Esophageal Cancer Chemoprevention: An Analysis of Food Consumption in Rats, Study Guides, Projects, Research of Statistics

Download Esophageal Cancer Chemoprevention: An Analysis of Food Consumption in Rats and more Study Guides, Projects, Research Statistics in PDF only on Docsity! A Study of Esophageal Cancer Jason Gershman Department of Statistics Rice University November 27, 2001 Final Project for Stat 421 A Brief History of Esophageal Cancer and Cancer Chemoprevention Esophageal cancer is an extremely deadly cancer in humans. The five-year survival rate for patients diagnosed with it is under ten percent. Approximately 12,000 new cases are diagnosed each year with tens of thousands more worldwide. Some of the causes of esophageal cancer include tobacco usage, consumption of alcoholic beverages, consumption of contaminated food and beverages, and ingestion of salt-cured, salt-pickled, and moldy food. The predominant form of esophageal cancer worldwide is Squamous Cell Carcinoma (SCC), which occurs as high as 140/100000 in parts of China. Cancer chemoprevention is the prevention of cancer by the administration of one or more chemical entities, either as individual drugs or as naturally occurring constituents of the diet. Chemoprevention is a new field, having only received growing consideration as a means of cancer control in the past decade. The traditional thought followed almost universally prior to about fifteen years ago is that chemicals cause cancer and hence one should not fight cancer with other chemicals. Those who work in chemoprevention have had to fight hard to get funding against those who believe in the traditional thought. My History Working With This Data This past summer, I participated in a Research Experience for Undergraduates program in Biostatistics at Ohio State University. As a result of my participation in this program, I was provided with the opportunity to analyze the data from cancer chemoprevention studies of esophageal cancer performed by the laboratories of Dr. Gary D. Stoner of the Ohio State University School of Public Health. Dr. Stoner has been using the Fischer 344 rat model of nitrosamine- induced tumorigenesis for the past decade. In other words, rats are given an agent in their diets that cause esophageal tumors to grow. In addition, some of these rats are fed a prospective chemopreventive agent. It is the hypothesis of the Stoner laboratories that the rats given the chemopreventive agent will develop smaller tumors as well as fewer tumors. In their model, weeks 5-24 (rescaled as weeks 1-19 since the carcinogen dosing ends). Figure 1 depicts the rescaled graph of these 19 weeks. Our ratio appears to start out at around 0.9 but increase up towards 1.0 by the end of the study. At first glance, it does not appear that the ratio is different from 1.0. Now, let us “normalize” our data by taking the logarithmic transformation of our ratio. This centers our values around 0, which is aesthetically pleasing. Hence, a log of the ratio equaling 0 indicates that we do not reject our null hypothesis while a highly negative ratio indicates that we reject our null hypothesis in favor of the alternative. Figure 2 depicts the graphs after the logarithmic transformation. Time 5 10 15 -0 .1 0 -0 .0 4 0 .0 2 Log of Ratio of fd2/fd1 -0.10 -0.05 0.0 0 2 4 6 Histogram Log of Ratio of fd2/fd1 Lag A C F 0 2 4 6 8 10 12 -1 .0 -0 .5 0 .0 0 .5 1 .0 ACF Lag A C F 0 2 4 6 8 10 -1 .0 -0 .5 0 .0 0 .5 1 .0 PACF Figure 2 Looking at ACF and the PACF, our data appears stationary in that our PACF appears to cut off after Lag1 while our ACF tails off. We can ignore the couple of larger values at lag 5 and higher order lags since our data set is so small (19 points), these large lag values are essentially meaningless. Now, let us fit our linear regression model to the data. Here, we have a model of the form y = a + bt + u where u is an AR(1). Here y is the log of the ratio we created above. We chose to model u as an AR(1), from which we can obtain the estimate of the coefficients by the PACF of y above, since the PACF appears to cut off after Lag 1 while our ACF tails off. We now create our model matrix and perform our regression. Let us check the diagnostics of our regression model in Figure 3. Here (18 out of 19) or 95% of our standardized residuals fall within two standard deviations, hence our regression appears to be well behaved. Our ACF and PACF plots both reveal that our process is stationary. The p- values of the Ljung-Box Chi-Squared test are all greater than 0.05. Hence, Plot of Standardized Residuals 5 10 15 -2 .5 -1 .0 0 .0 1 .0 ACF Plot of Residuals A C F 0 5 10 15 -1 .0 0 .0 0 .5 1 .0 PACF Plot of Residuals P A C F 5 10 15 -0 .4 0 .0 0 .4 P-values of Ljung-Box Chi-Squared Statistics Lag p -v a lu e 2 4 6 8 10 12 14 0 .0 0 .2 0 .4 0 .6 ARIMA Model Diagnostics: logfinratio ARIMA(1,0,0) Model with Mean 0 Figure 3 indeed our regression is well behaved and appears to be an acceptable model. Now, since our sample size is so small (n=19), in order to get accurate predictions of future weeks, we rely on Bootstrap inference procedures. Based on the bootstrap procedure (with 25 bootstrap replicates,) we can obtain estimates for the log of the ratio for food consumption for the six weeks following the conclusion of our study. 25 replicates is too few to get precise results in practice but 25 replicates should provide us with an indication of the results. We also obtain 95% Confidence Interval endpoints for these forecasted values. Conclusions As we can see from our graph above (Figure 4), the value of the log of the ratio of the two groups appears close to 0 throughout the latter part of our study and our predicted values are close to 0 as well. Note that I did not perform a one sample t-test to determine whether the log of the ratio equals Time 5 10 15 20 25 -0 .1 5 -0 .1 0 -0 .0 5 0 .0 0 .0 5 0 .1 0 L o g o f R a tio -0 .1 5 -0 .1 0 -0 .0 5 0 .0 0 .0 5 0 .1 0 Forecast for the Log of the Ratio for 6 weeks after the studyFigure 4