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Chapter 10: Problem 71

The percentage of women who get breast cancer sometime during their lifetime is higher now than in 1900 . Suppose that breast cancer incidence tends to increase with age, and suppose that women tend to live longer now than in \(1900 .\) Explain why a comparison of breast cancer rates now with the rate in 1900 could show different results if we control for the age of the woman.

Short Answer

Expert verified
Controlling for age may reduce perceived differences in breast cancer rates, as longer lifespans now increase exposure risk and improved diagnostics detect more cases.

Step by step solution

01

Understand the Context of Breast Cancer Incidence

Breast cancer incidence refers to the rate of new cases in a population. The comparison between now and 1900 is influenced by several socio-demographic factors, such as changes in longevity and medical diagnostics.
02

Identify Variables Affecting Breast Cancer Rates

Key variables include the average lifespan of women and the age at which breast cancer typically develops. In 1900, women had shorter lifespans, which limited the age range in which breast cancer could manifest. Presently, women live longer, increasing the likelihood of developing breast cancer over a prolonged period of risk exposure.
03

Analyze the Impact of Longevity on Cancer Rates

As women tend to live longer today, they are more likely to reach ages that have higher risks associated with breast cancer, thus increasing the observed incidence rate. Longevity impacts the calculation as it extends the period of susceptibility.
04

Consider Diagnostic Advancements

Medical advancements have improved the detection of breast cancer. In 1900, cases might have been underreported due to less effective diagnostic tools. The current higher reported incidence can thus partially reflect more accurate reporting rather than an absolute increase in cases.
05

Statistically Control for Age

If we control for age in statistical analyses, we compare the incidence of breast cancer among women of the same age group across both time periods. This could reveal that the difference in breast cancer rates is less than initially perceived, demonstrating that the apparent increase might be due to differences in age distribution and longevity rather than a genuine rise in incidence.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Breast Cancer Incidence
Breast cancer incidence measures the rate at which new cases of breast cancer occur in a given population over a specified period. It's a crucial statistics element that helps track the public health impact of breast cancer over time.
Women today face a different breast cancer landscape than those in the early 1900s, with many factors at play. Longevity, diagnostic capabilities, and even lifestyle choices affect the incidence rate.
In 1900, women's lifespans were considerably shorter, often not living past the age where breast cancer commonly occurs. This results in lower observed incidence rates from that era. In contrast, as women live longer today, they are more likely to reach ages with elevated breast cancer risks, hence contributing to higher current incidence figures.
Additionally, social awareness and healthcare accessibility have increased, encouraging more women to seek regular check-ups, potentially identifying more cases than a century ago.
Age Control in Statistical Analysis
Age control in statistics is vital when comparing data sets from different times or populations, especially when analyzing health-related data. By ensuring that comparisons are made within the same age groups, more accurate conclusions can be drawn about trends over time.
Let's break down the impact of age control:
  • If breast cancer incidence is higher now, it may simply relate to the longer average lifespan, allowing more women to reach ages where the risk is significant.
  • By grouping data according to age, statisticians can effectively control for longevity differences thereby highlighting whether increased incidence rates are genuine or simply an artifact of differing age demographics.
This method brings clarity, correcting potential misconceptions that could arise from raw comparisons and ensuring public health resources are appropriately allocated.
Advancements in Diagnostics
Medical advancements have significantly transformed breast cancer diagnostics from the 1900s to today. In earlier times, diagnosis was limited by the technology and medical knowledge of the era.
Some key advancements include:
  • The development of mammography and imaging technologies that allow for early detection and more accurate assessment.
  • Biotechnological progress that includes genetic testing and the identification of risk factors.
These improvements mean that more cases are identified today compared to the past when cases might not have been reported or recognized effectively. Thus, while it may appear breast cancer cases are surging, some of the increase is attributable to improved detection methods, not solely an increase in case numbers.
Recognizing the role of enhanced diagnostic tools helps in understanding data on breast cancer incidence, allowing health professionals and policymakers to make informed decisions about healthcare strategies and resource allocations.

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Most popular questions from this chapter

Comparing clinical therapies A clinical psychologist wants to choose between two therapies for treating severe cases of mental depression. She selects six patients who are similar in their depressive symptoms and in their overall quality of health. She randomly selects three of the patients to receive Therapy \(1,\) and the other three receive Therapy \(2 .\) She selects small samples for ethical reasons - if her experiment indicates that one therapy is superior, she will use that therapy on all her other depression patients. After one month of treatment, the improvement in each patient is measured by the change in a score for measuring severity of mental depression. The higher the score, the better. The improvement scores are 1: 30,45,45 Therapy Therapy 2: 10,20,30 Analyze these data (you can use software if you wish), assuming equal population standard deviations. a. Show that \(\bar{x}_{1}=40, \bar{x}_{2}=20, s=9.35, s e=7.64\), \(d f=4,\) and a \(95 \%\) confidence interval comparing the means is (-1.2,41.2) b. Explain how to interpret what the confidence interval tells you about the therapies. Why do you think that it is so wide? c. When the sample sizes are very small, it may be worth sacrificing some confidence to achieve more precision. Show that a \(90 \%\) confidence interval is \((3.7,36.3) .\) At this confidence level, can you conclude that Therapy 1 is better?

A USA Today story (May 22, 2010 ) about the medical benefits of moderate drinking of alcohol stated that a major French study links those who drink moderately to a lower risk for cardiovascular disease but challenges the idea that moderate drinking is the cause. "Instead, the researchers say, people who drink moderately tend to have a higher social status, exercise more, suffer less depression and enjoy superior health overall compared to heavy drinkers and lifetime abstainers. A causal relationship between cardiovascular risk and moderate drinking is not at all established." The study looked at the health status and drinking habits of 149,773 French adults. a. Explain how this story refers to an analysis of three types of variables. Identify those variables. b. Suppose socioeconomic status is treated as a control variable when we compare moderate drinkers to abstainers in their heart attack rates. Explain how this analysis shows that an effect of an explanatory variable on a response variable can change at different values of a control variable.

An AP story (April 9,2005\()\) with headline Study: Attractive People Make More stated that "A study concerning weight showed that women who were obese earned 17 percent lower wages than women of average weight." a. Identify the two variables stated to have an association. b. Identify a control variable that might explain part or all of this association. If you had the original data including data on that control variable, how could you check whether the control variable does explain the association?

According to the Bureau of Labor Statistics, the official unemployment rate was \(10.4 \%\) among blacks and \(4.7 \%\) among whites as of February 2015\. (www.bls.gov/). a. Identify the response variable and the explanatory variable. b. Identify the two groups that are the categories of the explanatory variable. c. The unemployment statistics are based on a sample of individuals. Were the samples of white individuals and black individuals independent samples or dependent samples? Explain.

Vegetarians more liberal? When a sample of social science graduate students at the University of Florida gave their responses on political ideology (ranging from \(1=\) very liberal to \(7=\) very conservative \(),\) the mean was \(3.18(s=1.72)\) for the 51 nonvegetarian students and \(2.22(s=0.67)\) for the 9 vegetarian students. Software for comparing the means provides the printout, which shows results first for inferences that assume equal population standard deviations and then for inferences that allow them to be unequal. \(\begin{array}{ccclc}\text { Sample } & \mathrm{N} & \text { Mean } & \text { StDev } & \text { SE Mean } \\ 1 & 51 & 3.18 & 1.72 & 0.24 \\ 2 & 9 & 2.220 & 0.670 & 0.22 \\ \text { Difference } & =\mu(1)-\mu(2) & & \end{array}\) Estimate for difference: 0.960 95?a CI for difference: (-0.210,2.130) T-Test of difference \(=0\) (vs \(\neq):\) T-Value \(=1.64\) \(\mathrm{P}\) -Value \(=0.106 \mathrm{DF}=58\) Both use Pooled StDev \(=1.6162\) 95? CI for difference: (0.289,1.631) T-Test of difference \(=0(\mathrm{vs} \neq):\) T-Value \(=2.92\) P-Value \(=0.007 \quad \mathrm{DF}=30\) a. Explain why the results of the two approaches differ so much. Which do you think is more reliable? b. State your conclusion about whether the true means are plausibly equal.
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