Forecasting Hepatocellular Carcinoma Mortality using a Weighted Regression Model to Estimate Cohort Effects in Taiwan

Summary

We depict a multistage method to measure a cohort effect with age data, thereby allowing data to be eliminated in many situations without sacrificing data quality. The protocol demonstrates the strategy and provides a weighted regression model for analyzing the hepatocellular carcinoma data.

Abstract

To eliminate the influence of age and period in age cycle contingency table data, a multistage method was adopted to evaluate the cohort effect. The most general primary malignant tumor of the liver is hepatocellular carcinoma (HCC). HCC is associated with liver cirrhosis with alcohol and viral etiologies. In epidemiology, long-term trends in HCC mortality were delineated (or forecasted) by using an age-period-cohort (APC) model. The HCC deaths were determined for each cohort with its weighted influence. The confidence interval (CI) of the weighted mean is fairly narrow (compared to the equally weighted estimates). Due to the fairly narrow CI with less uncertainty, the weighted mean estimation was used as a means for forecasting. With the multistage method, it is recommended to use weighted mean estimation based on a regression model to evaluate the cohort effect in the age-period contingency table data.

Introduction

The most common primary malignant tumor of the liver is hepatocellular carcinoma (HCC). Its mortality rate ranks fifth in men and eighth in women (6% of men and 3% of women) ¹ among all malignant tumors worldwide. In Taiwan, it is the most common cancer in men and the second most common cancer in women (21.8% of men and 14.2% of women) ². It is estimated that since 2000, the annual number of HCCs diagnosed worldwide is 564,000, among which 398,000 are men and 166,000 are women ³. In epidemiology, the most common way to explain the relationship between age, period, and cohort (APC) variables is that age and period influence each other to create a unique generational experience for the disease trend investigated.

Even though this conceptualization still has a precise linear connection of age + cohort = period, exposure (predictor) is not an inherent factor in a birth cohort. Instead, we propose that when changes cause different distributions of disease, there is a cohort effect. Nevertheless, since age + cohort = period, these three variables are linearly related; only if other restrictions are enforced is it impossible to generate an estimated age-period-cohort (APC) model using the linear effects of age, period, and cohort. In this study, we clarified this problem and the potential restrictions we imposed in our previous publications ^4,5,6,7.

With the slightest conjectures about the contingency table data, the multistage method ⁸ provides three stages to evaluate the cohort effect. In addition, since median polish does not depend on a specific distribution or framework, it was used for various types of data, such as ratios, logarithmic ratios, and counts. Median polishing is the prime technique used in the multiphase method.

Data from a two-way contingency table ⁹ were used to generate the development of the polished median. The median polishing procedure is used to eliminate the cumulative effects of age (i.e., row) and period (i.e., column) by iteratively subtracting the median from each row and each column. This procedure is often used in epidemiological data analysis ¹⁰. One advantage of this technique is that no assumptions about the distribution or structure of the data in the bidirectional contingency table are required. Therefore, this technique was broadly utilized for any type of data contained in the table, such as suicide data ¹¹. The APC model has also been used to describe the long-term trends of disease incidence or mortality ⁵. APC models often assume that age, period, and cohort have additive effects on the logarithmic transformation of disease/mortality. To evaluate cohort effects, the described protocol generates an APC model for complete hepatocellular carcinoma (HCC) mortality analysis with weighted regression, thereby supporting reliable predictions and moderate assessment of treatment effects.

Protocol

1. Data sources To demonstrate the calculations, we used annual data on HCC mortality from 1976 to 2015 for men and women in Taiwan. Statistical package for social sciences (SPSS) version 24.0 for Windows and Microsoft Excel were used to execute the protocols for this study. Have the HCC physician classify the patients' clinical symptoms, laboratory tests and medical imaging results to give a diagnosis code according to the International Classification of Disease (ICD) Code, IC…

Representative Results

The mortality data were demonstrated for 10 five-year age groups (40-44, 45-49, 50-54, 55-59, 60-64, 65-69, 70-74, 75-79, 80-84, and 85+) and 8 five-year time periods (1976-1980, 1981-1985, 1986-1990, 1991-1995, 1996-2000, 2001-2005, 2006-2010 and 2011-2015). The number of cohort groups was selected by subtracting one from the total number of age-period groups: 10 (five-year age groups) + 8 (five-year time periods) -1 = 17 birth cohorts, with the birth cohort groups denoted by mid-cohort years as 1891, 1896, 1901, 1906, …

Discussion

Due to the time trend of HCC mortality, conventional models underestimate some important features hidden in the data (such as cohort effects), and conventional analyses that use simple linear extrapolation of the observed logarithmic age correction rate show significantly reduced accuracy in their predictions. It is clear that this trend has continued for 35 years and will trend upwards in the next few years if we directly observe the long-term trend of HCC mortality in Taiwan from 1976 to 2015 (Figu…

Materials

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