Confidence intervals for ranks of age-adjusted rates across states or counties

A Comparison of Statistical Methods to Construct Confidence Intervals and Fiducial Intervals for Measures of Health Disparities

Health disparities are differences in health status across different socioeconomic groups. Classical methods, e.g., the Delta method, have been used to estimate the standard errors of estimated measures of health disparities and to construct confidence intervals for these measures. However, the confidence intervals constructed using the classical methods do not have good coverage properties for situations involving sparse data. In this article, we introduce three new methods to construct fiducial intervals for measures of health disparities based on approximate fiducial quantities. Through a comprehensive simulation study, We compare the empirical coverage properties of the proposed fiducial intervals against two Monte Carlo simulation-based methods-utilizing either a truncated Normal distribution or the Gamma distribution-as well as the classical method. The findings of the simulation study advocate for the adoption of the Monte Carlo simulation-based method with the Gamma distribution when a unified approach is sought for all health disparity measures.

Adolescent Behavioral Cancer Prevention in the United States: Creating a Composite Variable and Ranking States' Performance

Preventive behaviors established during adolescence can reduce cancer throughout the life span. Understanding the combinations of multiple behaviors, and how these behaviors vary across states, is important for identifying where additional interventions are needed. Using data on 2011-2015 vaccination, energy balance, and substance use from national surveys, we created state-level composite scores for adolescent cancer prevention. Hierarchical Bayesian linear mixed models were used to predict estimates for states with no data on select behaviors. We used a Monte Carlo procedure with 100,000 simulations to generate states' ranks and 95% confidence intervals. Across states, hepatitis B vaccination was 84.3% to 97.1%, and human papillomavirus vaccination was 41.8% to 78.0% for girls and 19.0% to 59.3% for boys. For energy balance, 20.2% to 34.6% of adolescents met guidelines for physical activity, 4.1% to 15.8% for fruit and vegetable consumption, and 66.4% to 82.0% for healthy weight. For substance use, 82.5% to 93.5% reported abstaining from binge alcohol use, 84.3% to 95.4% from cigarette smoking, and 62.9% to 92.8% from marijuana use. (1) Rhode Island, (2) Colorado, (4) Hawaii and New Hampshire (tied), and (5) Vermont performed the best for adolescent cancer prevention, and (47) Missouri, (48) Arkansas, Mississippi, and South Carolina (tied), and (51) Kentucky performed the worst. However, 95% CIs around ranks often overlapped, indicating lack of statistical differences. Adolescent cancer prevention behaviors clustered into a composite index. States varied on their performance on this index, especially for states at the high and low extremes, but most states did not differ statistically. These findings can inform decision makers about where and how to intervene to improve cancer prevention among adolescents.

Optimal Bayesian point estimates and credible intervals for ranking with application to county health indices

It is fairly common to rank different geographic units, e.g. counties in the USA, based on health indices. In a typical application, point estimates of the health indices are obtained for each county, and the indices are then simply ranked as if they were known constants. Several authors have considered optimal rank estimators under squared error loss on the rank scale as a default method for general purpose ranking, e.g. situations where ranking units across the full spectrum of performance (low, medium, high) is important. While computationally convenient, squared error loss on the rank scale may not represent the true inferential goals of rank consumers. We construct alternative loss functions based on three components: (1) the inferential goal (rank position or pairwise comparisons), (2) the scale (original, log-transformed or rank) and (3) the (positional or pairwise) loss function (0/1, squared error or absolute error). We can obtain optimal ranks for loss functions based on rank positions and nearly optimal ranks for loss functions based on pairwise comparisons paired with highest posterior density (HPD) credible intervals. We compare inferences produced by the various ranking methods, both optimal and heuristic, using low birth weight data for counties in the Midwestern United States, from 2006 to 2012.

State Prevalence and Ranks of Adolescent Substance Use: Implications for Cancer Prevention

Introduction

This study statistically ranked states’ performance on adolescent substance use related to cancer risk (past-month cigarette smoking, binge alcohol drinking, and marijuana use).

Methods

Data came from 69,200 adolescent participants (50 states and the District of Columbia) in the National Survey on Drug Use and Health (NSDUH) and 450,050 adolescent participants (47 states) in the Youth Risk Behavior Surveillance System (YRBSS). Adolescents were aged 14 to 17 years. For 2011–2015, we estimated and ranked states’ prevalence of adolescent substance use. We calculated the ranks’ 95% confidence intervals (CIs) using a Monte Carlo method with 100,000 simulations. Spearman correlations examined consistency of ranks.

Results

Across states, the prevalence of cigarette smoking was 4.5% to 14.3% in NSDUH and 4.7% to 18.5% in YRBSS. Utah had the lowest prevalence (NSDUH: rank = 51 [95% CI, 47–51]; YRBSS: rank = 47 [95% CI, 46–47]), and states’ ranks across surveys were correlated (r = 0.66, P < .001). The prevalence of binge alcohol drinking was 5.9% to 14.3% (NSDUH) and 7.1% to 21.7% (YRBSS). Utah had the lowest prevalence (NSDUH: rank = 50 [95% CI, 40–51]; YRBSS: rank = 47 [95% CI, 47–47]), but ranks across surveys were weakly correlated (r = 0.38, P = .01). The prevalence of marijuana use was 6.3% to 18.7% (NSDUH) and 8.2% to 27.1% (YRBSS). Utah had the lowest prevalence of marijuana use (NSDUH: rank = 50 [95% CI = 33–51]; YRBSS: rank= 46 [95% CI, 46–46]), and ranks across surveys were correlated (r = 0.70, P < .001). Wide CIs for states ranked in the middle of each distribution obscured statistical differences among them.

Conclusion

Variability emerged across adolescent substance use behaviors and surveys (perhaps because of administration differences). Most states showed statistically equivalent performance on adolescent substance use. Adolescents in all states would benefit from efforts to reduce substance use, to prevent against lifelong morbidity.

Ranking composite Cancer Burden Indices for geographic regions: point and interval estimates

PURPOSE

To develop a composite Cancer Burden Index and produce 95% confidence intervals (CIs) as measures of uncertainties for the index.

METHODS

The Kentucky Cancer Registry has developed a cancer burden Rank Sum Index (RSI) to guide statewide comprehensive cancer control activities. However, lack of interval estimates for RSI limits its applications. RSI also weights individual measures with little inherent variability equally as ones with large variability. To address these issues, a Modified Sum Index (MSI) was developed to take into account of magnitudes of observed values. A simulation approach was used to generate individual and simultaneous 95% CIs for the rank MSI. An uncertainty measure was also calculated.

RESULTS

At the Area Development Districts (ADDs) level, the ranks of the RSI and the MSI were almost identical, while larger variation was found at the county level. The widths of the CIs at the ADD level were considerably shorter than those at the county level.

CONCLUSION

The measures developed for estimating composite cancer burden indices and the simulated CIs provide valuable information to guide cancer prevention and control effort. Caution should be taken when interpreting ranks from small population geographic units where the CIs for the ranks overlap considerably.

Comparing percentages and ranks of adolescent weight-related outcomes among U.S. states: Implications for intervention development

Understanding statistical differences in states' percentages and ranks of adolescents meeting health behavior guidelines can guide policymaking. Data came from 531,777 adolescents (grades 9-12) who completed the Youth Risk Behavior Surveillance System survey in 2011, 2013, or 2015. We measured the percentage of adolescents in each state that met guidelines for physical activity, fruit and vegetable (F&V) consumption, and healthy weight status. Then we ranked states and calculated the ranks' 95% CI's using a Monte Carlo method with 100,000 simulations. We repeated these analyses stratified by sex (female or male) or race/ethnicity (non-Hispanic white, non-Hispanic black, Hispanic/Latino, or other). Pearson's and Spearman's correlation coefficients examined consistency in the percentages and ranks (respectively) across behaviors and subgroups. Meeting the physical activity and F&V consumption guidelines was relatively rare among adolescents (25.8% [95% CI=25.2%-26.4%] and 8.0% [95% CI=7.6%-8.3%], respectively), while meeting the healthy weight guideline was common (71.5% [95% CI=70.7%-72.3%]). At the state level, percentages of adolescents meeting these guidelines were statistically similar; states' ranks had wide CI's, resulting in considerable overlap (i.e., statistical equivalence). For each behavior, states' percentages and ranks were moderately to highly correlated across adolescent subgroups (Pearson's r=0.33-0.96; Spearman's r=0.42-0.96), but across behaviors, only F&V consumption and healthy weight were correlated (Pearson's r=0.34; Spearman's r=0.37). Adolescents in all states could benefit from initiatives to support cancer prevention behaviors, especially physical activity and F&V consumption. Programs in states that ranked highly on all assessed health behaviors could be adapted for dissemination in lower-performing states.

The number of key carcinogenic events can be predicted from cancer incidence

The widely accepted multiple-hit hypothesis of carcinogenesis states that cancers arise after several successive events. However, no consensus has been reached on the quantity and nature of these events, although “driver” mutations or epimutations are considered the most probable candidates. By using the largest publicly available cancer incidence statistics (20 million cases), I show that incidence of 20 most prevalent cancer types in relation to patients’ age closely follows the Erlang probability distribution (R² = 0.9734–0.9999). The Erlang distribution describes the probability y of k independent random events occurring by the time x, but not earlier or later, with events happening on average every b time intervals. This fits well with the multiple-hit hypothesis and potentially allows to predict the number k of key carcinogenic events and the average time interval b between them, for each cancer type. Moreover, the amplitude parameter A likely predicts the maximal populational susceptibility to a given type of cancer. These parameters are estimated for 20 most common cancer types and provide numerical reference points for experimental research on cancer development.

Ranking States on Coverage of Cancer-Preventing Vaccines Among Adolescents: The Influence of Imprecision

OBJECTIVES

Identifying the best and worst states for coverage of cancer-preventing vaccines (hepatitis B [HepB] and human papillomavirus [HPV]) may guide public health officials in developing programs, such as promotion campaigns. However, acknowledging the imprecision of coverage and ranks is important for avoiding overinterpretation. The objective of this study was to examine states' vaccination coverage and ranks, as well as the imprecision of these estimates, to inform public health decision making.

METHODS

We used data on coverage of HepB and HPV vaccines among adolescents aged 13-17 from the 2011-2015 National Immunization Survey-Teen (n = 103 729 from 50 US states and Washington, DC). We calculated coverage, 95% confidence intervals (CIs), and ranks for vaccination coverage in each state, and we generated simultaneous 95% CIs for ranks using a Monte Carlo method with 100 000 simulations.

RESULTS

Across years, HepB vaccination coverage was 92.2% (95% CI, 91.8%-92.5%; states' range, 84.3% in West Virginia to 97.0% in Connecticut). HPV vaccination coverage was 57.4% (95% CI, 56.6%-58.2%; range, 41.8% in Kansas to 78.0% in Rhode Island) for girls and 31.0% (95% CI, 30.3%-31.8%; range, 19.0% in Utah to 59.3% in Rhode Island) for boys. States with the highest and lowest ranks generally had narrow 95% CIs; for example, Rhode Island was ranked first (95% CI, 1-1) and Kansas was ranked 51st (95% CI, 49-51) for girls' HPV vaccination. However, states with intermediate ranks had wider and more imprecise 95% CIs; for example, New York was 26th for girls' HPV vaccination coverage, but its 95% CI included ranks 18-35.

CONCLUSIONS

States' ranks of coverage of cancer-preventing vaccines were imprecise, especially for states in the middle of the range; thus, performance rankings presented without measures of imprecision could be overinterpreted. However, ranks can highlight high-performing and low-performing states to target for further research and vaccination promotion programming.

International Ranking of Infant Mortality Rates: Taiwan Compared with European Countries

BACKGROUND

Rankings of infant mortality rates are commonly cited international comparisons to assess the health status of individual countries. We compared the infant mortality rate of Taiwan with those of European countries for 2004 according to two definitions.

METHODS

First, the countries were ranked on the basis of crude infant, neonatal, and postneonatal mortality rates. The countries were then ranked according to the mortality rates calculated after exclusion of live births with a known birth weight of <1000 g, which is the definition set by the World Health Organization.

RESULTS

Taiwan was ranked 11(th), 12(th), and 15(th) among 26 high-income countries for crude infant, neonatal, and postneonatal mortality rates, respectively. The ranks were 12(th), 16(th), and 15(th), respectively, for mortality rates, excluding live births with a birth weight of <1000 g. However, in only seven, four, and 10 countries were the mortality rate ratios statistically significantly lower than Taiwan in infant, neonatal, and postneonatal mortality, respectively, according to the second definition.

CONCLUSION

The ranking of Taiwan was similar (11(th) vs. 12(th)) according the two definitions. However, after consideration of the confidence interval, only six countries (Sweden, Finland, Czech Republic, Belgium, Austria, and Germany) had infant mortality rates statistically significantly lower than those of Taiwan in 2004.