This repository contains work done while an intern in the Etzioni Group at Fred Hutchinson Cancer Research Center. The goal of this project is to explain whether the uptake of surgery and radiation had different efficacies in black versus white men with prostate cancer, and, in more general terms, to determine the effect of different uptake and different efficacy of a treatment on disparity statistics in disease mortality.
Our model for mortality is a continuous time Markov chain, where a person can transfer between states of healthy, cancerous and dead (in that order only), with baseline age and race specific rates (calculated from people who did not receive treatments). Additionally, Each person is given a "c" value or a cutoff date. If a patient is diagnosed after their cutoff, they receive a treatment which increases mean survival by a constant multiplier, decreasing hazard by the inverse of that constant (a hazard ratio). We used uptake data and, assuming a monotonically increasing uptake, made a cdf of cutoff dates (with some at infinity), and thus created a treatment distribution for black and white men. Using known parameters of age-specific incidence rate, survival rate past past diagnosis, uptake of treatment based on year of diagnosis, each calculated for black and white men separately, we optimized our treatment efficacy parameter with a poisson likelihood (where a poisson distribution would give the number of deaths each year, and finding the likelihood of our observed data).
Through numerous iterations of our model (originally age independent incidence, optimizing for years before 1900, optimizing for ages above 85, etc.), it is clear that our model indicates a different treatment effect for surgery/radiation between black and white men, with white men getting a significantly better efficacy. Using a likelihood ratio test between our model of different efficacies and one optimized for the same treatment efficacy in both races, the p value attained was indistinguishable from 0 by RStudio.
Limitations of our model include the introduction of PSA screening in the 1990s. Our model is prepared to include only one treatment, and thus our question is truly "was there a different treatment effect of surgery and radiation among black and white men with prostate cancer ASSUMING PSA screening had no effect on mortality." A further step in this model would be to include a second or third or nth treatment possibility so that it could be more applicable to real situations for real diseases.
Furthermore, though our model fits mortality relatively well for individual birth cohorts between 1905 and 1965, for men under age 80, it fits poorly for ages over 80, and for entire population statistics such as age-adjusted mortality and various disparity statistics. For men over age 80, there is a slight age effect on treatment uptake in real data. Men past that age begin to decrease in treatment reception, so, when our optimization algorithm included those men, we were assuming that a certain percent were getting treatments, but the true percent was much lower, and our treatment efficacy was thus artificially lowered, so we had to exclude them. Our model only allowed for increasing probability of receiving treatment throughout time, independent of age. Because our model fails to fit men over age 80, who get a large increase in mortality, these errors compound and cause poor fits to population level data. Thus, another possible improvement would be to change the cutoff date approach in order to allow a date/age where people refuse treatment as well.
Another potential reason our model fits population level data poorly is because of certain trends in prostate cancer mortality, such as a seemingly constant increase in age-adjusted mortality rates before the mid 1990's, which may be due to artifact (more deaths being attributed to prostate cancer due to inflated diagnosis of cases in the PSA screening area) or some other reason, but our model cannot fit this increase and thus has to try to fit a treatment during an era in which mortality increased for a couple years. One possible next step would be to find a different cancer or non-reversible disease with clearer trends and a clear singular treatment introduction, which would fit the scope of our model better.
2000-Standard-Pop.csv: 2000 U.S. standard population data
SEERout1980-86.csv: Case level data for survival
agemort.csv: Data for death year and birth year specific mortality with modeled values as well
incidence-by-age.csv: Data for age-specific incidence rates
long-age-specific-mortality.csv: Data for creating agemort.csv, death year and age mortality rates
mortality-age-adjusted.csv: Age adjusted population mortality data
mortality-crude.csv: Not age adjusted population mortality data
treatment-type-race.csv: Data for rates of receiving different treatments\
2000-std-pop.R: Making a dataframe with standard population data
creating-population-data.R: Turning agemort from age-specific to age-adjusted population mortality
crude-vs-ageadjusted-exploration.R: Seeing how looking at crude versus age adjusted rates distorts population data
defining-simulation-functions.R: Defining functions which create our analytic model of mortality
real-world-age-specific-mortality.R: Creating a dataframe of values which we can compare our model to
real-world-parameter-dataframe.R: Creating a dataframe which contains incidence and survival values for each race and age group
real-world-uptake-trends.R: Creating uptake distributions for black and white men over time
selectedyears-optimizing-treatment-effect-likelihood.R: Optimizing treatment effect parameter with a poisson likelihood method
disparityreport-withoutagedependentincidence.Rmd: Old report before model was updated
disparity-report.Rmd: Most current report (in progress)