# Statistical testing

Statistical trends can be analyzed in many ways. The approaches used in Health, United States to analyze trends in health measures over time depend primarily on the data source (that is, National Center for Health Statistics surveys, vital statistics, and other data sources) but also consider the type of dependent variable and the number of data points. With enough data points, statistical analyses can detect not only whether an increase or decrease has occurred but also a change in trend. Some trends are analyzed using the weighted least squares regression method in the National Cancer Institute’s Joinpoint software version 4.8.0.1, which identifies the number and location of joinpoints (that is, inflection points) when changes in trend have occurred. For more information on Joinpoint, see: https://surveillance.cancer.gov/joinpoint. (Also see Sources and Definitions, Joinpoint trend analysis software; Statistical significance.)

## NCHS survey data

Trends in NCHS survey data: Based on record-level data and generally follow the steps laid out in the NCHS trends analysis guidelines. For more information, see Ingram DD, Malec DJ, Makuc DM, Kruszon-Moran D, Gindi RM, Albert M, et al. National Center for Health Statistics guidelines for analysis of trends. National Center for Health Statistics. Vital Health Stat 2(179). 2018. The presence of a nonlinear trend is first assessed using polynomial regression (SUDAAN PROC REGRESS). Linear, quadratic (7 or more time points), and cubic (11 or more time points) trends are tested in separate regression models. Quadratic trends are tested with both linear and quadratic terms in the model, and cubic trends are tested with linear, quadratic, and cubic terms in the model.

If a cubic trend is statistically significant and the analysis included at least 11 time points, Joinpoint software is used to search for up to two inflection points with as few as two observed time points allowed in the beginning, middle, and ending line segments (not counting the inflection points). Although this exceeds the software default of one inflection point for analyses using 11 time points, the NCHS trends analysis guidelines (see: https://www.cdc.gov/nchs/data/series/sr_02/sr02_179.pdf) state this is not a problem for the analysis of record-level survey data because appropriate survey analysis software is used as a follow-up to the Joinpoint software analysis. If a cubic trend is not statistically significant and a quadratic trend is, and the analysis included at least seven time points, Joinpoint is used to search for one inflection point in the trend. In each case, an overall p value of 0.05 and the grid search method are used. If neither a cubic nor quadratic trend is statistically significant—that is, there is no inflection point­—then Joinpoint is not used for further analysis. If a quadratic trend is statistically significant and the analysis included three to six time points, pairwise differences between percentages are tested using two-sided significance tests (z tests) to obtain additional information regarding changes in the trend.

In all Joinpoint analyses of survey data, the Bayesian information criterion (BIC) model is used because it increases the sensitivity to detect potential inflection points. Because Joinpoint is not able to fully account for the complex survey design, inflection points are verified in SUDAAN, which properly accounts for survey design. The difference in slopes between the two segments on either side of an inflection point is assessed using piecewise linear regression (SUDAAN PROC REGRESS). To conduct piecewise linear regression of age-adjusted estimates, survey weights are adjusted for age. For more information about this survey adjustment, see Li X, Bush MA. Approaches for performing age-adjustment in trend analysis. Joint Statistical Meetings 2019, Proceedings of the American Statistical Association: 741–50. Denver, Colorado. 2019. (Also see Sources and Definitions, Statistical reliability of estimates.)

## Vital records

Trends in vital statistics data: Analyses of birth data, infant mortality, and death rates using vital statistics data from the National Vital Statistics System also follow the NCHS trends analysis guidelines and use aggregated point estimates and their standard errors rather than record-level data. For more information, see Ingram DD, Malec DJ, Makuc DM, Kruszon-Moran D, Gindi RM, Albert M, et al. National Center for Health Statistics guidelines for analysis of trends. National Center for Health Statistics. Vital Health Stat 2(179). 2018. Increases or decreases in the estimates are assessed using Joinpoint with an overall p value of 0.05 and the grid search method. In analyses with fewer than 10 time points, BIC is used to select the model. In analyses with 10 or more time points, the permutation test is used to select the model. The maximum number of joinpoints searched is limited to 1, the software default when 11 time points occur in any analysis. The NCHS trends analysis guidelines (see: https://www.cdc.gov/nchs/data/series/sr_02/sr02_179.pdf) recommend against specifying a maximum number of joinpoints to search that exceeds the default for vital statistics, because this increases the likelihood of estimation issues. As few as two observed time points are allowed in beginning and ending line segments (not counting the inflection points). Trend analyses using Joinpoint are carried out on the log scale for birth, infant mortality, and death rates so that results provide estimates of average annual percent change.

Note that all calculations described in this section are performed on the most accurate, actual, unrounded values available while using SAS, SUDAAN, or Joinpoint to ensure the most accurate results. Where possible, estimates and standard errors are to five or more decimal places. Final published content (figures and trend tables) may have been rounded for presentation purposes. Using these rounded figures to reproduce calculations may lead to slightly different results.

## Other data sources

Trends in other data sources: The difference between two points is assessed for statistical significance using either z tests or the statistical testing methods recommended by the data systems. For analyses that show two time points, the differences between the two points are assessed for statistical significance at the 0.05 level using z tests without correction for multiple comparisons. For other data sources, significant comparisons are generally based on the recommendations of the sources. For health expenditure, physician, and dentist data, changes are based on absolute differences. For HIV cases, differences greater than 5% are generally discussed in the text. For life expectancy, changes of 0.1 year or greater are usually discussed. For other data sources with no standard errors, relative differences greater than 10% are generally discussed.