Comparing continuous and binary group-based trajectory modeling using statin medication adherence data

Ryan P Hickson; Izabela E Annis; Ley A Killeya-Jones; Gang Fang

doi:10.1097/MLR.0000000000001625

. Author manuscript; available in PMC: 2022 Nov 1.

Published in final edited form as: Med Care. 2021 Nov 1;59(11):997–1005. doi: 10.1097/MLR.0000000000001625

Comparing continuous and binary group-based trajectory modeling using statin medication adherence data

Ryan P Hickson ^1,^2,³, Izabela E Annis ¹, Ley A Killeya-Jones ¹, Gang Fang ¹

PMCID: PMC8525904 NIHMSID: NIHMS1734446 PMID: 34644285

Abstract

Background:

Of 58 medication adherence group-based trajectory modeling (GBTM) published studies, 74% used binary and 26% used continuous GBTM. Few studies provided rationale for this choice. No medication adherence studies have compared continuous and binary GBTM.

Objective:

Assess whether continuous versus binary GBTM (1) impacts adherence trajectory shapes, and (2) results in differential classification of patients into adherence groups.

Methods:

Patients were prevalent statin users with myocardial infarction hospitalization, 66+ years old, and continuously enrolled in fee-for-service Medicare. Statin medication adherence was measured 6 months pre-hospitalization using administrative claims. Final GBTM specifications beyond default settings were selected using a previously defined standardized procedure and applied separately to continuous and binary (proportion of days covered ≥0.80) medication adherence measures. Assignment to adherence groups was compared between continuous and binary models using percent agreement of patient classification and the kappa coefficient.

Results:

Among 113,296 prevalent statin users, 4 adherence groups were identified in both models. Three groups were consistent: persistently adherent, progressively nonadherent, and persistently nonadherent. The fourth continuous group was moderately adherent (progressively adherent in binary model). When comparing patient assignment into adherence groups between continuous and binary trajectory models, only 78.4% of patients were categorized into comparable groups (kappa 0.641; 95% confidence interval: 0.638–0.645). Agreement was highest in the persistently adherent group (~94%).

Conclusions:

Continuous and binary trajectory models are conceptually different measures of medication adherence. Choice between these approaches should be guided by study objectives and the role of medication adherence within the study—exposure, outcome, or confounder.

Keywords: Group-Based Trajectory Modeling, Health Behavior, Medication Adherence, Methods, Statistical Distributions

Introduction

Group-based trajectory modeling (GBTM) is a statistical method that categorizes individuals into groups with similar patterns of a longitudinal measure.^1,2 Originally developed in criminology and behavioral psychology,^1–6 GBTM has become increasingly popular in the medication adherence literature to better capture complex longitudinal adherence patterns.^7–17 Most medication adherence GBTM studies describe their process for selecting the number of adherence groups, but other practical decisions—such as functional form used to model medication adherence as a function of time (e.g. constant, linear, quadratic, etc.)—may alter the shape of adherence trajectories.¹⁸ In our previous work, we proposed a more standardized approach to making these decisions and selecting a final trajectory model.¹⁸ However, using continuous versus binary GBTM for medication adherence may also affect adherence trajectory shapes and patient assignment into adherence groups.

The proportion of days covered (PDC) is a standard summary measure in prescription claims data that measures adherence as the proportion of days that a patient had medication available, with values between 0 and 1 inclusive. For example, a patient with medication available for 270 days in a 360-day measurement period has PDC=270/360=0.75. Previous research has examined the pros and cons of dichotomizing PDC into a binary measure of being adherent (e.g. PDC ≥0.80) versus nonadherent,^19,20 as well as what that dichotomized cutoff should be.²¹ However, to our knowledge, no studies have compared using continuous adherence versus binary indicators of being adherent to probabilistically assign patients to adherence trajectory groups; e.g., when assigning patients to adherence trajectory groups, no research has compared using (A) 6 30-day continuous PDC measures between 0 and 1 versus (B) 6 binary indicators of monthly PDC ≥0.80 (≥24/30 days). See Appendix 1, Supplemental Digital Content 1 for a more detailed example comparing single summary measures and GBTM.

In a literature review updated in January 2021, 58 English-language peer-reviewed studies using GBTM to evaluate medication adherence and other medication utilization behaviors were identified; 43 used binary GBTM and 15 used continuous GBTM (see Appendix 2, Supplemental Digital Content 2 for further details). Besides studies where binary GBTM was the only option given how medication utilization was measured,^{14–17,22–28} very few studies provided a reasoned argument for choosing continuous versus binary GBTM.^7–9,12,13

Therefore, using our previously described approach to select a final GBTM specification,¹⁸ our objectives were to assess whether GBTM using continuous versus binary models (1) impacts the shape of adherence trajectories, and (2) results in differential classification of patients into adherence groups.

Methods

A 100% sample of US Medicare acute myocardial infarction (AMI) hospitalizations—with 2007–2011 enrollment summary, medical encounters, and prescription Part D event files—was used to identify a previously described cohort.²⁹ Patients met these eligibility criteria: 2008–2010 AMI hospitalization; ≥66 years old; survived hospitalization; 12 months pre-AMI continuous Medicare fee-for-service enrollment; and statin prescription fill within 12 months pre-AMI. The University of North Carolina at Chapel Hill Institutional Review Board approved this study.

Statin Adherence

Using PDC and adjusting for stockpiling and hospitalizations,^18,29 Part D prescription claims were used to measure adherence to any statin (switching allowed) in the 180 days pre-AMI hospital admission. For GBTM, adherence was measured in 30-day intervals over 6 months pre-AMI. During each 30-day interval, we measured adherence 2 different ways: (1) continuous adherence (PDC between 0 and 1 inclusive), and (2) binary indicator of being adherent (PDC ≥0.80). “New users” (first statin prescription <180 days pre-AMI) had missing adherence values before their first fill date (i.e., numerator and denominator were not counted).

Data Analysis

Group-Based Trajectory Modeling

Group-based trajectory modeling (GBTM) is an extension of finite mixture modeling used to describe the dynamic nature of repeated longitudinal measures like medication adherence and categorizes individuals into latent trajectory groups with similar patterns of the time-varying measure.^1–3,6,8 “Proc Traj,” a free downloadable SAS (Version 9.4) add-on package, was used.^30,31 Two categories of regression models are estimated simultaneously in GBTM: (1) a multinomial logit model estimating patient probabilities for group assignment, and (2) models estimating longitudinal trajectory shapes (e.g. adherence as a function of time).^2,8 For category (2), time is modeled with polynomials from zero-order (constant) to fourth-order (quartic), with third-order (cubic) being default.

GBTM Model-Building Procedure

To identify medication adherence trajectories, we used two separate approaches: (1) continuous monthly PDC using the censored normal (i.e. tobit) distribution, and (2) monthly binary indicators of being adherent using the logit distribution. Our medication adherence GBTM model-building procedure—built upon Nagin’s recommendations³—is outlined below.¹⁸ This procedure was applied separately to continuous and binary models.

All GBTM used 6 monthly adherence measures. We first modeled adherence using 2–7 groups, using second-order (quadratic) polynomials for all groups’ functional forms since we had fewer than 12 time points.^32,33 We then used Bayesian information criterion (BIC) and Bayes Factor to choose the optimal number of groups.^3,30 If these indices continued to improve with the addition of more groups,^6,8,12 then clinical meaningfulness was used to determine if a model with fewer than 7 groups should be chosen.¹⁸

After selecting the optimal number of groups, combinations of all plausible functional forms were specified—from zero-order (constant) to second-order (quadratic)—holding all other model specifications constant. Functional form combinations were limited based on content knowledge³ (e.g. constant for persistently adherent patients) and trajectory shapes from the all-quadratic models used to identify the number of groups. This approach is computationally practical: testing all combinations of zero- to second-order functional forms for 2–7 groups would require testing 3,276 (3²+3³+…+3⁷) different models. Models were then sorted by BIC from best fit to worst (see Appendix Table 1, Supplemental Digital Content 3 for BIC formula used in “Proc Traj”).^3,30

The model with the best fit according to the BIC meeting the following criteria was chosen as the final trajectory model: (1) p-values for model parameters <0.05 for each group; (2) ≥5% of population assigned to each adherence group;³⁴ (3) no polynomial overfitting (e.g. an essentially horizontal line modeled with quadratic polynomial); and (4) upon visual inspection, confidence intervals have a consistent width over time for each adherence group. For criterion (1), only the highest order polynomial needed a p-value <0.05; e.g., with the equation PDC = β₀ + β₁t + β₂t², where PDC is adherence and t is time, p<0.05 was only required for β₂.

Assessing Final GBTM Model Fitness

After selecting the final continuous trajectory model and the final binary trajectory model, we evaluated model fitness for each. Three of Nagin’s diagnostic criteria were applied: (1) the distribution of maximum posterior probabilities (average ≥0.7 in all groups); (2) the odds of correct classification (OCC >5.0 for all groups); and (3) comparison of (a) proportion of population estimated from model to belong to each group with (b) proportion of sample assigned to each group by maximum posterior probability rule (similar values suggest good model fit).³ Posterior probabilities estimate the likelihood of a patient belonging to each group in the model. We additionally calculated relative entropy, a measure of uncertainty in group classification for the entire model bound between 0 and 1 (high certainty ≥0.8, medium certainty 0.6–0.8, low certainty 0.4–0.6).^4,33–37 Finally, we evaluated spaghetti plots for a random sample of 200 patients within each group from the final models; a single spaghetti plot “strand” represents the longitudinal adherence for a single patient assigned to the trajectory group.^18,37,38

Comparing continuous and binary GBTM

The number of groups and overall shape of trajectories were qualitatively compared between the final continuous and binary models. For analogous groups in the continuous and binary models, the proportion of patients and average PDC in each group were compared. Finally, patient categorization into adherence groups was compared between the final continuous and final binary trajectory models using a kappa coefficient with 95% confidence interval (CI) and an “agreement plot,” which shows how many patients were assigned to similar adherence groups using the two GBTM approaches.³⁹

Results

Overall, 113,296 prevalent statin users were included.²⁹ Most patients were 66–85 years old (84.5%), White (84.3%), and female (54.3%); 10.1% were “new users”. Of 369,846 statin fills during the 6-month pre-AMI measurement period, 79.9% and 15.8% were 30- and 90-day fills, respectively.

Selecting Final GBTM Specifications

The final 4-group continuous trajectory model was previously described (as well as the 5-group model).¹⁸ The next section focuses on the selection process for the final binary trajectory model.

Similar to the continuous model, the BIC and Bayes Factor for the binary model continued to improve when adding more groups (Appendix Table 1, Supplemental Digital Content 3). Upon visual inspection (Appendix Figure 1, Supplemental Digital Content 4), we decided the 4-group binary model was the most clinically meaningful. The 5-group binary model was chosen as the second most meaningful. As in our previous study, 44 different combinations of specifications (functional forms) were modeled for the binary 4-group trajectory model (178 combinations for 5-group model).

The final 4-group continuous and binary models are presented in Figures 1A and 1B, respectively. No 5-group models met all model selection criteria; models with the best BIC fit that met all criteria except “no polynomial overfitting” were selected for final 5-group models (Appendix Figure 2, Supplemental Digital Content 5).

Figure 1. — Sample in group represents percent of patients assigned to group by maximum posterior probability rule. Population in group represents percent of patients estimated by model to be in adherence group (i.e. estimated group probabilities). The final 4-group continuous model (A) used the censored normal distribution. Predicted adherence and 95% CIs are plotted for each group. Functional forms (2 [quadratic], 1 [linear], 0 [constant]) for the persistently adherent, moderately adherent, progressively nonadherent, and persistently nonadherent groups, respectively: 0/0/1/0. The final 4-group binary model (B) used the logit distribution. Predicted probability of being adherent (i.e. PDC ≥0.80) and 95% CIs are plotted for each group. Functional forms for the persistently adherent, progressively adherent, progressively nonadherent, and persistently nonadherent groups, respectively: 0/1/1/0. Figure 1A is reprinted with permission from Hickson et al.¹⁸

Abbreviations: PDC, proportion of days covered; AMI, acute myocardial infarction; CI, confidence interval; IQR, interquartile range.

Assessing Final Model Fitness

The average of maximum posterior probabilities used for group assignment was ≥0.7 for all groups in both models, suggesting good model fitness (Figure 2).³ In the continuous model, more than 75% of patients in the persistently adherent and persistently nonadherent groups had posterior probabilities >0.9 (Figure 2A). However, posterior probabilities for the moderately adherent and progressively nonadherent groups were lower (Figure 2A), suggesting less certainty in patient assignment to these groups. The posterior probabilities were also lower for the binary model (Figure 2B) than the continuous model, suggesting less certainty in patients’ group assignments in the binary model. Similarly, the OCC were well above 5.0 in all groups in both models, suggesting good model fitness;³ however, the OCC were lower in the binary group, again suggesting less certainty in group assignments in the binary than the continuous model. Finally, the continuous model had a relative entropy of 0.870, suggesting high certainty in group classification; the binary model had a relative entropy of 0.757, suggesting medium certainty.^35,36 See Appendix Figure 3, Supplemental Digital Content 6 for 5-group results.

Figure 2. — Model fitness measures for the final 4-group continuous trajectory model (A) and binary trajectory model (B). Each patient is only represented in the group with their highest posterior probability (i.e. the maximum posterior probability rule). Standard rules of box-and-whisker plots were followed: middle line=median; x=mean; colored box=IQR; circles=outliers (>1.5*IQR below lower quartile or above upper quartile). Mean posterior probability ≥0.7 and OCC >5.0 for all groups suggests good GBTM model fitness.

Abbreviations: IQR, interquartile range; OCC, odds of correct classification; GBTM, group-based trajectory modeling.

Spaghetti plots for the 4-group continuous trajectory model (Figure 3) were previously presented and described.¹⁸ Briefly, individual patient adherence patterns in the persistently adherent (Figure 3A) and persistently nonadherent (Figure 3C) groups were concentrated close to group averages. This was not true for the other groups, but patients in the progressively nonadherent group (Figure 3D) did appear to have a consistent pattern of statin discontinuation. See Appendix Figure 4, Supplemental Digital Content 7 for 5-group continuous model spaghetti plots.

For the binary model, all group averages from spaghetti plots (Figure 4) were similar to trajectories from the binary model (Figure 1B). Individual patient adherent/nonadherent patterns in the binary spaghetti plots were weighted by the proportion of the group’s randomly selected 200 patients who followed that longitudinal pattern (Figure 4). Since binary GBTM models adherence as 0s (nonadherent) and 1s (adherent) to determine a probability of being adherent, group averages in the binary model spaghetti plots do not directly map to individual patient adherent/nonadherent patterns. See Appendix Figure 5, Supplemental Digital Content 8 for 5-group binary model spaghetti plots.

Comparing Continuous and Binary GBTM

When comparing continuous and binary trajectory models, the y-axes take on different meanings: the y-axis for the continuous model is the actual PDC (Figure 1A), while the y-axis for the binary model is the probability of being adherent (Figure 1B). Upon visual inspection, 3 groups appeared similar (persistently adherent, progressively nonadherent, and persistently nonadherent groups); however, the moderately adherent group from the continuous model was replaced by the progressively adherent group in the binary model. The sample proportion classified as persistently adherent was 59% and 58% in the continuous and binary models, respectively. However, the proportion of patients classified into the other groups was inconsistent between continuous and binary models. Additionally, while the average PDC was consistent for most groups, the average PDC differed between models for the progressively nonadherent groups.

Overall, 78.4% of patients were categorized into comparable groups between the two trajectory methods (Figure 5). The kappa coefficient was 0.641 (95% CI: 0.638–0.645), suggesting good agreement.^40,41 There was ~94% agreement between continuous and binary GBTM when classifying patients as persistently adherent. However, the average agreement percentages for persistently nonadherent and progressively nonadherent groups were 75.6% and 39.9%, respectively. See Appendix Figure 6, Supplemental Digital Content 9 for the 5-group agreement plot.

Discussion

When the same model-building procedure was applied to continuous and binary GBTM of statin medication adherence, several differences were observed. Even though continuous and binary trajectory models had the same number of groups and trajectories that appeared mostly similar, many patients were classified into different adherence groups between the 2 models; this was especially true among patients not assigned to the persistently adherent group. Also, the average adherence was vastly different between progressively nonadherent groups in the continuous and binary models even though their trajectories appeared visually similar. Spaghetti plots from the binary model showed that group averages for the probability of being adherent do not map directly to individual patient adherent/nonadherent values; trajectories from binary GBTM should be interpreted as the average probability of being adherent or the proportion of patients who will be adherent over time, not as the average of the actual longitudinal adherence patterns of those patients. Finally, model diagnostics of posterior probabilities, OCC, and relative entropy suggested greater certainty in group assignment and better model fitness in the continuous model than the binary model.

Of note, the interpretation of each model was different: the continuous model estimated average monthly PDC, whereas the binary model estimated the monthly probability of being adherent (PDC ≥0.80 in our study). Beyond this fact, when comparing patient categorization between models, only 78% of patients were categorized into comparable adherence groups, providing further evidence that these models represent inherently different measures of medication adherence. Nearly 60% of our sample were persistently adherent—the group with the greatest classification agreement between continuous and binary GBTM. Adherence to preventive therapies like statins is often poor, with up to 50% of patients discontinuing therapy within 12 months.⁴² Since study inclusion was conditional on filling a statin prescription, patients who had already discontinued statin therapy >12 months pre-AMI were excluded. In a new user study, the differential classification of patients into adherence groups between continuous and binary trajectory models may be an even greater concern.

Greater clarity and attention to detail is needed in the medication adherence GBTM literature. For example, one study used continuous GBTM to assess quarter-year adherence to glaucoma medications⁴³ and cited Franklin et al for their rationale.⁸ However, Franklin et al used binary GBTM; authors of the former article may have used the C-statistic from the simple continuous PDC measure in Table 1 of the Franklin paper to defend this decision, but, as Franklin et al explained, using a single adherence measure for the entire period (each patient has one adherence value held constant during the measurement period, but each patient has their own adherence value) is conceptually different than using continuous adherence measures in GBTM (adherence can change over time, but patients within a group assumed to have the same adherence). In other papers, it was difficult to determine if continuous or binary GBTM was used. Some papers mislabeled axes when using binary GBTM and used language suggesting they were directly modeling longitudinal adherence (as opposed to longitudinal probabilities of being adherent).^11,17 We recommend researchers explicitly state whether they used the censored normal or logit distributions and use clear language that appropriately describes the specific medication adherence measure modeled.

Given that continuous and binary trajectory models represent inherently different medication adherence measures, which model should be used? Franklin et al. suggested that GBTM may be more adept than standard measures at identifying specific types of nonadherence.⁸ Combining this information with Nagin’s recommendation that content knowledge is important for model selection,³ we suggest using study objectives to guide the decision of using continuous or binary trajectory models. We would argue that continuous trajectory models should be chosen in most scenarios, especially if the study purpose is to understand medication adherence trajectories as health behaviors of individual patients within a group or to develop/evaluate an intervention. As observed in spaghetti plots, the average adherence observed in continuous trajectories can directly map to homogeneous individual patient longitudinal adherence behaviors when certainty in patient classification is high.

Results from this study could be used to help develop and evaluate interventions when patients taking a preventative medication experience the negative event they were trying to prevent.^29,44 For persistently adherent patients, we want to develop an intervention implemented during or shortly after the index AMI hospitalization that reinforces the importance of continued adherence post-AMI. The choice between continuous and binary GBTM seems to make little difference when classifying these patients. For patients who were persistently nonadherent or progressively nonadherent, an intervention that leads to improved post-AMI adherence is desired, but different interventions may be needed to improve adherence in patients who discontinued statins months ago versus patients who just discontinued statins and then experienced an AMI. Given the greater classification certainty with continuous GBTM when assigning patients to these important adherence groups, we would hypothesize that continuous GBTM classifications may lead to a more efficient use of resources when implementing this hypothetical tailored intervention.

Binary trajectory models may be favored when investigating the relationship between adherence and outcomes, especially with a well-established cutoff for an adherence-outcome association in a given clinical area (e.g. PDC ≥0.80); however, this assumes no dose-response relationship with lower adherence (e.g. PDC 0.40–0.80 versus PDC <0.40).⁴⁴ While using binary⁴⁵ or categorical^29,44 cutoffs makes sense for simple summary adherence measures in terms of interpretability and because policies and clinical decision-making often use cutoffs, interpreting binary GBTM can be difficult. For example, patients are assigned to a group with a varying probability of adherence over time, and this group assignment is then attributed to a risk of experiencing the outcome of interest. But during each measurement period, individual patients are either adherent (PDC ≥0.80) or nonadherent (PDC <0.80)—they do not have an individual probability of being adherent. Given the difficulty in interpreting the outcome risk attributed to a changing probability of being adherent—in addition to the loss of information from dichotomization¹⁹—we would argue that even when investigating the relationship between medication adherence and clinical outcomes, continuous GBTM may be preferred.

With adherence to multiple medications, the simplicity of using binary GBTM (adherent to all versus nonadherent to at least one) may be preferred. However, other options may provide additional information about the adherence behavior of interest for the study, such as the zero-inflated Poisson distribution for number of medications adherent to or joint-GBTM using continuous PDC.⁴⁶

“Continuous” PDC—a proportion bound between 0 and 1—is likely to violate the censored normal distributional assumption. It is unclear how much this violation matters, but it may be worth investigating in the future. Even with this distributional assumption violation, posterior probabilities suggested better model fitness with continuous than binary GBTM in this study, even when 14.6% and 54.0% of person-month PDC values equaled 0 and 1, respectively. A post-hoc evaluation of arcsine-transformed PDC data⁴⁷ also appeared to violate the censored normal distributional assumption (Appendix Figure 7, Supplemental Digital Content 10). Using a zero- and one-inflated beta distribution for GBTM proportion data may be a more promising solution to this issue.⁴⁸

Limitations

Our results for prevalent users of a preventative medication in the 6 months before a hospitalization may not be generalizable to other GBTM adherence studies (e.g. study indexed on prescription fill looking forward in time, more time points, new users, non-preventative medication, other clinical scenarios). Also, administrative claims may overestimate adherence if patients fill but do not take medications and underestimate adherence if patients fill medications outside of their prescription plan. However, prescription claims have good validity and correlation with other adherence measures,⁴⁹ and out-of-plan prescription fills are not common among Part D beneficiaries.⁵⁰

Although our GBTM approach attempted to use objective rules to select a final model, the BIC and Bayes Factor were not useful in identifying the optimal number of adherence groups,^6,8,12 requiring a subjective approach using clinical/methodologic expertise. Because our findings may be heavily dependent on this subjective decision, we presented results for a scenario where a slightly different subjective decision to use 5 groups was made early in the GBTM model-building procedure. The overarching findings from 4-group and 5-group (appendix) models were similar.

Conclusions

To our knowledge, this is the first medication adherence study comparing continuous and binary GBTM. Both approaches use a longitudinal repeated measure to create a categorical variable and assign patients to adherence trajectory groups. However, continuous and binary GBTM produce inherently different measures of medication adherence; the choice between these approaches should be clearly communicated and guided by both study objectives and the specific role that medication adherence plays within the study (i.e. as an exposure, outcome, or confounder).

Supplementary Material

Supplemental Digital Content.doc

Appendix 1, Supplemental Digital Content 1. Example describing the difference between (1) GBTM to probabilistically assign patients to adherence groups, and (2) single summary adherence measures.

Appendix 2, Supplemental Digital Content 2. Previously published GBTM peer-reviewed studies and their use of continuous vs. binary trajectory models.

Appendix Table 1, Supplemental Digital Content 3. Bayesian information criterion (BIC) and Bayes Factor for 2- to 7-group adherence trajectory models fit with quadratic polynomials.

Appendix Figure 1, Supplemental Digital Content 4. Binary trajectory models fit with quadratic polynomials to identify appropriate number of groups.

Appendix Figure 2, Supplemental Digital Content 5. Final 5-group trajectory models.

Appendix Figure 3, Supplemental Digital Content 6. Assessment of final model fitness for 5-group trajectory models: distribution of maximum posterior probabilities, odds of correct classification, and relative entropy.

Appendix Figure 4, Supplemental Digital Content 7. Spaghetti plots of individual adherence (continuous PDC) patterns in the final 5-group continuous trajectory model.

Appendix Figure 5, Supplemental Digital Content 8. Spaghetti plots of individual adherent/nonadherent (binary PDC ≥0.80) patterns in the final 5-group binary trajectory model.

Appendix Figure 6, Supplemental Digital Content 9. Agreement plot comparing patient categorization into adherence groups between the 5-group continuous and 5-group binary trajectory models.

Appendix Figure 7, Supplemental Digital Content 10. Person-month distributions of continuous PDC and arcsine-transformed PDC in the full cohort and by adherence groups from final continuous GBTM specification.

NIHMS1734446-supplement-Supplemental_Digital_Content_doc.docx^{(2.1MB, docx)}

Acknowledgments

The authors would like to thank Stacie B Dusetzina, PhD and Maarit Jaana Korhonen, LicSci(Pharm), PhD for feedback on their previous experiences working with trajectory models and feedback on earlier versions of this work.

Funding

This study was supported in part by the NIH National Institute on Aging (NIA) grant 1R01AG046267-01A1 (PI: Fang) and 1R21AG043668-01A1 (PI: Fang). Dr. Hickson received support from the NIH National Heart, Lung, and Blood Institute (NHLBI) (NRSA Training Grant No. 4T32HL007055-42) as a post-doctoral research trainee with the Cardiovascular Disease Epidemiology Program at the University of North Carolina at Chapel Hill, the American Foundation for Pharmaceutical Education (AFPE) as a 2015 Phi Lambda Sigma First Year Graduate School Fellow, and AFPE as a 2018 Pre-Doctoral Fellow in Health Outcome Disparities. At the time of submission, Dr. Hickson was supported as a Postdoctoral Fellow in Advanced Geriatrics with the Geriatric Research, Education, and Clinical Center at the Veterans Affairs Healthcare System, Pittsburgh, PA. The contents do not represent the views of the U.S. Department of Veterans Affairs or the United States Government.

Footnotes

Conflicts of interest

The authors declare no conflicts of interest.

Previous presentations

An earlier version of this research was presented at the 2017 International Conference on Pharmacoepidemiology & Therapeutic Risk Management (ICPE) in Montreal, Canada.

References

1.Nagin DS. Group-based trajectory modeling: an overview. Annals of nutrition & metabolism. 2014;65(2–3):205–210. [DOI] [PubMed] [Google Scholar]
2.Nagin DS. Analyzing developmental trajectories: A semiparametric, group-based approach. Psychological methods. 1999;4(2):139. [DOI] [PubMed] [Google Scholar]
3.Nagin D Group-based modeling of development. Harvard University Press; 2005. [Google Scholar]
4.Nagin DS, Odgers CL. Group-based trajectory modeling in clinical research. Annual review of clinical psychology. 2010;6:109–138. [DOI] [PubMed] [Google Scholar]
5.Nagin DS, Odgers CL. Group-based trajectory modeling (nearly) two decades later. Journal of quantitative criminology. 2010;26(4):445–453. [DOI] [PMC free article] [PubMed] [Google Scholar]
6.Nagin DS, Tremblay RE. Analyzing developmental trajectories of distinct but related behaviors: a group-based method. Psychol Methods. 2001;6(1):18–34. [DOI] [PubMed] [Google Scholar]
7.Franklin JM, Krumme AA, Tong AY, et al. Association between trajectories of statin adherence and subsequent cardiovascular events. Pharmacoepidemiology and drug safety. 2015;24(10):1105–1113. [DOI] [PubMed] [Google Scholar]
8.Franklin JM, Shrank WH, Pakes J, et al. Group-based trajectory models: a new approach to classifying and predicting long-term medication adherence. Medical care. 2013;51(9):789–796. [DOI] [PubMed] [Google Scholar]
9.Lambert-Côté L, Bouhnik AD, Bendiane MK, et al. Adherence trajectories of adjuvant endocrine therapy in the five years after its initiation among women with non-metastatic breast cancer: a cohort study using administrative databases. Breast Cancer Res Treat. 2020;180(3):777–790. [DOI] [PubMed] [Google Scholar]
10.Modi AC, Rausch JR, Glauser TA. Patterns of nonadherence to antiepileptic drug therapy in children with newly diagnosed epilepsy. Jama. 2011;305(16):1669–1676. [DOI] [PMC free article] [PubMed] [Google Scholar]
11.Vadhariya A, Fleming ML, Johnson ML, et al. Group-Based Trajectory Models to Identify Sociodemographic and Clinical Predictors of Adherence Patterns to Statin Therapy Among Older Adults. Am Health Drug Benefits. 2019;12(4):202–211. [PMC free article] [PubMed] [Google Scholar]
12.Winn AN, Dusetzina SB. The association between trajectories of endocrine therapy adherence and mortality among women with breast cancer. Pharmacoepidemiology and drug safety. 2016;25(8):953–959. [DOI] [PubMed] [Google Scholar]
13.Winn AN, Fergestrom NM, Neuner JM. Using Group-based Trajectory Models and Propensity Score Weighting to Detect Heterogeneous Treatment Effects: The Case Study of Generic Hormonal Therapy for Women With Breast Cancer. Medical care. 2019;57(1):85–93. [DOI] [PMC free article] [PubMed] [Google Scholar]
14.Greenley RN, Karazsia B, Schurman JV, et al. Trajectories of oral medication adherence in youth with inflammatory bowel disease. Health Psychol. 2015;34(5):514–521. [DOI] [PubMed] [Google Scholar]
15.Gueorguieva R, Wu R, Krystal JH, Donovan D, O’Malley SS. Temporal patterns of adherence to medications and behavioral treatment and their relationship to patient characteristics and treatment response. Addictive behaviors. 2013;38(5):2119–2127. [DOI] [PMC free article] [PubMed] [Google Scholar]
16.Lo-Ciganic WH, Donohue JM, Kim JY, et al. Adherence trajectories of buprenorphine therapy among pregnant women in a large state Medicaid program in the United States. Pharmacoepidemiology and drug safety. 2019;28(1):80–89. [DOI] [PMC free article] [PubMed] [Google Scholar]
17.van Boven JFM, Koponen M, Lalic S, et al. Trajectory Analyses of Adherence Patterns in a Real-Life Moderate to Severe Asthma Population. J Allergy Clin Immunol Pract. 2020;8(6):1961–1969.e1966. [DOI] [PubMed] [Google Scholar]
18.Hickson RP, Annis IE, Killeya-Jones LA, Fang G. Opening the black box of the group-based trajectory modeling process to analyze medication adherence patterns: An example using real-world statin adherence data. Pharmacoepidemiology and drug safety. 2020;29(3):357–362. [DOI] [PMC free article] [PubMed] [Google Scholar]
19.Tueller SJ, Deboeck PR, Van Dorn RA. Getting less of what you want: reductions in statistical power and increased bias when categorizing medication adherence data. Journal of behavioral medicine. 2016;39(6):969–980. [DOI] [PMC free article] [PubMed] [Google Scholar]
20.Peterson AM, Nau DP, Cramer JA, Benner J, Gwadry-Sridhar F, Nichol M. A checklist for medication compliance and persistence studies using retrospective databases. Value Health. 2007;10(1):3–12. [DOI] [PubMed] [Google Scholar]
21.Karve S, Cleves MA, Helm M, Hudson TJ, West DS, Martin BC. Good and poor adherence: optimal cut-point for adherence measures using administrative claims data. Current medical research and opinion. 2009;25(9):2303–2310. [DOI] [PubMed] [Google Scholar]
22.Frank AS, Lupattelli A, Matteson DS, Meltzer HM, Nordeng H. Thyroid hormone replacement therapy patterns in pregnant women and perinatal outcomes in the offspring. Pharmacoepidemiology and drug safety. 2020;29(1):111–121. [Google Scholar]
23.Wen X, Kogut S, Aroke H, Taylor L, Matteson KA. Chronic opioid use in women following hysterectomy: Patterns and predictors. Pharmacoepidemiology and drug safety. 2020;29(4):493–503. [DOI] [PubMed] [Google Scholar]
24.Bateman BT, Franklin JM, Bykov K, et al. Persistent opioid use following cesarean delivery: patterns and predictors among opioid-naive women. American journal of obstetrics and gynecology. 2016;215(3):353.e351–353.e318. [DOI] [PMC free article] [PubMed] [Google Scholar]
25.Huang ST, Tseng LY, Chen LK, Peng LN, Hsiao FY. Does Long-Term Proton Pump Inhibitor Use Increase Risk of Dementia? Not Really! Results of the Group-Based Trajectory Analysis. Clinical pharmacology and therapeutics. 2019. [DOI] [PubMed] [Google Scholar]
26.Kim SC, Choudhry N, Franklin JM, et al. Patterns and predictors of persistent opioid use following hip or knee arthroplasty. Osteoarthritis and cartilage. 2017. [DOI] [PMC free article] [PubMed] [Google Scholar]
27.Murimi IB, Chang HY, Bicket M, Jones CM, Alexander GC. Using trajectory models to assess the effect of hydrocodone upscheduling among chronic hydrocodone users. Pharmacoepidemiology and drug safety. 2019;28(1):70–79. [DOI] [PubMed] [Google Scholar]
28.Harris GME, Wood M, Nordeng H. Modeling exposures of medications used episodically during pregnancy: Triptans as a motivating example. Pharmacoepidemiology and drug safety. 2020. [DOI] [PubMed] [Google Scholar]
29.Hickson RP, Robinson JG, Annis IE, et al. Changes in Statin Adherence Following an Acute Myocardial Infarction Among Older Adults: Patient Predictors and the Association With Follow-Up With Primary Care Providers and/or Cardiologists. Journal of the American Heart Association. 2017;6(10). [DOI] [PMC free article] [PubMed] [Google Scholar]
30.Jones BL, Nagin DS, Roeder K. A SAS procedure based on mixture models for estimating developmental trajectories. Sociological methods & research. 2001;29(3):374–393. [Google Scholar]
31.Jones BL, Nagin DS. Advances in group-based trajectory modeling and an SAS procedure for estimating them. Sociological Methods & Research. 2007;35(4):542–571. [Google Scholar]
32.Juarez DT, Williams AE, Chen C, et al. Factors affecting medication adherence trajectories for patients with heart failure. The American journal of managed care. 2015;21(3):e197–205. [PMC free article] [PubMed] [Google Scholar]
33.Librero J, Sanfelix-Gimeno G, Peiro S. Medication Adherence Patterns after Hospitalization for Coronary Heart Disease. A Population-Based Study Using Electronic Records and Group-Based Trajectory Models. PloS one. 2016;11(8):e0161381. [DOI] [PMC free article] [PubMed] [Google Scholar]
34.Dillon P, Stewart D, Smith SM, Gallagher P, Cousins G. Group-based trajectory models: assessing adherence to antihypertensive medication in older adults in a community pharmacy setting. Clinical pharmacology and therapeutics. 2018;103(6):1052–1060. [DOI] [PMC free article] [PubMed] [Google Scholar]
35.Clark SL. Mixture* modeling with behavioral data. University of California, Los Angeles; 2010. [Google Scholar]
36.Wang J, Wang X. Structural equation modeling: Applications using Mplus. John Wiley & Sons; 2012. [Google Scholar]
37.van der Nest G, Passos VL, Candel MJ, van Breukelen GJ. An overview of mixture modelling for latent evolutions in longitudinal data: Modelling approaches, fit statistics and software. Advances in Life Course Research. 2020;43:100323. [DOI] [PubMed] [Google Scholar]
38.Hargrove JL, Pate V, Casteel CH, et al. Antihypertensive Adherence Trajectories Among Older Adults in the First Year After Initiation of Therapy. American journal of hypertension. 2017. [DOI] [PMC free article] [PubMed] [Google Scholar]
39.Bangdiwala SI, Shankar V. The agreement chart. BMC medical research methodology. 2013;13(1):97. [DOI] [PMC free article] [PubMed] [Google Scholar]
40.Byrt T How good is that agreement? Epidemiology (Cambridge, Mass). 1996;7(5):561. [DOI] [PubMed] [Google Scholar]
41.Dawson B, Trapp RG. Basic & clinical biostatistics. 4th edn ed. New York: Lange Medical Books/McGraw-Hill, Medical Pub. Division; 2004. [Google Scholar]
42.Benner JS, Glynn RJ, Mogun H, Neumann PJ, Weinstein MC, Avorn J. Long-term persistence in use of statin therapy in elderly patients. Jama. 2002;288(4):455–461. [DOI] [PubMed] [Google Scholar]
43.Newman-Casey PA, Blachley T, Lee PP, Heisler M, Farris KB, Stein JD. Patterns of Glaucoma Medication Adherence over Four Years of Follow-Up. Ophthalmology. 2015;122(10):2010–2021. [DOI] [PMC free article] [PubMed] [Google Scholar]
44.Hickson RP, Robinson JG, Annis IE, Killeya-Jones LA, Fang G. It’s Not Too Late to Improve Statin Adherence: Association Between Changes in Statin Adherence from Before to After Acute Myocardial Infarction and All-Cause Mortality. Journal of the American Heart Association. 2019;8(7):e011378. [DOI] [PMC free article] [PubMed] [Google Scholar]
45.Choudhry NK, Glynn RJ, Avorn J, et al. Untangling the relationship between medication adherence and post-myocardial infarction outcomes: medication adherence and clinical outcomes. American heart journal. 2014;167(1):51–58.e55. [DOI] [PubMed] [Google Scholar]
46.Nagin DS, Jones BL, Passos VL, Tremblay RE. Group-based multi-trajectory modeling. Stat Methods Med Res. 2018;27(7):2015–2023. [DOI] [PubMed] [Google Scholar]
47.Lo-Ciganic WH, Donohue JM, Jones BL, et al. Trajectories of Diabetes Medication Adherence and Hospitalization Risk: A Retrospective Cohort Study in a Large State Medicaid Program. Journal of general internal medicine. 2016;31(9):1052–1060. [DOI] [PMC free article] [PubMed] [Google Scholar]
48.Elmer J, Jones BL, Nagin DS. Using the Beta distribution in group-based trajectory models. BMC medical research methodology. 2018;18(1):1–5. [DOI] [PMC free article] [PubMed] [Google Scholar]
49.Hansen RA, Kim MM, Song L, Tu W, Wu J, Murray MD. Comparison of methods to assess medication adherence and classify nonadherence. The Annals of pharmacotherapy. 2009;43(3):413–422. [DOI] [PubMed] [Google Scholar]
50.Roberto PN, Stuart B. Out-of-plan medication in Medicare Part D. The American journal of managed care. 2014;20(9):743–748. [PubMed] [Google Scholar]

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