Elementary Statistics and Inference. Elementary Statistics and Inference. 1.) Introduction. 22S:025 or 7P:025. Lecture 1.

Transcription

1 Elementary Statistics and Inference 22S:025 or 7P:025 Lecture 1 1 Elementary Statistics and Inference 22S:025 or 7P:025 Introduction 2 1.) Introduction A. The course will be based on the text: Statistics, Fourth Edition, Freedman, Pisani, and Purves published by Norton & Company (2007) IMU Bookstore B. The syllabus for the course is provided as a separate handout to each student 3 1

2 1.) Introduction (cont.) C. This course provides an overview of the logic and techniques involved in analyzing and interpreting empirical data. Methods for displaying data graphically and for describing characteristics of data will be covered in the first part of the course dealing with descriptive statistics. The second part of the course includes topics in elementary probability theory and sampling, forming a basis for techniques of statistical inference. The problem of inference, attempting to make generalizations that go beyond the data at hand, is the focus of the third part of the course. 4 2

3 Elementary Statistics and Inference 22S:025 or 7P:025 Chapter One 10 2.) Chapter One A. Salk Vaccine Field Trial NFIP Years ago Polio was a dreaded and often crippling disease that attacked many young people often in the summer. Jonas Salk, in the 1950s, developed a promising drug that would protect an individual from contracting polio. His drug was tested by the National Public Health Service and the National Foundation for Infantile Paralysis (NFIP) in The drug was tested with a treatment group, against a control group, using a double blind experiment. Neither the research subjects (persons) nor the doctors who measured the responses knew who was in the treatment group (those who received the drug), or the control group (those who did not receive the drug). The Experiment 2 x 10 6 children, treatment group were vaccinated, control group not vaccinated experiment run by National Foundation for Infantile Paralysis (NFIP) grades 1, 2,

4 Refused to Participate Agreed to Participate Treatment 500,000 Control 1,000, ,000 1,500,000 2,000,000=Total 13 Parents who were from higher SES would be more willing to have child participate than those from lower SES however, lower income families probably had children exposed to polio more often than children from higher income high risk children have more antibodies. The design was flawed because it included more children from higher income families, and they were more likely to contract polio. The treatment and control groups should be as nearly alike as possible. 14 B. Outcome of the Salk Vaccine Trials Likelihood of being assigned to treatment group was same as for control group. Doctors not told which children were in treatment or control group. 15 4

5 Randomized Double Blind Experiment N Rate Treatment 200, Control 200, No Consent 350, (See page 6.) 16 National Federation of Infantile Paralysis (NFIP) Experiment N Rate Grade 2 225, Grade 1 and 3 (Control) 725, Grade 2 (No Consent) 125, Grade 2 students received the vaccine. (see page 6.) 17 NFIP biased because students it was given only to children who were volunteered by their parents and in grade 2. (Reduced from 54% to 25%) Double Blind less biased because given across grades, and randomly given to those who were volunteered. Some volunteered children (Control) did not receive vaccine. (Reduced from 71% to 28%) Bottom Line Salk Vaccine was found to be very good. Polio is now extremely rare, compared to

6 C. Portacaval Shunt Chapter One In some cases of cirrhosis of the liver, the patient may start to hemorrhage and die. The portacaval shunt is a risky surgical procedure that redirects the blood flow to reduce damage from hemorrhage. 19 Table 2: 51 Studies on Portacaval Shunt Degree of Enthusiasm % Marked Design Marked Moderate None Enthusiasm No Controls /32 Controls, Not Randomized /15 Randomized Controls /3 Poor study design can lead to misleading results. 20 D. Possible Research Designs Experiments Randomized Controls Patient Population Controls Not Randomized Patient Population Eligible Ineligible (two side, wrong disease, etc.) Healthier Sicker Surgery Control Surgery Control Best Design 21 6

7 Table 3: Three-Year Survival Rates in Studies of Portacaval Shunt Randomized Not Randomized Surgery 60% 60% Controls 60% 45% Two designs lead to different conclusions when randomized, surgery not more effective; when not randomized, the surgery seems better. 22 E. Historical Controls When it is awkward, repugnant, or difficult to develop randomized control group of subjects the treatment group might be compared against the historical group with the disease / or skill level. Comparisons with the historical control group are not as defensible as using a contemporary control group for comparing effectiveness of treatment. 23 Table 4: A Study of Coronary Therapy Randomized Controlled Historically Controlled Therapy Coronary Bypass Surgery FU BCG DES Randomized controls 17 of 20 studies treatments not effective. Historical controlled 27 of 32 studies treatments effective. 24 7

8 Table 5: 3 Year Survival Rates Group Randomized Historical Surgery 87.6% 90.9% Controls 82.2% 71.1% Using Historical controls misleading, because only more healthy patients received treatment. 25 F. See Summary at End of Chapter One pages Terms to note: method of comparison, treatment group, control group, confounding, randomized controlled experiment, placebo, and double blind. 26 8