From acute to chronic back pain: Using linear mixed models to explore changes in pain intensity, disability, and depression

Rebecca Bendayan; Carmen Ramírez-Maestre; Emilio Ferrer; Alicia López; Rosa Esteve

doi:10.1016/j.sjpain.2017.02.009

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From acute to chronic back pain: Using linear mixed models to explore changes in pain intensity, disability, and depression

Rebecca Bendayan , Carmen Ramírez-Maestre , Emilio Ferrer , Alicia López and Rosa Esteve

Published/Copyright: July 1, 2017

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From the journal Scandinavian Journal of Pain Volume 16 Issue 1

Abstract

Background/aims

This longitudinal study investigated the pattern of change in pain intensity, disability, and depression in 232 chronic pain patients who were followed up for 2 years since pain onset. Most studies that have investigated changes in these variables over time have used participants who had already been in pain for more than 3 months. Few studies have followed up individuals from the acute phase onward and such studies used traditional statistical methods that cannot identify transition points over time or measure inter-individual variability.

Methods

We followed up individuals with chronic pain from pain onset up to 18 months and we examined their pain intensity, disability and depression trajectories using a modelling approach that allows to account for between and within-individual variability. We compared three patterns of change based on theoretical criterions: a simple linear growth model; a spline model with a 3-month transition point; and a spline model with a 6-month transition point. Time with pain was selected as time metric to characterise the change in these variables in the transition from acute to chronic pain. Sex and age differences were also examined.

Results

The results showed that the pain intensity trajectory was best represented by the spline model with a 3-month transition point, whereas disability and depression were best explained by linear growth models. There were sex differences at intercept level in all the models. There were age differences at baseline for pain intensity. No sex or age differences were found for the slope.

Conclusions

Pain intensity decreased in the first 3 months but underwent no further change. Disability and depression slightly but constantly decreased over time. Although women and older individuals are more likely to report higher pain intensity or pain-related disability in the first three months with pain, no differences by sex or age appear to be associated with the changes in pain intensity, depression and disability through the process of chronification.

Implications

Our findings suggest that pain chronification could be considered a continuous process and contribute to the ongoing discussion on the utility of standard classifications of pain as acute or chronic from a clinical point of view. Clinical and intervention decisions based in these standard classifications should consider the differences in the trajectories of pain related variables over time. In addition, this article illustrates a statistical procedure that can be of utility to pain researchers.

Keywords: Chronic pain onset; Pain intensity; Depression; Disability; Change

1 Introduction

Chronic pain is commonly defined as any pain lasting more than 3 months (IASP, 1994) and is one of the most disabling health problems [1]. A recent review suggested that pain decreases from the moment of pain onset [2]. However, these findings are not consistent across studies. Some authors found prevalence rates and pain intensity to be fairly stable over time [3,4], whereas others suggested that the course of pain can fluctuate [5]. Moreover, some studies have tried to group their participants according to reported changes in pain over time [6,7]. Elliot et al. [6] investigated changes in pain intensity over 4 years and found that 49% reported no change in pain intensity, whereas the rest only reported slight changes. Tamcan et al. [7] investigated pain intensity every week for 1 year and found that it remained fairly constant in those who reported mild and severe persistent pain intensity.

These studies mainly addressed pain and pain intensity prevalence rates, and only a few also investigated the course of adjustment variables, such as disability [6,8] or depression [9,10]. Regarding disability, Elliot et al. [6] investigated changes in chronic pain between baseline and 18-month follow-up and found significant changes in bodily pain and physical functioning over time. McGorry et al. [8] investigated daily self-reports of pain intensity and disability over a 6-month period. Their results suggested that chronic pain should not be considered a static phenomenon, and that intermittent increases in pain intensity might be associated with disability. Studies that have investigated depression trajectories have found inconsistent results. Mitchell and Adkins [9] found that levels of depression increased over time, whereas Saunders et al. [10] found that depression appeared to remain stable over a 5-year period.

Most of these studies included individuals with pain of more than 3-months duration, but none measured these three variables in chronic pain patients since the time of pain onset (i.e., when pain was acute). Although many studies have measured variables at pain onset to predict adjustment when pain becomes chronic, few have investigated their course from acute to chronic pain [11,12]. Casey et al. [11] evaluated pain intensity and disability at pain onset and at 3 months. They found that acute disability, but not acute pain intensity, predicted disability at 3 months. Philips and Grant [12] investigated participants with acute back pain at 3 and 6 months. Their results suggested that: pain intensity appeared to decrease slightly over time; depression mainly changed during the first 3 months, followed by stabilisation; and disability sharply decreased during the first 3 months followed by an increase at 6 months. To the best of our knowledge, these studies were the first to investigate changes from pain onset to its chronic phase in samples of chronic pain patients. However, they mainly used traditional analytical strategies (i.e., multiple regressions, traditional repeated measures analysis), which provide limited information about the pain trajectories, and did not address inter-individual variability. More recent studies have acknowledged this variability and classified chronic pain patients by their pain intensity trajectories [13,14,15]. For example, Dunn et al. [13,14] classified back pain patients attending primary care services into 4–5 groups by their monthly pain levels over 6 months, being these similar seven years later. Kongsted et al. [15] followed a similar approach and described pain intensity trajectories based on weekly measurements over a year. They identified 5–12 sub-groups in a sample with a recent episode of low back pain via latent class models. These studies [13,14,15] not only highlight the great inter-individual variability in pain intensity trajectories but the complexity of characterising the course of low back pain [13,14,15]. It should be noted that the majority of the individuals considered in these studies had pain for more than three months or had previous episodes of back pain.

Within this context, research studies aiming to characterise the course of pain should consider statistical techniques that can measure the pattern of change taking into account inter-individual variability (e.g., linear mixed models) so as individuals who have suffered pain for less than three months at baseline. Our study investigates the pattern of change in pain intensity, depression, and disability from pain onset up to 2 years of chronic pain, using linear mixed models. We propose a specific modelling approach to explore change not only in pain intensity but in relevant adjustment variables.

2 Methods

2.1 Participants

A total of 254 patients with an acute back pain episode were recruited by general practitioners in five Primary Care Units in Málaga (Spain). Exclusion criteria were: pain lasting more than 3 months; being treated for a malignancy, terminal illness, or psychiatric disorder; the presence of back pain that was related with or secondary to a specific medical condition (e.g. tumours, trauma, infection, fractures, and inflammatory disorders), presence of specific back pain; operation in the lumbar area; pregnancy; and not being able to understand Spanish.

The participants were assessed on five occasions, the first when pain duration was less than 3 months. Subsequently, they were assessed four times at 6-month intervals. After screening for eligibility, the overall response rate was 91% of the initial sample. The overall attrition rate was of 36% from wave 1 to wave 2, 12% from wave 2 to wave 3, 6% from wave 3 to wave 4, and 3% from wave 4 to wave 5. Reasons for attrition were as follows: 36% of the missing participants did not reply to the phone calls; 36% stated they “had no time” for the assessment session; 14% expressly refused participation; 10% had made four appointments but did not attend; 3% moved away; and 0.8% died.

2.2 Instruments

Pain intensity. Patients were asked to rate their highest, average, and lowest level of pain over the past 2 weeks, as well as their current pain, on a 0–10 scale, with 0 indicating no pain and 10 pain as intense as the individual could imagine. A composite score was calculated for each individual by averaging the highest, average, lowest, and current level of pain intensity. Jensen et al. [16] showed that composites of 0–10 ratings are reliable measures of pain intensity in chronic pain patients.

Depression. The 7-item Hospital Anxiety and Depression Scale [17] subscale for depression was administered. Higher scores indicate higher levels of depression. The Spanish version of the scale shows appropriate reliability and validity [18]. The internal consistency of the HADS is high (α = .86). In the present study the depression subscale showed an adequate internal consistency (α = .81).

Disability. The Roland–Morris Questionnaire [19] was used. It consists of 24 items, which reflect limitation in different daily activities attributed by the patient to low back pain. The patient marks each item that applies to his or her current status. The Spanish version showed adequate internal consistency (between α = .83 and α = .94). In the present study, these showed high internal consistency (α = .89)

2.3 Procedure

To guarantee the standardisation of the recruitment process across the five centres, and prior to data collection, the researchers held a meeting with the participating doctors in which the eligibility criteria were explained and the procedures were decided.

At the end of their visit to their doctor, each patient who fulfilled the eligibility criteria (i.e., the individuals had to be suffering back pain at least one week and less than 3 months and pain intensity had to be equal to or higher than 3 on a 10-point scale) was informed of the objectives of the study and their participation was requested. Some patients were interviewed after their visit, whereas others left their telephone number to make an appointment on another day. In order to guarantee the standardisation of the procedure, psychologists were specifically trained for the data collection. Each participant was interviewed by a trained psychologist to obtain demographic, social, or medical history data, and a set of questionnaires were administered. The first assessment session took place when the pain duration was less than 3 months; after this initial session, the patients were contacted by telephone four times at 6- month intervals to make an appointment for further evaluation. These phone calls to set up the next appointment were the only contact with the participants in between the 6 months intervals. If a patient failed to attend the appointment it was re-scheduled up to four times. If the patient did not attend the appointment after four attempts their responses were coded as missing data. The participants were always interviewed in their usual primary care centre.

2.4 Data analyses

The main aim of this study was to investigate patterns of change in pain intensity, depression, and disability from pain onset up to 2 years with chronic pain. Traditional repeated measures analyses (e.g., t-tests or repeated measures ANOVA) provide limited information about change over time. Understanding change as the simple difference between scores assessed on two measurement occasions does not allow us to accurately describe the process of change, nor does it provide information about individual trajectories over time. Furthermore, it does not specify when change occurred, whether it occurred just after the first measurement occasion or just before the second one, or if the rate of change was steady or changeable. Moreover, these traditional analyses are based in mean differences over time and do not account for inter-individual variability (i.e., each individual can have a different baseline score and have a different rate of change over time).

Recent advances in longitudinal data analysis research have provided useful techniques, such as linear mixed models, to investigate different patterns of change that take into account inter-individual variability [20,21,22]. This study investigated three models of change: a linear growth model; a spline model with a transition point at 3 months; and a spline model with a transition point at 6 months. The linear growth model assumes that there is a constant rate of change over time. That is, this model assumes that each month with there is the same rate of change. The spline model with a transition point at 3 months divides the data into two segments of time and fits a linear model to each of the segments. Thus, spline 1 represents the linear change from the onset of pain to the transition point – at 3 months – whereas spline 2 represents the linear change starting at the transition point. The spline model with a transition point at 6 months divides the data into two segments of time and fits a linear model to each of the segments. Thus, spline 1 represents the linear change from the onset of pain to the transition point – at 6 months – whereas spline 2 represents the linear change starting at the transition point. These models have been used in previous research and could in theory capture changes in the pain process overtime [23,24]. Detailed information on each model is provided in Appendix A.

Time with pain in months was selected as time metric for these models. The choice of time metric when modelling longitudinal data is not only a statistical issue but a theoretical one. The time metrics assumed are not only a measure of time but a theoretical assumption of the processes which drive the change in our outcomes. Therefore, when the aim is to understand changes associated to the experience of pain and its chronification, time with pain is the ideal time metric to represent change in pain-related variables. In order to account for inter-individual variability at baseline and trajectories, the baseline levels of each outcome variable (intercepts) and individual slopes were random in the models. That is, these models consider that each individual may start at a different level and their rate of change might be different from other individuals. Each individual has a different time with pain in the first assessment (intercept), always less than three months, and each individual has a different trajectory of change (slope) in disability, pain intensity and depression over the two years. This allows considering monthly fluctuations and reducing potential variation associated to the pain duration at the first measurement occasion, which are relevant issues from a clinical perspective [25].

We first examined the linear model; then, the splines model with a transition point at 3 months; and, finally, the splines model with a transition point at 3 months. This study also aims to describe the process to explore the shape of the trajectories in three relevant variables to understand the transition from acute and chronic pain. This process has to be driven by theory considering that the best model will be the one that provides a more parsimonious representation and clearer substantive insights [22]. Therefore, the first model considered was the simplest: the linear model, which was used as base model to examine whether there was any change over time in pain intensity, disability and depression. This first step aims to answer to a first question: Are there any changes in pain intensity, disability and depression scores from pain onset up to 2 years of chronic pain? Visual examination of the data and the results of a linear model provide an overall response to this first question. When change was identified in this first step, the two splines models were examined and compared. Bayesian Information Criterion (BIC) indexes were used to compare those models that captured the change over time (i.e., significant individual coefficients for intercept and slope) and those with lower BIC were selected. This approach has also been useful to address a further understanding of the process of change in developmental studies [23,26]. We used SAS PROC MIXED software with the Kenward–Roger procedure for adjusting the degrees of freedom for reduced sample sizes [27,28,29]. As previous research highlighted the need to carefully consider sex and age differences in chronic pain studies [30,31,32,33,34] all the models were adjusted for baseline age and sex. An unstructured covariance structure was assumed. SAS codes for each model are available to interested researchers.

3 Results

Preliminary analyses investigated missing data patterns. The expectation maximisation algorithm was used to perform multiple imputation in order to provide the most accurate estimates with our percentages of missing data [34,35]. There were no significant differences between the initial sample and the participants who completed the five assessments in any of the demographic variables, clinical pain-related variables, or the variables considered in the models. Following Carpenter and Kenward [36] recommendations, sensitivity analyses were performed by comparing multiple imputed data and complete cases; the results based on multiple imputations were in line with those of the complete cases.

The study sample comprised 157 women and 75 men whose average age on the first measurement occasion was 45.41 years (SD = 16.21). Most participants were married (50%), never married (30%), cohabiting (8%), widowed (4%), separated (4%), and divorced (3%). In total, 40% had completed high school and 22% had a university degree. With regard to employment status, the largest single group of patients were in full-time employment (46%), followed by homemakers (23%), unemployed (13%), retired (13%), and students (4%). From those that were not in full-time employment only 1.3% pointed out as a cause their general health status. With regards to pain, median pain duration at baseline was 24 days and the most common site of pain was cervical (45%), followed by vertebral-lumbar (37%), sacral (29%), thoracic (22%), and lumbar-renal (21%); and only 3% did also report knee pain.

Table 1 shows descriptive statistics for pain intensity, pain related disability, and depression in the sample. Estimates for the final models are shown in Table 2 and Figs. 1–3 show individual trajectories of a subsample and the predicted average trajectory for the better fitting model for pain intensity, disability and depression respectively. Estimates for each model for the three variables can be found in Supplemental Table 1. On the one hand, a comparison of the different models of change in pain intensity showed that the spline model with a transition point at 3 months had the best fit. As it can be seen in Table 2 and Fig. 1 there was a significant decrease in pain intensity scores during the first 3 months with pain, but no significant change thereafter.

Fig. 1

Trajectories for pain intensity scores (Y-axis) over 24 months since pain onset (X-axis). Average predicted trajectory indicated by red line.

Fig. 2

Trajectories for disability scores (Y-axis) over 24 months since pain onset (X-axis). Average predicted trajectory indicated by red line.

Fig. 3

Trajectories for depression scores (Y-axis) over 24 months since pain onset (X-axis). Average predicted trajectory indicated by red line.

Table 1

Mean and standard deviations (SD) for pain intensity, disability and depression at each measurement occasion (MO).

	MO1	MO2	MO3	MO4	MO5
Pain IntensityMean (SD)	5.49 (1.81)	3.64 (2.57)	3.64 (2.99)	3.83 (2.94)	3.45 (2.78)
Disability Mean (SD)	10.40 (5.93)	6.13 (5.48)	5.67 (5.64)	5.65 (5.77)	5.06 (5.28)
Depression Mean (SD)	11.03 (3.80)	10.50 (4.25)	9.86 (3.69)	10.07 (3.69)	9.69 (3.31)

Table 2

Estimates, standard errors (SE) and confidence intervals (CI) for final models for pain intensity, disability and depression over five measurement occasions (N = 232).

	Pain intensity		Disability		Depression

	Estimate (SE)	CI	Estimate (SE)	CI	Estimate (SE)	CI

	Splines model – 3 months		Linear model		Linear model
Intercept	1.78 (.66)^[**]	.46, 3.10	6.43 (1.28)^[***]	3.90, 8.96	10.76 (.82)^[***]	9.14,12.38
Time			−.23 (.08)^[**]	−.39, −.06	−.10 (.05)^[*]	−.21, .003
Splinel	−1.20 (.26)^[***]	−1.73, −.68
Spline2	−.02 (.04)	−.11, .06
Sex (female)	1.25 (.42)^[**]	.41, 2.08	1.72 (.82)^[*]	.10, 3.34	.28 (.52)	−.75, 1.33
Baseline age	.02 (.01)^[*]	.002, .04	.04 (.02)	−.001, .09	.0008 (.01)	−.02, .03
Slopel
Sex (female)	.22 (.17)	−.11, .56	−.02 (.05)	−.12, .08	.05 (.03)	−.01, .12
Age	.008 (.004)	−.001, .01	.0003 (.001)	−.002, .003	.0003 (.009)	−.001, .002
Slope2
Sex (female)	−.005 (.02)	−.06, .05
Age	.0002 (.0007)	−.001, .001
-2LL	2845.3		4037		3530.2
BIC	2910.7			4058.8		3552

On the other hand, a comparison of the different models of change in disability and depression showed that the linear model had the best fit; there was a slight but significant decrease in both variables over time. Regarding the covariates, women reported higher pain intensity and disability scores than men at baseline; however, there were no sex differences in depression at baseline. There were no age differences in any of the models at baseline, and no slope differences in sex or age at baseline.

4 Discussion

The aim of this study was to investigate the pattern of change in pain intensity, depression, and disability from pain onset up to 2 years of chronic pain, taking into account inter-individual variability. A total of 232 patients who attended five primary health services for an acute back pain episode were followed up five times over 2 years. Three models of change were investigated: a simple linear growth model; and two spline models with a 3-month transition point and a 6-month transition point, respectively.

Regarding pain intensity, the spline model with a 3-month transition point had the best fit. There was a significant decrease in pain during the first 3 months and no significant changes in pain intensity after the fourth month. These results are in line with studies that have found that pain intensity appears to stabilise once pain becomes chronic [3,4,6]. Moreover, the results provide additional empirical support to the current definition of chronic pain (pain that lasts more than 3 months; IASP, 1994). The “stabilisation” of perceived pain intensity after 3 months could be associated with the use of more effective coping strategies, such as pain acceptance, or other key factors in the pain-adjustment process. Research studies have highlighted the relevance of pain acceptance in chronic pain [37,38,39,40] and recent studies have found a negative association between pain acceptance and pain intensity [37,41]. To date, studies which have investigated the association between pain acceptance and pain intensity have only used individuals with chronic pain (i.e., more than 3 months with pain), but our findings suggest that it would be of interest to investigate any short-term changes in these variables during the third and fourth month. Our results appear to be in the line with those of Dunn et al. [13,14], who identified four subgroups among individuals with low acute back pain attending primary care centres based on their trajectories of pain intensity over 6-month periods. The authors found that 37% of the participants had persistent mild pain; those who reported higher initial levels of pain intensity and subsequently reported a slight decrease. This pattern of change in individuals with chronic pain is supported by the fact that the pain intensity trajectory found in our sample is similar to those found by Dunn et al. [13,14].

The pattern of change in the adjustment variables disability and depression were best explained by a linear model. Although the decrease in these variables was very slight, our results are consistent with those that suggest that these variables change over time [6]. Our findings suggest that the process of adjustment to chronic pain appears to be very slow in terms of depression and disability and might be better described by non-linear models not considered in this study. Studies with longer follow-ups are needed to examine whether these patterns are persistent over time, as Dunn et al. [13] found in pain intensity after 7 years. Moreover, future studies with larger sample sizes should explore whether pain intensity, disability and depression trajectories are interrelated.

Regarding the covariates, the results showed that women were more likely to report higher pain intensity and disability scores than men at baseline, although no sex differences were found for depression at baseline. Previous studies on pain intensity have found similar results [42]. Our results are also in line with those of previous studies which suggest that women are more sensitive than men to threat-related stimuli and that this would generally lead to increased pain perception [42,43,44]. Moreover, it is of special interest that older individuals who had an acute pain episode were more likely to perceive greater pain intensity levels when this lasted for 3 months. This finding is consistent with previous research that has found an association between age and chronic pain [45]. However, we found no sex or age differences in the rate of change. These results suggest that although women and older individuals are more likely to report higher pain intensity or pain-related disability in the first three months with pain, no differences by sex or age appear to be associated with the changes in pain intensity, depression and disability through the process of chronification. Further research with greater sample sizes is needed to explore whether these findings could be explained by other relevant demographic variables.

The main strength of the present study is that we followed up individuals with chronic pain from pain onset up to 18 months and we examined their pain intensity, disability and depression trajectories using a modelling approach that allows to account for between and within-individual variability.The modelling approach here illustrated has been widely used in developmental research [23,24] but to date has not been applied to pain research. However, it seems a suitable one when the aim is characterising the course of pain taking into account that each individual is unique and different from others. On the one hand, these models allow researchers to formally test different patterns of change described, hypothesised or suggested in previous literature. The present study compared three models of change (linear, splines models with a 3-month transition point and splines model with a 6-month transition point) which have been discussed by previous studies focused on the first months since pain onset [11,12]. In addition, this approach, in general, and our results, in particular, contributes to the ongoing discussion on the utility of standard classifications of pain as acute or chronic. In 1994, the IASP stated that three months was the most convenient point of division between acute and chronic pain, and suggested a six months transition point for research purposes. Our results found that it appears to be a transition point at three months when examining pain intensity trajectories but there is no clear transition point when examining the trajectories of relevant adjustment variables. Although previous studies have also highlighted issues derived of defining chronic pain solely by duration [13,46], clinical practice and epidemiological research classify individuals by the three month standard definition of chronic pain. On the other hand, we proposed an approach for examining trajectories in pain studies where each individuals’ trajectory was aligned to each individuals’ pain duration, which allows to capture between and within individual variability (i.e., some individuals may have been already two months suffering pain while other individuals have just had pain for two weeks). This is not only a statistical issue but a theoretical one, using pain duration as time metric assume that changes in pain intensity, disability and depression are driven by the time that the individual has been suffering pain. For our purpose of describing the trajectories of change since pain onset through its chronification, this time metric seems to be the most appropriate. However, when the aim of the study is, for example, to describe trajectories of disability in pain sufferers who underwent a specific treatment, using time since the beginning of the treatment would be a sensible decision.

Some limitations should be also acknowledged, the present study did not aim to identify any patients’ subgroups or predict risk of developing chronic pain but to describe the trajectories of pain intensity, disability and depression over the first two years suffering chronic pain in a sample that is representative of individuals who suffer chronic back pain. However, both approaches could be combined. Future studies with larger samples sizes could first identify sub-groups of their interest and then explore the trajectory of change in any adjustment variable within each group. Moreover, it should be noted that no specific data on major life events, health-related event, or pain-related treatments was collected. Examining how the co-occurrence of these events can shape the trajectories of pain intensity, disability and depression in individuals who develop chronic pain would be extremely interesting. In addition, although the present study used adequate measures of disability and depression for individuals with pain, it should be noted that only self-report measures were used. It would be of interest to conduct future studies with different assessment methods, for example, objective measures as walking speed.

To sum up, although the results on the pain intensity trajectory suggest that the standard cut-off of 3 months seems adequate to define chronic pain, this transition point in time cannot be clearly identified when pain-related disability and depression trajectories because this transition is gradual. Our findings suggest that pain chronification could be considered to be a continuous process and contribute to the ongoing discussion on the utility of standard classifications of pain as acute or chronic from a clinical point of view. In fact, Dunn et al. [13] also raised the clinical implications of using standard definitions, as some interventions might be more effective if performed during the first 3 months of acute pain. In addition to the theoretical and clinical implications of these results, the present article also illustrates how linear mixed models can allow us to better understand the underlying theoretical models of change in chronic pain. We hope that researchers on chronic pain are encouraged to follow this approach.

Highlights

Changes in pain intensity, disability, and depression since pain onset were investigated.
Changes in pain intensity are found only over the first three months.
Disability and depression slightly decrease following a linear trend.
The results suggest that pain chronification is a continuous process.
The utility of standard classifications of pain as acute or chronic is further discussed.

DOI of refers to article: http://dx.doi.org/10.1016/j.sjpain.2017.05.008.

Departmento de Psicobiologia y Metodologia de las CC. Del C., Faculted de Psicologia, Campus de Teatinos s/n, Malaga 29071, Spain

Ethical issues: This research project was approved and registered by the Carlos Haya Hospital Ethics Committee. Informed consent was obtained prior to data collection.
Conflict of interest: None declared.

Acknowledgements

This study was supported by grants from the Spanish Ministry of Science and Innovation (PSI2008-01803/PSIC and PSI2012-32662); and the Regional Government of Andalusia (HUM-566; P07-SEJ- 3067).

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Appendix A

Let Y be a variable measured on an individual (i =1 to N) over time (t = 1 to T), where Y is pain intensity, depression, and disability in each model, respectively; time is time with pain.

The first model is a linear growth model, which can be written as

Yit=yi0+yis⋅timeit+eit

where Y_it is the observed score on individual i at measurement t, y_i0 is the latent initial level score of an individual i, y_is is a latent score of individual i, representing the slope or change in the individual over time, time_it is the observed time with pain of individual i at measurement t, and e_it is the latent error score of individual i at measurement t. This model includes sources of individual differences in the level and slope, as

yi0=μ0+3i0 andyis=μs+eis

where the level and slope scores have fixed group means (μ₀ and μ_s and residuals (e_i₀ and e_i_s), and these residuals have variance components (σ02,σs2 and σ_0s; u ~ N(0, G)). Similarly, the error term associated with the within-person residual e_it also has a zero mean and a variance term σ02, (e_i ~ N(0, R)).

The next model allows a change of direction in the trajectory at a specific point in time (i.e., a linear spline model). Two linear spline models with two pre-determined transition points were investigated; one with a transition point at 3 months with pain (according to the standard definition of chronic pain), and the second at 6 months with pain (as suggested by Philips and Grant [12]). These models can be written as

Yit=yi0+yis1⋅time1it+yis2⋅time2it+eit

where time1 and time2 represent the time with pain before and after the transition point, y_is₁ and y_is₂ are the regression coefficients associated with the linear changes before and after that transition point, and y_i₀ represents the score at that point. This model has been found to be useful to evaluate hypotheses on differential rates of change across various periods of time. For further information on these models see Kail and Ferrer [23] and McArdle et al. [24].

Appendix B. Supplementary data

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.sjpain.2017.02.009.

Received: 2016-09-10

Revised: 2017-02-03

Accepted: 2017-02-21

Published Online: 2017-07-01

Published in Print: 2017-07-01

Supplementary Material Details

Articles in the same Issue

https://doi.org/10.1016/j.sjpain.2017.02.009

Keywords for this article

Chronic pain onset; Pain intensity; Depression; Disability; Change

From acute to chronic back pain: Using linear mixed models to explore changes in pain intensity, disability, and depression

Article

Abstract

Background/aims

Methods

Results

Conclusions

Implications

1 Introduction

2 Methods

2.1 Participants

2.2 Instruments

2.3 Procedure

2.4 Data analyses

3 Results

4 Discussion

Highlights

Acknowledgements

References

Appendix A

Appendix B. Supplementary data

Supplementary Material

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Articles in the same Issue

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