Pain when it “counts”: hurdle analysis of clinical pain ratings improves data model performance

Appraising performance characteristics of the pain Numerical Rating Scale using marginal distribution analysis we identify efficient pain metrics that represent clinical data more precisely than prior methods.

Abstract

Objectives:

The Numerical Rating Scale is widely used for patient-reported appraisals of pain intensity; however, scale properties have limited utility for assessing chronic pain. Specifically, single pain ratings demonstrate high intraindividual variability. We propose an efficient alternative, termed hurdle analysis, separately analyzing zero and nonzero pain ratings.

Methods:

This retrospective study of 23,480 US Veterans diagnosed with low back pain (LBP) included 2.1 million unique pain ratings. Marginal distributions comprised of all pain ratings for each individual were parametrized with usual and hurdle analysis methods to holistically assess scale utilization.

Results:

The population was 87% male and 13% female; 41% Black, 38% White, and 2% Hispanic; modal age range was 65 years to 84 years (45 years–64 years) for men (women). Focusing on statistically informative records, ie, those with ≥100 pain ratings (22% of the total), the median [interquartile range] pain rating was 3.5 [2.3–4.7] (4.0 [3.0–5.1]) for men (women). Marginal distributions were non-normal, with zero being the modal value in 79% (73%) of men (women). In hurdle analysis, the average proportion of zeroes was 0.39 (0.31) for men (women); the average nonzero pain rating was 5.9 [5.1–6.6] (6.0 [5.3–6.7]) for men (women). The nonzero averages, in contrast to standard averages, were normally distributed for the population and compared with data showed less bias and variance.

Conclusion:

Analysis of clinical pain ratings from Veterans with LBP with hurdle analysis yielded improved estimates of pain when-pain-is-present (ie, nonzero pain) and also demonstrated the variable presence of pain in this population. Further study of this approach appears warranted.

1. Introduction

Pain assessment remains challenging despite the development of many approaches.^{4,9,11,13,36,56,58} Studied since the mid-20th century, pain intensity measures are essential to acute care and research on analgesic efficacy.^18,33 Nonetheless, concerns about the utility and interpretability of pain intensity ratings persist.^35,58 One approach, the Numerical Rating Scale (NRS) of pain intensity has been used widely for decades.^15,27 In diverse clinical settings, the NRS is rapidly administered, functions reliably, and is responsive to acute analgesia.^9,28,60 Nonetheless, the NRS has features that limit use, especially for chronic pain.^{3,21,25,34,61}

Numerical Rating Scale performance in chronic care settings demonstrates high variability.^{7,17,21,53,54} The variability within and between individuals experiencing the same “type” of pain prevents clearer interpretation.¹² Repeated NRS ratings obtained from individuals over time, and ratings from cross-sectional populations demonstrate large variation and non-normality.^14,23,24 This has stymied data interpretation and study design.^12,14 As an alternative to single point-in-time NRS ratings as outcomes, some researchers have proposed averaging multiple NRS ratings to produce average pain scores (APS).^14,26 Viewed as “smoothing out” the variability of single NRS ratings, APS may also be suboptimal.⁵⁷ Averaging can introduce bias, especially when data do not fit a unimodal distribution.¹⁰ Averaging can obscure key information regarding intraindividual as well as interindividual variability.³⁹ One important source of pain data variability that may be lost by averaging pain ratings is the occurrence of “low” or zero-value pain ratings.^22,59,63 Zero-value pain ratings potentially represent a tendency to be “pain-free” or “pain-resistant,” which may have special salience.⁴³ In short both APS and single (point) NRS ratings are unreliable and biased estimators of clinical pain data; alternatives are needed.²¹

In 2017, Goulet et al.²³ analyzed single NRS ratings from a cross-sectional cohort of US Veterans with musculoskeletal diagnoses enrolling in primary care clinics. The ratings demonstrated “excess” zeroes, ie, although some patients had pain at the time of their intake visit, others did not. They concluded that a method termed zero-inflated analysis was potentially superior to standard unimodal distributions, such as the binomial distribution, for fitting cross-sectional pain ratings data. Further application of this approach to pain has been limited.^2,38,51,62 In mental health research and other fields, zero-inflated data models have gained wider adoption.^2,30,49,51 More complex models of pain ratings data have also been proposed.⁵⁵ Pragmatically, however, model complexity can limit implementation.⁴⁸ The nature of clinical NRS data, collected at irregular intervals (having variable gaps), means that the computational burdens of time-based models are profound.⁵⁵ Considering these factors, we wanted to explore whether simplified zero-inflated analysis might work for individual longitudinal data. Focusing here on the scale properties of the NRS, we analyze marginal distributions of NRS pain ratings gathered over time from individuals. Our goal is to determine whether individual pain ratings data distributions from those with low back pain reveal key features of NRS usage. We specifically did not target persons without a pain diagnosis, as infrequent pain produces distributions that are statistically uninformative. The primary outcome of this analysis is a comparison of the statistical fit of the proposed Hurdle Pain Score (HPS) vs the fit of ordinary average and standard deviation parameters as models of pain ratings data.^16,45 Assessing the residual model error, we find that HPS yields far better statistical precision than usual analysis.

2. Methods

2.1. Data source

We conducted a retrospective analysis of pain ratings obtained and recorded at the Baltimore Veterans Affairs (VA) Medical Center (VA Maryland Health Care System [VAMHCS], Station 512) for all Veterans with a diagnosis of low back pain (LBP) with at least one clinical encounter between the dates of January 1, 2018, and May 31, 2022. Since 1995, VA healthcare facilities have recorded pain ratings at many clinical encounters across a range of settings including inpatient vital signs, procedural visits, recovery room admissions, and outpatient visits (encounters), using an 11-point NRS.²⁰ Most VA pain ratings are accessioned into the electronic health record directly by nursing assistants who are trained to conduct “pain screenings” using standard NRS scales.⁵⁰ In this study, all pain rating data of each individual, without consideration of assessment setting, were included for analysis. Data, including NRS pain ratings, were processed within the VA Integrated Network Computing Infrastructure. Demographic features were defined as those in the VA EHR. Data were extracted using Microsoft SQL Server 2022 and SQL Server Management Studio 2018 (Redmond, WA) and analyzed using SAS (Cary, NC).

2.2. Subject ascertainment

Veterans with one or more visits to VAMHCS during the ascertainment period and at least one diagnosis of LBP, as determined by the presence of an ICD-10 code of M54.5, were included, as previously published.^31,32 The study cohort excluded patients for whom demographic data were not available, and patients whose only pain ratings were outside of range (eg, a pain rating >10 [exclusively “99”] or missing).

2.3. Statistics

Marginal distributions were calculated using all available NRS ratings starting with the first recorded rating for the Veteran and extending until the date of data extraction.⁴⁵ We used over 2.1 million NRS pain ratings from a cohort of over 23 thousand US Veterans diagnosed with LBP.

The primary aim of this article was to compare zero-inflated pain rating analysis, implemented here as HPS, to the analysis of pain ratings as conducted using an ordinary average and standard deviation (termed here point pain score [PPS] analysis). The goal was to determine whether and to what extent HPS is a more precise representation of NRS utilization by Veterans with LBP, compared to usual average analysis. Point pain score is premised on the assumption that clinical pain rating values arise from a unimodal pain distribution, whereas the HPS is premised on the assumption that pain ratings arise from bimodal distributions, here consisting of zero-valued ratings and other ratings being all nonzero pain ratings values. We planned a priori to use a model variance to evaluate precision.

All the available ratings were used to compute a subject-by-subject average and standard deviation, as well as the variance (PPS parameters). For “zero-inflated” pain rating analysis, some researchers have used machine learning algorithms iteratively fitting the proportion of data which are likely to arise from a data distribution inclusive of nonzero values (this may include some zeroes), finding the mean value of that distribution. Data not included in this distribution must meet criteria for inclusion in the “other” distribution which consists exclusively of data with the value of “0.”^16,37 In lieu of this machine learning approach, we used a technique known as hurdle analysis in which all values falling below a threshold value are partitioned in a “data below threshold” group (DBT), and all values falling above a threshold value are portioned into a “data above threshold” group (DAT). Here, we set the threshold at 0.5 so that the DBT included all pain ratings with a value of zero; DAT included all pain ratings with a value in the range of 1 to 10 inclusive. For the DBT, the number of ratings (with a value of zero) was counted; for the DAT, the number of ratings (with nonzero values) was counted (HPS-proportion), and the average of the nonzero ratings (HPS-average) was computed. A variance of the HPS parameters for each Veteran was also determined. Variance for HPS-proportion depends inversely on the number of values included in the estimate. Here, the variance of HPS-proportion was small (many data for each individual). Finally, we calculated a sum of squares for the entirety of each Veteran's NRS pain ratings.⁸ Goodness of fit was determined by calculating a sum square of error for PPS and HPS-average for each Veteran and determining the reduction in the sum of squares attributable to HPS for every study subject over the 1 to 10 NRS range. Separate analyses were performed and reported for women and men. For this study, we limited the analysis to those patients with 100 or more pain ratings so that the variance estimates would be sufficiently well-determined; those with smaller number of data will require additional study.

2.4. Ethics oversight

This study was approved by the University of Maryland Human Rights Protection Office and the VA Maryland Health Care System Research and Development Committee.

3. Results

3.1. Study population

In total, 23,561 Veterans diagnosed with low back pain had an encounter at our medical center during the period January 1, 2018, until May 31, 2022 (Figure 1). Of these, 23,480 (99.6%) had demographic data (Table 1). Most patients were noted to be male; 20,378 (86.8%) and 3,102 (13.2%) were noted to be female (Table 1). Women were younger than men. Race and ethnicity data were available for 98.2% of women and 89.2% of men. Black/non-Hispanic or Latino was the most common race and ethnicity group in women and men, 56.1% and 44.9%, respectively, White/non-Hispanic or Latino being the second most common group, 28.3% and 44.7%, respectively.

Figure 1.

Population and pain rating flow diagram. Total pain scores exclude 5630 missing values. Pain scores 0 to 10 exclude 4995 values of “99.”

Table 1.

Demographics.

Sex	Female	Male
	3,102	20,378
Age
≤24	2	3
25–44	991	2987
45–64	1570	6039
65–84	518	7095
85+	21	1046
Race/Ethnicity
Black/non-Hispanic	1710	7592
Black/Hispanic	36	73
Black/other	35	115
White/non-Hispanic	861	7558
White/Hispanic	75	305
White/other	24	156
American Indian or Alaska Native	35	73
Asian	54	233
Native Hawaiian or other Pacific Islander	33	118
Unknown or declined to answer	183	675

3.2. Numerical Rating Scale values across the total population

In total, 2,105,412 pain assessments were documented; 5,630 (0.3%) were missing rating values. A total of 4,995 (0.2%) NRS ratings were recorded as “99,” outside of range, and were excluded from study. The remaining 2,094,787 NRS ratings were analyzed on a subject-by-subject basis. The number of pain ratings for each patient ranged from 0 to 17,026 with an average (median) NRS count of 85.3 (28) for women and 89.8 (35) for men. For the total population, the average pain rating (± standard deviation) was 3.6 ± 1.8 for women and 3.3 ± 1.9 for men (excluding 239 men and 47 women without pain ratings). Across the population, zero was the most frequent rating and 2 was the least for both sexes. For further analysis, we excluded those with <100 pain ratings because of resulting statistical uncertainty. Six hundred twenty-six women and 4,294 men had ≥100 pain ratings, 20.2% and 21.1% of total ratings, respectively. For these, zero was the most frequent rating and 2 was the least, for both sexes; the nonzero mode at the median was 7 for women and men (Table 2).

Table 2.

Percent of women and men having specified Numerical Rating Scale ratings expressed as percentiles.

NRS	Women (percentile percent)					Men (percentile percent)
	5th	25th	50th (median)	75th	95th	5th	25th	50th (median)	75th	95th
0	9.3	19.5	31.1	45.1	68.5	10.7	23.3	38.8	57.5	81.1
1	0.5	1.7	2.9	4.5	7.2	0.4	1.7	3.0	4.7	8.4
2	0.0	1.3	2.5	4.2	9.1	0.0	1.3	2.4	4.0	8.4
3	0.7	2.3	3.8	6.6	12.3	0.6	2.0	3.7	6.1	11.9
4	0.9	2.9	4.7	8.2	16.0	0.8	2.5	4.3	7.0	13.2
5	2.0	4.9	7.4	10.9	18.5	1.6	3.9	6.4	9.6	16.4
6	1.6	4.8	7.9	11.2	17.5	0.9	3.7	6.2	9.8	16.9
7	1.8	5.7	9.6	14.3	21.0	0.9	4.0	7.7	12.6	21.9
8	1.0	5.1	8.8	15.0	25.0	0.8	3.6	7.6	13.3	24.1
9	0.0	1.5	3.2	6.5	15.0	0.0	0.9	2.4	5.1	12.3
10	0.0	1.7	3.7	8.5	18.5	0.0	1.0	2.8	6.3	18.0

For example, the median percent of assessments for which the NRS was recorded as zero for women was 31.1% that for men was 38.8%. In this cohort with LBP, zero is distinctive the most commonly documented rating, 2 is the least common. Notably, 9 and 10 are not used with high frequency (∼20% of ratings) except in a modest percentage of the population. Bold font indicates median values.

LBP, low back pain; NRS, Numerical Rating Scale.

3.3. Point pain score for individuals

Numerical Rating Scale ratings for the Veterans with at least 100 pain ratings totaled 197,300 for women and 1,452,386 for men (1,649,686 total), comprising 78.4% of the pain ratings extracted. The ratings for individual Veterans were plotted as a function of time; 2 examples are shown in Figure 2A and B. We observed that NRS ratings vary over time and that pain ratings of zero (meaning that “no pain” is perceived at the time of assessment), are relatively common. To evaluate pain scale utilization by Veterans in clinical settings, we applied marginal distribution analysis, constructing histograms including all the pain ratings of a single patient (see examples in Figures 2C and D). The marginal distributions demonstrated that most Veterans had a substantial proportion of pain ratings of zero. Zero was the modal pain rating for 73% of women and 79% of men. The proportion of zero-value pain ratings for each Veteran showed a median percent (interquartile range) of 31.3% (19.8%-45.2%) and 38.8% (23.3%-57.5%) for women and men, respectively; meaning a “median” Veteran with LBP would report “zero” pain at approximately a third of pain assessments.

Figure 2.

Example pain rating records and histograms. (A) All NRS pain ratings for 71-year-old female veteran, N = 357, (B) all pain ratings for 77-year-old male veteran, N = 338. (C) Pain rating marginal distribution for data shown in (A, D) pain rating marginal distribution for data shown in (B). Pain ratings were assessed at specific times shown as filled (black) data points in panels (A and B). These data points are shown as connected with dashed lines (which do not indicate continuous pain assessment) to facilitate visualization as a series of data. NRS, Numerical Rating Scale.

3.4. Standard statistical parameters for individual study subjects and the population

Averaging all a patient's pain ratings, an overall APS was computed. The population distribution of APS for women and men is shown in Figure 3A and B. The median of the APS distribution (interquartile range) was 4.0 (3.0–5.1) for women and 3.5 (2.3–4.7) for men, with 95% of the data ranging (2.5 percentile–97.5 percentile) from 1.2 to 6.8 and 0.61 to 6.4, respectively. The distribution of APS values for women was generally symmetrical with wide variation; the distribution for men was not symmetrical, also showing wide variation. The variance associated with each individual APS was determined; this variance of the APS estimates varied across the population and was slightly different for women and men, being generally symmetrical (Fig. 3G and H). The variance associated with APS estimates was substantial with median (interquartile range) values of 10.1 (8.2–12.3) for women and 9.7 (7.6–12.1) for men, with 95% of the data ranging (2.5 percentile–97.5 percentile) from 4.4 to 15.7 and 2.9 to 16.6, respectively.

Figure 3.

Pain rating parameters determined using averaging and HPS methods, by sex. (A) Average of all pain ratings for individuals, all women, (B) HPS-averages for individuals, all women, (C) proportion of nonzero pain rating values across all females (HPS-proportion); (D) comparison of variance of individual average determinations and HPS-average determinations for individuals, all women; (D) average of all pain ratings for individuals, all men, (E) HPS-averages for individuals, all men, (F) proportion of nonzero pain rating values across all men (HPS-proportion); (G) comparison of variance of individual average determinations and HPS-average determinations for individuals, all men. Analyses limited to those with 100 or more pain rating assessments, details in text. HPS, hurdle pain score.

3.5. Hurdle pain score parameters for individual study subjects and the population

Hurdle pain score analysis was performed by calculating the average of all nonzero NRS values (HPS-average) as well as the proportion of nonzero pain ratings (HPS-proportion) (Fig. 4). For the population, the median HPS-average (interquartile range) was 6.0 (5.3–6.7) for women and 5.9 (5.1–6.6) for men, with 95% of the data ranging (2.5 percentile–97.5 percentile) from 4.0 to 7.8 and 3.5 to 7.9, respectively. The population distribution of HPS-averages for women and men was generally symmetrical (Figs. 3C and D). The variance of individual HPS-averages was similar for both women and men, with a median (interquartile range) of 5.1 (4.2–6.2) and 5.4 (4.3–6.5), respectively, with 95% of the data ranging (2.5 percentile–97.5 percentile) from 2.5 to 8.5 and 2.4 to 9.0, respectively. The distributions of these variances were generally symmetrically distributed (Figs. 3G and H). The median HPS-proportion (interquartile range) was 0.69 (0.55–0.89) for women and 0.61 (0.43–0.77) for men ranging (2.5 percentile–97.5 percentile) from 0.25 to 0.92 and 0.14 to 0.92, respectively. The population distribution of HPS-proportions is shown in Figure 3E and F. The distributions of HPS-proportions were not symmetrical; both female and male distributions showed a longer left tail. Notably, male–female comparison indicated that percentage-wise more men are represented in the lower range of HPS-proportions.

Figure 4.

Hurdle–average (HPS-average) values vs. hurdle–proportion (HPS-proportion) values for each veteran with over 100 pain ratings. Men shown as blue dots and women as magenta dots. The HPS is determined as the expected value of data above threshold (E [DAT]), ie, average of NRS ratings above zero, and the HPS-proportion is determined as the proportion of pain ratings above threshold (P [DAT]), ie, proportion of all NRS ratings, for an individual, that are greater than zero. HPS, hurdle pain score; NRS, Numerical Rating Scale.

3.6. Comparison of average pain scores and hurdle pain score in terms of fit to the data

Comparing the population distributions of individual APS and HPS-average values (Fig. 3A compared with Fig. 3C and Fig. 3B compared with Fig. 3D) demonstrated that HPS-average values are higher overall and less dispersed. The population distributions for APS scores show substantive dispersion, and the distribution for men is not symmetrical. By contrast, the HPS-average scores are generally symmetrical for both women and men. Taking the HPS-proportion distribution data together with the HPS-average data, we find that the asymmetry of the male APS distribution may reflect the fact that there are more men who have HPS-proportion below 0.5. By contrast, the HPS-average population distribution is symmetrical for both male and female Veterans. The variance of APS values was compared with the variance of HPS values using an F-statistic which demonstrated that the variance of HPS-average estimates was significantly smaller for both women and men (P < 0.001).

The representation of the data by the HPS and standard data models was assessed using a sum of squares approach. We determined that the average reduction in sum of squares, evaluated across nonzero pain ratings, for the HPS-average was 50.7% for women and 55.8% for men compared with the total sum of squares as determined for PPS. To assess the degree of bias arising from the usual (PPS) and HPS methods regarding the estimation of expected pain intensity when pain is present, we selected the nonzero mode as a “gold standard,” post hoc. The mean (± standard deviation) estimated bias of the average pain score was −2.7 (±1.8) for women and −3.0 (±1.9) for men, whereas that for the HPS was −0.7 (±1.3) and −0.6 (±1.5), respectively.

4. Discussion

This analysis of >1 million pain ratings demonstrates that NRS pain ratings of individual Veterans with low back pain are not unimodal; rather, a constrained bimodal model yields improved data representation. Specifically, by evaluating pain-when-present, we determined that the resulting “hurdle pain score-average” demonstrates reduced variance and bias compared with usual methods. In addition, we show that the proportion of nonzero pain ratings is an important source of interindividual variation in the population. Using robust statistical methods, we found that the model error arising from the APS/PPS methods is substantially larger than for HPS, ie, HPS is a better model. We find that HPS analysis, by providing a metric of pain intensity that is computationally parsimonious (efficient), associated with less intraindividual model variance and bias (more precise), and characterized by markedly reduced interindividual variance (reliable), is potentially highly useful as a pragmatic alternative. We conclude from this that hurdle pain score analysis, focusing on “expected pain when pain is present” and the “proportion of assessments with nonzero pain,” may be an efficient approach to assessing pain rating data.

Several observations from this study have direct clinical application: (1) pain was commonly, but not always, present on assessment; (2) women were more likely to report (nonzero) pain; (3) when pain was present, it was typically in the high-moderate range, substantially higher than estimates derived from “usual” averaging⁵⁰; (4) the intensity of pain-when-pain-is-present (HPS-average) was indistinguishable for women and men; and (5) an HPS-proportion above 50% (pain more often) was more common for women, this may have important implications for clinical studies of pain relief.

To explain differences between APS and HPS in conceptual terms, we superimpose curves representing real data and real model predictions for averaging and HPS (Fig. 5). This illustrates that (1) averaging assumes that pain rating distributions are unimodal, but most are not; (2) the outcomes of usual averaging results in substantive bias in estimating pain-when-pain-is-present, ie, distance from the nonzero (data) mode to the total data average is large, whereas the HPS-average is closer to the nonzero mode; and (3) comparison of the data to the average of all data produces variance that is greater than that for HPS, indicating that APS is an error-prone representation of data. The observation that HPS-averages have much less variance than APS-averages, as in Figure 4C and G, may affect how treatment effects are assessed. By decreasing variance in the manner proposed here, for studies which seek to use clinical pain ratings as a pragmatic assessment of pain experience, increased power would be expected.¹⁹ Also, HPS analysis will shed new light on patterns of pain recurrence. For example, some conditions respond to specific treatments by having a reduction in pain intensity “when-pain-is-present” (reduced HPS-average), while others may have less frequent pain (reduced HPS-proportion, eg, migraine).⁴⁰ In short, we show intrinsic bias in APS and PPS as estimators of patient pain experience.²⁶ By formally reappraising the performance characteristics of the NRS using marginal distributions of pain ratings, we see that HPS describes patient-reported pain ratings data with greater precision.

Figure 5.

Example of data, fit based on averaging of all ratings data, and HPS model fit. A Veteran's pain rating marginal distribution is shown as solid gray-filled vertical bars. The “fitted model” based on data averaging (APS) is a normal curve reflecting the values of the average and standard deviation (specified in the legend) for all pain ratings provided by the individual (red dashed line). The model is clearly very different from the data. The “HPS-fitted model” is a normal curve reflecting the nonzero data (Hurdle Pain Score) average and standard deviation (blue dashed line). The line represents an objectively better fit of the data in this example with model error reduced by approximately 50%. APS, average pain scores; HPS, hurdle pain score.

Hurdle pain score analysis operationalizes a bimodal model of pain intensity, where pain may be viewed as categorically different when absent vs when present. As alluded to above, average scores are generally only appropriate when data cluster around a single central tendency.⁸ It is not necessarily the case that averages are only useful when distributions are symmetrical, but the meaning of the average will be distinctly different (and biased as a measure of central tendency) for asymmetrical distributions such as the Poisson and the negative binomial and may be uninterpretable for bimodal and multimodal distributions.^16,23,38 When data exhibit abundant zeros and the remaining data appear to arise from a distinct nonzero distribution, the hurdle technique may work well in representing data. There is growing interest in zero-inflated models, such as the hurdle model, as representations of patient-reported outcomes.^2,6,16,37,49 In mental health research, interest in zero-inflated data models has expanded; for example, drug cravings research.⁴⁹ Our data suggest that “0” pain may be categorically distinct from pain of 1 to 10, but further study is needed.

Although there has been considerable controversy over NRS “appropriateness” in some quarters, there has been relatively little formal study of NRS characteristics since Electronic Health Record expansion.⁵² Goulet examined single NRS pain ratings in a cross-sectional cohort of Veterans with musculoskeletal pain diagnoses at primary care intake.²³ That cross-sectional study demonstrated single point ratings for a population may follow a zero-inflated distribution. Our research demonstrates this phenomenon at the level of the individual. Whereas the cross-sectional study could be interpreted as showing that some individuals “feel pain” and others “do not,” the data here indicate that almost everyone feels “0” pain sometimes, and individuals vary both in terms pain intensity and presence. This finding, validated by additional study, could yield breakthroughs in understanding the NRS system while yielding insight into how individuals experience pain differently from one another. The shape of the data distributions observed in the Veterans in our informative subset of several thousand indicates that most patients used the NRS scale in a manner that produced bimodal distributions; most were “zero-inflated,” a term of the art from industrial engineering studies of the 1960s. This does not mean that patients “inflate” their zeroes or necessarily that providers are suppressing pain, it is simply a technical term describing the shape of the distribution. More work may be required to optimally define the distributions observed.¹⁶ Our data showed a paucity of low-value nonzero pain ratings, eg, very few “1”s and “2”s, and a preference for pain rating values ranging 4 to 8, predisposing hurdle analysis to work well as a step towards even greater precision.

Further research would be needed to ready this method for clinical use. Steps in this process might include feasibility and user experience testing and further methodological development. Potential clinical benefits include improved recognition of sentinel pain events and more accurate and actionable characterizations of pain intensity, and the proportion of time that pain is present.

Limitations of this study include studying a population from a single medical center. The host medical center has a strong and stable relationship with a multiprofessional university-based healthcare campus and hospital system that provides training to diverse clinical providers, meaning that consistency in clinical education and care delivery contextualizes these data.^5,46 The scale of available data supported our exploratory data analysis which can now be validated through multisite studies. The choice of marginal distribution analysis was intentional, supporting focus on pain scale utilization agnostic to temporal data features. Because pain is often assessed at irregularly irregular intervals, with variably long gaps between assessments, analytical methods based on regular data “sampling” cannot be used.⁵⁵ Time-based analysis with variable “sampling” is computationally intensive. Schneider, for example, reported “regime-switching” analysis of ecological momentary assessment pain ratings using a bimodal analytical model; because they reported results as a single average, direct comparison is not possible.⁵⁵ Another limitation is that this study focuses on those with LBP diagnosis exclusively, but because the prevalence of LBP is very high in Veterans, this is an important population.⁴⁴ We cannot exclude that Veterans may report more (or fewer) zeroes than civilians. We opted for a population not including those without a pain diagnosis as determination of HPS properties has intrinsic statistical limitations in those with small amounts of informative (ie, both zero and nonzero) data. Studies comparing broader populations, with and without a variety of pain diagnoses, are clearly of interest and will need study. In this LBP cohort, we intentionally did not exclude those with other pain conditions; the results represent a wide range of patient experience.

The demographic features of our study population overcome a limitation of many other studies; we focus on majority Black, urban-dwelling population which has been subject to diverse disparities with multidimensional health impacts.^1,42 Many of those who receive care at the studied medical center experience profound socioeconomic and environmental disadvantages, and the impacts of these factors warrant detailed study, including impact on pain and pain relief.⁴⁷ It may be that the patients in our study have increased pain associated with LBP due to the above factors, but we cannot exclude the possibilities that pain ratings are reduced due to healthcare disparities; race was not separately examined here.^29,41

In this report, we demonstrate the potential value of HPS analysis, a rapidly implemented, pragmatic alternative to data averaging and other more resource intensive methods. Finding that HPS parameters demonstrate increased precision, we conclude that the HPS is a potentially useful approach. We also find that those with LBP vary widely in terms of the proportion of pain assessments that are associated with nonzero pain. Adopting a pain rating analysis technique that reflects the intensity and presence features of longitudinal pain rating data will result in less unexplained variance and less intrinsic bias. We posit that the intensity of pain-when-pain-is-present and the proportion nonzero pain ratings, represented separately in HPS analysis, both describe important features of patient-reported pain experience and that people vary substantively in experiencing these features.

5. Summary

Appraising performance characteristics of the pain Numerical Rating Scale using marginal distribution analysis we identify efficient metrics that represent clinical pain ratings more precisely than prior methods.

Disclosures

The authors have no conflict of interest to declare.