous predictors in the current study are applicable to such polygenic scores. Similarly, the continuous biomarker results can be applied to any linear combination of multiple biomarkers and clinical variables in a predictive score [1,28].

The relationship between the distribution of a biomarker in the population and its clinical usefulness may change dramatically in the future. If genetic biomarkers become routinely available and do not require additional testing, the absolute effect size of the prediction in a given individual becomes more important than the population-based explanatory power that is primarily considered in this article. However, the proportion of variance explained will remain a useful measure as it is applicable to multivariate models that may combine a large number of genotypes or other biomarkers to achieve a clinically meaningful prediction [1,18].

The applicability of the present results is limited to studies of similar character to those that served as a basis for the simulation. However, since the two studies that were considered were real-world pragmatic trials with relatively broad inclusion criteria [12,13], the conclusions should relatively well generalize to the population of patients treated in routine primary and secondary care settings. Our conclusions about the benchmark for clinical significance are based on the assumption that similar effect size is relevant for predictive biomarkers as for drug–placebo differences. Since the proposed clinical significance is based on a difference that is noticeable for patients, people close to the patient and clinicians [2,6], this assumptions appears reasonable. The simulations of genetic biomarkers in the present study have been limited to an additive genetic model, which assumes that heterozygotes are intermediate between the two homozygous groups. We chose an additive model, since this is the most commonly applied genetic model in practice and most recessive or dominant effects can be seen with an additive test. Extension of the present results to additive and dominant models depends on minor allele frequency and would be difficult to estimate for genetic markers with very low minor allele frequency owing to the very low number of homozygotes. In the present study, we have not separately considered the role of additional clinical variables that may contribute to prediction of outcome, such as number of previous episodes, duration of present episode, age, subtypes of depression and symptom dimensions [1,29–31]. Similar estimates for biomarker effects that are conditional on any such variables will have to be calculated with respect to the distribution of each such additional variable. When interpreting the results, it is important to keep in mind that the outcome of antidepressant treatment is measured with a certain error. Therefore, 100% of variance could never be explained even by a perfect predictor and the relatively low percentage of variance explained may represent a relatively larger proportion of what is explainable. For example, with a typical reliability of measurement of 0.80, 36% of variance in outcome is owing to measurement error and a clinically significant predictor would explain 10% rather than 6.3% of the theoretical outcome that is measured with perfect accuracy. However, since it is unlikely that depression severity will ever be measured without error, we keep the results in the raw metrics that of necessity is attenuated by measurement error. A final limitation is that the conclusions regarding the proportion of variance explained in categorical outcomes depend on the estimation of pseudo r^{2} from logistic models, which is inexact, and should therefore be treated only as approximation.

## Conclusion

In conclusion, we propose a set of standards for clinical significance of biomarkers predictive of depression treatment outcome. The clinical applicability of biomarkers will depend on a cost– benefit analysis where the effect size of prediction is weighted against the cost and risk of testing.

## Future perspective

We hope that the current study will highlight the need for robust prediction with a sufficiently large effect size for biomarker research to significantly inform clinical practice. We expect that this will lead to two important developments in biomarker research. First, since it appears unlikely that a single common biomarker will achieve the effect size needed to significantly inform clinical decision-making, the research will move towards combining multiple biomarkers into predictive score or algorithms that may achieve clinically significant prediction [1]. The estimates for continuous biomarkers can be used to assess the clinical significance of such multivariate prediction. Second, the applicability of any prediction increases if an alternative treatment is available for those with a predicted poor treatment outcome. It is therefore likely that biomarker research will move to comparative studies of different treatments. The comparison of psychological and pharmacological approaches may be especially promising [28].

### Background

- The benefits of any biomarker-based prediction for an individual patient depend on effect size rather than on statistical significance.
- Three points difference on the Hamilton Rating Scale for Depression (HRSD) has been proposed as a consensus criterion for clinical significance in drug comparisons. A similar criterion is needed to assess the clinical significance of biomarkers.

### Materials & methods

- To translate the clinical significance criterion to biomarker research, we have simulated datasets modeled on large pragmatic clinical trials.
- We used proportion of variance explained as a common metric to translate explanatory power between variously distributed predictors, including genotypes and continuous biomarkers.

### Results

- Clinically significant drug–placebo difference corresponds to 6.3% of variance in outcome explained.
- Genotypes with minor allele frequencies of 5, 10, 20, 30 and 50% need to attain a per-allele difference of 4.7, 3.6, 2.8, 2.4 and 2.2 HRSD points, respectively, to reach clinically significant prediction.
- A normally distributed continuous biomarker (or a predictive score composed from multiple biomarkers) will need an effect size of 1.5 HRSD points per standard deviation to reach clinical significance.
- A number needed to asses of three suggests that, with this effect size, a biomarker will significantly improve the prediction of outcome in one out of every three patients assessed.

### Discussion

- The clinical applicability of a predictive biomarker also depends on other factors including test availability, cost and treatment delays associated with testing.

### Future perspective

- It is likely that multiple biomarkers combined in predictive scores or algorithms will be needed to achieve clinically meaningful prediction.
- Biomarker research should move towards comparative studies of different treatments (e.g., comparison of psychological and pharmacological treatment).

## Acknowledgements

The authors thank M Gray, who has provided technical support with creating an online calculator that accompanies this article.

The research leading to these results has received support from the Innovative Medicine Initiative Joint Undertaking (IMI-JU) under grant agreement No. 115008, of which, resources are composed of EU and the European Federation of Pharmaceutical Industries and Associations (EFPIA) in-kind contribution and financial contribution from the EU’s Seventh Framework Program (FP7/2007-2013). RH Perlis is supported by the National Institute of Mental Health MH086026. R Uher consults for the WHO. RH Perlis has received consulting fees from Proteus Biomedical, Concordant Rater Systems and RIDventures and research funding from National Institute of Mental Health. None of these organizations have direct interest in the content of this publication.

## Footnotes

**Financial & competing interests disclosure**

The authors have no other relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript apart from those disclosed.

No writing assistance was utilized in the production of this manuscript.

## References

Papers of special note have been highlighted as:

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- Biomarkers predicting treatment outcome in depression: what is clinically signif...Biomarkers predicting treatment outcome in depression: what is clinically significant?NIHPA Author Manuscripts. Jan 2012; 13(2)233PMC

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