Patient Response Trajectories in Major Depressive Disorder

Abstract

Objective

To investigate whether the efficacy of antidepressants can be understood in terms of patient response-trajectory classes.

Experimental Design

Patient-level data were analysed from 1357 adults with MDD randomised to either escitalopram 20 mg/day (n = 676) or placebo (n = 681) in five 8-week randomised placebo-controlled trials. Growth mixture models (GMMs) were used to identify the response trajectories; longitudinal latent class analysis (LLCA) was used to corroborate the findings.

Principal Observations

Three classes of response were identified for escitalopram and placebo based on the trajectory of the patients’ Montgomery-Åsberg Depression Rating Scale (MADRS) total scores during treatment. All three classes had similar mean baseline MADRS scores, but the change from baseline after 8 weeks differed: –4.2 MADRS points for non-responders, –18.4 MADRS points for slow responders, and –26.7 points for fast responders. The proportions of non-responders, slow responders and fast responders were 53%, 38% and 9%, respectively, with placebo and 27%, 58% and 14%, respectively, with escitalopram. Receiver operating curve analysis showed that a cut-off of ≥43% improvement from baseline to week 2 predicted fast responders, and a cut-off of ≥28% improvement from baseline to week 4 predicted responders (fast or slow). There were no clinically useful differences at baseline that predicted the trajectory class to which a patient would belong.

Conclusions

The presence of fast-, slow- and non-responder classes has a clear clinical relevance for guiding treatment decisions; individual patients can be classified by the change in their MADRS score from baseline at 2 or 4 weeks.

Introduction

Early detection of the effect of treatment in patients with major depressive disorder (MDD) is important, particularly if the treatment proves not to be sufficiently efficacious for the patient. However, no biomarkers are currently available for the prediction of response and traditional intention-to-treat analysis is not helpful in separating patients who subsequently respond to treatment from those who are non-responders. The traditional method uses an analysis of covariance (ANCOVA) model which assumes that all patients benefit from treatment. Thase et al. analysed patient-level data from five randomised placebo-controlled studies in MDD using a mixture model and identified two patient subgroups (benefiting versus not benefiting from treatment) at the end of short-term treatment (week 8).¹ This bimodal model gave a considerably better fit to the data than the ANCOVA model, but other methods are potentially more powerful as they use data from all visits to identify different patient trajectory classes.

Gueorguieva et al. used growth mixture models (GMMs) to analyse data from 2515 patients in short-term MDD trials with duloxetine, paroxetine, escitalopram and placebo arms and found two trajectory classes in the active-treatment group and one class in the placebo group.² From a clinical viewpoint, this is a challenging finding because the ‘average effect’ of the antidepressant obscures the robust effect on the ‘responder group’. While it is possible – and even quite likely – that a fit index or a formal test may suggest a different number of classes within the groups, caution should be exercised before drawing conclusions. It is certainly useful to do ‘by-treatment’ analyses, however, it is important that to ensure consistent interpretation, patient-level data from both treatment groups are analysed simultaneously, so that model assumptions are inferred that make comparisons across treatment groups viable.

Using longitudinal latent class analysis (LLCA) of depression scores from 811 patients treated with either escitalopram or nortriptyline in the Genome-Based Therapeutic Drugs for Depression (GENDEP) database, Uher et al. identified nine distinct trajectories.³ This was in contrast to the results reported by Gueorguieva et al., which might be explained by differences in the model assumptions underlying GMM and LLCA methods.²

Based on GMMs, patients can be classified into one of several response trajectory groups. The change from baseline in Montgomery-Åsberg Depression Rating Scale (MADRS) total score in the first 1 or 2 weeks can be used to predict the outcome of acute treatment for each patient.⁴ Early MADRS total scores can also be used as predictors of trajectory-class membership, and the value of these scores can be quantified in terms of specificity, sensitivity, and positive and negative predictive value (PPV and NPV, respectively). These scores can provide a basis for clinically useful criteria to predict the probable effect of treatment and identify patients who may benefit from a change in treatment.

The approach taken in the present study was to start with a joint analysis of both treatment groups (escitalopram and placebo) and use ‘by-treatment’ analyses as a supportive method to investigate the robustness of the finding from the joint analysis. LLCA was used to contrast and support the findings from GMMs. Optimal criteria for classification were developed using receiver operating curve (ROC) methodologies, and differences in baseline characteristics between trajectory groups were investigated. We discuss how some of these criteria (early response/non-response) could be used in clinical practice for choosing further treatment for each patient.

Methods

Patients

Patient-level data were pooled from all five of the Forest Laboratories Inc.- and H. Lundbeck A/S-sponsored, randomised placebo-controlled trials in MDD in which it was possible to receive escitalopram 20 mg/day.¹ In order to optimize the signal-to-noise ratio for the analyses, only treatment groups using the highest recommended dose of 20 mg/day were included. All patients who participated in the trials provided written informed consent. Analyses were based on the full analysis set, comprising all patients (n = 1357) who took ⩾1 dose of study medication and had ⩾1 valid post-baseline MADRS assessment. MADRS total scores from all timepoints (baseline, weeks 1, 2, 4, 6 and 8) were analysed using mixture models/latent class models.⁵ All analyses were based on all observed data and provide unbiased estimates under the ‘missing at random’ assumption.⁶

By using these six repeated measurements from each patient, we sought to identify typical response trajectories and characterise the patients in each trajectory class in terms of baseline characteristics. The aim was to identify criteria (either at baseline or during early treatment) that would predict which patients belonged to each trajectory class. GMMs were used as the primary method for identifying the response trajectories; LLCA was used an alternative methodology to confirm (or reject) the GMM findings. Based on the class memberships determined by the best fitting GMM, prediction of trajectory-class membership was investigated using standard prediction methodology, such as calculation of sensitivity, specificity, PPV and NPV, as well as ROCs.

The Growth Mixture Model

The focus was to use the repeated measurements of the MADRS total scores to identify typical trajectories among the patients. Two types of GMMs were used:

• 1. The quadratic:

  MADRS_ti = α_ci + β_ci t + γ_ci t² + error_ti

• 2. The piecewise linear (using the convention that x⁺= x when x>0 and x⁺= 0 when x⩽0):

  MADRS_ti = α_ci + β_ci t + γ_ci (t−2)⁺ + δ_ci (t−4)⁺ + error_ti

Where i = individual, t = assessment time (baseline, weeks 1, 2, 4, 6 and 8) and c = the unobserved class variable in each model.

Each class is thereby defined by its mean trajectory, which is assumed to be quadratic or piecewise linear, respectively. It was assumed that error variance was constant over all post-baseline measurements, as the error term represents the time-/patient-specific measurement error for that assessment.

In the quadratic GMM, all individual trajectories were assumed to be parabolic, which allowed for straight lines (if γ_ci=0), as well as trajectories that started with improvement but gradually flattened by week 8 (e.g. β_ci ≈−16γ_ci). Parabolas are the most commonly used trajectories for GMMs, but they do not allow for a rapid improvement followed by a long flat trajectory. Therefore, a piecewise linear model was used, which assumed linearity between baseline and week 2, between weeks 2 and 4, and between weeks 4 and 8.

In both models, it was assumed that the individual trajectory parameters followed a multivariate normal distribution specific to the class. The model allows for different proportions of patients in each trajectory class, depending on treatment. Hence, the trajectory classes are assumed to be the same for the groups receiving escitalopram and placebo, but the distribution of patients in classes can differ between treatments. By-treatment analyses were also performed to investigate whether the classes are defined similarly in the treatment groups.

Longitudinal Latent Class Analysis

LLCA is an alternative to GMM analysis and is more flexible with respect to the mean structure and more rigid with respect to the covariance structure. LLCA is conditional on trajectory class and patient scores at different timepoints being independent (no patient-specific trajectory, only class-specific).

The LLCA is:

MADRS_ti = α_ct + error_ti

Where i = individual, t = assessment time (baseline, weeks 1, 2, 4, 6 and 8) and c = unobserved class variable (as detailed for the GMM above). It was assumed that patients belonging to the same class would have the same expected trajectory (except for the error term) and not merely similar trajectories (as is the case with the GMM). Here, LLCA was used as sensitivity analysis of the GMM analyses.

Prediction

To translate the results of these statistical models into models with clinical utility, ROCs were constructed using the MADRS total score at weeks 2 and 4, either as the percent change from baseline or using a cut-off. The optimal point on the ROC was calculated using the Youden index (J = sensitivity+specificity−1). The diagnostic sensitivity is the ability to correctly assign patients to the correct trajectory and the diagnostic specificity is the ability to correctly identify patients who do not belong to a particular trajectory.

The PPV is the probability that a patient who satisfies a classification criterion is in the right trajectory class, while the NPV is the probability that a patient who does not satisfy the criterion is not in the wrong trajectory class. When the sensitivity and specificity are known, the PPV and NPV can be calculated using Bayes’ rule:

PPV = sensitivity*probability of belonging to the trajectory class/probability of satisfying the criterion

NPV = specificity*probability of not belonging to the trajectory class/probability of not satisfying the criterion.

To investigate if combining information from weeks 2 and 4 would increase predictability, the Youden index was optimised as a function of both scores using Boolean “OR” and “AND” criteria. The “OR” criterion was satisfied if either the week 2 or the week 4 criterion was satisfied. The “AND” criterion was satisfied if both the week 2 and the week 4 criteria were satisfied. This cannot be depicted using an ROC, as it is necessary to optimise Youden’s index as a function of both week 2 and 4 scores simultaneously, so only the optimal combinations are shown.

Estimation

The GMM and LLCA calculations were estimated using Mplus.⁷ All other statistical analyses were carried out in R.⁸ The model can be estimated conditional on the number of unobserved classes, and the number of classes can be investigated using fit indices or other tools. More detail about GMMs is provided by Muthén and Brown.⁹

Results

The Growth Mixture Model

For the different GMMs, the Bayesian information criterion (BIC) was 47,407 and 47,391 for the two- and three-class models, respectively, using quadratic trajectories. For the two- and three-class models with piecewise linear trajectories, the BIC values were 47,231 and 47,205, respectively. These data suggested that a three-class model offered a better description of the data than a two-class model within both types of trajectories and that the piecewise linear models provided a better fit to the data than the quadratic models (a lower BIC value is better).

It was not possible to obtain estimates from four-class models for either of the trajectory types, as the models did not converge despite our best attempts with the estimation algorithm. Thus, the data did not support more than three typical trajectories (Figure 1).

Figure 1.

Growth Mixture Model Trajectory Classification and Class Sizes Based on Most Likely Trajectory-Class Membership Using a Three-Class Model With Piecewise Linear Trajectories

A. Non-responders; B. Slow responders; C. Fast responders. Solid lines indicate patients receiving placebo and dotted lines indicate patients receiving escitalopram. MADRS: Montgomery-Åsberg Depression Rating Scale. The coloured lines indicate mean trajectories.

A three-class model identified non-responders, slow responders and fast responders. This model explained more of the variance than the previously reported two-class model,¹ and the piecewise linear model captured more variance than the quadratic model, also suggesting that the three-class piecewise linear model is the better model for these data (Table 1).

Table 1. Variance Explained by Different Models at Week 8.

		Two-class mixture modela		Three-class quadratic GMM		Three-class piecewise linear GMM
Variance explained (ESC)		64%		78%		82%
Variance explained (PBO)		63%		83%		86%
SD (benefiters)		5.6%		–		–
SD (non-benefiters)		6.7%		–		–
SD (fast, slow, non-responders)		–		4.3%		3.9%

^aThase et al.¹ ESC: escitalopram; GMM: growth mixture model; PBO: placebo; SD: standard deviation.

Analysis of the escitalopram and placebo groups revealed similar trajectory shapes using the piecewise linear three-class model (results not shown). The largest difference between the groups was for the fast-responder cohorts, which appeared to have earlier improvements in the placebo group than in the escitalopram group.

Patients were subsequently assigned to the class for which they had the largest posterior probability of belonging. The distribution of non-responders, slow responders and fast responders by treatment for the piecewise linear model is shown in Table 2. This shows that it is necessary to treat four patients [1/(0.53−0.28)] to move one patient from the non-responder group, and to treat 20 patients [1/(0.14−0.09)] to achieve one additional fast responder. The individual trajectories for non-, slow and fast responders are shown in Figure 1.

Table 2. Patient Withdrawals by Trajectory Class and Treatment Group (full analysis set).

Primary reason	Non-responders	Slow responders	Fast responders
				Placebo (n = 362; 53%)	Escitalopram (n = 185; 27%)	Placebo (n = 261; 38%)	Escitalopram (n = 393; 58%)	Placebo (n = 58; 9%)	Escitalopram (n = 98; 14%)
Withdrawn, n (%)	75 (20.7)	36 (19.5)	27 (10.3)	68 (17.3)	8 (13.8)	12 (12.2)
Adverse event	9 (2.5)	18 (9.7)	4 (1.5)	19 (4.8)	0 (0)	6 (6.1)
Lack of efficacy	18 (5.0)	6 (3.2)	2 (0.8)	2 (0.5)	1 (1.7)	0 (0)
Protocol violation	4 (1.1)	2 (1.1)	0 (0)	7 (1.8)	1 (1.7)	2 (2.0)
Consent withdrawn	15 (4.1)	3 (1.6)	6 (2.3)	12 (3.1)	2 (3.4)	2 (2.0)
Lost to follow-up	20 (5.5)	6 (3.2)	13 (5.0)	28 (7.1)	3 (5.2)	1 (1.0)
Other	9 (2.5)	1 (0.5)	2 (0.8)	0 (0)	1 (1.7)	1 (1.0)

Longitudinal Latent Class Analysis

For the LLCA, the BIC decreased monotonically for models with 1–12 classes and was not a convincing tool for choosing the number of latent classes. Instead, the size of the smallest class was used as a criterion. For models with 7, 8, 9, 10 and 11 classes, the expected number of patients in the smallest class was 34, 28, 29, 2 and 2, respectively, suggesting that adding a tenth or eleventh class did not substantively improve the description of the data. For this reason, the results from the nine-class LLCA are reported (Figure 2). The results from this model were consistent with those from the GMM, as the two LLCA fast-responder trajectories could be interpreted as corresponding to the GMM fast-responder class, the four flat LLCA trajectories to the GMM non-responder class, and the three LLCA slow-responder trajectories to the GMM slow-responder class. The differences between LLCA classes within GMM responder-type classes appear to reflect differences in baseline severity. The numbers of patients in the joint classification based on the GMM and LLCA models are shown in Table 3. A comparison of the grouping of the nine classes from the LLCA with the fast, slow and non-responder classes from the GMM gave a Cohen’s kappa of 0.603, which can be interpreted as showing that the two classifications are in ‘substantial agreement’.¹⁰ In addition, 75% (1021 of 1357) of the patients were categorised consistently across the two models.

Figure 2.

Longitudinal Latent Class Analysis Trajectories and Class Sizes Using a Nine-Class Model

There are four non-responder classes (red), three slow-responder classes (orange) and two fast-responder classes (green). The overlap between trajectories (eg, a fast-responder and a slow-responder curve) explains why the receiver operating characteristic analysis will never be perfect. ESC: escitalopram; PBO: placebo; MADRS: Montgomery-Åsberg Depression Rating Scale.

Table 3. Numbers of Patients in Each Trajectory Class Based on the Three-Class Piecewise Linear Growth Mixture Model (GMM) versus the Nine-Class Longitudinal Latent Class Analysis (LLCA).

LLCA class		1		2		1		2		3		1		2		3		4
GMM class		Fast responder				Slow responder						Non-responder
Fast responder		75		41		18		15		0		7		0		0		0
Slow responder		68		72		202		168		33		85		25		1		0
Non-responder		0		0		2		10		33		94		177		211		20

Prediction of Responders versus Non-Responders

ROC analysis was used to determine the optimal diagnostic parameters at weeks 2 and week 4 that identify non-responders or fast responders (Figure 3). The absolute values, as well as the relative improvement from baseline of the MADRS total scores at weeks 2 and 4, were analysed first. For predicting fast responders, the relative improvement from baseline to week 2 using a cut-off of ⩾43% decrease from baseline in MADRS score had the highest Youden index (of the four potential predictors), with a sensitivity of 93% and a specificity of 87%. For predicting responders (fast or slow), the relative improvement from baseline to week 4 using a cut-off of ⩾28% improvement had the highest Youden index (of the four), with a sensitivity of 81% and a specificity of 73%. For predicting fast response, this corresponds to a PPV of 49% and an NPV of 99% and for predicting response (fast or slow), a PPV of 82% and an NPV of 72%. To investigate whether combining information from weeks 2 and 4 would increase predictability, the Youden index was optimised as a function of scores at weeks 2 and 4 using Boolean criteria (Table 4). For the prediction of fast responders, the week 2 criterion was approximately the same, regardless of the joint criterion being “AND” or “OR”. Furthermore, the fact that the optimal week-4 criterion was strict under the “OR” and relaxed under the “AND” criterion, means that if the week-2 score is known, then little additional information is gained by knowing the week 4 score when predicting whether the patient is a fast responder or not. From the Youden indices, it seems that relative improvement is a substantially better predictor than the absolute measures. For the prediction of responders (versus non-responders), the optimal week-4 criterion was approximately the same regardless of the joint criterion being an “AND” or an “OR” criterion, and there seems to be little to gain by including week-2 scores in the prediction. Thus, for prediction of responders (fast or slow), knowledge of the week-2 score provides little extra information when the relative improvement from baseline to week 4 is known. For this prediction, an absolute criterion of having a MADRS total score <19 at week 4 performs only slightly worse than the relative criterion (improvement of ⩾28% at week 4; Table 4).

Figure 3.

Receiver Operating Curves for Identifying Fast Responders versus Slow or Non-Responders and Fast or Slow Responders versus Non-Responders

Fast responders are distinguished from slow or non-responders (blue line) using the change from baseline at week 2 (the optimal cut-off is ⩾43% improvement); and fast or slow responders versus non-responders (red line) using the change from baseline at week 4 (the optimal cut-off is ⩾28% improvement). The points represent the optimal values on each curve.

Table 4. The Effect of Percentage Change from Baseline in MADRS Total Score and Cut-offs on the MADRS on Diagnostic Sensitivity and Specificity.

Gold standard		Week 2		Boolean criterion		Week 4		Sens		Spec		PPVa		NPVb		J
Fast versus slow/non-responders
Cut-off		⩽15		and		⩽40		75		88		44		96		0.63
Cut-off		⩽16		or		⩽5		83		82		84		69		0.65
Decrease		⩾38%		and		⩾8%		95		82		42		99		0.77
Decrease		⩾44%		or		⩾78%		93		85		46		99		0.78
Fast/slow versus non-responders
Cut-off		⩽40		and		⩽19		75		79		84		68		0.51
Cut-off		⩽10		or		⩽19		76		78		84		69		0.54
Decrease		⩾8%		and		⩾28%		74		79		84		67		0.53
Decrease		⩾42%		or		⩾28%		84		71		81		74		0.55

J: Youden index (sensitivity+specificity−1); NPV: negative predictive value; PPV: positive predictive value; Sens: sensitivity; Spec: specificity.

Prevalence is calculated from the patient numbers in Table 4. Bold text indicates the criterion that yields the highest value of the Youden index of the four selected criteria

Baseline Characteristics Associated with Response Trajectory Class

The three classes of patients differed significantly across all baseline characteristics investigated (Table 5). There was a tendency for fast-responding patients to be younger and non-responding patients to be older than slow responders, and there was a tendency for a relatively larger proportion of men to be non-responders compared with women. There was also a tendency towards more non-responders and fewer slow responders in the studies carried out in the USA compared with those conducted in other countries. Baseline depression and anxiety scores performed poorly as predictors of fast response and non-response, as they did not consistently correlate across the trajectory classes. Although age was predictive in so far as older patients were more likely to follow the non-responder trajectory, while younger patients were more likely to follow the fast-responder trajectory, the mean difference was very small compared with the standard deviation, making age a poor predictor of trajectory-class membership.

Table 5. Patient Baseline Characteristics.

Characteristic		Non-responders (n = 547)		Slow responders (n = 654)		Fast responders (n = 156)		P-value
Age, mean (SD), years		41.3 (11.2)		40.7 (12.1)		38.1 (11.3)		<0.001
Sex, female, n (%)		308 (56.3)		427 (65.3)		100 (64.1)		0.005
BMI, mean (SD), kg/m2		28.8 (7.1)		27.5 (6.5)		28.6 (7.5)		0.006
US patients, n (%)		454 (83.0)		471 (72.0)		123 (78.8)		<0.001
MADRS, mean (SD)		30.4 (4.5)		28.4 (4.2)		31.4 (4.4)		<0.001
HAM-Aa, mean (SD)		17.1 (5.4)		15.6 (5.0)		17.0 (5.4)		<0.001
HAM-D anxa,b, n (%)		238 (52.4)		200 (42.5)		68 (55.3)		0.003

^aOnly measured in the US studies. ^bSomatic/anxiety subscale score ⩾7 (sum of items 10, 11, 12, 13, 15, 17). BMI: body mass index; HAM-A: Hamilton Anxiety Rating Scale; HAM-D anx: anxiety subscale (sum of items 10, 11, 12, 13, 15, 17) of the Hamilton Depression Rating Scale; MADRS: Montgomery-Åsberg Depression Rating Scale; SD: standard deviation.

The clinical characteristics of these three patient classes were compared at weeks 2, 4 and 8 (Table 6). Response and remission rates differed greatly, as did mean change from baseline in MADRS total score, particularly at week 8. For example, the week-8 response rate was 0.5% for non-responders, 78.4% for slow responders and 97.8% for fast responders, demonstrating that almost all patients who were most likely to belong to the trajectory class of non-responders would be defined as non-responders according to the standard criterion (⩾50% improvement in MADRS total score from baseline to end of study); almost a quarter of the patients in the trajectory class of slow responders did not meet the ‘responder’ criterion; and almost all patients in the fast-responder trajectory class did meet the criterion.

Table 6. Clinical Characteristics of Non-, Slow and Fast Responders Over Time in All Patients for The Piecewise Linear Growth Mixture Models.

		Non-responders		Slow responders		Fast responders
Week 2
No. of patients		515		624		149
MADRS, mean (SD)		26.9 (6.1)		21.0 (6.4)		11.5 (5.9)
MADRS, mean CFB (SD)		−3.5 (5.2)		−7.4 (5.1)		−19.9 (4.1)
Remitters, n (%)a		3 (0.6)		32 (5.1)		69 (46.3)
Responders, n (%)b		13 (2.5)		72 (11.5)		121 (81.2)
Week 4
No. of patients		490		593		143
MADRS, mean (SD)		24.9 (7.1)		15.6 (7.4)		9.9 (7.5)
MADRS, mean CFB (SD)		−5.4 (6.4)		−12.9 (6.8)		−21.5 (7.5)
Remitters, n (%)a		15 (3.1)		162 (27.3)		86 (60.1)
Responders, n (%)b		44 (9.0)		263 (44.4)		121 (84.6)
Week 8
No. of patients		440		564		137
MADRS, mean (SD)		26.1 (5.4)		10.1 (5.3)		4.6 (4.2)
MADRS, mean CFB (SD)		−4.2 (5.3)		−18.4 (5.8)		−26.7 (5.5)
Remitters, n (%)a		0 (0)		286 (50.7)		124 (90.5)
Responders, n (%)b		2 (0.5)		442 (78.4)		134 (97.8)

^aDefined as MADRS total score ⩽10. ^bDefined as ⩾50% improvement in MADRS total score from baseline. CFB: change from baseline; MADRS: Montgomery-Åsberg Depression Rating Scale; SD: standard deviation.

Withdrawal Associated with Response Trajectory Class

Reasons for withdrawal are shown in Table 2. Withdrawal rates were similar for non-responders and fast responders in both treatment groups. Non-responders treated with escitalopram withdrew primarily due to adverse events (AEs), while patients receiving placebo mainly withdrew due to lack of efficacy or were lost to follow-up. In the fast-responder class, patients receiving escitalopram also withdrew primarily due to AEs, while those receiving placebo withdrew mainly due to withdrawal of consent or were lost to follow-up. Slow responders treated with escitalopram had a higher rate of withdrawal than patients receiving placebo, mainly due to AEs and loss to follow-up.

Adverse Events Associated with Response Trajectory Class

AEs were more frequent in escitalopram-treated patients than in those receiving placebo in all three trajectory classes. The incidences of individual AEs were similar in non- and slow responders (data not shown). Among patients receiving placebo, fast responders tended to have a higher incidence of dry mouth and increased appetite, and a lower incidence of diarrhoea compared with non- and slow responders. In patients receiving escitalopram, fast responders tended to have a higher incidence of headache, diarrhoea and flatulence versus non- and slow responders.

Discussion

Comparison of GMM Analysis with Latent Class Analysis

GMM analysis of data from all visits during the 8-week treatment period shows that patients can be classified into one of three classes on the basis of the trajectory of their scores. The three classes (non-, slow and fast responders) have a similar baseline MADRS total mean score, but the change from baseline after 8 weeks differs, from −4 MADRS points for non-responders, to −18 MADRS points for slow responders, and −27 points for fast responders. The non-responders correspond to the ‘non-benefiters’ reported by Thase et al.,¹ while the fast and slow responders correspond to the ‘benefiters’. GMM analysis using a piecewise linear model explains ∼84% of the variance in the dataset versus 64% using latent class analysis (and 6% using ANCOVA).

The difference between treatment groups lies in the proportion of patients belonging to each trajectory class: 53% in the placebo group were non-responders versus 27% in the escitalopram group, corresponding to a number needed to treat of four. The higher proportion of responders in the GMM analysis is partly due to the use of repeated measures, in contrast to last observation carried forward, as used by Thase et al.,¹ and partly because GMM identifies patients whose trajectory indicates a slow but consistent improvement (for both placebo and escitalopram groups).

Growth Mixture Model

Gueorguieva et al. also analysed data from short-term placebo-controlled depression studies using polynomials and piecewise linear GMMs and found that a piecewise linear model provided a better description of the data.² They found two trajectories in patients treated with antidepressants (selective serotonin reuptake inhibitors or duloxetine), but only one in patients receiving placebo. In contrast to the conclusions drawn by Gueorguieva et al.,² our analysis revealed three typical inherent trajectory classes in each treatment group, suggesting that treatment changes the patient distribution between the trajectory classes rather than creating substantively different ones. Slightly lower mean anxiety and depression scores were associated with slow response to treatment and there were proportionately more men than women in the non-responder class. Neither of our analyses found a separate class of patients whose condition worsened with time, which means that there are few such patients and they do not follow a typical trajectory. Hence, they are a minor, heterogeneous subgroup of the non-responders.

In another study, GMM techniques were used to investigate the trajectories of relapse in an analysis of data from four placebo-controlled discontinuation trials of antidepressants in patients with MDD.¹¹ The study analysed trajectories of depression severity (measured using the 17-item Hamilton Depression Rating Scale) for up to 26 weeks in patients who entered a double-blind phase in which they remained on active treatment or were switched to placebo after having responded to treatment with duloxetine or fluoxetine. The analysis identified three relapse trajectory classes in both the active-treatment and placebo (discontinuation) groups, with no evidence of any difference in trajectory classes between the groups.

Marques et al. used the GMM method in a pooled analysis of two trials in patients with schizophrenia.¹² These authors identified four trajectory classes, described as non-responders (20%), partial responders (48%), responders (22%) and dramatic responders (10%). Responders had a lower baseline MADRS score than the other classes and dramatic responders were only observed in the active-treatment group. In the present study, all three trajectory classes are present in each treatment group, indicating that – in patients with depression – this may be an inherent feature of the course of treated illness. The trajectory class of fast responders identified in the current study corresponds to the dramatic responders identified by Marques et al. (10% of patients with schizophrenia but not found in the placebo group),¹² the rapid treatment responders reported by Levine and Rabinowitz¹³ (15% of patients with schizophrenia), and the ‘reducers’ reported by Litten et al.¹⁴ (30% of patients with alcohol dependency) who reduced their drinking by ⩾50% before even starting treatment.

Longitudinal Latent Class Analysis

LLCA was used in the current study to contrast and support the findings from the GMMs, and nine different trajectories were identified using this technique, as also found by Uher et al.³ LLCA provides a ‘lower level’ description because it does not allow for variation between patients within each class (i.e. classes are more homogeneous). In contrast, GMM is more flexible on the covariance structure and provides a ‘higher level’ description of trajectory classes. This results in a ‘higher resolution’ when using LLCA compared with GMM; hence LLCA will tend to detect smaller trajectory classes with more subtle differences. Consequently, LLCA is more likely to find spurious classes or classes without clinical relevance. In the analyses presented here, the two methods complement each other, and our clinical interpretation is that there are three main types of responders (non-responders, slow responders and fast responders) that can be further divided into four, three and two subclasses, respectively, each subclass differing primarily in the level of baseline severity. Thus, despite the fact that the LLCA allows for much less within-class heterogeneity (and hence finds more trajectory classes) than the GMM, it also picks up the general pattern of non-responders, slow responders and fast responders.

The clinical relevance of the subclasses is probably low. Interestingly, this is consistent with the findings reported by Smagula et al., who found three, two and one subclasses for the same three types of responders identified in the current study based on the GMM.¹⁵

Interpretation of NPV and PPV for Each Trajectory Class

In a diagnostic test, the NPV is the proportion of subjects with a negative test result who do not have the disease, and the PPV is the proportion of those with a positive test result who actually have the disease. The PPV and NPV are direct functions of the sensitivity and specificity (together with the proportion of patients satisfying the criterion and the proportion of patients in the specific trajectory class in the sample) and depend on the choice of the Youden index as the criterion for optimising the cut-offs. PPV and NPV have clinical utility for the psychiatrist because these are the probabilities of a patient belonging to either of the trajectories given the patient’s actual scores. When predicting those patients with MDD who will be fast responders to treatment, a relative change from baseline to week 2 of ⩾43% improvement corresponds to an NPV of 99% and a PPV of 49%. The high NPV means that only 1% of patients identified as non- or slow responders are actually fast responders; however, the low PPV means that only about half of the patients identified as fast responders are actually fast responders. This is probably because there is an overlap between a fast-responder and a slow-responder trajectory, as seen in the nine-class LLCA model in Figure 2. These results are consistent with those of Szegedi et al.,¹⁶ who showed that early improvement (⩾20% from baseline) by week 2 predicated stable response (⩾50% from baseline) by week 4 and beyond.

Similarly, when predicting responders (fast or slow), the relative change from baseline to week 4 using a cut-off of ⩾28% improvement corresponds to a PPV of 82% and an NPV of 72%. This means that more than four out of five patients identified as responders are actually responders, but more than one in four patients who are identified as non-responders are actually responders. This is because baseline demographics and clinical assessments are significantly different between patients in the three trajectory classes, but are too small to be clinically useful. These results extend conclusions made by Kennedy et al.,¹⁷ who used response and remission at end of study as outcomes, rather than the full individual trajectories.

Clinical Implications of the Current Findings

The current study did not identify any baseline variables that even moderately predicted latent trajectory-class membership, although such indicators may exist. Previous studies have explored the potential for baseline variables (including individual symptoms of depression¹⁸) and early improvements to predict later disease severity as assessed by response and/or remission, but such studies failed to identify strong predictors.^18,19 As proposed by Stassen et al.,²⁰ in the current analysis we made use of the longitudinal study design, and investigated the trajectories over the whole course of the treatment period rather than basing the analysis on patients’ end-of-treatment status (of remission/response), but this approach did not reveal predictors of trajectory class. However, the current study did find that patients who were fast responders to treatment could be identified by week 2, had the best outcome and had an 88% study-completion rate. By contrast, 4 weeks of treatment were needed to reliably differentiate slow responders from non-responders. Our findings suggest that people with depression who have experienced <28% improvement by week 4 are unlikely to respond by week 8, whether treated with escitalopram or receiving placebo. It remains to be seen, however, whether such empirically derived decision rules can be used prospectively to improve patient outcomes. Specifically, are such patients more likely to benefit if they changed treatment, such as the addition of an adjunctive therapy, than if they continued to receive 4 additional weeks of antidepressant monotherapy? Additional biomarkers could improve treatment selection for an individual.

Limitations

Our analysis has several limitations. First, the model is based on data from individuals with MDD who were recruited on the basis of strict inclusion and exclusion criteria and who provided informed consent for participation in randomised placebo-controlled trials. It is not clear if our findings would hold true in a more heterogeneous group of patients with depression, such as those recruited into the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) study, or if data were used from studies with a significant level of heterogeneity. Second, our analysis was limited to studies of a single antidepressant (escitalopram) and was further limited to studies that permitted use of the maximum approved daily dose of that medication (20 mg). As molecular analyses for genetic markers were not included in this analysis, we do not know if these three trajectories of response are associated with any potential biomarkers of non-, slow and fast response.

Conclusions

The existence of three trajectory classes has clear clinical relevance, and patients in each class can be identified by their change in MADRS total score from baseline at week 2 or week 4 with relatively high NPVs. In addition, all three classes are found in both treatment groups (placebo and escitalopram), but with differences in the relative proportions of patients in each class. Finally, the results of the LLCA were consistent with the three trajectory classes found by the GMM.