Clusters of pain trajectories among patients with sickle cell disease hospitalized for vaso‐occlusive crisis: A data‐driven approach

Abstract Background Vaso‐occlusive crises (VOCs) are the hallmark of sickle cell disease (SCD), with higher severity among hospitalized patients. Clustering hospitalizations with similar pain trajectories could identify vulnerable patient subgroups. Aims were to (a) identify clusters of hospitalizations based on pain trajectories; (b) identify factors associated with these clusters; and (c) determine the association between these clusters and 30‐day readmissions. Methods We retrospectively included 350 VOC hospitalizations from 2013 to 2016 among 59 patients. Finite mixture modeling identified clusters of hospitalizations from intercepts and slopes of pain trajectories during the hospitalization. Generalized estimating equations for multinomial and logistic models were used to identify factors associated with clusters of hospitalizations and 30‐day readmissions, respectively, while accounting for multiple hospitalizations per patient. Results Three clusters of hospitalizations based on pain trajectories were identified: slow (n = 99), moderate (n = 207), and rapid (n = 44) decrease in pain scores. In multivariable analysis, SCD complications, female gender, and affective disorders were associated with clusters with slow or moderate decrease in pain scores (compared to rapid decrease). Although univariate analysis found that the cluster with moderate decrease in pain scores was associated with lower odds of 30‐day readmissions compared to the cluster with slow decrease, it was nonsignificant in multivariable analysis. SCD complications were associated with higher odds of 30‐day readmissions and older age was associated with lower odds of 30‐day readmissions. Conclusions Our results highlight variability in pain trajectories among patients with SCD experiencing VOC and provide a novel approach for identifying subgroups of patients that could benefit from more intensive follow‐up.


INTRODUCTION
Sickle cell disease (SCD), which is the most common inherited blood disorder in the United States, primarily affects people of African descent and Hispanics of Caribbean ancestry [1]. The hallmark of SCD is acute, painful vaso-occlusive crisis (VOC), which can be frequent and difficult to treat, and result in high healthcare utilization [2]. Many patients attempt to manage their VOC at home, potentially resulting in underestimation of the pervasiveness of VOC [3,4]. On the other hand, patients seeking medical care for VOC may represent more severe cases [5].
When patients with VOC present acutely to healthcare providers, they have usually exhausted home care options and require more aggressive pain management, typically delivered inpatient [6]. Prior studies described trends in pain scores during VOC hospitalizations, observing that pain scores decrease as the patient approaches discharge, sometimes reaching a plateau without complete resolution [7][8][9]. These studies primarily plotted or reported individual or mean pain scores for each hospitalization day. Although these methods produce visualizations of pain scores, they do not allow grouping or clustering of hospitalizations with similar pain trajectories, which could identify subgroups of vulnerable patients. In addition, the pain experience during a hospitalization may predict future hospitalizations and readmissions, further illustrating the potential use of grouping pain trajectories [9].
Growth mixture modeling and latent class growth analysis provides data-driven approaches for identifying unobserved ("latent") growth curves or trajectories, based on variables (eg, pain scores) collected over time [10]. However, using these methods for creating pain trajectories during a VOC hospitalization is challenging when length of stay (LOS) varies and missing data due to shorter LOS are not missing at random [10,11]. Recent studies have introduced methods to create pain trajectories during hospitalizations, but have focused on portions of the hospitalization (eg, first 48 h, 3 days leading up to discharge) rather than the full hospitalization [12,13]. Building on these approaches, we propose estimating the intercept and slope of pain score trajectories for each hospitalization and then using finite mixture modeling to identify clusters of hospitalizations based on these intercepts and slopes [14].
The overall goal of our study was to use our proposed methods to identify clusters of hospitalizations with similar pain trajectories among patients with SCD hospitalized for VOC. We then assessed whether patient (eg, gender) and clinical characteristics (eg, affective disorder, SCD complications, use of hydroxyurea, and genotype) were associated with these clusters. Based on prior research, we hypothesized that hospitalizations among patients with more severe SCD, patients with affective disorders, and patients prescribed hydroxyurea would have worse pain trajectories [15][16][17][18][19][20]. Finally, we tested the association between clusters of pain trajectories and 30 [23,24]. We excluded transfer hospitalizations if patients spent >2 days at an outside hospital, as this would limit information about the early pain crisis. Hospitalizations <3 days were excluded because there were too few pain scores to create trajectories; hospitalizations >14 days were also excluded as their pain experience was hypothesized to be different (see Table A1 for comparison of hospitalization characteristics based on LOS exclusions). Exclusion of hospitalizations >14 days was based on statistical criteria (sparse data) and existing ranges of cutoffs used to define prolonged hospitalizations [7,25,26]. This study was approved by the Tufts Health Sciences Institutional Review Board.

Data
The study database had three levels of information: patient, hospital-

Descriptive analysis
Patient and hospitalization characteristics were described for the full sample at the patient and hospitalization level using means, standard deviations (SD), medians, 25th-75th quartiles (Q1, Q3), frequencies, and percentages. For patient characteristics that could vary over time, characteristics at the first hospitalization were used for the patientlevel description. Data were analyzed using R (3.6.2 for Windows)/R

Identifying clusters of pain trajectories
We used a two-step approach to identify clusters of VOC hospitalizations with similar pain trajectories: (a) estimate intercepts and slopes of maximum daily pain scores for each hospitalization and (b) estimate finite mixture models using these intercepts and slopes for each hospitalization to identify clusters [14]. Briefly, a linear regression model was fit for each hospitalization with daily maximum pain score as the outcome and hospitalization day as the only covariate. Intercepts and slopes for each hospitalization were output from the linear regression models and included as input for the Gaussian finite mixture model, which allows different covariance structures and different numbers of mixture components (ie, clusters) (see Appendix for detailed description of this analysis and the sensitivity analysis).
To plot the pain trajectories by cluster, predicted values and 95% confidence intervals were estimated using a mixed effects model with random intercepts and slopes for each hospitalization (proc mixed in SAS). Maximum daily pain score was regressed on cluster, hospitalization day, and their interaction, assuming an autoregressive covariance structure (based on Akaike information criteria). Pain trajectories by cluster were plotted from hospitalization day 1 to 7, with 7 representing the 75th percentile of LOS.
When interpreting differences in pain scores, research suggests that 1-point changes on the 0 to 10 pain scale represent minimally important change, whereas 2-point changes represent more meaningful decreases in pain [28].

Analysis of factors associated with clusters of pain trajectories
We identified patient and hospitalization characteristics that were associated with clusters of pain trajectories, while accounting for the correlation of hospitalizations within patients using generalized estimating equations (proc GEE in SAS) with a multinomial distribution (glogit link) and an independent covariance structure [29]. Hospitalization characteristics LOS in days, median (Q1, Q3) n/a 7 (5,9) Admission pain score, median (Q1, Q3) n/a 9 (8, 10)

TA B L E 1 Patient and hospitalization characteristics
Discharge pain score, median (Q1, Q3) n/a 5 (4, 6) a For time-varying patient characteristics, only the first hospitalization was included. b Other includes Hb Sβ + thalassemia, Hb Sβ 0 thalassemia, unknown genotype (two patients and three hospitalizations are unknown). c One patient and three hospitalizations did not have information in the EMR about their home medication regimen. d Seven patients and 38 hospitalizations were missing ADI score.
The following covariates were included in the multivariable model based on a priori hypothesized relationships with pain experience: gender, affective disorder, number of SCD complications, home use of hydroxyurea, and genotype (Hb SS vs all others).
We hypothesized that daily use of opioids would be associated with clusters of pain trajectories. However, we were unable to assess for this relationship because nearly all hospitalization days (98%) involved opioid use and daily morphine equivalent dose (MED) was not available for all patients during the study period.

Analysis of relationship between clusters of pain trajectories and 30-day readmission
This analysis was restricted to patients who were established at Tufts MC because they would be expected to be readmitted at Tufts MC (see Table A2 for characteristics of established patients). Using GEE with a binomial distribution and logit link (with an autoregressive covariance structure based on quasi-likelihood criteria) [30] to account for the correlation of hospitalizations within patients, we tested the association between clusters of pain trajectories and 30-day readmissions. The multivariable model was fit adjusting for gender, age, affective disorder, number of SCD complications, home use of hydroxyurea, and genotype (Hb SS vs all others).

Sample
Initially, 568 hospitalizations among 90 patients with SCD were identified as potentially eligible. After applying inclusion/exclusion criteria, the analytic cohort included 350 hospitalizations for VOC among 59 patients ( Figure 1).

Clusters of pain trajectories
Across all hospitalizations, the mean intercept was 9.03 (SD = 1.06) and the mean slope was -0.43 (SD = 0.58). Three distinct clusters of hospitalizations with similar pain trajectories were identified using finite mixture models and were described based on the steepness of the pain slope over the course of hospitalization: (a) slow decrease (n = 99, intercept = 9.58, slope = -0.14); (2) moderate decrease (n = 207, intercept = 8.89, slope = -0.36); and rapid decrease in pain scores (n = 44, intercept = 8.60, slope = -1.13) (Figure 2). Hospitalizations with slow decrease in pain scores (ie, shallow slope) had the highest initial pain score (ie, intercept), followed by hospitalizations with moderate decrease in pain scores, and then hospitalizations with rapid decrease in pain scores. Among the 40 patients who had more than one hospitalization, only eight had hospitalizations that were always classified in the same cluster; the remaining 32 patients had hospitalizations in at least two different clusters. See Table A3 for results of sensitivity analysis.

Factors associated with clusters of pain trajectories
Patient and hospital characteristics were described by clusters of pain trajectories (Table 2), and univariate and multivariable analyses identified factors associated with the clusters (Table 3)

DISCUSSION
Based on 350 VOC hospitalizations among 59 patients with SCD, we identified three clusters of hospitalizations with similar pain trajectories (rapid, moderate, and slow decrease); the cluster with moderate decrease in pain scores was the most common. Hospitalizations among females, patients with more SCD complications, or patients with affective disorders had higher odds of being in the cluster with worse pain trajectories (ie, slow or moderate decrease in pain scores).
Although hospitalizations in the cluster with moderate decrease in pain scores had lower odds of 30-day readmissions than the cluster with slow decrease, this was no longer significant in the multivariable model. Younger age and more SCD complications were associated with higher odds of 30-day readmissions.
This analysis provides an advancement over prior studies of pain trends during VOC hospitalizations, which were primarily descriptive [7][8][9]. We used a data-driven approach to uncover clusters of hospitalizations with similar pain trajectories, highlighting variability in pain experiences. As previously observed, we found that pain tended to decrease from admission to discharge, although at different rates across the clusters. Our approach also allowed us to test whether patient and clinical characteristics were associated with pain trajectory clusters. By its nature, the use of finite mixture models to identify clusters of hospitalizations with similar pain trajectories is exploratory, so there is no correct number of clusters. Although our primary analysis identified three clusters, our sensitivity analysis found only two, indicating that the number of clusters is sensitive to the criteria we used to fit the model. Differences in pain scores across the three clusters, as well as differences in patient and clinical characteristics across the clusters, provide initial justification for the use of three clusters. Additional research that includes more patients from multiple hospitals should be conducted to further validate these findings. The number of clusters of hospitalizations with similar pain trajectories could also be determined by how the results will be used, and clinical criteria should also be incorporated.
Although a widely used and validated measure of SCD severity does not currently exist, frequent VOCs and more SCD-related complications likely represent higher disease severity [15][16][17]. Our results confirmed that hospitalizations for patients with more SCD complications had slower decreases in pain scores and more SCD complications were associated with 30-day readmissions. In fact, the relationship between clusters of pain trajectories and 30-day readmissions likely attenuated from statistically significant to nonsignificant after adjustment for SCD complications. LOS is closely related to pain trajectories and disease severity, as patients with rapid decreases in pain scores have shorter LOS. Given this relationship, we did not include LOS in our primary analysis. However, sensitivity analyses found that LOS was not associated with 30-day readmissions and that pain trajectory clusters alone were better at predicting 30-day readmissions than LOS alone. Hospital discharge often depends on a return to baseline pain level, rather than complete resolution. Unfortunately, we were unable to collect information about the baseline pain experience outside the hospital.
Aside from SCD complications, we found that affective disorders and female gender were associated with less rapid resolution of pain trajectories. The relationship between affective disorders and the pain experience is complicated and bidirectional; pain may lead to an increase in anxiety or depression, whereas anxiety or depression may lead to differences in the pain experience [18,19]. Prior research shows that males have more severe SCD and lower life expectancy than females [31,32]. However, other studies found no differences in the pain experience by gender or possible differences related to the menstrual cycle [33,34]. A possible explanation is that females experience more anxiety and depression, which could result in different pain experiences, but our results adjusted for affective disorder [18,35].
Age was the only factor besides SCD complications that was associated with 30-day readmissions. Older age was actually associated with lower 30-day readmission rates, which has been observed in other studies of SCD [1]. Interestingly, the univariate relationship between age and 30-day readmissions was not significant, but became significant after adjustment for SCD complications. Given life expectancy in the 40s or 50s, we hypothesize that patients with more severe SCD die sooner, so patients who survive to older adulthood have less severe disease and lower healthcare utilization [32,36,37]. Of note, this study only included patients ≥18 years old so this age-based relationship may be different for pediatric patients. other studies [39,40].
In conclusion, we identified three unique clusters of pain trajectories among VOC hospitalizations using a novel, data-driven approach. SCD complications were associated with slower decreases in pain scores as well as increased 30-day readmissions. These results highlight the variability in pain trajectories among patients with SCD experiencing VOC and provide a novel approach for identifying subgroups of patients who are most vulnerable and could benefit from interventions, such as more intensive follow-up. helped acquire the data; and reviewed and edited the paper. NSS helped acquire the data and reviewed and edited the paper. SKP conceptualized the study; helped acquire the data; helped acquire funding support; and reviewed and edited the paper.

CONFLICT OF INTEREST
The authors declare no conflict of interest.

Identifying clusters of pain trajectories
We used a two-step approach to identify clusters of VOC hospitalizations with similar pain trajectories: (a) estimate intercepts and slopes of maximum daily pain scores for each hospitalization and (b) estimate finite mixture models using these intercepts and slopes for each hospitalization to identify clusters [14]. For each individual hospitalization, we fit a linear regression model with daily maximum pain score as the outcome and hospitalization day as the only covariate (using the lm function in R). Visual inspection of plots of observed daily pain scores over the course of each hospitalization justified the use of linear regression. Intercepts and slopes for each hospitalization were output from the linear regression models and included as input for the finite mixture model (using mclust package in R). Gaussian finite mixture models were fit via the expectation-maximization (EM) algorithm, allowing for different covariance structures and different numbers of mixture components (ie, clusters). Clusters are ellipsoidal, centered at the mean, with volume, shape, and orientation determined by the covariance matrix.
In the multivariate setting, the volume, shape, and orientation of the covariance can be equal or unequal across clusters. The number of clusters was based on the following criteria: Bayesian information criteria (BIC) and ≥10% of sample in each cluster. BIC was also used to determine the covariance structure. As a sensitivity analysis, the integrated complete-data likelihood (ICL) was used instead of the BIC to