Analyzing the Duration of Untreated Psychosis: Quantile Regression

Prolonged duration of untreated psychosis (DUP) is associated with poorer outcomes across multiple health care systems.¹ Early detection (ED) efforts can reduce these delays² but face a challenge: typically skewed DUP distributions are poorly managed by commonly used statistical methods. This limits the strength and scope of inferences about ED’s effectiveness.¹ Also, while reducing DUP will improve outcomes for most patients, there are some for whom a particularly long DUP is a byproduct of an insidiously unfolding illness rather than a modifiable prognostic factor.³ This highlights the need for a tool to interrogate the effect of ED across the full range of DUP.

Various strategies can be used to analyze the effect of ED on DUP. Categorical divisions of DUP into long and short subgroups use arbitrary cutoffs (eg, <3 months, <12 months, or a median split). However, the absence of adequate evidence for a threshold (above which DUP is consequential for outcomes) limits validity. Alternatives include transformation (eg, square-root) to approximate normality or nonparametric statistical tests to compare across the entire distribution of DUP. However, the results can be difficult to interpret or translate into practice. More importantly, the skewness of DUP may reflect meaningful heterogeneity. Conventional statistical methods, with a focus on mean estimates, fail to capture the differential effects of covariates across different sections of the DUP distribution.

We propose an alternative. Quantile regression (QR) can model conditional quantiles of response using independent variable(s).⁴ Quantiles split a frequency distribution into equal-sized partitions (eg, 10 deciles or 100 percentiles). Unlike ordinary least-squares regression, QR can estimate the heterogeneous effects of predictors (eg, age, sex, education, or ED) across different quantiles of outcome (DUP), rather than presuming a uniform mean effect. The effectiveness of a particular ED strategy will likely vary across different levels of DUP. Unlike conventional analysis of mean DUP, QR can quantify these variations. Furthermore, unlike linear regression that relies on a normality assumption, QR can provide more accurate estimates in samples with extreme outliers, as is common in DUP distributions. The Yale Human Investigations Committee approved the trial from which these data were extracted.

We illustrate the value of this strategy, with a post hoc analysis of the effect of age, sex, and years of education on DUP, measured at a first-episode service in the 6 years prior to the launch of an ED campaign. To test our theory that growing awareness of the service would affect DUP over this period, the analysis was stratified by early (2006-2009) and late (2010- 2012) epochs. Ordinary least-squares regression obtained a significant coefficient (SE) of −3.0 (1.3) (P = .02) on predicted mean DUP during the early vs late epoch (coefficient [SE], 0.1 [0.7]; P = .90). However, fit diagnostics implied severe violation of the normality assumption, invalidating this test. In contrast, QR revealed a significant differential effect of education by DUP quantile (Figure). Specifically, while no effect was found for the other demographic variables, more education was correlated with lower levels of extreme DUP during the early but not the late epoch (eg, coefficient [SE] at 90% percentile, −7.9 [3.0]; P = .01). As the service became better known to referral sources, the effect of greater educational attainment on improved access was likely muted. While this post hoc analysis can reveal only tentative inferences, it demonstrates the value of QR in interrogating actionable associations derived from clinical theory.

Quantile regression analyses can inform messaging and outreach efforts for first-episode services that are contemplating ED efforts in their communities. A similar analysis, using ED as an independent variable, awaits results from an ongoing study⁵ and will allow prospective assessment of the differential effect of this ED campaign across different subpopulations and across the full distribution of DUP.

Published Online: August 31, 2016. doi:10.1001/jamapsychiatry.2016.2013.

Author Contributions: Dr Srihari had full access to all the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis.

Concept and design: Guloksuz, Li, Tek, Woods, McGlashan, Srihari.

Acquisition, analysis, or interpretation of data: Guloksuz, Li, Woods, Friis, Srihari.

Drafting of the manuscript: Guloksuz, Li, Tek, Srihari.

Critical revision of the manuscript for important intellectual content: Guloksuz, Li, Woods, McGlashan, Friis, Srihari.

Statistical analysis: Guloksuz, Li, Srihari.

Obtaining funding: Srihari.

Administrative, technical, or material support: Guloksuz, McGlashan.

Study supervision: Tek, McGlashan, Srihari.

Conflict of Interest Disclosures: None reported.

Funding/Support: This work was supported by grants R01MH103831 and RC1 MH088971 from the National Institutes of Health (Dr Srihari, principal investigator).

Role of the Funder/Sponsor: The National Institutes of Health had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.