Comparing Propensity Score Methods for Creating Comparable Cohorts
of Chiropractic Users and Nonusers in Older, Multiply Comorbid
Medicare Patients With Chronic Low Back Pain

This section is compiled by Frank M. Painter, D.C.
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FROM:   J Manipulative Physiol Ther. 2015 (Nov); 38 (9): 620–628 ~ FULL TEXT

William B. Weeks, MD, PhD, MBA, Tor D. Tosteson, ScD, James M. Whedon, DC, MS, Brent Leininger, DC, Jon D. Lurie, MD, MS, Rand Swenson, DC, MD, PhD, Christine M. Goertz, PhD, DC, Alistair J. O'Malley, PhD

The Geisel School of Medicine at Dartmouth,
The Dartmouth Institute for Health Policy and Clinical Practice,
Lebanon, NH;

OBJECTIVE:   Patients who use complementary and integrative health services like chiropractic manipulative treatment (CMT) often have different characteristics than do patients who do not, and these differences can confound attempts to compare outcomes across treatment groups, particularly in observational studies when selection bias may occur. The purposes of this study were to provide an overview on how propensity scoring methods can be used to address selection bias by balancing treatment groups on key variables and to use Medicare data to compare different methods for doing so.

METHODS:   We described 2 propensity score methods (matching and weighting). Then we used Medicare data from 2006 to 2012 on older, multiply comorbid patients who had a chronic low back pain episode to demonstrate the impact of applying methods on the balance of demographics of patients between 2 treatment groups (those who received only CMT and those who received no CMT during their episodes).

RESULTS:   Before application of propensity score methods, patients who used only CMT had different characteristics from those who did not. Propensity score matching diminished observed differences across the treatment groups at the expense of reduced sample size. However, propensity score weighting achieved balance in patient characteristics between the groups and allowed us to keep the entire sample.

CONCLUSIONS:   Although propensity score matching and weighting have similar effects in terms of balancing covariates, weighting has the advantage of maintaining sample size, preserving external validity, and generalizing more naturally to comparisons of 3 or more treatment groups. Researchers should carefully consider which propensity score method to use, as using different methods can generate different results.

KEYWORDS:   Chiropractic Manipulation; Medicare; Propensity Score

From the FULL TEXT Article:


Health Services research methods, such as analysis of large claims databases, are an important tool for research on effectiveness and efficiency of complementary and integrative health services (CIHS) such as spinal manipulative therapy (SMT). [1] These methods may be particularly useful when determining whether patients who use such care for certain conditions might have lower overall care costs when compared to patients who do not, [2] a so called ‘medical care cost offset’ that has been demonstrated, for instance, with pharmaceutical [3, 4] and mental health [5, 6] treatment.

The very high variability of healthcare expenditures for individuals [7] might distort cost-offset analysis when sample sizes are small, as they frequently are in randomized controlled trials (RCTs) that examine the effectiveness of SMT. As a recent report on RCTs that studied the clinical effectiveness of SMT for neck and low back pain found a median sample size of 95, and an interquartile range of 47–199, [8] research efforts searching for medical care cost offsets might need to use large databases or nationally weighted surveys [9] to conduct observational comparative effectiveness studies with adequate sample sizes.

However, the use of observational data from large datasets or surveys to compare groups that do or do not use a particular treatment modality may be confounded by selection bias. [10, 11] For instance, studies that have compared users to non-users of a common type of SMT that is provided by doctors of chiropractic (DCs) (known as chiropractic manipulative treatment (CMT)) show that CMT users are younger, wealthier, and healthier than non-users and more likely to be insured and female. [12–14] These demographic characteristics have been associated with different health and cost outcomes when comparing CMT to medical care for treatment of low back pain. [15] Therefore, it is critical to recognize potential selection bias when attempting to compare treatment groups in observational studies of patients who use CMT.

While traditional risk-adjustment for demographic differences in patient populations through risk stratification and regression adjustment have narrowed cost differences between patients who obtained CMT and those who sought conventional medical care for back pain, [16] newer statistical methods that calculate the propensity of patients to self-select into 1 treatment group or another, based on a variety of demographic and utilization variables, and use those calculations for further analysis, are increasingly used in light of their improved performance in estimating causal effects. [17, 18]

To date, several studies have applied propensity score methods to analysis of survey data in an effort to compare CIHS users to non-users. In a study that found that most CIHS treatment for back and neck problems was provided by DCs, Martin et al. used the Medicare Expenditure Panel Survey to compare costs of treatment for back and neck problems for patients who did and did not use CIHS: propensity scores for the 2 groups were used to match patients who had propensity scores within a ‘region of common support’ and then identify the ‘nearest neighbor’ as a method to develop 2 matched groups for comparison. [19] Weigel et al. have applied inverse propensity score weighting to data from ‘Medicare Current Beneficiary Survey’ [20] respondents and to ‘Assets and Health Dynamics among the Oldest Old’ interviews [21] when comparing utilization and outcomes of chiropractic and conventional medical treatment of back pain in the Medicare population. However, to date, propensity score methods have not been applied directly to Medicare claims data to evaluate costs of care for patients seeking back pain treatment.

This study has 2 purposes. Firstly, the paper provides an overview and brief tutorial on how propensity score methods work and the different types of propensity score methods that are commonly used in order to help readers of the CIHS literature understand these fairly complex methods. Secondly, the study uses Medicare data from 2006–2012 on older, multiply comorbid patients who had a chronic low back pain episode to demonstrate the impact of applying different propensity score methods on the balance of demographics of patients who were in one of 2 treatment groups: those who received only CMT and those who received no CMT during their episodes.



Overview of propensity score methods Propensity scoring methods can be used to address possible confounding in observational studies where investigators have no control over treatment assignment, such as when they retroactively analyze health care claims databases. Conditional on a set of observed covariates, the propensity score for a patient is defined as the probability of a patient with the same observed characteristics being in the treatment group. [22] The application of propensity score methods is designed to construct a new analytic dataset in which treatment groups are balanced on observed confounders so that the outcomes for the different treatment groups can be directly compared.

For instance, imagine that there were 100 patients with low back pain who used CMT and 200 who did not, and the 2 groups differed in their age and sex distributions (Figure 1). When examining the actual data, it is evident that the numbers, proportions of males and females, and ages of the 2 different treatment groups differed. Propensity scores based on age and sex could be used to identify and match patients who have a similar likelihood to be in a particular treatment group even if those cases differed individually on age and sex (shown in red in the figure). [23] However, using such a matching process limits the analysis to those with similar scores, and the number of cases that can be used for analysis will decline in both treatment groups. This is generally true whether one uses a 1–to-many (where 1 case from the smaller group is matched to several from the larger group) [23] or a 1–to–1 ‘closest neighbor’ matching mechanism. [19] With the limited number of cases, the age- and gender-distributions of the larger group will begin to resemble those of the smaller group. When using this method, it must be then acknowledged that the reduced dataset used to analyze outcomes may not be representative of the original study dataset. That is, external validity may be sacrificed to improve internal validity.

An alternative method that allows researchers to retain all of the data and maintain generalizability to the larger groups is propensity score weighting [24] (Figure 2). Here, cases are weighted according to the inverse of the propensity of a patient to self-select into a particular treatment group, based on demographics and other variables. In effect, this method relatively over-weights results for patients who are least likely to have self-selected into their respective treatment group, given their characteristics. In the example, one can see that older female patients are less likely to be in the CMT group; by over-weighting the older patients (and the females) and under-weighing the younger patients (and the males), one can generate a distribution that approximates the demographics of the non-CMT treatment group.

The variables that should be used to calculate propensity scores differ from study to study, and even the number of variables used is open to consideration. While some authors advocate broad use of all variables, others suggest that experts use the literature and the data to determine which variables are likely to represent important differences that might affect the outcome between treatment groups. Recent studies indicate that a combination of those methods is probably the most effective way of determining propensity score variables. [25] However, the trimmed propensity score methodology, wherein only statistically significant differences in the characteristics of the comparison groups are included in the propensity score calculation, has generated the best predictive models when examining rare events. [26]

Analysis becomes much more challenging when comparing multiple treatment groups. In this case, multinomial regression or alternative approaches to analysis of ordinal or nominal data are required to generate propensity scores that allow comparison of multiple treatment groups. Matching would then require application of algorithms to identify closest matches across the several treatment groups. [27] However, propensity score weighting methods generalized more easily to comparisons of 3 or more treatment groups than methods for propensity score weighting methods, but either method can be used to address selection bias with, [28] or without, [29] stratification.

      Impact of applying propensity score methods on the balance of demographics
      of older, multiply comorbid patients with a chronic back pain episode
      who were in one of two treatment groups

A. Identification of patients and assignment to treatment groups   Using Medicare fee-for-service files from 2006–2012, we identified older patients who had an episode of chronic low back pain (cLBP) during which they also had an additional musculoskeletal disorder diagnosis and a mental health disorder diagnosis. We focused on patients with multiple comorbidities because they consume a disproportionate amount of healthcare resources. [30] We then identified patients who exclusively used CMT and who did not use CMT during their cLBP episodes. The sections below provide the methodology that we used to identify the multiply comorbid patients with a cLBP episode that we examined, to determine whether each of these used or did not use CMT, to calculate propensity scores, and to apply them using the different methods described above. Dartmouth College’s Committee for the Protection of Human Subjects approved the study.

Following Cherkin’s methodology, [31] we eliminated patients with ICD-9-CM codes that are unlikely to be responsive to non-surgical treatment: neoplasms (CPT-9-CM codes 140–239.9), intra-spinal abscess (324.1), osteomyelitis (730–730.99), vertebral fractures with spinal cord injury (806.0–806.9), open vertebral fractures without spinal cord injury (805.1, 805.3, 805.5, 805.7, 805.9), vertebral dislocations (839–839.59), chordotomy (03.2–03.29), and cervical and dorsal fusions (81.01–81.03). Because DCs frequently use ICD-9-CM diagnostic codes 839–839.59, we did not exclude patients who had these codes if the code was recorded during a chiropractic visit.

Guided by Martin’s analysis of the Medical Expenditures Panel Survey (MEPS) prevalence of diagnostic categories of back problems, [32] we identified back pain patients as those who had a primary ICD-9-CM diagnosis code in the 724 series: 724.2 (lumbago), 724.3 (sciatica), 724.4 (thoracic or lumbosacral neuritis or radiculitis, unspecified), 724.5 (backache, unspecified), 724.8 (other symptoms referable to back), and 724.9 (other unspecified back disorders). These conditions account for approximate 55% of spine disorders. [32] However, because DCs frequently use additional ICD-9-CM codes, we included diagnoses in the 722 (intervertebral disc disorders), 739 (non-allopathic subluxation), and 839 (other multiple and ill-defined dislocations) series if such diagnoses were made during a chiropractic visit.

Consistent with the literature, [33] we defined a cLBP episode as beginning with the recording of a low back pain diagnosis at least twice over at least a 90–day period following a period of 6 months during which no such diagnosis was recorded; the episode was defined to end on the day that the last such diagnosis was followed by at least 180 days without any such diagnosis. Although we had access to 7 years of data, our inclusion criteria required a 1–year look back and a 1–year follow up period. Thus, our analyses included episodes of chronic low back pain that occurred during 5 years, between 2007–2011.

To identify a multiply comorbid cohort, we limited the study population to patients who had an ICD-9-CM code indicating at least 1 of the following additional musculoskeletal comorbidities during the episode or in the 12 months preceding episode onset: other back and neck pain (307.89, 722.3, 722.32, 722.8, 722.83, 846 series, 847.2, 847.3, 847.9, 996.41), non-back rheumatism (729.0), arthritis and other arthropathies (716.19, 716.68, 716.95) osteoarthritis (715.00, 715.09, 715.18, 715.21, 715.22, 715.28, 715.98), and diffuse diseases of the connective tissue (728.89, 728.9, 729.1, 729.3, 729.4). We further limited the study population to patients who had an ICD-9-CM code indicating at least 1 of the following psychological comorbidities during the episode or in the 12 months preceding episode onset: depression (296.3, 300.4, 309.0, 309.2, 309.8, 311), anxiety (293.84, 300.00, 300.09), or insomnia (327.01, 327.02).

Patients who used CMT were identified as having as at least 1 visit to a DC during the year (code 35 in the provider specialty field) and generating at least 1 CPT based charge for chiropractic manipulative treatment of the spine (code 98940 (1 or 2 regions), 98941 (3 to 4 regions), or 98942 (5 regions)) with a concurrent diagnosis of low back pain, defined above.

Therefore, we were able to identify patients who did and did not use CMT. Because the timing of CMT in the context of concurrently received medical care matters, [16, 34] we subdivided patients who used CMT into those who used only CMT, those who used CMT followed by medical care, and those who used medical care followed by CMT during their chronic low back pain episode. While we generated propensity scores for all treatment groups, for the purposes of this example, we limited analyses to patients who used only CMT and those who did not use CMT.

B. Calculation of propensity scores   Because we anticipated that we would find that the different groups studied would have different patient characteristics, [19, 35, 36] we used multinomial stepwise logistic regression [37] (with criteria to enter the stepwise regression set at p<0.05 and criteria to exit set at p >0.10, and with statistically significant interaction terms retained) to generate the propensity for each patient to be in 1 of the 4 particular treatment groups, based on the following variables and their interactions, all of which were included in calculation of propensity scores:

  1. From Medicare files:

    1. Socio-demographic variables (patient sex, patient race, whether the patient was concurrently enrolled in Medicaid, whether the patient was originally enrolled in Medicare by virtue of disability or age, and whether the beneficiary has a low-income subsidy for Medicare Part D (a measure of patient poverty)); and

    2. Diagnostic codes which we used to identify patients who had the aforementioned categorically defined comorbidities that defined our study population and from which we calculated modified Deyo-Charlson [38] scores and Iezzoni [39] scores.

    3. The per-capita supply of DCs in the Dartmouth Atlas Defined Hospital Referral Region. We included this in the propensity score because the supply of DCs has been associated with CMT utilization in the Medicare population; [40, 41] therefore, the supply of DCs represents a confounder that should be included in propensity score generation as it might be associated with both treatment exposure and outcomes.

    4. The regional carrier that was used by Medicare to process CMT claims in the region where the patient lived as a variable in generating propensity scores.

  2. From ZIP Code-linked datasets:

    1. An estimate of patient income (ZIP Code specific median annual household income in 2010) as well as the proportion of the population that lived under the federal poverty level.

C. Application of propensity scores and comparisons of the two methods   For the 2 treatment groups we examine here – patients who used only CMT and patients who used no CMT during their cLBP episode – we compared results from 2 different propensity score application methods: propensity score matching and inverse propensity score weighting. Further, we examined 2 methods of propensity score matching: 1 in which we used the best single match,19 and a 1–to-many methodology in which we used the closest 4 matches from the larger group. [23] For propensity score weighting, we inversely weighted cases by a patient’s propensity to self-select into their respective treatment group.


The top lines of Table 1 show demographics, measures of poverty and income, and the per-capita supply of DCs in the hospital referral region for patients in the 2 treatment groups examined, before application of the different propensity scoring methods. As expected, when compared to those who did not use CMT during their back pain episode, patients who used only CMT were younger, more likely to be white, more likely to have a greater than high school education, less likely to identified as being impoverished through Medicare Part D, and less likely to be Medicaid enrolled. In this subpopulation of multiply comorbid patients that we examined, we were surprised to find that patients who used only CMT were somewhat more likely to be male and to live in ZIP Codes with lower incomes than patients did not use CMT. As predicted from studies that have shown a relationship between chiropractic care use and the supply of DCs in the community, [40, 41] patients in our cohort who used CMT lived in hospital referral regions that had a higher per-capita supply of DCs.

The bottom lines of Table 1 show that, after application of the different propensity score methods, the 2 comparison treatment groups looked more similar. As anticipated, when propensity score matching was used, the total numbers of cases dropped (dramatically so when only the single best match method was used). When 1–to–1 matching was used, demographic values of the 2 groups were more similar to those in the treatment group with the smaller number of patients (in this case, the group that only used CMT). When 4–to–1 matching was used, results that were intermediate between the 2 groups were found. In contrast, when inverse propensity score weighting was used, all of the cases remained in the analysis, and the demographic values were more similar to the treatment group with the larger number of patients (in this case, the group that did not use CMT).

Table 2 shows the prevalence of the diagnostic groups and indicators of illness burden that were used to generate our propensity scores before and after application of the different propensity score methods. As expected, before application of propensity scores, patients who used only CMT were less likely to be obese, had lower illness burdens (as measured by Charlson and Iezzoni scores), were less likely to be disabled, and how lower Medicare spending levels in the prior year than patients who used no chiropractic services during their back pain episodes. Patients who sought only CMT during their episodes had a lower prevalence of osteoarthritis, non-back pain, other arthritis, depression, and anxiety but a higher prevalence of other back and neck pain and diffuse connective tissue disease. Again, all uses of propensity scores reduced differences between groups. Also, when 1–to–1 matching was used, the values for both comparison groups were more similar to those for the group that used only CMT; when 4–to–1 matching was used, values were between the 2 groups, seemingly not representative of either. Propensity score weighting resulted in values that were more similar to the group that did not use any CMT and diminished differences across treatment groups.


Propensity score methods have proven to be useful in observational studies that compare treatment groups when there is the possibility of selection bias. We described the application of 3 propensity score methods to generate balanced key variables across 2 cLBP treatment exposures in the older, multiply comorbid Medicare population. We showed that application of propensity score methods markedly diminished differences in baseline characteristics across the 2 treatment groups examined, thereby permitting balanced comparison of outcome variables between these groups. However, we found that, as a method, inverse propensity score weighing had 2 advantages: it retained all of the cases and it generated more balanced demographic values that were more like the treatment group with a larger number of patients, thereby preserving external validity.

Our findings suggest that propensity score calculation and application should be considered when conducting observational trials of CIHS service utilization and outcomes any time investigators have no control over treatment assignment that may be susceptible to selection bias. While findings may differ in other studies, we found that application of inverse propensity score weighting created comparison groups that were more similar to the larger group and generated findings that were more generalizable than application of propensity score matching algorithms. Further, our results indicate that different propensity score methods may generate different results.

Limitations and suggestions for future studies

Our study has several limitations. First, as is always the case when conducting retroactive analyses of claims databases, we were limited by data availability. There remain potentially confounding variables for which we were unable to correct. Second, our inclusion criteria were dependent on the accuracy and completeness of data reporting; we did not have the ability to independently verify diagnostic accuracy, for instance. To the extent that diagnostic inaccuracies were present in our data, our results are inaccurate. Third, we studied a very narrow subset of the Medicare population; findings may vary when examining broader cohorts of patients with back pain episodes.

Future studies might reexamine observational studies that did not use propensity scoring methods by generating and applying propensity scores and then comparing new to original findings. If original findings held, they might be considered much more robust and policy relevant. Future observational studies that examine the clinical or economic impact of CIHS should use propensity scoring methods and should provide justification for the particular method used.


This study shows that propensity score methods are useful in making comparisons across treatment groups in observational studies. Such analytic methods can make treatment groups more comparable and, therefore, improve the accuracy and generalizability of studies utilizing databases to compare outcomes across groups of patients. Further, application of propensity score methodologies approaches the main goal of randomization in controlled studies: to assure the comparability of groups for which outcomes are being assessed.

Practical Applications

  • Patients who use CMT often have different characteristics than patients who do not, and
    these differences can confound attempts to compare outcomes across treatment groups.

  • Propensity score methods reduce differences across treatment groups in observational
    studies and may lead to different policy ramifications than alternative approaches.

  • Propensity score calculation and application should be considered when conducting
    observational analyses of service utilization and outcomes when investigators have
    no control over treatment assignment,

Funding Sources 

The National Institutes of Health National Center for Complementary and Integrative Health (1R21AT008287-01) National Center for Advancing Translational Sciences (1UL1TR001086); and the National Institute of Arthritis and Musculoskeletal Skin Diseases (1P60AR062799) funded this work.

Conflicts of Interest

No conflicts of interest were reported for this study.


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