Purpose of this article

Since the medical system in Canada is socialized, many (if not all) of the free market, capitalist forces that might automatically improve quality of care are not in effect. This is a result of the government control over the system. Debate over whether or not this occurs is quite high, especially as the United States considers a similar system under President Obama. Many critics of socialized medicine argue that it decreases quality of care and increases wait times, especially for the poor. The purpose of this study is to determine if the wait times for breast cancer treatment in Canada is different for people with low income as opposed to those with high incomes.

Statistical Concepts Discussed

The study uses preexisting data in their analysis. To obtain data about wait-times, demographics, survival times, etc., the researchers use a 10-year study of cancer survival that was conducted in Ontario and California. The focus of this study was women who were diagnosed with cancer between 1998 and 2000. The sample size of this study was sufficient to detect a 15% increase in survival rates with probability 0.8. In particular, there were around 990 observations in each observational study group. In addition to disease information and survival rates, the data set includes demographic data that includes home address. Using this information, the study uses census data to determine the income level of the participants. That is, the census data provides information regarding average income for each neighborhood within the neighborhoods of interest. For this study, a person’s income is set to be that of the neighborhood in which they live. This may be an ecological fallacy. That is, the study assumes that the characteristics of the individual match the average characteristics of the place in which they live. Nonetheless, since neighborhoods tend to be fairly homogenous, this assumption may not be unreasonable.

The distribution of wait times were highly right skewed. That means that most patients experienced short wait times while there were a few patients who experienced much longer wait times. For this reason parametric tests were not appropriate. Parametric tests, like the t-test, assume that the individual populations follow a normal distribution. Even though the samples appear to be quite large, the researchers do not appeal to the central limit theorem. Instead, they employ nonparametric tests to perform their analysis. The Mann-Whitney U-test, also know as the Wilcoxon Rank-Sum test (not identical, but mathematically equivalent. I.e., they differ by adding a constant value), is used to compare the medians of the two groups. The U-test differs from the t-test in this way. The t-test focuses on the difference between means, but the U-test tests for differences between medians. This is a more reasonable approach since the observations are so right-skewed. In addition, the Mantel-Haenszel chi-square test is used to test for correlation between categorical variables that are displayed in a two-way table. The variables analyzed in the two-way tables are location (Ontario or California) and income (low, middle, or high).

As an illustration of the Mantel-Haenszel test, here is the two way table shown in Table I of the paper. The table is as follows:

Ontario / California / Total
Urban / 624 / 656 / 1280
Rural / 305 / 328 / 633
Total / 929 / 984 / 1913

The paper doesn’t display the stratified breakdown so that the reader can calculate the test statistic (the test is used for determining correlation using stratified data). In this case, the strata would be the income levels.

Based on the above table, though, we can perform a chi-square test for independence. In this case, the null hypothesis is that the variables are independent, and the alternative is that they aren’t. The expected frequencies are calculated using the marginal counts. The expected table is as follows:

Ontario / California
Urban / 621.60 / 658.40
Rural / 307.40 / 325.60

So we calculate the test statistic to be (621.6-624)^2/621.6+(658.4-656)^2/658.4+(305-307.4)^2/307.4+(325.6-328)^2/325.6 = 0.0545. The critical value in this case (1 degree of freedom) is 3.84, so we do not reject the null hypothesis. There is not enough evidence to suggest that variables are not independent.

Conclusion

The results of the study found that there was a difference between wait times in large metropolitan areas. Specifically, Canadians had to wait longer (by about 3 days) than Californians who lived in large areas. Those living in more rural places did not demonstrate a significant difference in their wait times. In addition, they found that women in Ontario were also significantly more likely to experience very long waits.

In addition, the study found that income was a significant factor in wait times for treatment in California where it was not a significant factor in Ontario. In addition to this, wait times to receive radiation treatment were longer for those in more rural places in California.

The authors point out some limitations with their methods. In particular, several of their results are based on quite small samples. In addition, there may be a problem with data collection. That is, missing values, (i.e., incomplete cancer treatments), may affect the analysis of data, though the authors of the study argue that these missing values did not affect their analysis in a significant way. Finally, the study is not yet complete. It is a 10 year study that did not begin until the year 2000. Hence the results will not be fully available for a few more years, though they argue that their results should not be affected by this problem either.