Abstract
Objective.
Knee replacement rates are increasing exponentially in the US and straining insurance budgets. We investigated how many knee replacements (KRs) would be prevented at different levels of pain improvement, a major target of osteoarthritis trials.
Methods.
We used data from the Osteoarthritis Initiative (OAI) to emulate a trial of knee pain interventions on KR risk changes. We modeled hypothetical 1-, 2- or 3-unit reductions of the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) pain subscale whenever a person reported a pain score ≥ 5 (out of 20) in an affected knee at any clinic visit. We used causal inference-based targeted learning to estimate treatment effects for hypothesized pain intervention strategies adjusted for time-dependent confounding. Sensitivity analyses assessed interventions at WOMAC pain scores ≥ 4 and ≥ 7.
Results.
Of 9592 knees studied (4796 participants; 58.5% female; baseline age = 61.2 years), 40.7% experienced WOMAC pain ≥ 5. The estimated knee-level (reference) risk of a KR, adjusted for loss to follow-up and death, was 6.3% (95% CI: 5.0%, 7.7%) in the OAI. Reductions of WOMAC pain scores by 1, 2, or 3 units decreased KR risk from 6.3% to 5.8%, 5.3% and 4.9%, respectively. Larger reductions in KR risk were achieved when interventions were applied at WOMAC pain ≥ 4.
Conclusion.
Modest pain reductions from OA interventions would substantially reduce the number of KRs with greater reductions achieved when pain decreased more and when interventions were introduced at lower pain levels.
INTRODUCTION
Rates of knee replacement (KR), which are primarily performed for osteoarthritis (OA) when medical and rehabilitative remedies fail, are rising in the United States and worldwide (1,2). The Global Burden of Disease (GBD) reports OA as a leading cause of disability and the most common form of arthritis that affects roughly 91.2 million adults in the United States (3). The rising rates of obesity and aging of the population will only exacerbate the need for a KR that is expected to overwhelm the US healthcare system in coming decades. Painful knee OA affects about 4.9% of the United States population age 26 and over, and 16.7% of those age 45 and above (4,5). Randomized trials testing efficacy of OA treatments often consider pain improvement as the primary efficacy target (6–10). It is uncertain however, what amount of pain improvement would be needed to ultimately reduce the risk of a KR.
Studying the amount of pain reduction needed to affect KR rates through trials is problematic for a variety of reasons beyond the prohibitive sample size and costs of using KR as an outcome in trials. Trials often assess short-term interventions, and treatment assignment in trials is often based on a one-time randomization that does not allow treatment modification or switching in response to the observed course of a disease. This is especially problematic for the assessment of long-term interventions for conditions such as chronic knee pain in OA. Patient characteristics may change over time, violating the balance of confounders among intervention groups achieved with the initial randomization. Further, a substantial proportion of trial participants may switch to another intervention strategy given a change in health status or disease progression.
One approach to addressing these challenges is through use of a multi-step sequential study that allows participants to be re-assigned to a different treatment level or strategy as their health status changes over time (11). Observational studies are uniquely positioned to address the long-term assessment of dynamic intervention strategies for chronic or progressive conditions (12).
In this study, we used data from an observational cohort to examine whether a strategy that reduced pain when participants’ knee pain reached a certain threshold could reduce the risk of a KR and if so, by how much. We do not examine one specific treatment but rather assessed intervention strategies that led to a prespecified reduction in pain. We used causal inference-based methods to provide an assessment of several long-term pain intervention strategies where hypothetical intervention decisions were tailored to a patient’s evolving characteristics.
METHODS
Setting.
We included data from the Osteoarthritis Initiative (OAI), a NIH-sponsored multi-center longitudinal cohort of persons with or at risk of knee OA. The OAI study visits that were included were from baseline, 12-, 24-, 36-, 48-, 72-, and 96-month that consisted of clinical, radiographic, and medication data.
Measurements.
Our study outcome was defined as an incident KR (either total or partial) that was recorded in the OAI by medical reports or radiographic adjudication.
Our study exposure used to define “hypothetical interventions” was based on knee pain quantified by the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) pain subscale at each visit. The term “intervention” in the context of our analytic method refers to any hypothetical treatment that reduces WOMAC pain (e.g., by medication, physical activity, weight loss, etc.).
Covariates consisted of demographics, body mass index, Kellgren and Lawrence grade, WOMAC stiffness and function scores, objective functional performance measures of chair stand time, 20- and 400-meter walk tests, malalignment, Charlson comorbidity index, Center for Epidemiologic Studies Depression (CES-D) scale, Physical Activity Scale for the Elderly (PASE) score, knee injury, hip pain or stiffness in the past 12 months, a family history of a knee or a hip replacement, regular use of prescription nonsteroidal anti-inflammatory drugs (NSAIDs) or COX-2 inhibitors in the past 12 months, and regular use of prescription opioids in the past 12-months. The regular use of a prescription pain medication for a given OAI study visit was determined based on the Medical Inventory Form where duration of use (up to 12 months prior to a given OAI study visit) and use frequency (i.e., regular vs. as needed) were recorded.
Analytic Approach.
We summarized the study sample’s baseline characteristics by frequencies for binary and categorical variables and by distribution summaries of continuous variables.
We used the causal inference-based method of targeted learning (13,14) to estimate the effect of “following an intervention strategy” (15). Interventions were dynamic based on time-evolving patient characteristics (16). Specifically, at an exam at which an OAI participant’s knee attained a pain score that triggered the intervention, they hypothetically received it. All knees in the OAI were included in the analyses. The intervention protocol was specified as hypothetical pain intervention strategies consisting of knee pain reduction by 1, 2, and 3 units on 0–20 WOMAC pain subscale for an individual with a painful knee at a given OAI study visit (i.e., an intervention-decision point). We chose these hypothetical levels of pain reduction for several reasons. The minimal clinically important difference or improvement for pain varies by the circumstances (e.g., KR vs. medical treatment) and by study. For example, Angst et al (17) suggested values approximating 8–10% of the scale that corresponds to a reduction in pain of ≥2 in our study which uses the 0–20 scale. Further, a KR would be unlikely to be carried out in those with low pain levels; thus, we implemented interventions whenever knee pain reached or exceeded 5 (out of 20).
Our initial goal was to estimate the risk of a KR based on observed WOMAC pain data without any hypothetical intervention which we shall label the ‘reference risk’. We then aimed to quantify how much this reference risk would have changed if we could hypothetically intervene and reduce WOMAC pain. Thus, at each intervention-decision point, an intervention could change according to a patient’s knee pain level (Figure 1). Assume an OAI participant presented with knee pain at one or more clinic visits. Our goal was to compare the participant’s observed real-world outcome (i.e., KR risk) with the outcome if we would have intervened to reduce knee pain (by any means such as pain medication, physical activity, weight loss, etc.) whenever knee pain level ≥5 on WOMAC subscale. In sensitivity analyses, we further tested intervention strategies where a hypothetical pain intervention was triggered at ≥4 and also ≥7 WOMAC pain cutoff points to allow us to compare KR risk if we could initiate or maintain knee pain interventions at lower or higher levels of pain.
Figure 1.
Schematic design of the study design. The top row depicts observed data where no (hypothetical) intervention was applied. The bottom row depicts the same knees; however, hypothetical interventions were applied if knees experienced pain ≥ 5 on WOMAC scale. The risk of knee replacement was compared between the hypothesized intervention strategy (bottom row) and observed data (top row).
Estimating the Effect.
Targeted learning (18,19) is a semi-parametric statistical method in which a potential misspecification of either the outcome model or the exposure based model can still yield a consistent estimate of the treatment effect. In this regard, targeted learning (20) has advantages over traditional parametric regression-based models (21). Other strengths of targeted learning have been noted (22). We followed the method proposed by Diaz in which we compute a statistical estimand referred to as longitudinal modified treatment policy that relies on the observed value of an exposure (i.e., in the absence of an intervention) to measure treatment effect for an intervention strategy (23).
Targeted learning-based estimation of the treatment effect to reduce the risk of KR allowed us to adjust for both time-dependent confounding and selection bias due to informative censoring because of loss to follow-up or death in the OAI cohort. We considered the time sequence of exposure, outcome, and confounders across all OAI visits such that any intervention-decision point was adjusted for the preceding confounders. Time-dependent confounding adjustment avoided the bias of adjusting for intermediate factors (24). Missing data were imputed by R’s mice library (25) that implemented the multiple imputation by chained equations approach using a random forest algorithm (26).
The specific steps of our analytic approach were as follow: We first calculated the risk of KR for a knee in the OAI cohort under a “no intervention” strategy (i.e., the reference risk) in all knees regardless of pain score. If there were no loss to follow-up or death in the OAI cohort, the reference risk would have equaled the observed proportion of KR among all knees. By accounting for loss to follow-up and death, the reference risk for a KR in the OAI cohort was estimated using observed data without pain modification (i.e., “no intervention” strategy).
In the second step of our analysis, we compared this reference risk of a KR with those under hypothetical intervention strategies of reducing pain to estimate the treatment effect. We adjusted for the following fixed confounders: sex, race, education, family history of knee or hip replacements, and income variables from baseline visit. For time-dependent confounding, adjustment at each study visit used the lagged variables approach (27–29) where measurements from the preceding visit (or from the current visit if the variable was defined based on an event before the current visit) was included. For example, at the 36-month visit, time-dependent confounding factors included NSAIDs and an opioid use variable from the 36-month visit because it was ascertained by a questionnaire on pain medication use in the 12 months preceding the 36-month visit. This ensured confounding measurements preceded WOMAC pain assessment during the 36-month visit. We created 3 different models, one in which the strategy assumed a reduction of 1 WOMAC point when pain reached a score of ≥5, one in which it assumed a reduction in 2 and a third in which, it assumed a reduction of 3.
Finally, we calculated an E-value to quantify the potential effect of unmeasured or residual confounding on our estimated effect sizes (30). A large E-value suggests that it would be unlikely that an unknown or unmeasured factor could exist at a magnitude necessary to totally explain away (i.e., nullify) our estimated effect size.
RESULTS
The baseline characteristics of our study sample that included 9592 knees from 4796 OAI participants are summarized in Table 1. The outcome of KR was observed in 5.5% (528/9592) of knees after the baseline visit (i.e., no OAI participant had a KR at baseline). The “reference risk” of KR in the OAI (i.e., estimated mean population of KR outcome under a “no intervention” strategy), after adjustment for loss to follow-up and death, was estimated to be 6.3% (95% CI: 5.0%, 7.7%).
Table 1.
Baseline characteristics of the knee-level study data (n = 9592).
| Baseline characteristic | Mean (SD) or frequency (%) |
|---|---|
|
| |
| Age, years | 61.2 (9.2) |
| Female Sex, no. (%) | 5608 (58.5) |
| Race, no. (%) | |
| - White (Ref.) | 7580 (79.1) |
| - African-American | 1748 (18.2) |
| - Asian | 90 (0.9) |
| - Other | 164 (1.7) |
| Education, no. (%) | |
| - Less than high school graduate (Ref.) | 336 (3.5) |
| - High school graduate | 1214 (12.8) |
| - Some college | 2292 (24.1) |
| - College graduate | 2002 (21.1) |
| - Some graduate school | 794 (8.3) |
| - Graduate degree | 2872 (30.2) |
| Income, no. (%) | |
| - <$10K (Ref.) | 320 (3.6) |
| - $10K to <$25K | 908 (10.2) |
| - $25K to <$50K | 2270 (25.6) |
| - $50K to <$100K | 3220 (36.3) |
| - ≥$100K | 2150 (24.2) |
| Marital status, no. (%) | |
| - Married (Ref.) | 6356 (66.8) |
| - Widowed | 768 (8.1) |
| - Divorced | 1358 (14.3) |
| - Separated | 172 (1.8) |
| - Never married | 856 (9.0) |
| BMI, kg/m2 | 28.62 (4.84) |
| KL grades, no. (%) | |
| - 0 (Ref.) | 3448 (38.5) |
| - 1 | 1597 (17.8) |
| - 2 | 2374 (26.5) |
| - 3 | 1239 (13.8) |
| - 4 | 295 (3.3) |
| Alignment, no. (%) | |
| - Neither (Ref.) | 2770 (29.7) |
| - Varus | 2522 (27.1) |
| - Valgus | 4026 (43.2) |
| Charlson comorbidity index | 0.39 (0.84) |
| WOMAC pain score | 2.4 (3.3) |
| WOMAC stiffness score | 1.5 (1.7) |
| WOMAC disability score | 8.1 (11.0) |
| Chair stand time averaged across 2 trials, seconds | 11.55 (3.98) |
| 20-meter walk test averaged across 2 trials, meter/second | 29.40 (4.05) |
| 400-meter walk time, seconds | 307.06 (57.38) |
| 400-meter walk test total walked distance, meter | 397.79 (22.62) |
| CES-D score | 6.6 (7.0) |
| PASE score | 160.8 (82.5) |
| History of a knee injury with walking difficulty for at least 2 days, no. (%) | 2584 (27.2) |
| Hip pain, aching, or stiffness in the past 12-month, no. (%) | 3951 (41.3) |
| Family history of a knee replacement, no. (%) | 1326 (14.0) |
| Family history of a hip replacement, no. (%) | 858 (9.1) |
| Regular user of prescription NSAIDs or COX-2 inhibitors in the past 12 months, no. (%) | 392 (4.1) |
| Regular user of prescription opioids in the past 12 months, no. (%) | 22 (0.2) |
Except where indicated otherwise, values are the mean (standard deviation). BMI = body mass index; CES-D = Center for Epidemiologic Studies Depression scale; KL = Kellgren and Lawrence; NSAIDs = nonsteroidal anti-inflammatory drugs; PASE = Physical Activity Scale for the Elderly; Ref. = reference level for a categorical variable; WOMAC = Western Ontario and McMaster Universities Osteoarthritis Index.
In the OAI, 40.8% (3911/9592) of knees experienced pain that reached or exceeded 5 on the WOMAC pain scale at at least one study visit (with median of 2 study visits, mean 2.4, and range of 1–6) during follow-up; thus, these knees were subject to hypothetical pain interventions. In total, there were 57,552 instances (i.e., intervention-decision points), in which a knee in OAI was assessed for pain to see if it reached or exceeded the threshold (i.e., 5 out of 20 on WOMAC pain subscale) that we set for the hypothetical intervention (i.e., 9592 knees * 6 follow-up visits = 57,552). Of these, the knee pain level reached or exceeded 5 on the WOMAC scale in 9509 (16.5%) instances across all visits; thus, knee pain level was hypothetically reduced by 1, 2, or 3 WOMAC units in these instances. Table 2 presents distributions of WOMAC pain across our study sample’s OAI visits for all knees and those with WOMAC pain ≥5.
Table 2.
Knee-level distributions of time-varying exposure and frequencies of loss to follow-up and death across the Osteoarthritis Initiative cohort visits in our study setup.
| OAI visit | Knee pain WOMAC score, mean (SD), median | Loss to follow-up, no. participants | Death, no. participants | |
|---|---|---|---|---|
|
| ||||
| All knees | Knees with WOMAC pain ≥ 5 | n/a | n/a | |
|
| ||||
| Baseline | 2.4 (3.3), 1.0 | 7.9 (2.9), 7.0 | n/a | n/a |
| 12-month | 2.1 (3.2), 1.0 | 7.8 (2.8), 7.0 | 0 | 16 |
| 24-month | 2.1 (3.1), 1.0 | 7.7 (2.8), 7.0 | 125 | 24 |
| 36-month | 2.1 (3.1), 1.0 | 7.9 (2.9), 7.0 | 104 | 30 |
| 48-month | 2.1 (3.1), 1.0 | 7.9 (2.9), 7.0 | 116 | 21 |
| 72-month | 2.2 (3.2), 1.0 | 7.8 (2.9), 7.0 | 420 | 65 |
| 96-month | n/a | n/a | 176 | 76 |
N/A = not applicable in this study due to time precedence of time-dependent confounders, time-varying exposure, and outcome; OAI = Osteoarthritis Initiative; WOMAC = Western Ontario and McMaster Universities Osteoarthritis Index.
The risk of KR in the OAI under our strategies consisting of a pain reduction by 1, 2, and 3 WOMAC pain units in knees that had a WOMAC pain score of ≥ 5, was reduced from 6.3% to 5.8%, 5.3%, and 4.9%, respectively. Estimated treatment effects corresponding to our estimands for pain reduction strategies of 1, 2, and 3 units on WOMAC scale suggested a risk ratio of 0.91, 0.84, and 0.77, respectively. Table 3 presents the number of KRs that could have been prevented if OAI participants followed the corresponding intervention strategies, compared to observed data representing no modification in pain.
Table 3.
Estimated knee-level risk of a knee replacement in the Osteoarthritis Initiative cohort under dynamic intervention strategies of pain reduction by 1, 2, or 3 units on the WOMAC subscale whenever a knee pain score reached or exceeded 5.
| Pain intervention strategy | Risk ratio (95% CI) | Absolute risk (95% CI) by following a strategy; risk difference (95% CI) | Number of KRs prevented in OAI by following a strategy |
|---|---|---|---|
| “whenever WOMAC ≥ 5, reduce it by …” | Reference risk = 6.3% | (no. knees = 9592; no. KR = 528) | |
|
| |||
| 1 | 0.91 (0.88, 0.95) | 5.8% (4.5%, 7.1%); −0.6% (−0.8%, −0.4%) | 55 |
| 2 | 0.84 (0.76, 0.92) | 5.3% (3.8%, 6.8%); −1.0% (−1.6%, −0.5%) | 101 |
| 3 | 0.77 (0.64, 0.92) | 4.9% (2.7%, 7.0%); −1.5% (−2.4%, −0.6%) | 142 |
KR = knee replacement; OAI = Osteoarthritis Initiative; WOMAC = Western Ontario and McMaster Universities Osteoarthritis Index.
In sensitivity analyses we investigated interventions triggered at WOMAC pain scores of ≥4 and ≥7. Findings were consistent with the primary analyses except that larger reductions in KR risks were observed in strategies that triggered an intervention at a lower WOMAC pain level (i.e., WOMAC pain ≥ 4) (see Supplemental Table).
Sensitivity analyses to estimate the strength of a potential unmeasured confounder needed to nullify our estimated risk ratios for the intervention strategies showed E-values of 1.42, 1.67, and 1.92 for pain reduction by 1, 2, and 3 on WOMAC scale, respectively. This means that, for example, for the strategy of reducing WOMAC pain by 1 unit, an unmeasured factor must have a minimum risk ratio of 1.42 beyond those already adjusted for in the analysis to nullify our estimated effect size of 0.91. This suggests that as pain reduction increases, substantial unmeasured confounding above and beyond confounders already adjusted for in our analyses would be needed for our estimated effect measure confidence intervals to include the null.
DISCUSSION
By testing hypothetical pain intervention strategies, we found that the absolute long-term risk of a KR was reduced from 6.3% to at least 5.8% when pain interventions that actually reduced pain were applied whenever knee pain reached 5 or above on the WOMAC pain subscale (This translates into 6 KRs avoided per 1000 painful knees). As knee pain affects millions of Americans and given the rising burden of KR in the United States that is accompanied by growing obesity rates and population aging, these findings suggest that developing long-term intervention strategies to successfully address chronic knee pain will have significant but modest public health and economic benefits.
Our study is the first to quantify the long-term expected risk of KR for a time-varying (i.e., dynamic) intervention trajectory. Approaches such as our have been used for many conditions (31–34), especially for study settings that are impractical to implement through randomized trials such as quantifying the multi-decade long risk of chronic conditions by modifiable lifestyle factors (35).
Our tested intervention strategies assumed a fixed reduction in pain severity. Our approach has parallels with the ‘treat to target’ approach in rheumatoid arthritis. However, treatments are inconsistent in their effectiveness. While our analysis mandated a specific level of pain reduction, a similar average pain reduction would yield comparable results. Few studies have used WOMAC pain to quantify the effects of various interventions and have focused on similar levels of pain reduction. For example, a meta-analysis of high vs. low intensity exercise on OA pain found that, compared with low intensity exercise, there was approximately a 1-unit (point) reduction in WOMAC pain score in the high intensity group but that effect diminished after 40 weeks (36). In a tanezumab vs. placebo trial testing low doses of tanezumab, the active treatment group’s advantage over placebo was <1 WOMAC pain unit (37). In another large trial of exercise vs. education, the difference in WOMAC pain was 2.5 units (38). If treatments don’t reduce pain by as much as our models assumed, there will be less reduction in knee replacement risk.
Also, we studied reductions in the WOMAC score as a target of OA interventions, our results suggest, as noted in Tubach et al. (39), that absolute levels of knee pain at which interventions are triggered is as important as the extent of pain reduction to decrease KR risk. Specifically, our findings suggest that the same extent of pain reduction would diminish KR risk more effectively when triggered at a lower knee pain level, likely due to patients attaining lower absolute levels of pain.
Our study assessed the relation of long-term pain reduction to KR risk and tested a hypothetical intervention that reduced pain. Other studies have addressed specific interventions that target pain but have not reported a decrease in KRs. For example, a study on a long-term prescription analgesics such as NSAIDs, cyclooxygenase-II inhibitors, acetaminophen, salicylates and narcotic in the OAI cohort reported that analgesics use was associated with an increased risk of KR (40). The aforementioned study, however, did not adjust for time-dependent confounding and only compared users of analgesics at all timepoints with never-users (which included both non-painful knees and painful knees). In contrast, in another study assessing the effects of prescription NSAIDs on OA progression in the OAI cohort, pain interventions resulted in a decreased rate of OA progression defined by joint space width reduction (41).
Our study cannot rule out the existence of residual confounding that may have biased our estimated effect measures. For example, there may be factors that affect both the receipt of a pain intervention and the decision to have a knee replacement. We implemented an analytic approach that enables time-dependent confounding adjustment by a comprehensive set of factors and also quantified the magnitude of extra potential confounding needed to nullify our estimated effect sizes. One advantage of our analytic approach is that it includes more participants and their visits and evaluates real world patterns of exposure to treatments compared with models that only compare outcomes of patients who are assumed to be treated at all timepoints versus those who are untreated during the entire study period. Few real-world patients would exist in these extreme levels of interventions across strata of evolving comorbidities. Our study did not focus on a specific pain remedy, and the findings are assumed to be broadly applicable to any intervention that reduces pain that could be helpful in future randomized trials design that target OA pain by medications, exercise, weight loss (e.g., through bariatric surgery in extremely obese patients), or future treatments. Our results may be limited by the modest reduction in pain experienced by those with knee pain in the OAI cohort. If widely-used intervention strategies produced larger reductions in pain, they likely would have reduced KR risks more.
About 20% of OAI participants were persons of Black, Asian or other racial/ethnic backgrounds. There may be differences in perception, tolerance, or reporting of pain among different groups or there may be disparities in knee replacement therapy. The number of non-White participants in OAI was not large enough to allow us to generate race-specific estimates of pain intervention effects on knee replacement risk; thus, the findings may not be generalizable to other groups.
We note that pain improvement is not the only factor that can affect KR risk; for example, improvements in function may likely also impact KR risk. Further, the effect of pain improvement on KR risk may be mediated by function or other mediating factors. We focused here on pain improvements as a proof-of-concept illustration of this type of study design and approach to addressing clinically relevant questions that are infeasible to address in traditional randomized trials.
In conclusion, KR rates are increasing, straining the capacity of the health care system and also health care budgets. While trials of potential treatments for OA do not generally have long enough follow-up or sufficient size to evaluate the effect of pain reduction on KRs, our findings suggest that treatments with even modest reductions in pain commensurate with current treatments would substantially decrease KR rates. These data provide additional strong evidence that effective treatments for OA are critically needed.
Supplementary Material
Acknowledgments
Supported by NIH grants R03AG060272, R21AR074578, K24AR070892 (to Dr. Neogi), U01AG018820 and P30AR072571 along with a Pfizer Global Award for Advancing Chronic Pain Research (award number: WI243952 to Dr. Jafarzadeh), and Innovative Research Award from Rheumatology Research Foundation (to Dr. Jafarzadeh)
REFERENCES
- 1.Losina E, Thornhill TS, Rome BN, Wright J, Katz JN. The dramatic increase in total knee replacement utilization rates in the United States cannot be fully explained by growth in population size and the obesity epidemic. J Bone Joint Surg Am 2012;94:201–207. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 2.Ackerman IN, Bohensky MA, de Steiger R, Brand CA, Eskelinen A, Fenstad AM, et al. Substantial rise in the lifetime risk of primary total knee replacement surgery for osteoarthritis from 2003 to 2013: an international, population-level analysis. Osteoarthritis Cartilage 2017;25:455–461. [DOI] [PubMed] [Google Scholar]
- 3.Jafarzadeh SR, Felson DT. Updated estimates suggest a much higher prevalence of arthritis in United States adults than previous ones. Arthritis Rheumatol Hoboken NJ 2018;70:185–192. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 4.Lawrence RC, Felson DT, Helmick CG, Arnold LM, Choi H, Deyo RA, et al. Estimates of the prevalence of arthritis and other rheumatic conditions in the United States. Part II. Arthritis Rheum 2008;58:26–35. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 5.Zhang Y, Jordan JM. Epidemiology of osteoarthritis. Clin Geriatr Med 2010;26:355–369. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 6.Juhl C, Christensen R, Roos EM, Zhang W, Lund H. Impact of exercise type and dose on pain and disability in knee osteoarthritis: a systematic review and meta-regression analysis of randomized controlled trials. Arthritis Rheumatol Hoboken NJ 2014;66:622–636. [DOI] [PubMed] [Google Scholar]
- 7.Fransen M, McConnell S, Harmer AR, Van der Esch M, Simic M, Bennell KL. Exercise for osteoarthritis of the knee: a Cochrane systematic review. Br J Sports Med 2015;49:1554–1557. [DOI] [PubMed] [Google Scholar]
- 8.Machado GC, Maher CG, Ferreira PH, Pinheiro MB, Lin C-WC, Day RO, et al. Efficacy and safety of paracetamol for spinal pain and osteoarthritis: systematic review and meta-analysis of randomised placebo controlled trials. BMJ 2015;350:h1225. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 9.Liu X, Machado GC, Eyles JP, Ravi V, Hunter DJ. Dietary supplements for treating osteoarthritis: a systematic review and meta-analysis. Br J Sports Med 2018;52:167–175. [DOI] [PubMed] [Google Scholar]
- 10.Megale RZ, Deveza LA, Blyth FM, Naganathan V, Ferreira PH, McLachlan AJ, et al. Efficacy and safety of oral and transdermal opioid analgesics for musculoskeletal pain in older adults: A systematic review of randomized, placebo-controlled trials. J Pain 2018;19:475.e1–475.e24. [DOI] [PubMed] [Google Scholar]
- 11.Bembom O, van der Laan MJ. Statistical methods for analyzing sequentially randomized trials. J Natl Cancer Inst 2007;99:1577–1582. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 12.Bembom O, van der Laan MJ. Analyzing sequentially randomized trials based on causal effect models for realistic individualized treatment rules. Stat Med 2008;27:3689–3716. [DOI] [PubMed] [Google Scholar]
- 13.van der Laan MJ, Rose S. Targeted Learning - Causal Inference for Observational and Experimental Data. New York, NY: Springer New York; 2011. Available at: http://link.springer.com/10.1007/978-1-4419-9782-1. Accessed October 22, 2015. [Google Scholar]
- 14.van der Laan MJ, Rose S. Targeted Learning in Data Science: Causal Inference for Complex Longitudinal Studies. Springer International Publishing; 2018. Available at: //www.springer.com/us/book/9783319653037. Accessed April 5, 2018. [Google Scholar]
- 15.Hernán MA, Robins JM. Per-protocol analyses of pragmatic trials. N Engl J Med 2017;377:1391–1398. [DOI] [PubMed] [Google Scholar]
- 16.Zhang Y, Young JG, Thamer M, Hernán MA. Comparing the effectiveness of dynamic treatment strategies using electronic health records: An application of the parametric g-formula to anemia management strategies. Health Serv Res 2018;53:1900–1918. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 17.Angst F, Benz T, Lehmann S, Aeschlimann A, Angst J. Multidimensional minimal clinically important differences in knee osteoarthritis after comprehensive rehabilitation: a prospective evaluation from the Bad Zurzach Osteoarthritis Study. RMD Open 2018;4:e000685. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 18.van der Laan MJ. Targeted maximum likelihood based causal inference: Part I. Int J Biostat 2010;6:Article 2. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 19.van der Laan MJ. Targeted maximum likelihood based causal inference: Part II. Int J Biostat 2010;6:Article 3. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 20.van der Laan MJ, Luedtke AR. Targeted learning of the mean outcome under an optimal dynamic treatment rule. J Causal Inference 2015;3:61–95. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 21.Neugebauer R, Schmittdiel JA, van der Laan MJ. Targeted learning in real-world comparative effectiveness research with time-varying interventions. Stat Med 2014;33:2480–2520. [DOI] [PubMed] [Google Scholar]
- 22.Petersen ML, Porter KE, Gruber S, Wang Y, van der Laan MJ. Diagnosing and responding to violations in the positivity assumption. Stat Methods Med Res 2012;21:31–54. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 23.Díaz I, Williams N, Hoffman KL, Schenck EJ. Nonparametric causal effects based on longitudinal modified treatment policies. J Am Stat Assoc 2021;0:1–16. [Google Scholar]
- 24.Cole SR, Platt RW, Schisterman EF, Chu H, Westreich D, Richardson D, et al. Illustrating bias due to conditioning on a collider. Int J Epidemiol 2010;39:417–420. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 25.Buuren S Flexible Imputation of Missing Data. Chapman and Hall/CRC; 2012. Available at: http://www.crcnetbase.com/isbn/9781439868256#/doi/book/10.1201/b11826. Accessed November 3, 2014. [Google Scholar]
- 26.Shah AD, Bartlett JW, Carpenter J, Nicholas O, Hemingway H. Comparison of random forest and parametric imputation models for imputing missing data using MICE: a CALIBER study. Am J Epidemiol 2014;179:764–774. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 27.Daniel RM, Cousens SN, De Stavola BL, Kenward MG, Sterne JAC. Methods for dealing with time-dependent confounding. Stat Med 2013;32:1584–1618. [DOI] [PubMed] [Google Scholar]
- 28.Robins JM, Hernán MA. Estimation of the causal effects of time-varying exposures. In: Longitudinal Data Analysis. Chapman & Hall/CRC Handbooks of Modern Statistical Methods. Chapman and Hall/CRC; 2008:553–599. Available at: http://www.crcnetbase.com/doi/abs/10.1201/9781420011579.ch23. Accessed July 8, 2015. [Google Scholar]
- 29.Mansournia MA, Naimi AI, Greenland S. The implications of using lagged and baseline exposure terms in longitudinal causal and regression models. Am J Epidemiol 2019;188:753–759. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 30.Ding P, VanderWeele TJ. Sensitivity analysis without assumptions. Epidemiol Camb Mass 2016;27:368–377. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 31.Danaei G, Rodríguez LAG, Cantero OF, Logan R, Hernán MA. Observational data for comparative effectiveness research: An emulation of randomised trials of statins and primary prevention of coronary heart disease. Stat Methods Med Res 2013;22:70–96. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 32.Danaei G, Rodríguez LAG, Cantero OF, Hernán MA. Statins and Risk of Diabetes An analysis of electronic medical records to evaluate possible bias due to differential survival. Diabetes Care 2013;36:1236–1240. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 33.Picciotto S, Chevrier J, Balmes J, Eisen EA. Hypothetical Interventions to Limit Metalworking Fluid Exposures and Their Effects on COPD Mortality: G-Estimation Within a Public Health Framework. Epidemiol Camb Mass 2014;25:436–443. [DOI] [PubMed] [Google Scholar]
- 34.Mokhayeri Y, Hashemi-Nazari SS, Khodakarim S, Safiri S, Mansournia N, Mansournia MA, et al. Effects of hypothetical interventions on ischemic stroke using parametric g-formula. Stroke 2019:STROKEAHA119025749. [DOI] [PubMed] [Google Scholar]
- 35.Danaei G, Pan A, Hu FB, Hernan MA. Hypothetical Midlife Interventions in Women and Risk of Type 2 Diabetes. Epidemiol January 2013 2013;24:122–128. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 36.Regnaux J-P, Lefevre-Colau M-M, Trinquart L, Nguyen C, Boutron I, Brosseau L, et al. High-intensity versus low-intensity physical activity or exercise in people with hip or knee osteoarthritis. Cochrane Database Syst Rev 2015:CD010203. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 37.Schnitzer TJ, Easton R, Pang S, Levinson DJ, Pixton G, Viktrup L, et al. Effect of Tanezumab on joint pain, physical function, and patient global assessment of osteoarthritis among patients with osteoarthritis of the hip or knee: A randomized clinical trial. JAMA 2019;322:37–48. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 38.Bennell KL, Nelligan R, Dobson F, Rini C, Keefe F, Kasza J, et al. Effectiveness of an internet-delivered exercise and pain-coping skills training intervention for persons with chronic knee pain: A randomized trial. Ann Intern Med 2017;166:453–462. [DOI] [PubMed] [Google Scholar]
- 39.Tubach F, Ravaud P, Baron G, Falissard B, Logeart I, Bellamy N, et al. Evaluation of clinically relevant states in patient reported outcomes in knee and hip osteoarthritis: the patient acceptable symptom state. Ann Rheum Dis 2005;64:34–37. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 40.Hafezi-Nejad N, Guermazi A, Roemer FW, Eng J, Zikria B, Demehri S. Long term use of analgesics and risk of osteoarthritis progressions and knee replacement: propensity score matched cohort analysis of data from the Osteoarthritis Initiative. Osteoarthritis Cartilage 2016;24:597–604. [DOI] [PubMed] [Google Scholar]
- 41.Lapane KL, Yang S, Driban JB, Liu S-H, Dubé CE, McAlindon TE, et al. Effects of prescription nonsteroidal antiinflammatory drugs on symptoms and disease progression among patients with knee osteoarthritis. Arthritis Rheumatol Hoboken NJ 2015;67:724–732. [DOI] [PMC free article] [PubMed] [Google Scholar]
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.

