Hempel S, Newberry SJ, Maher AR, et al. Probiotics for the prevention and treatment of antibiotic-associated diarrhea: a systematic review and meta-analysis. JAMA. 2012;307(18):1959-1969.
eFigure 1. PubMed Search Strategy
eFigure 2. Flow Diagram
eTable1. Evidence Table Probiotics for AAD
eReferences. Included RCTs
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Hempel S, Newberry SJ, Maher AR, et al. Probiotics for the Prevention and Treatment of Antibiotic-Associated Diarrhea: A Systematic Review and Meta-analysis. JAMA. 2012;307(18):1959–1969. doi:10.1001/jama.2012.3507
Author Affiliations: Southern California Evidence-based Practice Center, RAND Health, Santa Monica (Drs Hempel, Newberry, and Shekelle, and Ms Shanman and Ms Johnsen); RAND, Santa Monica (Drs Maher, Wang, and Miles); West Los Angeles VA Medical Center, Los Angeles (Dr Shekelle); and Cedars-Sinai Medical Center, Los Angeles (Dr Maher), California.
Context Probiotics are live microorganisms intended to confer a health benefit when consumed. One condition for which probiotics have been advocated is the diarrhea that is a common adverse effect of antibiotic use.
Objective To evaluate the evidence for probiotic use in the prevention and treatment of antibiotic-associated diarrhea (AAD).
Data Sources Twelve electronic databases were searched (DARE, Cochrane Library of Systematic Reviews, CENTRAL, PubMed, EMBASE, CINAHL, AMED, MANTIS, TOXLINE, ToxFILE, NTIS, and AGRICOLA) and references of included studies and reviews were screened from database inception to February 2012, without language restriction.
Study Selection Two independent reviewers identified parallel randomized controlled trials (RCTs) of probiotics (Lactobacillus, Bifidobacterium, Saccharomyces, Streptococcus, Enterococcus, and/or Bacillus) for the prevention or treatment of AAD.
Data Extraction Two independent reviewers extracted the data and assessed trial quality.
Results A total of 82 RCTs met inclusion criteria. The majority used Lactobacillus -based interventions alone or in combination with other genera; strains were poorly documented. The pooled relative risk in a DerSimonian-Laird random-effects meta-analysis of 63 RCTs, which included 11 811 participants, indicated a statistically significant association of probiotic administration with reduction in AAD (relative risk, 0.58; 95% CI, 0.50 to 0.68; P < .001; I2, 54%; [risk difference, −0.07; 95% CI, −0.10 to −0.05], [number needed to treat, 13; 95% CI, 10.3 to 19.1]) in trials reporting on the number of patients with AAD. This result was relatively insensitive to numerous subgroup analyses. However, there exists significant heterogeneity in pooled results and the evidence is insufficient to determine whether this association varies systematically by population, antibiotic characteristic, or probiotic preparation.
Conclusions The pooled evidence suggests that probiotics are associated with a reduction in AAD. More research is needed to determine which probiotics are associated with the greatest efficacy and for which patients receiving which specific antibiotics.
The use of antibiotics that disturb the gastrointestinal flora is associated with clinical symptoms such as diarrhea, which occurs in as many as 30% of patients.1,2 Symptoms range from mild and self-limiting to severe, particularly in Clostridium difficile infections, and antibiotic-associated diarrhea (AAD) is an important reason for nonadherence with antibiotic treatment.3
Probiotics are microorganisms intended to have a health benefit when consumed. Synbiotics refer to preparations in which probiotic organisms and prebiotics (nondigestible food ingredients that may benefit the host by selectively stimulating bacteria in the colon) are combined.
Quiz Ref IDPotentially, probiotics maintain or restore gut microecology during or after antibiotic treatment through receptor competition, competition for nutrients, inhibition of epithelial and mucosal adherence of pathogens, introduction of lower colonic pH favoring the growth of nonpathogenic species, stimulation of immunity, or production of antimicrobial substances.4,5
There is an increasing interest in probiotic interventions, and evidence for the effectiveness of probiotics in preventing or treating AAD is also increasing.6,7 Previous reviews have been nonsystematic, have focused on specific patient populations or probiotic genera, and have not included the latest clinical trials.1,8 A 2006 meta-analysis9 on probiotic use for AAD included 25 RCTs and a 2006 review10 included 16 relevant RCTs. Both studies suggested that probiotic use was associated with reduced risk of AAD. Yet, more than 30 additional RCTs on the topic have been published in the international literature since. A recent Cochrane review on pediatric AAD suggested a protective association of probiotic use in preventing AAD in children. Most studies of probiotics include adult participants, which suggests the evidence in adult AAD prevention should also be revisited.11
The objective of this systematic review and meta-analysis is to evaluate broadly the available evidence on probiotics and synbiotic interventions including the genera Lactobacillus, Bifidobacterium, Saccharomyces, Streptococcus, Enterococcus, and Bacillus, alone or in combination, for the prevention or treatment of AAD.
The review protocol has been registered in PROSPERO International Prospective Register of Systematic Reviews (crd.york.ac.uk/prospero/index.asp Identifier: CRD42011001296).
Parallel RCTs that compared probiotic use as adjunct antibiotic treatment with a concurrent control group receiving no treatment, placebo, or a different probiotic or probiotic dose were eligible for inclusion in the review. Participants of all ages treated with antibiotics, regardless of the indication and the patients' underlying symptomatology, were included. Interventions based on the genera Lactobacillus, Bifidobacterium, Saccharomyces, Streptococcus, Enterococcus, and/or Bacillus alone or in combination, using live (active or lyophilized) microorganisms in probiotic or synbiotic preparations, were eligible. RCTs of prevention as well as treatment of AAD were included. Trials were also included if probiotics were given alongside antibiotics to enhance treatment effects (eg, Helicobacter pylori eradication), rather than to prevent adverse effects of antibiotics, if the outcome of diarrhea was reported. All reports of diarrhea were considered (as main treatment effects, reasons for dropouts, or adverse effects). This analysis used the original study's definition of diarrhea, which ranged from uncomplicated diarrhea to severe diarrhea with complications such as electrolyte imbalance, and included outcomes such as watery stool, stool consistency, self-reported diarrhea, and physician-defined diarrhea.
As part of a larger project on the safety of probiotic use,6 we searched 12 electronic databases (DARE, Cochrane Library of Systematic Reviews, CENTRAL, PubMed, EMBASE, CINAHL, AMED, MANTIS, TOXLINE, ToxFILE, NTIS, AGRICOLA), from database inception to February 2012 without language restriction, to identify probiotics publications. The search was broad and not restricted to individual genera used as probiotics or to any clinical indications or outcomes; the exact search terms for PubMed are shown in eFigure 1. In addition, we searched clinicaltrials.gov, screened references of included studies and reviews, and hand-searched the International Journal of Probiotics and Prebiotics.
Two reviewers independently assessed publications for inclusion in the review. Discrepancies were resolved through discussion by the review team.
Two independent reviewers extracted trial details pertaining to the participants, antibiotics and probiotics interventions and comparators, and results regarding diarrhea, using a standardized form. Discrepancies were resolved through discussion. The primary outcome was the number of participants with diarrhea in each treatment group. We also extracted other relevant outcomes such as the severity of diarrhea or measures of stool consistency. We extracted probiotics-related adverse effects such as infections because of the administered organism. When more than 1 active treatment group was investigated, we selected the group first mentioned as the main treatment group.
We applied the Cochrane Risk of Bias tool to assess sequence generation; allocation concealment; participant, personnel, and outcome assessor blinding; attrition bias; incomplete outcome data; selective outcome reporting; and other sources of bias.12 In addition, we assessed the reporting and ascertainment of included strains, the statistical power, and the funding and potential for conflict of interest associated with individual trials.
We combined trials in a random-effects meta-analysis calculating the relative risk (RR) and the 95% CI in trials reporting the number of patients with diarrhea, using the DerSimonian-Laird algorithm in The Metafor Package—a meta-analysis package for R.13,14 In addition, we computed the risk difference (RD) and the number needed to treat (NNT) for the number of participants with AAD based on an analysis using RD. Other study characteristics and results were summarized narratively.
Subgroup analyses were based on the probiotic genus, participants' age, clinical condition, and setting. To investigate whether any observed differences between subgroups were statistically significant, meta-regressions were undertaken to compare the ratio of relative risks (RRR) using the presence of the subgroup-defining variable as a moderator. To assess heterogeneity, we computed the I2 statistic. We explored potential sources of heterogeneity and the robustness of results further for the aim of the study, study quality, the comparator, antibiotic treatment duration, and publication year. Potential for publication bias was assessed with Egger regression and the Begg rank test.15,16
The search for publications on probiotic use identified 15 214 titles and abstracts, of which 2426 were obtained as full-text publications and screened for inclusion in the review. A total of 82 RCTs met inclusion criteria. Details of the study flow are documented in eFigure 2. The citations and the characteristics of all RCTs meeting inclusion criteria for the review are documented in detail in the eTable. The included RCTs primarily enrolled adults for studies in which age was described (52/82 RCTs). The clinical indication for antibiotics varied; the most common reason was H pylori eradication (24/82), but studies with this indication still comprised a minority of the studies. Sixteen trials reported the use of single antibiotics such as amoxicillin, azithromycin, and clarithromycin, while others included numerous antibiotics or were otherwise unspecified. Two trials were identified that explicitly investigated probiotics for the treatment, rather than the prevention or potential treatment of AAD, with all participants experiencing AAD at study commencement.
Most RCTs randomized a moderate number of participants (median, 93.5; mean [SD], 161.3 [192.3]) to either adjunctive probiotics treatment or placebo (56/82), no treatment (ie, antibiotics only, 23/82), heat-killed organisms matching the probiotics (3/82), or standard treatment (diosmectite, 1/82). The probiotic interventions were primarily Lactobacillus based, either alone or combined with other genera, (57/82), eg, Bifidobacterium (32/82). Sixteen studies used an exclusively yeast-based intervention (Saccharomyces boulardii [cerevisiae] or Hansen CBS 5926). Few studies used Enterococcus, Streptococcus, or Bacillus strains.
The quality of the reporting was low; 59 trials lacked adequate information to assess the overall risk of bias. Results of the quality assessment for individual features are shown in Table 1. Half the RCTs reported only the genus and species that were used in the intervention but not the strain (41/82), and many did not state that treatment allocation was concealed (64/82), or did not report an intention-to-treat analysis (31/82). Nearly half did not report a power calculation (39/82). However, 53 of the 82 trials reported that participants and outcome assessors were blind to the intervention. Seventeen trials were classified as industry sponsored; 52 did not clarify the role of funding, questions about conflict of interest remained, or both; and 13 trials explicitly stated no competing interest.
Details of included double-blind placebo-controlled trials aiming to reduce or treat AAD and reporting the number of participants with AAD in both treatment groups are shown in Table 2 and Table 3.17-51
Of all included trials, 63 reported the number of participants with diarrhea and the number of participants randomized to both treatment groups.17-78 The RR (95% CI) results of each trial are shown in the Figure17-78; most trials did not show a statistically significant advantage of probiotic use. However, across 63 RCTs (N = 11 811 participants), probiotic use was associated with a lower RR of developing diarrhea compared with a control group not using probiotics, (pooled RR, 0.58; 95% CI, 0.50 to 0.68; P < .001; I2, 54%). To test the robustness of this result, we omitted each trial, in turn, from the analyses; the pooled result remained statistically significant at P < .001 for all 63 analyses. The pooled RD of developing AAD was −0.07 (95% CI, −0.10 to −0.05; P < .001); the NNT was 13 (95% CI, 10.3 to 19.1). There was no evidence of publication bias (Egger regression test P = .26; Begg rank test P = .34).
Most studies (62/82) explicitly administered probiotics to prevent or treat AAD. However, all trials that reported the outcome of interest and described an intervention in which antibiotics and probiotics were given simultaneously were included (eg, to enhance effectiveness of H pylori eradication), regardless of the study objective. When the meta-analysis was restricted to the trials explicitly aiming to prevent or treat AAD (52 RCTs), results were similar (RR, 0.58; 95% CI, 0.49 to 0.68; P < .001; I2, 55%; NNT, 12). Approximately half of the trials (43 RCTs) reported a definition of the diarrhea outcome. Favorable results for probiotics were also shown in these selected trials (RR, 0.56; 95% CI, 0.47 to 0.68; P < .001; I2, 57%; NNT, 10).
This analysis also investigated whether studies with a lower risk of bias reported outcomes associated with probiotics supplementation. Trial quality was generally low; however, the substantial number of double-blind RCTs (N=44) showed a statistically significant combined RR of 0.61 (95% CI, 0.52 to 0.73; P < .001; I2, 50%; NNT, 14). These associations were sustained in the small number of trials that reported allocation concealment as well as double-blinding (12 RCTs [RR, 0.62; 95% CI, 0.41 to 0.95; P = .029; I2, 76%; NNT, 14]). A meta-regression showed that associations regarding treatment benefits for nonblinded trials were not significantly larger (RRR, 1.24; P = .25). The beneficial association of probiotic use was also shown in 12 RCTs that declared the funding source and claimed to be free of conflict of interest (RR, 0.63; 95% CI, 0.42 to 0.92; P = .018; I2, 68%; NNT, 15). There was no statistically significant difference in results between studies with conflict of interest compared with other studies (RRR, 1.14; P = .49).
Quiz Ref IDMany trials used blends of various probiotic genera, primarily Lactobacillus, alone or in combination with other probiotics. The exclusively Lactobacillus- based interventions (17 RCTs) reporting on the number of participants with AAD showed a pooled RR of 0.64 (95% CI, 0.47 to 0.86; P = .004; I2, 56%; NNT, 14). The exclusively yeast-based interventions (15 RCTs, Saccharomyces) showed a pooled RR of 0.48 (95% CI, 0.35 to 0.65; P < .001; I2, 56%; NNT, 10). The pooled result for 3 older studies using Enterococcus [Streptococcus ] faecium SF68 was 0.51 (95% CI, 0.38 to 0.68; P < .001; I2, 0%; NNT, 12). Subgroup analyses did not explain a substantial amount of heterogeneity across studies. Heterogeneity remained evident when analyses were restricted to individual genera. The results of the subgroups of distinct genera did not have statistically significant difference (Q (5) = 4.7; P = .45). The identified studies that provided head-to-head comparisons of different probiotics showed no clear signal. Comparing Lactobacillus LGG, Saccharomyces boulardii, and Lactobacillus acidophilus plus Bifidobacterium lactis, one study concluded that none of the species or combinations showed substantial superiority over the others.79 A study using 6 different probiotic preparations (S boulardii, Enterococcus SF68, Lactobacillus LGG, 3 different Lactobacillus strains, a combination of Bifidobacterium and Lactobacillus strains, or a mixture of different lactic acid bacteria) reported no difference in intestinal concerns.80
Subgroup analyses for each of the 6 investigated genera analyzed as ingredients of the probiotics interventions (including blends) showed statistically significant associations with the number of patients with AAD compared with control participants for all genera. Indirect comparisons across studies comparing the risk ratios of trials with and without each genus found no difference between studies associated with the genus ([Bacillus ; RRR, 0.62; P = .18], [Bifidobacterium ; RRR, 1.18; P = .16], [Enterococcus ; RRR, 1.03; P = .92], [Lactobacillus ; RRR, 1.14; P = .09], [Saccharomyces ; RRR, 0.79; P = .18], and [Streptococcus ; RRR, 1.05; P = .82]). The number of trials by genus ranged from 40 (Lactobacillus) to 3 (Bacillus). Most interventions were blends of probiotics, which did not allow us to establish an independent association for each genus.
Forty-five placebo-controlled trials (excluding no adjunct treatment trials) also showed a statistically significantly lower RR of AAD for participants using probiotics (RR, 0.59; 95% CI, 0.50 to 0.70; P < .001; I2, 48%; NNT, 13).
We distinguished 3 subgroups based on participant age: children (0-17 years), adults (18-65 years), and elderly adults (>65 years). A large number of studies included participants from 2 or more age groups. In the 16 RCTs that targeted children specifically, the association of probiotics with risk for AAD was 0.55 (95% CI, 0.38 to 0.80; P = .002; I2, 68%; NNT, 11). In the 14 RCTs that included only participants aged 18 to 65 years, the association was an RR of 0.54 (95% CI, 0.34 to 0.85; P = .008; I2, 45%; NNT, 13). Only 3 studies were identified exclusively in elderly adults that reported the number of participants with AAD. The pooled result for these trials was an RR of 0.81 (95% CI, 0.40 to 1.63; P = .55; I2, 65%; NNT, 25). A meta-regression did not indicate statistically significant differences in associations between age groups, whether comparing all 3 age groups (Q (2) = 0.95; P = .62), or only RCTs in children and adults, exclusively (Q (1) = 0.01; P = .93).
The majority of RCTs enrolled outpatients, but 24 RCTs included hospitalized patients. In 20 RCTs, adjunct probiotics treatment was associated with a statistically significant benefit on the number of participants with AAD (RR, 0.55; 96% CI, 0.42 to 0.72; P < .001; I2, 47%; NNT, 10). The indications for antibiotic use varied across participants in the included studies. The most common indication for antibiotic use in the identified studies was H pylori treatment. In these 15 RCTs, adjunct probiotic use was associated with benefit (RR, 0.55; 95% CI, 0.35 to 0.86; P = .009; I2, 65%; NNT, 17). The beneficial association of probiotic use was also demonstrated in the remaining 48 RCTs (RR, 0.58; 95% CI, 0.49 to 0.69; P < .001; I2, 56%; NNT, 12), and the 2 subgroups were not significantly different (RRR, 1.01; P = .96). For trials in which a treatment schedule was reported, antibiotics were administered between 1 and 14 days, with 22 of 82 trials specifying a 7-day treatment schedule; however, neither a dichotomous analysis for the 1-week cutoff, nor a continuous-variable meta-regression for treatment duration influenced the result (dichotomized duration RRR, 0.85; P = .61; continuous duration RRR/d, 1.00; P = .95). Included studies were published over a period of more than 30 years. Newer studies may have chosen antibiotics with a better safety record. However a meta-regression did not indicate that the ratio of AAD incidences in the treatment and control groups was significantly affected by publication year (RRR/y, 1.02; P = .07).
Most trials either did not specify the follow-up period, or the assessment was explicitly limited to the time of antibiotics treatment. Trials that reported AAD incidence after cessation of antibiotic therapy (7 RCTs) indicated that the number of participants experiencing AAD was lower in the probiotics groups than in control groups (RR, 0.44; 95% CI, 0.20 to 0.99; P = .047; I2, 0%; NNT, 75).
In 31 RCTs, it was specified which AAD incidences required treatment, were classified by the authors as severe, led to participants stopping the antibiotics and probiotics treatment, or involved patients testing positive for C difficile. Adjunct probiotics treatment was associated with reductions in the number of participants experiencing severe occurrences in the studies that reported the presence or absence of these events (RR, 0.52; 95% CI, 0.36 to 0.75; P < .001; I2, 0%; NNT, 69). In 14 RCTs, the pooled RR for preventing C difficile diarrhea was 0.29 (95% CI, 0.17 to 0.48; P < .001; I2, 0%; NNT, 25), but several studies cautioned that adherence for testing was low or the number of tested samples per group was not reported.
Of the 82 trials, 4 publications reported the absence of infections and serious adverse events due to the administered probiotics organism and the absence of pathogenic growth in stool samples. Nineteen RCTs reported that no adverse events were judged to be associated with probiotics intake, the intervention was considered safe, or no adverse events were observed. Fifty-nine RCTs did not report on probiotics-specific adverse events.
Quiz Ref IDThe principal finding of this review is that using probiotics as adjunct therapy reduces the risk of AAD, with an RR of 0.58. The result was consistent across a number of subgroup and sensitivity analyses. The treatment effect equates to an NNT of 13. The main limitations to this result are residual unexplained heterogeneity, poor documentation of the probiotic strains, and lack of assessment of probiotic-specific adverse events.
The existing evidence base for the prevention or treatment of AAD consists primarily of Lactobacillus interventions, either alone or in combination with other genera. Although RCTs of interventions of Streptococcus, Enterococcus, or Bacillus were eligible for inclusion in the review, few trials were identified. The included trials predominantly used lactic acid–producing bacteria such as Lactobacillus rhamnosus, or L casei with few exceptions, the Saccharomyces trials used the yeast S boulardii [cerevisiae]. The relative efficacy of probiotic interventions may be strain specific81; however, this analysis found no evidence that the effectiveness varies systematically even by probiotic genus. Most documented interventions used blends of genera, species, and strains, and interventions were poorly documented. Few trials described the strains used, and fewer indicated that the potency of the product was tested for the study.
In rare cases, probiotics have been linked to serious adverse effects such as fungemia82-87 and bacterial sepsis88; hence, potential adverse effects of probiotics must be reviewed with the efficacy data, especially because little research attention has focused on adverse effects of probiotics used in clinical practice.6 Although none of the included trials reported such adverse events, it is noteworthy that few trials addressed these outcomes, especially because cases of such infections suspected to be associated with the administered organisms were reported decades ago.6
The objective of this study was to evaluate broadly the available evidence on probiotic interventions for the prevention and treatment of AAD, building on previous nonsystematic overviews and systematic reviews on selected applications.1,2,8,11,89-91Quiz Ref IDA large number of subgroup and sensitivity analyses were carried out to identify sources of statistical heterogeneity among trials. No systematic differences in results were identified across trials using different age groups, clinical indications, duration of antibiotics, included probiotics, and other study characteristics.
A substantial number of RCTs have addressed the prevention of AAD with probiotics; however, few trials were adequately powered. Trials aiming to demonstrate a reduction of a relatively rare event (probability 0.3) with an RR of 0.58 need sample sizes of 178 per group to achieve a power of 0.80. Only 10% of included trials fall into this category, suggesting the need for larger samples, eg, multisite trials.92 Associations were shown through systematically identifying pertinent trials and pooling results across inadequately powered trials.
Quiz Ref IDDetermining which populations would benefit most from adjunct probiotics therapy8 is an ongoing challenge; it must be considered that AAD does not occur in the majority of patients and when it occurs, it is usually self-limiting.93 We identified only a small number of RCTs that targeted elderly participants, and more research is needed in particular for this participant group. Some antibiotics are more likely to cause diarrhea as an adverse effect,94,95 but included studies rarely specified the antibiotics used or included patients taking a variety of different antibiotics, hindering an analysis of differential effectiveness by antibiotic taken.
A further limitation to this review is that we did not specifically solicit experts for published or unpublished research. Additional questions for future research include the optimal dose of the probiotic preparation and the comparative effectiveness of different probiotic interventions for the prevention or treatment of AAD. These questions should be explored in direct, head-to-head comparisons.
In summary, our review found sufficient evidence to conclude that adjunct probiotic administration is associated with a reduced risk of AAD. This generalized conclusion likely obscures heterogeneity in effectiveness among the patients, the antibiotics, and the probiotic strains or blends. Future studies should assess these factors and explicitly assess the possibility of adverse events to better refine our understanding of the use of probiotics to prevent AAD.
Corresponding Author: Susanne Hempel, PhD, Southern California Evidence-Based Practice Center, RAND Health, 1776 Main St, Santa Monica, CA 90401 (firstname.lastname@example.org).
Author Contributions: Dr Hempel had full access to all of the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis.
Study concept and design: Hempel, Newberry, Maher, Wang, Shekelle.
Acquisition of data: Hempel, Newberry, Maher, Wang, Shanman, Johnsen.
Analysis and interpretation of data: Hempel, Newberry, Maher, Wang, Miles, Johnsen, Shekelle.
Drafting of the manuscript: Hempel, Johnsen.
Critical revision of the manuscript for important intellectual content: Hempel, Newberry, Maher, Wang, Miles, Shanman, Johnsen, Shekelle.
Statistical analysis: Miles.
Obtained funding: Shekelle.
Administrative, technical, or material support: Johnsen.
Study supervision: Shekelle.
Conflict of Interest Disclosures: All authors have completed and submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest and none were reported.
Funding/Support: The RAND Corporation internally funded this review, building on the literature database established for contract HHSA 290-2007-10062-I, an evidence report on the safety of probiotics commissioned by the Agency for Healthcare Research and Quality and funded jointly by the National Institutes of Health (NIH) Office of Dietary Supplements, the NIH National Center for Complementary and Alternative Medicine, and the US Food and Drug Administration (USFDA) Center for Food Safety and Applied Nutrition. Dr Shekelle reports support from the Department of Veterans Affairs.
Role of the Sponsor: The sponsors had no role in the conduct of this review; collection, management, analysis, and interpretation of the data for this review topic; or in the preparation, review, or approval of this manuscript.
Additional Contributions: Alexandria Smith, MPH, and Ning Fu, MA, provided assistance with the database, and Tanja Perry, BHM, provided administrative assistance for the manuscript. All of these individuals are employees of RAND and received no additional compensation in association with their contributions to this article.