Use of latent growth curve models for assessing the effects of darbepoetin alfa on hemoglobin and fatigue

Contemporary Clinical Trials 31 (2010) 172–179

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Contemporary Clinical Trials j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c o n c l i n t r i a l

Use of latent growth curve models for assessing the effects of darbepoetin alfa on hemoglobin and fatigue Donald E. Stull a,⁎, Margaret K. Vernon b, Jason C. Legg c, Hema N. Viswanathan c, Diane Fairclough d, Dennis A. Revicki b a b c d

Center for Health Outcomes Research, United BioSource Corporation, 20 Bloomsbury Square, London WC1A 2NS, UK Center for Health Outcomes Research, United BioSource Corporation, 7101 Wisconsin Ave, Suite 600, Bethesda, MD 20814, USA Amgen Inc., One Amgen Center Dr. Thousand Oaks, CA 91320-1799, USA University of Colorado, 2570 S Jackson Street, Denver, CO 80210, USA

a r t i c l e

i n f o

Article history: Received 2 April 2009 Accepted 30 December 2009 Keywords: Chemotherapy-induced anemia Darbepoetin alfa Latent growth models Patient-reported fatigue

a b s t r a c t Background: The relationship between darbepoetin alfa and fatigue in chemotherapy-induced anemia (CIA) patients is complex because of patients receiving transfusions and the mediating effect of hemoglobin. Latent growth models (LGMs) were used to examine simultaneously relationships among drug exposure, fatigue outcomes, covariates, and mediating factors. Methods: Data from four CIA studies (AMG 20010145: small cell lung cancer, n = 547; AMG 980297: lung cancer, n = 288; AMG 20000161: lymphoproliferative malignancies, n = 339; AMG 20030232: non-myeloid malignancies, n = 320) were analyzed separately. Patients reported fatigue using the FACT-Fatigue. The effect of darbepoetin alfa on FACT-F changes mediated through hemoglobin changes was examined with LGMs controlling for transfusions, age, sex, baseline ECOG performance status, and health status (EQ-5D VAS). Model fit was assessed using multiple indices including the comparative fit index (CFI). Results: Darbepoetin alfa increased hemoglobin levels which were associated with decreases in fatigue. Increases in hemoglobin were statistically significantly (p b 0.05) related to decreases in fatigue in the studies (AMG 20030145: β̂ = 0.28; AMG 980297: β̂ = 0.46; AMG 20000161: β̂ = 0.59; and AMG 20030232: β̂ = 0.39). Darbepoetin alfa statistically significantly increased hemoglobin (AMG 20010145:β̂ = 0.50, AMG 980297:β̂ = 0.53, AMG 20000161:β̂ = 0.47, and AMG 20030232:β̂ = 0.30) while controlling for covariates. Model fit was acceptable (CFI ≥ 0.89) in all studies. Conclusions: Results indicate LGMs may be a valuable statistical method for modeling complex relationships among clinical and patient reported outcomes. A statistically significant effect of darbepoetin alfa on fatigue change through hemoglobin change occurred across four studies, after modeling the effects of transfusions, age, sex, EQ-5D VAS and ECOG. © 2010 Elsevier Inc. All rights reserved.

1. Introduction

⁎ Corresponding author. 20 Bloomsbury Square, London, WC1A 2NS, UK. Tel.: +44 20 7299 4558; fax: +44 20 7299 4555. E-mail addresses: [email protected] (D.E. Stull), [email protected] (M.K. Vernon), [email protected] (J.C. Legg), [email protected] (H.N. Viswanathan), [email protected] (D. Fairclough), [email protected] (D.A. Revicki). 1551-7144/$ – see front matter © 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.cct.2009.12.006

Anemia affects 70% to 90% of cancer patients receiving concomitant myelosuppressive chemotherapy [1] and significantly impairs patient functioning, activities of daily living, and occupational functioning [2–5]. Fatigue is one of the most frequently experienced symptoms of chemotherapy induced anemia (CIA) [6–8]. Erythropoiesis stimulating agents (ESAs), namely, Epoetin alfa and darbepoetin alfa are indicated for

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the treatment of anemia in patients receiving myelosuppressive chemotherapy and have been demonstrated to increase hemoglobin levels in CIA patients [9–13]. Clinical trials involving ESAs allow for physician discretion regarding administration of red blood cell (RBC) transfusions and typically recommend transfusions when hemoglobin levels fall to 8 g/dL, which is indicative of severe anemia. Previous trials have shown that ESAs significantly reduce the need for RBC transfusions [10,11,14–17]. The effect of ESAs on patient reported fatigue is not hypothesized to be direct, since CIA treatments increase hemoglobin levels, which can then lead to decreased fatigue [9], and is difficult to examine in placebo controlled trials because of the administrations of RBC transfusions. Given that ESAs are known to reduce transfusion rates, differential transfusion rates for each treatment group can confound analyses of the effect of ESAs on fatigue. Common statistical methods for assessing the effect of treatment on fatigue in clinical trials have a number of shortcomings [18]. Comparing mean fatigue change from baseline to the end of the study between treatment groups provides an assessment of the average change in each treatment group. Analyses using overall change ignore potentially useful data captured at intermediate time points during the study. Thus, modeling the relationship between fatigue outcomes over time and ESA treatment, transfusions, and hemoglobin levels over time is of interest. Latent growth models (LGMs) relate changes over time in observations to random curves. Each subject has a curve, called the growth curve, for each variable monitored over time describing change over time. LGMs can model direct and indirect relationships among the random curve variables, covariates that can vary over time, treatment groups, and observations over time in the structural equation model (SEM) framework [18–20]. A SEM analysis involves fitting sample means and covariances of the observations to hypothesized relationships among observations, covariates, and random curve variables, resulting in an overall test of fit. The objective of this analysis was to apply latent growth curve methods to evaluate the effect of darbepoetin alfa on patient reported outcomes in four randomized placebo controlled trials. 2. Methods 2.1. Research design and subjects This analysis used clinical and patient reported outcome data from four randomized, placebo-controlled clinical trials of patients with CIA comparing darbepoetin alfa (Aranesp®; Amgen Inc., Thousand Oaks, CA) against placebo: (1) AMG 20010145, patients with extensive stage small cell lung cancer and planned multicycle platinum based chemotherapy (N = 600); (2) AMG 980297, patients with lung cancer receiving platinum containing chemotherapy (N = 320); (3) AMG 20030232, patients with non-myeloid malignancies receiving multicycle chemotherapy (multiple tumor types; N = 391); and (4) AMG 20000161, patients with lymphoprofilerative malignancies receiving chemotherapy (N = 349) [10,11,14,17]. All studies had a treatment group and a control group. Patients were randomized to experimental treatment (darbepoetin alfa) or placebo at 1:1. The primary endpoints for AMG 20010145 were change in hemoglobin and overall

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survival. Incidence of transfusions was the primary endpoint for studies AMG 980297 and AMG 20030232. For study AMG 20000161, hemoglolobin response defined as N=2 g/dL was the primary endpoint. The institutional review boards of the participating centers approved the protocols, and all patients gave written informed consent before any study specific procedures were carried out. Additional details of the studies are shown in Table 1. Inclusion criteria were similar across the clinical trials. All eligible patients were 18 years old or older and had the study defined cancer type and chemotherapy status. All patients were anemic (hemoglobin ≤ 11 g/dL) from receiving chemotherapy. Patients with anemia due to iron, folate or B12 deficiency, hemolysis, bleeding, or active infection, and those with transferrin saturation b15% or serum ferritin concentration b10 ng/mL were excluded from the study. Patients receiving an RBC transfusion within two weeks of study entry were also excluded. During the active treatment period, RBC transfusions were recommended if hemoglobin concentration decreased to ≤8.0 g/ dL. Some subjects received an RBC transfusion with hemoglobin concentration N8.0 g/dL because of signs or symptoms of severe anemia (e.g., lethargy, congestive heart failure, angina, or dyspnea). Administration of an RBC transfusion when the hemoglobin concentration was N8.0 g/dL without accompanying signs or symptoms was not recommended. Treatment durations, study treatment weeks, and timing of clinical and patient reported outcome assessment varied across the four clinical trials (Table 1). Studies were analyzed separately because of differences in cancer types and study designs. 3. Measures 3.1. Demographic and clinical characteristics Patient gender and age were recorded at baseline. In addition, the Eastern Cooperative Oncology Group (ECOG) performance status measure was recorded at baseline [21]. The ECOG measure assesses a patient's performance status using a 6-point scale ranging from 0 (“Fully active, able to carry on all pre-disease performance without restriction”) to 5 (“Dead”). Hemoglobin (g/dL) was assessed weekly. Transfusions were recorded as they were received throughout the treatment periods. The number of transfusions during the treatment period for each participant was used as a predictor of changes in hemoglobin and patient-reported fatigue outcomes to help account for changes in hemoglobin throughout the trial. 3.2. Patient reported outcome (PRO) measures Patients were administered two PRO measures: the Functional Assessment of Cancer Therapy-Fatigue (FACT-F), which assesses a patient's level of fatigue and the EuroQol Health State Index (EQ-5D), which assesses a patient's general health state. 3.2.1. FACT-F The 13-item FACT-F scale [22,23] was used in these analyses as the primary measure of patient reported fatigue. The FACT-F asks a patient to rate responses to 13 questions on fatigue and how fatigue affects their daily activities. The items

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Table 1 Study descriptions. AMG 20010145

AMG 980297

AMG 20030232

AMG 20000161

N Analyzable n a Age mean (sd) Gender, n (%) Male Female Population/ cancer type

600 547 61.0 (8.8)

391 288 61.4 (8.9)

320 320 64.1 (12.1)

349 339 64.7 (13.0)

350 (64%) 197 (36%) Extensive stage small-cell lung cancer treated with platinum plus etoposide chemotherapy

300 mcg QW for the first four weeks and 300 mcg Q3W until end of study US, Australia, Europe

114 (36%) 206 (64%) Non-myeloid malignancies receiving multicycle chemotherapy (multiple tumor types) 300 mcg Q3W

165 (49%) 174 (52%) Lymphoproliferative malignancies

Treatment regimen Location

206 (72%) 82 (28%) Lung cancer patients receiving multicycle platinum-containing chemotherapy 2.25 mcg/kg QW Australia, Canada, Europe

US and Australia

Study duration (Weeks) Treatment weeks

up to 24

16 followed by open label

16

Australia, Canada, Europe 16

1, 4, 7, 10, 13

weekly (12 weeks)

≥14 g/dl stop therapy; b 13 g/dl restart therapy

N13 g/dl stop therapy; b12 g/dl restart therapy

1, 10, 16

1, 5, 9, 13, 16

Treatment 58 (29.6%) Placebo 63 (32.3%)

Treatment 29 (16.5%) Placebo 27 (15.6%)

weekly Study drug (darbepoetin alfa or placebo) administration commenced on study day 1 immediately before first cycle of on-study chemotherapy. Patients received chemotherapy (cisplatin or carboplatin plus etoposide), every three weeks for up to 6 cycles. Study drug administration continued throughout the 6 cycles of chemotherapy and for a 3-week period after the last dose of chemotherapy. N 15 g/dl (men) stop therapy; N14 g/dl (women) N 15 g/dl (men) stop Hemoglobin stop therapy; b 13 g/dl restart therapy therapy; N14 g/dl (women) treatment stop therapy; b 13 g/dl target restart therapy Study week for 1, 7, 13, 24 1, 4, 7, 13 FACT-F assessment b Treatment 150 (50.2%) Treatment 49 (30.8%) Number with Placebo 145 (48.2%) Placebo 52 (32.3%) at least one missing FACT-F

2.25 mcg/kg QW

FACT-F, Functional Assessment of Cancer Therapy-Fatigue. a Number of patients used for analysis, based on availability of FACT-F and EuroQol Health State Index (EQ-5D) visual analog scale scores at baseline. b Week1 = baseline.

are scored from 0 (not at all) to 4 (very much). The scale score is computed by summing the item scores after reversing two items that are positively worded. The FACT-F scale scores range from 0 to 52, where higher scores represent less fatigue. 3.2.2. EQ-5D The EQ-5D is a preference based instrument designed to assess impact on health-related quality of life in five domains: mobility, self-care, usual activities, pain/discomfort, and anxiety/depression [24]. The EQ-5D contains a visual analogue scale (VAS) that asks the patient to rate their current health state from 0 to 100, where 0 represents the worst imaginable health state and 100 represents the best imaginable health state. The baseline EQ-5D VAS score was used in these analyses as a measure of baseline health status. 4. Statistical analysis The LGM framework, provides a convenient way to estimate simultaneously effects of darbepoetin alfa on changes in fatigue directly and indirectly through changes in hemoglobin levels, modeling the effect of transfusions on hemoglobin levels. Using LGMs allow us to explore differences in trajectories of change in

fatigue and hemoglobin by treatment group (darbepoetin alfa versus placebo) and the relationship between changes in hemoglobin and fatigue. The hypothesized model contains a growth curve for hemoglobin level and a growth curve for fatigue for each patient. Each growth curve is characterized by two variables: a variable for the curve at the first time point labeled as baseline and a variable for changes in the curve over time labeled slope of change (Fig. 1). It is important to note that the baseline (i.e., intercept) variable is not the value of the initial observation for a patient, but rather the value of the growth curve at the initial time point for the patient. Consequently, the baseline and slope variables have means and variances reflecting the mean intercepts and mean slopes of change. The coefficients for the baseline latent variables are fixed at 1 since the baseline is acting as an intercept to the curve and contributes the same value to the mean at every time point. The coefficients for the slope latent variables can be fixed according to the timing of the assessment points, or some can be left free to be estimated to allow for non-linearity in the growth curve [18]. Under the model assessed (Fig. 1), the baseline for FACT-F is regressed on the baseline for hemoglobin. Each baseline

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Fig. 1. Hypothesized relationships between latent growth curve variables, hemoglobin observations, and FACT-F observations. (Numbers on paths between hemoglobin and FACT-F observations at each visit and respective growth curve variables represent coefficients for measurements at each time point. One to two paths from the slopes to the visits can be freed up to allow for non-linear slopes.)

variable is hypothesized to be correlated with the corresponding slope of change variable i.e., a change in the slope variable can be related to the value of the baseline variable. For example, a higher baseline for hemoglobin variable likely is associated with a flatter slope of change since patients are treated to a specified target. Baseline hemoglobin is hypothesized to influence the slope of change for FACT-F. The baseline hemoglobin also is hypothesized to have an impact on the number of transfusions over the study. Assignment of the treatment drug is hypothesized to impact the slope for hemoglobin. The number of transfusions is hypothesized to be correlated with the slope for hemoglobin. Transfusions were modeled both as time-varying covariates and as a total count variable. Results were nearly identical perhaps because most transfusions occurred early in all trials. Use of a total count variable simplified the models and allowed for consistent modeling across trials. Lastly, we hypothesized that the slope for hemoglobin affects the slope for FACT-F. This last hypothesis was based on the assumption that the hemoglobin curve for a patient is a good predictor of the FACT-F curve and represents the effect of changes in hemoglobin on change in fatigue outcomes. Structural paths determine how the means and variances of changes in hemoglobin and fatigue are related to treatment, number of transfusions, and the covariates of EQ-5D VAS, ECOG status, age, and sex (see Fig. 2). Each path on the diagram has an associated β coefficient to be estimated that characterizes the relationship, as in regression. In addition to the correlation between the slopes of change in hemoglobin and fatigue, three additional paths relating darbepoetin alfa use, transfusions, and the slope for FACT-F were included in the model for testing. The slope of change for FACT-F was regressed on treatment drug assignment, the number of transfusions was regressed on treatment drug assignment, and FACT-F was correlated with the number of transfusions. The associated coefficients for these paths are hypothesized to be 0 since we hypothesize that treatment effect on change in FACT-F is mediated through changes in hemoglobin. We tested the working hypothesis of

these coefficients being zero in the LGM. A statistically significant value for these coefficients would indicate that we are potentially missing important variables in the model. The baseline and slope variables and the number of transfusions were regressed on the covariates. Initial descriptive analyses indicated that the growth curves for hemoglobin and/or FACT-F were not linear over time for all of the trials. Each study had its own growth curve shapes due, at least in part, to differences in protocols, cancer types, and assessment times. As an example, Fig. 1 shows the growth curve model used to analyze the data from the four trials. The numbers on the paths from the slope of the latent variables to the individual assessments represent coefficients relating the observations at each assessment point to the growth curve variables. In AMG 20010145, a linear in time growth curve would have coefficients of 0, 6, 12, and 23 on the slope latent variables. When combined with the coefficient of 1 on the baseline latent variables, a simple linear curve over time for each patient is specified. Based om preliminary analyses, we considered departures from linearity between particular assessments in the form of parameters that are free to be estimated [18]. In order to incorporate nonlinearity, some of the coefficients on the slope latent variables are estimated rather than fixed. Having the coefficients estimated by the LGM allows for departures from linearity in the growth curves between particular assessment periods in each study. Specifically, the coefficients indicated by alpha are the ones that were freely estimated in Fig. 1. In Study AMG 20010145, information on mean scores at each assessment indicated that the slopes of change increased rapidly from baseline to first assessment followed by a decrease in the rate of change. The nonlinearity can be thought of as first modeling a rise in hemoglobin and allowing for less change in hemoglobin as the level is maintained by treatments. Similarly, using the mean scores at each assessment, the curves for FACT-F were hypothesized as nonlinear from Week 1 to Week 13, but linear after that. The nonlinearity for the FACT-F allowed for an unknown change in linearity at the second assessment followed by a steady change

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Fig. 2. Hypothesized relationships between latent growth curve variables, darbepoetin alfa, and baseline covariates. (The hypothesized model for hemoglobin level and FACT-F score growth curves is shown. Baseline latent variables [circles] represent the value of the growth curve at the initial observation for each patient.)

in FACT-F as time passed. The use of nonlinear curves instead of linear curves was supported by model diagnostics. In contrast, for AMG 20000161 the curve for FACT-F was linear throughout the trial, but the curve for hemoglobin was linear from baseline through week 9 (third assessment) and then departed from a straight linear slope. There was some attrition due to death recorded in the studies. However, there was no differential dropout between the treatment and placebo groups in the 4 studies. The range of overall missing data across studies at the end of the study was 16% in AMG 20000161 and 49% in AMG 20010145. The higher attrition rate in AMG 20010145 can be attributed to the fact that the trial was conducted in patients with small-cell lung cancer with overall survival as the co-primary endpoint. The analysis was based on all available data and missing data due to death were not imputed. We explored whether missing data would affect parameter estimates in our hypothesized models by examining two methods for handling missing data. The LGMs were fit using two methods for handling missing data: listwise deletion and full information maximum likelihood (FIML) [25] in Mplus Version 5.1 [26]. Using FIML produces consistent maximum likelihood estimators when the data are missing at random and the missing data mechanism is included in the model covariates. Parameter estimates were nearly identical for both analytic approaches, though sample sizes were reduced for listwise deletion. Results of FIML are presented here. All available clinical and PRO data collected up to end of study were used. Models were evaluated using several fit indices. The fit indices detect differences in describing the data between

estimated covariances under the model and estimated covariances under alternative models. Fit indices are often used to evaluate SEMs rather than the likelihood ratio tests common in multiple regression models. The goal in evaluation is to find a model that reasonably explains the data while adhering to subject matter hypotheses and being parsimonious for clarity. The comparative fit index (CFI) measures the improvement in fit from using the hypothesized model over using a model with independence assumed among the variables. A model is considered a good improvement over the independence model if the CFI is ≥0.90, where the maximum possible value is 1.00 [27]. The root mean square error of approximation (RMSEA) measures model misspecification in comparison to the sample covariances while adjusting for model size and sample size. A model is considered well specified if RMSEA is ≤0.08 [28]. The standardized root mean residual (SRMR) measures the average squared difference between sample correlations and estimated correlations under the model. A SRMR b0.1 is considered an acceptable difference between observed and fitted correlations [27]. We conducted mixed effects regressions that are commonly used to analyze such data. Two regressions were conducted. Multiple assessments of fatigue were regressed on hemoglobin, total number of transfusions across the trial, and the baseline covariates in the first mixed effects regression. In the second mixed effects regression, multiple hemoglobin assessments were regressed on the treatment, total number of transfusions across the trial, and the baseline covariates. While these regressions are useful for assessing the overall effect of treatment on hemoglobin and fatigue, the LGM by contrast

D.E. Stull et al. / Contemporary Clinical Trials 31 (2010) 172–179

provides information about the relationship between hemoglobin and fatigue. Obtaining information on the relationship between hemoglobin and fatigue from the two regressions is difficult since it is inferred through the difference in treatment effects from the two regressions. 5. Results Results show that darbepoetin alfa significantly increased hemoglobin levels, and increased hemoglobin levels were associated with improvements in patient-reported fatigue outcomes in patients with CIA. The hypothesized LGMs across three of the four trials had acceptable fit to the data according to the CFI, RMSEA, and SRMR estimates (Table 2); study AMG 20010145 was marginal. The main paths of interest for this study (treatment to change in hemoglobin, and change in hemoglobin to change in patient-reported fatigue outcomes) were statistically significant across the four clinical trials (Table 3). Numbers reported are standardized coefficients using the STDXY standardization in Mplus 5.1. The STDXY option standardizes both the responses and predictors in the model. In all of the four trials, the slope for hemoglobin had a statistically significant (p b 0.05) relationship with the darbepoetin alfa treatment. Patients receiving darbepoetin alfa had greater increases in hemoglobin levels than patients receiving placebo as indicated by the sign on the coefficients for the slope for hemoglobin on darbepoetin alfa treatment. Also, changes in hemoglobin levels were statistically significantly related (p b 0.05) to improvements in patient reported fatigue in all 4 trials (Table 4). A positive coefficient indicates that the FACT-F score increases (indicating improvements in fatigue) as hemoglobin increases. The standardized coefficients for the statistically significant paths were of moderate effect size (Table 4). The number of transfusions received throughout the trial was used as a covariate since the number of transfusions was hypothesized to be correlated with the slope for hemoglobin and the slope for FACT-F. By including the correlations with the number of transfusions, part of the variation in hemoglobin levels and FACT-F scores across time were accounted for by transfusion information. Consequently, the effect of darbepoetin alfa directly on hemoglobin and indirectly on fatigue through hemoglobin is statistically significant after taking into account the number of transfusions. The coefficient for the slope for FACT-F regressed on darbepoetin alfa treatment was not statistically significantly different from 0 in any of the four studies, as expected. However, the correlation between the number of transfusions and the slope for FACT-F was statistically significant in AMG 20000161 and AMG 980297 and the regression coefficient of number of Table 2 Model fit statistics. Study

CFI

SRMR

RMSEA

90% RMSEA CI

AMG AMG AMG AMG

0.890 0.941 0.979 0.940

0.079 0.074 0.037 0.065

0.081 0.055 0.043 0.058

(0.070, (0.037, (0.013, (0.046,

20010145 980297 20030232 20000161

0.093) 0.073) 0.068) 0.070)

CFI, Comparative fit index; CI, Confidence interval; RMSEA, Root mean square error of approximation; SRMR, Standardized root mean residual.

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Table 3 Standardized coefficients for statistically significant paths between darbepoetin alfa to slope of change in Hemoglobin and FACT-F. Path

Standardized coefficient (standard error) AMG AMG AMG AMG 20010145 980297 20030232 20000161

Darbepoetin alfa to slope 0.501 of change in hemoglobin (0.053) Slope of change in 0.284 hemoglobin to slope of (0.100) change in FACT-F

0.526 0.301 (0.080) (0.058) 0.462 0.388 (0.137) (0.097)

0.467 (0.057) 0.594 (0.118)

FACT-F, Functional Assessment of Cancer Therapy-Fatigue.

transfusions on darbepoetin alfa use was statistically significant in AMG 20010145. These coefficients indicate that additional variables, such as disease severity, could be useful in explaining the relationship between treatment, change in hemoglobin, and change in FACT-F. Including darbepoetin alfa in the model resulted in indirect effects of 0.12 to 0.28 of the variation in fatigue outcomes (calculated by multiplying the standardized coefficient for slope for hemoglobin on darbepoetin alfa use by the standardized coefficient for slope for FACT-F on the slope for hemoglobin). The indirect effect was 0.14 in AMG 20010145 and 0.24 in AMG 980297, which were both studies of patients with lung cancer; 0.12 in AMG 20030232 in patients with nonmyeloid cancer; and 0.28 in AMG 20000161, in patients with lymphoproliferative malignancies. The minimally important difference (MID) is the smallest change in a variable that is meaningful to patients. The published MID for the FACT-F is 3.0 [23]. The average change in FACT-F from baseline to end of the study for patients receiving darbepoetin alfa treatment can be estimated using unstandardized coefficients estimated in the LGM. The estimated change in the FACT-F from baseline to the end of the study for patients receiving darbepoetin alfa was 2.9 in AMG 20020145, 1.1 in AMG 980297, 0.9 in AMG 20030232, and 3.5 in AMG 20000161. Results of the mixed effects regressions and LGM for AMG 20010145 are presented in Tables 4 and 5 for side-by-side comparisons. The coefficients are unstandardized regression coefficients in both tables. The mixed effects regressions indicate that baseline hemoglobin is significantly associated with changes in patient-reported fatigue outcomes (see Table 5). However, neither treatment nor number of transfusions over the course of the trial was significantly associated with changes in fatigue outcomes. Treatment and number of transfusions over the course of the trial were, however, highly significantly associated with changes in hemoglobin, controlling for baseline covariates (see Table 4). Thus, while there is some indication of an indirect effect of treatment on patientreported fatigue outcomes, it was seen by combining inference from two separate regressions. There are some sizeable differences in coefficients between the mixed effects regression compared with the LGMs, likely the result of the modeling measurement and time-specific error variance. 6. Discussion and conclusions Various techniques are available for examining the relationship between treatment and PROs. Meta-analyses have

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Table 4 Mixed-Effects Regression versus Latent Growth Model (LGM) of hemoglobin on darbepoetin alfa, total number of transfusions, and baseline covariates (unstandardized coefficients). Dependent variable: change in hemoglobin

Mixed effects regression Coeff.

Treatment Baseline ECOG Assessment week EQ-5D VAS Gender Age Total # of transfusions Constant Log restricted-likelihood = − 3143.6355

LGM

SE

− 0.671 0.075 − 0.145 0.060 − 0.017 0.004 0.003 0.002 − 0.032 0.077 − 0.011 0.004 − 0.364 0.033 13.666 0.320 Wald chi2(7) = 295.24 Prob N chi2 b 0.0001

z

P N |z|

95% CI

− 8.99 − 2.41 − 4.65 1.48 − 0.42 − 2.47 − 10.91 42.69

b 0.001 0.016 b 0.001 0.140 0.675 0.014 b 0.001 b 0.001

− 0.818 − 0.263 − 0.024 − 0.001 − 0.184 − 0.019 − 0.429 13.039

− 0.525 − 0.027 − 0.010 0.006 0.119 − 0.002 − 0.298 14.293

Coeff.

SE

− 1.047 0.281 – 0.001 0.216 − 0.039 − 0.413 –

0.112 0.085 – 0.003 0.108 0.007 0.059 –

increase in hemoglobin following a transfusion, the effect can be modeled as a departure from a linear trend and can be tied to a time-varying event, such as the incidence of the transfusion in the time period prior to a fatigue assessment. The findings of these analyses are consistent with clinician observations and previous research on ESAs in cancer populations. Previous clinical trials have demonstrated that darbepoetin alfa and the other ESAs reduce transfusion rates and improve hemoglobin levels in oncology patients with anemia who are undergoing chemotherapy [10–12,14–16]. Several studies have demonstrated that improvements in hemoglobin levels have concomitant effects on reducing patient reported fatigue [4,10,17,31–33]. Consistency in direction of the effect of darbepoetin alfa on changes in hemoglobin and the relationships between changes in hemoglobin and fatigue scores was found across the four clinical trials. There was variation in the size of the effect of darbepoetin alfa on fatigue and the amount of change in patient reported fatigue outcomes across the four clinical trials. These differences may be due to different inclusion criteria, different cancer types, varying chemotherapy regimens, and different fatigue assessment schedules. The largest effects were observed in the three clinical trials with more frequent assessments of patient reported fatigue. In particular, AMG 20030232 showed the weakest overall effect of darbepoetin alfa on fatigue and the smallest change in the FACT-F (0.9). AMG 20030232 also had the fewest FACT-F assessments and the longest time between the baseline and first assessment post-baseline. Including

shown that small yet significant improvements in patient reported fatigue are related to ESA use [29,30]. Often the approach to estimate the effect is to compare mean change by treatment group [4,12]. There is evidence from the LGM analysis that darbepoetin alfa improves patient reported fatigue outcomes and that this effect is mediated through increasing hemoglobin levels. Latent growth models can be used to estimate simultaneously changes in multiple variables and the relationships, direct and indirect, among those changes. Alternative methods like baseline-to-end-of-study change analyses can lose valuable information obtained at intermediary time points. Linear mixed effects models that estimate the conditional mean effect can include information from each assessment, but in the case of indirect effects, such as the present study, the common estimators from separate regression functions to analyze these effects are difficult to interpret. An LGM, however, is useful when the relationship between changes in multiple variables or variation in individual responses over time is of interest. The LGM approach is an important tool for clinical trial analysis since clinical trials often monitor changes in several variables. The interplay and variability of changes in clinical trial variables and other covariates can provide insight into the variable relationships that may not be parameterized in an analysis of the difference between means. An LGM analysis is flexible since model building approaches used in regression are available. Nonlinearity in a variable's change can be built into the growth curve models. For example, if there is a steep

Table 5 Mixed-Effects Regression versus Latent Growth Model (LGM) of fatigue on darbepoetin alfa, hemoglobin, total number of transfusions, and baseline covariates (unstandardized coefficients). Dependent variable: change in fatigue

Mixed effects regression Coeff.

Treatment Baseline hemoglobin Baseline ECOG Assessment week EQ-5D VAS Gender Age Total # of transfusions Constant Log restricted-likelihood = − 6284.6077

SE

0.747 0.597 0.621 0.133 − 2.790 0.474 0.001 0.019 0.335 0.011 1.536 0.615 − 0.035 0.034 − 0.411 0.265 4.526 3.035 Wald chi2(8) = 1165.27 Prob N chi2 b 0.0001

LGM z

P N |z|

95% CI

1.25 4.68 − 5.88 0.05 31.31 2.5 − 1.02 − 1.55 1.49

0.211 b 0.001 b 0.001 0.957 b 0.001 0.012 0.307 0.121 0.136

− 0.423 0.361 − 3.720 − 0.036 0.314 0.331 − 0.102 − 0.931 − 1.422

1.918 0.881 − 1.861 0.038 0.356 2.740 0.0321 0.109 10.475

Coeff.

SE

1.021 1.051 0.114 – − 0.006 − 0.914 0.048 − 0.128 –

0.559 0.038 0.392 – 0.011 0.467 0.031 0.228 –

D.E. Stull et al. / Contemporary Clinical Trials 31 (2010) 172–179

frequent assessments of fatigue outcomes can yield gains in precision on coefficient and slope parameter estimates and can result in improved clarity and accuracy in the models describing the relationship between darbepoetin alfa use and patient reported outcomes. The spacing of the quality of life assessments in AMG 20030232 makes it difficult to capture changes in fatigue scores and the relationship of the changes to treatment. In addition to these factors, there may be some differential response to treatment. Specifically, changes in fatigue scores for patients receiving darbepoetin alfa were mixed across the trials. The variability in hemoglobin and FACT-F scores suggests that there may be subgroups of patients who are less likely to respond to treatment or transfusions. This subset of the population may not fit the proposed LGM well and including them in the model decreases the estimated effect of darbepoetin alfa. Understanding the factors that can predict clinically effective response and hypo-response in patients receiving ESAs is an important future direction for study. The analysis of trial data using LGM offers a valuable opportunity to estimate the impact of ESAs on patient reported fatigue in future clinical trials and patient level meta-analyses. References [1] Groopman JE, Itri LM. Chemotherapy-induced anemia in adults: incidence and treatment. J Natl Cancer Inst 1999;91:1616–34. [2] Curt GA, Breitbart W, Cella D, et al. Impact of cancer-related fatigue on the lives of patients: new findings from the Fatigue Coalition. Oncologist 2000;5:353–60. [3] Hamilton J, Butler L, Wagenaar H, et al. The impact and management of cancer-related fatigue on patients and families. Can Oncol Nurs J 2001;11: 192–8. [4] Cella D, Kallich J, McDermott A, Xu X. The longitudinal relationship of hemoglobin, fatigue and quality of life in anemic cancer patients: results from five randomized clinical trials. Ann Oncol 2004;15:979–86. [5] Morrow GR, Shelke AR, Roscoe JA, Hickok JT, Mustain K. Management of cancer-related fatigue. Cancer Invest 2005;23:229–39. [6] Henry DH, Viswanathan HN, Elkin EP, Traina S, Wade S, Cella D. Symptoms and treatment burden associated with cancer treatment: results from a cross-sectional national survey in the U.S. Support Care Cancer 2008;16: 791–801. [7] Cella D, Davis K, Breitbart W, Curt G, for the Fatigue Coalition. Cancerrelated fatigue: prevalence of proposed diagnostic criteria in a United States sample of cancer survivors. J Clin Oncol 2001;19:3385–91. [8] Irvine D, Vincent L, Graydon JE Bubela N, Thompson L. The prevalence and correlates of fatigue in patients receiving treatment with chemotherapy and radiotherapy. A comparison with the fatigue experienced by healthy individuals. Cancer Nurs 1994;17:367–78. [9] Engert A. Recombinant human erythropoietin in oncology: current status and further developments. Ann Oncol 2005;16:1584–95. [10] Hedenus M, Adriansson M, San Miguel J, et al. Efficacy and safety of darbepoetin alfa in anaemic patients with lymphoproliferative malignancies: a randomized, double-blind, placebo-controlled study. Br J Haematol 2003;122:394–403. [11] Pirker R, Ramlau RA, Schuette W, et al. Safety and efficacy of darbepoetin alpha in previously untreated extensive-stage small-cell lung cancer treated with platinum plus etoposide. J Clin Oncol 2008;26:2342–9. [12] Chang J, Couture F, Young S, McWatters K-L, Lau CY. Weekly epoetin alfa maintains hemoglobin, improves quality of life, and reduces transfusion in breast cancer patients receiving chemotherapy. J Clin Oncol 2005;23: 2597–605.

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