# Melanoma U.S. Mortality Trends

Found in NCI’s 2018 Cancer Statistics Review Results from the Standard Joinpoint Model, Jump Model, and Comparability Ratio Model

The jump model and comparability ratio (CR) model in the Joinpoint software provide a direct estimation of trend data (e.g. cancer rates) where there is a coding or other type of scale change, which causes a "jump" in the rates, but is assumed not to affect the underlying trend.

While some causes of death other than cancer have large ICD-9/ICD-10 coding changes, most cancer causes of death have relatively small comparability ratios (a measure of the ratio of the number of death certificates coded to a specific cause under the ICD-10 divided by the number coded to that cause under ICD-9). All the cancer sites published in the Cancer Statistics Review (CSR) have comparability ratios that fall between 0.99 and 1.01 except for 10 cancer sites (Table 1).

Site | CR | SE(CR) |
---|---|---|

Oral Cavity and Pharynx | 0.9603 | 0.0040 |

Liver and Intrahepatic Bile Duct | 0.9634 | 0.0023 |

Lung and Bronchus | 0.9837 | 0.0005 |

Melanoma of the Skin | 0.9677 | 0.0032 |

Corpus and Uterus NOS | 1.026 | 0.0040 |

Prostate | 1.0134 | 0.0015 |

Brain and Other Nervous System | 0.9691 | 0.0025 |

Non-Hodgkin Lymphoma | 0.9781 | 0.0018 |

Leukemia | 1.0119 | 0.0019 |

Myeloma | 1.0383 | 0.0030 |

For many of these cancer sites, the impact of the comparability ratio is too small to impact the trends in any meaningful way. However, it is possible that a relatively modest comparability ratio can change the overall conclusions about the trends.

## Melanoma Trends

For melanoma, the published ICD-9 to ICD-10 comparability ratio is 0.9677 (SE = 0.0032, 95% CI = (0.9614, 0.9741)). Figure 1 shows US melanoma mortality for all races and both genders from 1992 through 2015 using the standard joinpoint model, the comparability ratio model, and the jump model.

The standard joinpoint model shows a joinpoint in 2013 with a flat trend of 0.00% APC per year prior to 2013 and a significant fall from 2013 to 2015 of 5.40%. A comparability ratio less than one (i.e. 0.9677) forces a sudden drop in the trend line between 1998 and 1999. With this shift, the comparability ratio model shows a joinpoint in 2011 with a significant rise of 0.28% per year prior to 2011 and a significant fall from 2011 to 2015 of 2.68% per year. The jump model estimates a similar comparability ratio of 0.9455, and finds a joinpoint at 2010 with a significant rise of 0.48% per year prior to the joinpoint, and a significant decline of 2.17% after. These are qualitatively different results when the coding change from ICD-9 to ICD-10 is taken into account.

**Figure 1. Standard joinpoint model, jump model, and comparability ratio model for all races and both genders US Mortality for Melanoma, 1992-2015. The estimate of the comparability ratio from the jump model is 0.9455 with standard error = 0.0147 (the estimate of the comparability ratio is statistically different than 1). The comparability ratio (input from a double coding study) is 0.9677 with standard error = 0.0032 (the comparability ratio is statistically different than 1).**

Motivated by this example, an alternate table of US melanoma mortality results in NCI's 2018 Cancer Statistics Review (CSR) that corresponds to the mortality portion of Tables 16.1, 16.2 and 16.3 from CSR has been computed. The alternate table shows Joinpoint results for US mortality from 1975-2015 and 1992-2015 by gender and racial/ethnic groups. The standard joinpoint models, jump models, and comparability ratio models have up to five and four joinpoints for 1975-2015 and 1992-2015, respectively. In these tables the preferred model is indicated for each cohort. The standard joinpoint model is the one currently in use in the Cancer Statistics Review.

## Choice of Selected Model

For causes of death with comparability ratios less than a certain threshold (e.g. between 0.99 and 1.01) the standard joinpoint model may be sufficient. For causes of death with comparability thresholds less than 0.99 or greater than 1.01 the following criteria are provided to choose between the comparability ratio and jump models, and have been used to select the model of choice for melanoma trends.

- If the underlying cohort size is small, the comparability ratio (CR) estimated using the jump model can be quite variable. Therefore, as a first step, if the statistical test that the comparability ratio from the jump model indicates that the CR estimate is not statistically different than 1, use the comparability ratio model. However, if the comparability ratio provided by a double coding study (and directly input into the comparability ratio model) is also not statistically different than 1, then use the standard joinpoint model.
- Even in situations where the jump is statistically significant, if there is large variability, and the comparability ratio is small, one should be wary of estimates of the comparability ratio estimated from the jump model which differ widely from the comparability ratio estimated using a double coding study and input into the comparability ratio model. The underlying variability of the data may make estimation of a small or modest jump size impossible, and there may be confounding between the estimation of the size of the APC, the location of the joinpoints, and the size of the jump. In small subpopulations (e.g. API, AI/AN, rare cancer sites, or small geographic areas), such situations may occur. To avoid this, if the cohort size represents less than some threshold (we utilized 5000 deaths per year as a cutoff) then the comparability ratio model should be used rather than the jump model.

For the US Mortality Melanoma mortality trends 1992-2015 for both genders all races (Figure 1), the comparability ratio (CR) estimate from the jump model is 0.9455, and a statistical test shows that the CR is significantly different from one. The 2015 death counts for this cohort is 8885, which is larger than 5000, therefore, a jump model is selected as the final model.

The example below demonstrates one of the situations.

Figure 2 shows the three models for the same cohort (U.S. Melanoma mortality, both sexes, all races) but for a longer series, 1975-2015. The standard joinpoint model now shows two joinpoints, the jump model shows 5 joinpoints, and the comparability ratio model shows three joinpoints. For trend analysis, the last segment tends to draw the most interest for its important indication on the most recent trend. All three models show a downward trend in the last segment: APC for the jump model, comparability ratio model and standard joinpoint model are -4.51 (significant), -4.65 (significant), and -5.30 (significant), respectively. The standard joinpoint model has a flat trend between 1989 and 2013 (APC=-0.03, not statistically significant). On the other hand, both jump model and comparability ratio model show upward trend for the majority part of this period: Between 1987 and 2009, comparability ratio model has APC = 0.27 (statistically significant) and jump model has two joinpoints -- between 1977 and 1990, and between 1994 and 2009, the APCs are 1.34 and 0.50 respectively, both statistically significant. During1990-1994, the jump model has APC = -0.30, but not statistically significant. In this example, the CR estimate from the jump model is 0.9466, and a statistical test shows that the CR is significantly different from one. The 2015 death counts for this cohort is 8885, which is larger than 5000, therefore, a Jump model is selected as the final model.

**Figure 2. Standard joinpoint model, jump model, and comparability ratio model for all races and both genders US Mortality for Melanoma, 1975-2015. The estimate of the comparability ratio from the jump model is 0.9466 with standard error = 0.0102 (the estimate of the comparability ratio is statistically different than 1). The comparability ratio (input from a double coding study) is 0.9677 with standard error = 0.0032 (the estimate of the comparability ratio is statistically different than 1). **