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Chapter 14: Problem 32

14.32 Women diagnosed with breast cancer whose tumors have not spread may be faced with a decision between two surgical treatments-mastectomy (removal of the breast) or lumpectomy (only the tumor is removed). In a long-term study of the effectiveness of these two treatments, 701 women with breast cancer were randomly assigned to one of two treatment groups. One group received mastectomies, and the other group received lumpectomies and radiation. Both groups were followed for 20 years after surgery. It was reported that there was no statistically significant difference in the proportion surviving for 20 years for the two treatments (Associated Press, October 17,2002 ). Suppose that this conclusion was based on a \(90 \%\) confidence interval for the difference in treatment proportions. Which of the following three statements is correct? Explain why you chose this statement. Statement 1: Both endpoints of the confidence interval were negative. Statement 2: The confidence interval included \(0 .\) Statement 3 : Both endpoints of the confidence interval were positive.

Short Answer

Expert verified
Statement 2 is correct because a confidence interval that includes 0 indicates that there is no statistically significant difference in the proportions, consistent with the study's reported findings.

Step by step solution

01

Understanding Confidence Intervals

A confidence interval provides a range of values that likely contains the true parameter value in the population. In this case, the parameter is the difference in survival proportions between women receiving different treatments. A 90% confidence interval means that the difference in proportions can lie within this range 90% of the time if the study were to be repeated many times under the same conditions.
02

Analyzing the Problem Statement

According to the problem, it was reported that there was no statistically significant difference in the proportion surviving for 20 years for the two treatments. This means that the confidence interval for the difference in treatment proportions must include 0. Because if 0 is in the confidence interval, it says that there is a chance that the true difference in proportions is 0, which means there is no difference.
03

Making the Final Decision

With an understanding of confidence intervals and the problem statement, it is possible to determine which statement is correct. Only Statement 2: 'The confidence interval included 0.' is correct because it indicates that there was no statistically significant difference in the survival proportions.

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Key Concepts

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

Breast Cancer Treatment
Breast cancer treatment involves medical procedures and strategies aimed at removing or destroying cancerous cells from the breast. Two common surgical treatments are mastectomy and lumpectomy.
  • Mastectomy: A surgical procedure where the entire breast is removed to ensure that cancerous tissues are entirely eliminated.
  • Lumpectomy: Also known as breast conservation surgery, involves removing only the tumor and a small amount of surrounding tissue.
Both treatments aim to prevent cancer from spreading further. The choice between them can depend on multiple factors such as the stage and type of cancer, patient preferences, and additional treatments like radiation therapy. In long-term studies, comparing these treatments helps understand their effectiveness and impact on survival rates.
Statistical Significance
Statistical significance helps us determine whether a specific result from a study is due to a real effect or just by chance. It's a crucial concept in analyzing medical treatments and outcomes.
  • A result is statistically significant if the findings are unlikely to have occurred randomly, and thus, there is likely a true effect or difference.
  • In the context of breast cancer treatments, the conclusion that there is no statistically significant difference implies that either treatment leads to similar survival outcomes.
The measure of statistical significance is often guided by a p-value or a confidence interval. If the effect is not statistically significant, the observed data could realistically happen by chance.
Survival Analysis
Survival analysis is a statistical method used to analyze the expected duration until one or more events happen, such as death or cancer recurrence.
  • It is particularly important in medical studies for understanding how long patients survive after treatment.
  • This multifaceted technique enables researchers to estimate survival rates and see how different factors, like treatment type, influence survival over time.
In the case of breast cancer treatment, survival analysis over a 20-year period provides critical insights into long-term survival rates post-surgery, helping refine treatment options for future patients.
Lumpectomy vs Mastectomy
The choice between lumpectomy and mastectomy is significant and personal for women diagnosed with breast cancer. Both have different approaches and implications.
  • Lumpectomy: Often followed by radiation, it is less invasive, allows for breast conservation, and has a shorter recovery time.
  • Mastectomy: Removes more tissue; might be recommended if cancer is in multiple areas or if there's a high risk of recurrence.
Studies comparing the two help ensure patients have detailed information on survival outcomes, empowering them to make informed treatment decisions.
90% Confidence Interval
A 90% confidence interval provides a range where the true difference in treatment outcomes is expected to lie with 90% certainty. It helps in assessing the effectiveness of breast cancer treatments.
  • The confidence interval's endpoints give a statistical range for understanding the potential difference between two groups (e.g., survival rates for lumpectomy vs. mastectomy).
  • In the given breast cancer study, the interval includes 0, indicating no observed statistical difference in long-term survival between the two treatments.
This analysis highlights whether the difference in treatment outcomes is practically significant, guiding patients and healthcare professionals in decision-making.

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Most popular questions from this chapter

The paper "Matching Faces to Photographs: Poor Performance in Eyewitness Memory" Uournal of Experimental Psychology: Applied [2008]: \(364-372)\) described an experiment to investigate whether people are more likely to recognize a face when they have seen an actor in person than when they have just seen a photograph of the actor. The paper states that there was no significant difference in the proportion of correct identifications for people who saw the actor in person and for those who only saw a photograph of the actor. In the context of this experiment, explain what it means to say that there is no significant difference in the group means.

In the paper "Happiness for Sale: Do Experiential Purchases Make Consumers Happier than Material Purchases?" (Journal of Consumer Research [2009]: \(188-197\) ), the authors distinguish between spending money on experiences (such as travel) and spending money on material possessions (such as a car). In an experiment to determine if the type of purchase affects how happy people are after the purchase has been made, 185 college students were randomly assigned to one of two groups. The students in the "experiential" group were asked to recall a time when they spent about \(\$ 300\) on an experience. They rated this purchase on three different happiness scales that were then combined into an overall measure of happiness. The students assigned to the "material" group recalled a time that they spent about \(\$ 300\) on an object and rated this purchase in the same manner. The mean happiness score was 5.75 for the experiential group and 5.27 for the material group. Standard deviations and sample sizes were not given in the paper, but for purposes of this exercise, suppose that they were as follows: \begin{tabular}{|ll|} \hline Experiential & Material \\ \hline\(n_{1}=92\) & \(n_{2}=93\) \\ \(s_{1}=1.2\) & \(s_{2}=1.5\) \\ \hline \end{tabular} Using the following Minitab output, carry out a hypothesis test to determine if these data support the authors' conclusion that, on average, "experiential purchases induced more reported happiness." Use \(\alpha=0.05\) Two-Sample T-Test and Cl Sample \(\begin{array}{rrrrr}\text { ple } & \text { N } & \text { Mean } & \text { StDev } & \text { SE Mean } \\ 1 & 92 & 5.75 & 1.20 & 0.13 \\ 2 & 93 & 5.27 & 1.50 & 0.16\end{array}\) Difference \(=\operatorname{mu}(1)-\operatorname{mu}(2)\) Estimate for difference: 0.480000 \(95 \%\) lower bound for difference: 0.149917 T-Test of difference \(=0(\mathrm{vs}>): \mathrm{T}\) -Value \(=2.40 \mathrm{P}\) -Value \(=\) \(0.009 \mathrm{DF}=175\)

The paper "If It's Hard to Read, It's Hard to Do" (Psychological Science [2008]: \(986-988\) ) described an interesting study of how people perceive the effort required to do certain tasks. Each of 20 students was randomly assigned to one of two groups. One group was given instructions for an exercise routine that were printed in an easy-to-read font (Arial). The other group received the same set of instructions but printed in a font that is considered difficult to read the time (in minutes) they thought it would take to complete the exercise routine. Summary statistics follow. The authors of the paper used these data to carry out a twosample \(t\) test and concluded at the 0.10 significance level that the mean estimated time to complete the exercise routine is significantly lower when the instructions are printed in an easy-to-read font than when printed in a font that is difficult to read. Discuss the appropriateness of using a twosample \(t\) test in this situation.

The article "An Alternative Vote: Applying Science to the Teaching of Science" (The Economist, May 12,2011 ) describes an experiment conducted at the University of British Columbia. A total of 850 engineering students enrolled in a physics course participated in the experiment. Students were randomly assigned to one of two experimental groups. Both groups attended the same lectures for the first 11 weeks of the semester. In the twelfth week, one of the groups was switched to a style of teaching where students were expected to do reading assignments prior to class, and then class time was used to focus on problem solving, discussion, and group work. The second group continued with the traditional lecture approach. At the end of the twelfth week, students were given a test over the course material from that week. The mean test score for students in the new teaching method group was \(74,\) and the mean test score for students in the traditional lecture group was \(41 .\) Suppose that the two groups each consisted of 425 students. Also suppose that the standard deviations of test scores for the new teaching method group and the traditional lecture method group were 20 and 24 , respectively. Estimate the difference in mean test score for the two teaching methods using a \(95 \%\) confidence interval. Be sure to give an interpretation of the interval.

(C1) The paper "Effects of Caffeine on Repeated Sprint Ability, Reactive Agility Time, Sleep and Next Day Performance" (Journal of Sports Medicine and Physical Fitness [2010]: 455 - 464) describes an experiment in which male athlete volunteers who were considered low caffeine consumers were assigned at random to one of two experimental groups. Those assigned to the caffeine group drank a beverage which contained caffeine 1 hour before an exercise session. Those in the no- caffeine group drank a beverage that did not contain caffeine 1 hour before an exercise session. That night, participants wore a device that measures sleep activity. The researchers reported that there was no significant difference in mean sleep duration for the two experimental groups. In the context of this experiment, explain what it means to say that there is no significant difference in the group means. In particular, explain if this means that the mean sleep durations for the two groups are equal.
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