Different regression equations relate age to the incidence of Lauren types 1 and 2 stomach cancer in the SEER database: these equations are unaffected by sex or race

Data acquisition

Hence, SEER generated 160 numbers pairs. Each pair comprised a number of persons who developed stomach cancer and a number of persons in the denominator. For each set a rate was calculated by dividing the number of persons with stomach cancer by the number of persons in the denominator. For example, from 1992–1996, 35 Lauren type 1 stomach cancers were observed among 2,752,873 non-Asian men ages 40–44: the rate was 1.27 × 10^-5. From 1997–2001, of 366,766 Asian women aged 65–69, 55 developed Lauren type 1 gastric cancer: the rate was 1.60 × 10^-4.

Software

R was used for data analysis.

Model selection

All models tested were linear regression models with the response variable being the logarithms of the cancer rates, as defined above. Analysis of variance determined which model best reflected the data. Covariates were always added to regression; the ratio of the change in the residual sum of squares (ΔRSS) to the RSS before the covariate was added was compared with an F test. Independent (explanatory or predictor) variables included: A) Five year period (1992–1996 = 0, 1997–2001 = 1), B) Sex (men = 0, women = 1), C) Race (Non Asian = 0, Asian = 1), D) Lauren type (type 1 = 0, type 2 = 1), E) Age Group (40–44 = 1, 45–49 = 2, 50–54 = 3, etc.). All ten possible two-way variable interactions were assessed. The null hypothesis was rejected if P < 0.05. Neither higher-order explanatory variable interactions nor non-linear relationships of explanatory variables to the response variable were considered in this analysis.

Evaluation of the data precluded the performance of Poisson regression: the mean number of patients with cancer was 49; the variance was 2224. When Poisson regression was tried with population as an offset, with or without the zero cell, all five potential explanatory variables (five year period, sex, race, Lauren type, and age) and all ten potential first order interactions were associated with the counts; each explanatory variable had an associated z > 600, P < 1 × 10^-10. A residual plot showed the model lacked a good fit.

Model adequacy

Standardized residuals were calculated by R. To test the assumption that the standardized residuals were normally distributed, a Shapiro-Wilks test was performed. To test the assumption that the mean of the standardized residuals was 0, a t-test was performed. To test the assumption that the standardized residuals had constant variance with respect to the fitted values, the standardized residuals were divided into quartiles and Bartlett's test for homogeneity of variances was performed. A data point was considered an outlier if its studentized residual, calculated by R, was greater than 3; dffits (a measure which gives greater weight to outlying observations) and Cook's distance (a measure of impact of the respective case on the regression equation), calculated by R were used to assess leverage; outliers that are found to have high leverage, large dffits and/or Cook's distances, are considered bad leverage points and are removed from the analysis.

Raw data

Summary of model building

Final model

Two regression equations, using the values for the final model without the outlier, express the results:

Lauren type 1

ln(ca) = -14.15 - 1.07 × sex + 1.74 × race + 0.52 × age group

Lauren type 2

ln(ca) = -11.55 - 0.23 × sex + 0.97 × race + 0.28 × age group

For the above equations:

• ln(ca) is the response variable, the natural logarithm of the stomach cancer rates.

• Sex, Race, and Age are explanatory variables (sometimes called risk factors)

• The numbers in front of the explanatory variables are called regression coefficients or beta weights. Coefficients are interpreted as follows: if Sex and Age are held constant (or "controlling for" Sex and Age), then, for Lauren type 1 stomach cancer, mean ln(ca) increases by about 1.74 if the group is Asian; for Lauren type 2 stomach cancer, the corresponding increase is 0.97.

Figures 1, 2, 3 and 4 plot predicted and observed logarithms of stomach cancer rates versus age comparing Asian and non-Asian men and Asian and non-Asian women. Actual data confirms the regression equations: data points pretty closely approximate the lines in all cases. Although the races and sexes may start off with different incidences at age 40, changes in incidence with respect to age are quite similar. Because the incidence of patients with Lauren type 1 tumors 1) starts out lower than and 2) rises at almost twice the rate of the incidence of patients with Lauren type 2 tumors, the ratio of Lauren type 1 to type 2 incidences strongly depends on age. Compare Asian and non-Asian men: at age 40 both groups show a greater incidence of patients who developed Lauren type 2 tumors; at age 85 Asians show a greater incidence of patients who developed Lauren type 1 tumors, which is not true for non-Asians.

Model adequacy

There was only one outlier, a data point with a studentized residual over 3. No non-Asian women, aged 45–49 years, developed Lauren type 1 stomach cancer; it was the only zero cell. The studentized residual, -5.40, corresponded with the largest Cook's distance, 0.183, and the dffit, -1.316, with the largest absolute value. The outlier was a bad leverage point. Although results for the outlier are displayed in the tables, the high leverage meant that the outlier should be excluded from the final analysis. Removing the outlier yielded the same choice of covariates.

Year of diagnosis

Boyle [4] found stomach cancer in general was declining in incidence in Europe, as did Faycal [5], Pineros [6] in Columbia, Ardanaz [7] in Navarro, and Stracci [8] and Crocetti [9] in Italy. Liu's [10] results showed that over time, for both sexes, there were different trends for stomach cancer depending on the third of the stomach involved and the age of the patient. Henson [11] studied Lauren type 2 and Lauren type 1 incidences over time, revealing that the changes over time differed between the two Lauren types. Sunny's [12] study of Indian men and women revealed different rates of decline in stomach cancer, demonstrating an interaction of time of diagnosis and sex. Levi [13], using joinpoint regression analysis, found that the fall over time in gastric cancer rates was proportionally greater for older than for younger persons, although all showed a decline. The results of the study of Kobayashi [14], by contrast, gave the lion share of the decrement in gastric cancer for the young. For the Greenland Inuit, stomach cancer rates appear to have increased [15]. This study of SEER data did not show time of diagnosis or an interaction of any factor and time of diagnosis to be an important explanatory variable for the incidence of stomach cancer over the decade 1992–2001 in the United States.

Sex

Marmo [16], Turkdogan [17], Faycal [5], Bani-Hanu [21], and Dobru [18] all showed men at greater risk for stomach cancer than women. Among Epstein Barr Virus positive cancers, the gender difference exists, but is only statistically significant for Lauren type 2 gastric cancers [19]. A family history of stomach cancer would appear to place women, but not men at increased risk [20]. Alaskan Native American men differ less from other American men than do Alaskan Native American women, demonstrating an interaction of sex and race [22]. Green tea consumption appears to protect women, but not men, from gastric cancer [23]. Japanese men appear to have a greater increase in risk as they age than do Japanese women [24]. Khan [25] found that different foods for men than for women increased the risk of gastric cancer. This study of SEER data identified gender as an important explanatory variable for the incidence of stomach cancer.

Race

Ciliated metaplasia, a precursor to stomach cancer, occurs at different rates in the Pacific and Atlantic basins [26]. Yao [27] showed that Hispanics with stomach cancer differed in age than other persons and that Asians differed in survival than other persons. Multiple studies have placed Asians at greater risk of gastric cancer [28–30]. When a known risk factor, such as H. pylori, becomes universally acquired, it ceases to be a risk factor; this has been shown to have occurred in Koirea [31]. This study of SEER data did not find an interaction between race and sex, but did identify race as an explanatory variable for stomach cancer incidence.

As to black race, some have suggested that Caucasians are more likely than blacks to develop gastric cancer that arises in the cardia and that blacks are more likely than Caucasians to develop gastric cancer that arises outside the cardia [32, 33]. There were insufficient patients in this study to subdivide the analysis by site within the stomach or to separately analyze black persons. To evaluate the importance of black race, studies would need 1) to have more black patients and 2) to take into account whether the cancer originated in the gastric cardia or not. The location of origin would be of interest in itself as immunohistochemical patterns of cardia and non-cardia gastric cancers differ [34].

Age

Older persons more likely develop ciliated metaplasia than do young persons [26]. Multiple studies have shown that age is a vitally important factor to consider as regards the risk of stomach cancer [18, 35, 21]. In terms of other risk factors, there is good reason to think that H pylori's effect declines with age [36] and that acquisition of H pylori after age 1 may be less important in carcinogenesis than is acquisition before age 1 [37]. Marmo [16] and Tanaka [24] demonstrated an interaction of age and sex. Levi [13], Kobayashi [14], and Liu [10] showed an interaction of age and time of diagnosis. A prior study [38] suggested that the effect of environmental carcinogens is largely limited to childhood. The latter is in accord with our study, which would suggest that a person's risk of cancer is set at or below the age of 40 and that its expression occurs at predictable increments thereafter. This study of SEER data found age to be an explanatory variable for stomach cancer incidence.

Lauren type

Loss of CDX2 may represent a marker of tumor progression in early gastric cancer and carcinomas with an intestinal, but not a non-intestinal phenotype [39]. The frequency of ciliated metaplasia differs between intestinal and non-intestinal stomach cancer types [26]. For some nations, Lauren type 1 cancer was more common than Lauren type 2 [18, 40]. Yao [27] showed Hispanics differed in Lauren type from other persons. An interaction with between time of diagnosis and Lauren type exists [5, 11]. van Beek [41] found that Epstein Barr Virus associated cancer was more frequently associated with Lauren type 1 than with Lauren type 2 adenocarcinoma. This study of SEER data found interactions of Lauren type and race, age, and gender to be of such importance that two different regression equations had to be created to describe the data. The importance of separating Lauren types from one another lies in part in the demonstrated multiple interactions between Lauren type and so many other variables, both those found in this study and those found in recent epidemiologic studies.

The above discourse allows one to appreciate the limitations and utility of the study. SEER is, like many of the sources of the other studies, an administrative database. Administrative databases lack a review of histopathology; the added loss of precision is unavoidable because such a review would increase the expense of any such study and decrease participation by hospitals, largely invalidating its results. As expected, specific program codes are not available on line for investigators, reviewers, readers, and editors to explore issues that may be important to them, such as the means of creation of a denominator in rate calculations. The website is excellent, but might also include readily accessible links to the data registries themselves and their policies and procedures, so investigators, reviewers, editors, and readers can satisfy any questions they might have as to such matters as data collection or the particular manner of dealing with multiple primaries for a particular study. No administrative database can keep a record of such things as H pylori rates, genetic markers, food intake, or any of the other above miscellaneous factors identified. As with any study, the number of factors that can be evaluated is limited both for reasons of data collection and for statistical reasons having to do with sample size; for this reason, a global explanation encompassing all potential factors cannot be expected. The most any epidemiologic study can offer is a partial explanation of complex phenomena. Most vital, the above referenced recent studies show that any conclusion derived by examination of a particular population must be verified by evaluation of multiple populations. This is because factors that are important in one population may be unimportant in another population; only by repeating an analysis in multiple populations can an epidemiologic conclusion be considered verified. Notwithstanding these caveats, such studies of epidemiology have great practical significance; Marmo [16] used such results to design a screening protocol for stomach cancer based on age and sex so as to reduce cost.