BMS 511 Biostats & Statistical Analysis Lecture Notes PDF

BMS 511 Biostats & Statistical Analysis Chapter 6 Samples and observational studies Guang Xu, PhD, MPH Assistant Professor of Biostatistics and Public Health College of Osteopathic Medicine Marian Univ...

BMS 511 Biostats & Statistical Analysis Chapter 6 Samples and observational studies Guang Xu, PhD, MPH Assistant Professor of Biostatistics and Public Health College of Osteopathic Medicine Marian University  Previous Learning Objectives Demonstrate Regression The least-squares regression line Facts about least-squares regression Outliers and influential observations Working with logarithm transformations Cautions about correlation and regression Association does not imply causation Copyright © 2018 W. H. Freeman and Company  Learning Objectives Determine samples and observational studies Observational study versus experiment Population versus sample Randomness and bias The simple random sample (SRS) Other probability samples Sample surveys Comparative observational studies Copyright © 2018 W. H. Freeman and Company Observational versus experimental studies (1 of 2) Observational study: record data on individuals without attempting to influence the responses. – In 1992, several major medical organizations said that women should take hormones such as estrogen after menopause, because women who took hormones seemed to reduce their risk of a heart attack by 35% to 50%. Copyright © 2018 W. H. Freeman and Company Observational versus experimental studies (2 of 2) Experimental study: Deliberately impose a treatment on individuals and record their responses. Influential factors can be controlled. – By 2002, several studies concluded that hormone replacement does not reduce the risk of heart attacks. These studies had assigned women to either hormone replacement or to placebo pills. The assignment was done by a coin toss. Copyright © 2018 W. H. Freeman and Company Observational study or experiment? (1 of 2) A 2013 Gallup study investigated how phrasing affects the opinions of Americans regarding physician-assisted suicide. Telephone interviews were conducted with a random sample of 1,535 national adults. Using random assignment, 719 heard the question in Form A and 816 the one in Form B. – Form A: When a person has a disease that cannot be cured, do you think doctors should be allowed by law to end the patient’s life by some painless means if the patient and his or her family request it? Copyright © 2018 W. H. Freeman and Company Observational study or experiment? (2 of 2) – Form B: When a person has a disease that cannot be cured and is living in severe pain, do you think doctors should or should not be allowed by law to assist the patient to commit suicide if the patient requests it? 70% of those given Form A answered “should be allowed”, compared with only 51% of those given Form B. What type of study is this? A. Observational study B. Randomized experiment C. Neither. This is just anecdotal evidence. Copyright © 2018 W. H. Freeman and Company  Confounding Two variables are confounded when their effects on a response variable cannot be distinguished. Observational studies often fail to yield clear causal conclusions, because the explanatory variable is confounded with lurking variables. Copyright © 2018 W. H. Freeman and Company  Population versus sample Population: The entire group of individuals in which we are interested but can’t usually assess directly A parameter is a number summarizing a characteristic of the population. Sample: The part of the population we actually examine and for which we do have data A statistic is a number summarizing a characteristic of a sample. Copyright © 2018 W. H. Freeman and Company  The role of randomness in sampling How do you select the individuals/units in a sample? Probability sampling: individuals or units are randomly selected; the sampling process is unbiased. Copyright © 2018 W. H. Freeman and Company  Bias Bias is the systematic tendency for a study to favor certain outcomes. In the diagram featured on this slide, you can see how the lower right figure is “off target,”, while the other three are, on average, centered around their target. Figure 6.3 Baldi/Moore, The Practice of Statistics in the Life Sciences, 4e, © 2018 W.H. Freeman and Company Copyright © 2018 W. H. Freeman and Company  Examples of bad sampling (1 of 2) Ann Landers summarizing responses of readers: 70% of (~10,000) parents wrote in to say that having kids was not worth it—if they had to do it over again, they wouldn’t. But a random sample showed that 91% of parents WOULD have kids again. What do you think explains such drastically different responses? Copyright © 2018 W. H. Freeman and Company  Examples of bad sampling (2 of 2) Would you expect very different responses on the potential legalizing of marijuana if you asked the first people you saw on the parking lot of a university or the first people you saw on the parking lot of a church? Copyright © 2018 W. H. Freeman and Company  The simple random sample A simple random sample (SRS) is made of randomly selected individuals. Each individual in the population has the same probability of being in the sample. All possible samples of size n have the same chance of being the sample drawn. How to choose an SRS? Draw from a hat (lottery style). Use a table of published random numbers (Table A). Use software that generates random numbers. Copyright © 2018 W. H. Freeman and Company Choosing a simple random sample (1 of 2) We need to select a random sample of 5 from a class of 20 students. 1) List and number all members of the population, which is the class of 20 students, listed to the right. 2) Use Table A or technology to get 5 random numbers. Assume we got the number 17, 9, 13, 7, and 2. 3) The first five random numbers matching numbers assigned to people make the SRS. The first individual selected is Ramon, number 17. Then Henry (9). The next three to be selected are Moe, George, and Amy (13, 7, and 2). Copyright © 2018 W. H. Freeman and Company Choosing a simple random sample (2 of 2) 01 Alison 11 Kate 02 Amy 12 Max 03 Brigitte 13 Moe 04 Darwin 14 Nancy 05 Emily 15 Ned 06 Fernando 16 Paul 07 George 17 Ramon 08 Harry 18 Rupert 09 Henry 19 Tom 10 John 20 Victoria Copyright © 2018 W. H. Freeman and Company  Other probability samples (1 of 2) A stratified random sample: Make sure your sample has known percentages of individuals of certain types (strata). America's State of Mind report was based on a probability sample of Medco's de-identified database of members with 24 months of continuous insurance enrollment. Sampling was stratified by age group and sex to match the demographics of the whole customer base. A multistage sample: Select your final sample in stages, by sampling successively within a sample within a sample. Copyright © 2018 W. H. Freeman and Company  Other probability samples (2 of 2) The National Youth Tobacco Survey administered in schools uses a sampling procedure to generate a nationally representative sample of students in grades 6– 12. Sampling is probabilistic and consists of selecting: 1) Counties as Primary Sampling Units (PSU) 2) Schools within each selected PSU 3) Classes within each selected school Copyright © 2018 W. H. Freeman and Company  Sample surveys A sample survey is an observational study that relies on a random sample drawn from the entire population. – Opinion polls are sample surveys that typically use voter registries or telephone numbers to select their samples. – In epidemiology, sample surveys are used to establish the incidence (rate of new cases per year) and the prevalence (rate of all cases at one point in time) of various medical conditions, diseases, and lifestyles. These are typically stratified or multistage samples. Copyright © 2018 W. H. Freeman and Company  Some survey challenges Undercoverage: Parts of the population are systematically left out. Nonresponse: Some people choose not to answer/participate. Wording effects: Biased or leading questions, and complicated/confusing statements can influence survey results. Response bias: Fancy term for lying or forgetting (especially on sensitive/personal issues). Can be amplified by the survey method (in person vs. by phone or online). Copyright © 2018 W. H. Freeman and Company  How bad is nonresponse in surveys? (1 of 2) The Census Bureau’s American Community Survey (ACS): ~2.5% via mail with reminders. Response is mandatory. University of Chicago’s General Social Survey (GSS): ~30%—in person. Pew Research Center methodology survey up to ~90% in 2012 Private polling firms such as SurveyUSA: ~90% as of 2002 (stopped showing after that) phone (with interviewer or automated call) or online. Copyright © 2018 W. H. Freeman and Company How bad is nonresponse in surveys? (2 of 2) Copyright © 2018 W. H. Freeman and Company  Wording effects (1 of 2) A 2013 Gallup study investigated how phrasing affects the opinions of Americans regarding physician-assisted suicide. Telephone interviews were conducted with a random sample of 1,535 national adults. Using random assignment, 719 heard the question in Form A and 816 the one in Form B. – Form A: When a person has a disease that cannot be cured, do you think doctors should be allowed by law to end the patient’s life by some painless means if the patient and his or her family request it? Copyright © 2018 W. H. Freeman and Company  Wording effects (2 of 2) – Form B: When a person has a disease that cannot be cured and is living in severe pain, do you think doctors should or should not be allowed by law to assist the patient to commit suicide if the patient requests it? Question wording resulted in a substantial difference in opinions: 70% of those given Form A answered “should be allowed,” compared with only 51% of those given Form B. Copyright © 2018 W. H. Freeman and Company An example of response bias (1 of 2) Copyright © 2018 W. H. Freeman and Company  An example of response bias (2 of 2) From this data we see that men tend to over report their height by 1.22 cm, and overreport their weight by 0.3 kg. Women tend to overreport their height by 0.68 cm, but underreport their weight by 1.39 kg. Copyright © 2018 W. H. Freeman and Company  Comparative observational studies Case-control studies start with 2 random samples of individuals with different outcomes, and look for exposure factors in the subjects’ past (“retrospective”). – Individuals with the condition are cases, and those without are controls. – Good for studying rare conditions. Selecting controls is challenging. Cohort studies enlist individuals of common demographic and keep track of them over a long period of time (“prospective”). Individuals who later develop a condition are compared to those who don’t develop the condition. – Cohort studies examine the compounded effect of factors over time. – Good for studying common conditions. Very expansive. Copyright © 2018 W. H. Freeman and Company  A case-control study example (1 of 2) Aflatoxicosis epidemics Aflatoxins are secreted by a fungus found in damaged crops and can cause severe poisoning and death. The Kenya Ministry of Health investigated a 2004 outbreak of aflatoxicosis resulting in over 300 cases of liver failure. A sample of 40 case-patients and 80 healthy controls were asked how they had stored and prepared their maize. Copyright © 2018 W. H. Freeman and Company  A case-control study example (2 of 2) The case-patients were randomly selected from a list of individuals admitted to a hospital during the 2004 outbreak for unexplained acute jaundice. Control individuals were selected to be as similar to the case-patients as possible, yet randomly selected. Preliminary data suggested that soil, microclimate, and farming practices might have played a role, but not age or gender. For each case-patient, two individuals from the patient’s village with no history of jaundice symptoms were randomly selected. Copyright © 2018 W. H. Freeman and Company  Examples of cohort studies (1 of 2) The Nurses’ Health Study is one of the largest prospective observational studies designed to examine factors that may affect major chronic diseases in women. Since 1976, the study has followed a cohort of over 100,000 registered nurses. Every two years, they receive a follow-up questionnaire about diseases and health-related topics. Response rate: ~90% each time. Copyright © 2018 W. H. Freeman and Company  Examples of cohort studies (2 of 2) 2007 report on age-related memory loss: About 20,000 women ages 70+ had completed telephone interviews every two years to assess their memory with a set of cognitive tests. One of the findings: the more women walked during their late 50s and 60s, the better their memory score was at age 70 and older. However, because this is an observational study, we cannot unambiguously conclude that walking has a protective effect against memory loss. Copyright © 2018 W. H. Freeman and Company Application of SPSS: Least-square Regression Line Application of SPSS: Least-square Regression Line Application of SPSS: Least-square Regression Line Double click the plot at the Output window to open Chart Editor  Application of SPSS: Least-square Regression Line Method 1: Click the “Element” and choose “Fit Line at Total” Method 2: Right click the plot and choose “Add Fit Line at Total” Application of SPSS: Least-square Regression Line  Learning Objectives Determine samples and observational studies Observational study versus experiment Population versus sample Randomness and bias The simple random sample (SRS) Other probability samples Sample surveys Comparative observational studies Copyright © 2018 W. H. Freeman and Company