Class Note for STAT 528 at OSU 32
Class Note for STAT 528 at OSU 32
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Date Created: 02/06/15
Stat 528 Autumn 2008 Elly Kaizar Obtaining Data Reading Sections 31 32 33 0 Where do we get information 0 Experiments Confounding Replication o Observational Studies Confounding Selection bias Other problems in sampling Data Collection in Context 0 Data collection Design of experiments and sampling Chapter 3 0 Analysis of data Describing and summarizing data Chapter 1 everywhere 0 Probability Formalizing randomness and uncertainty Chapters 4 and 5 0 Statistical inference Drawing conclusions from data Chapters 6 through 9 Study Type Classi cation 0 ln an experiment we impose a treatment on units and observe their response We can often do a good job of con trolling confounding in experiments Used to estimate treatment effects 0 ln an observational study we observe units and measure variables on them Without imposing any treatment A sam ple survey is usually a kind of observational study Used to estimate treatment effects Used to estimate population characteristics De nitions of treatment effects 0 The ef cacy of a treatment is its ability to produce a change in outcome 0 The effectiveness of a treatment is its ability to produce a desirable effect When applied to a population Example Researchers Wish to study how time until death is associated With CABG vs PCl for patients recently suffering a heart attack Two study designs 1 Researchers recruit patients after having a heart attack They randomly assign them to CABG or PCl They follow them and record time until death 2 Researchers ask physicians to record characteristics of heart attack sufferers including treatment with CABG or PCl in a database called a registry Researchers search through death certi cates to determine the time until death for the patients Showing Ef cacy Core Ideas of a Simple Experiment o The ideal counterfactual Apply a treatment to a unit and record the outcome Go back in time Don7t apply the treatment to that unit and record the outcome Compare the outcomes With and Without treatment This approach gives you the treatment effect for that unit 0 The usual Consider a collection of units Apply treatments to some units and record all outcomes Compare the average outcome for treated and untreated units lf applied well this approach estimates the average treat ment effect for this collection of units Making the Usual Mimic the Ideal o The ideal is good because the only difference between the treated and untreated units is the treatment Thus any dif ference in outcome must be due to the treatment 0 The goal of experimental design is to create an ef cient experiment where average differences in outcomes are due to either 1 treatment 2 chance Then we can use statistics to approximate the likelihood that the difference is due to chance If this is an unlikely option we can conclude that the data contains evidence that the average treatment effect is different from zero o If there is another explanation for the size of the average difference we say there is confounding 0 ln the usual set up why else might we see a difference Confounding o Lurking variables are variables that affect the outcome and have not been somehow controlled in the experiment There are many kinds of lurking variables Characteristics of Units and Environments gtllt To deal with lurking unit characteristics we would like to split the lurking pro les evenly between those with and without treatment Then the effect of the lurking variables averages out This necessitates an appropriate control group gtllt Match groups of treated and untreated units on val ues of lurking variables This is called blocking Matched pairs is a special kind of blocking where only two units form a block gtllt Within blocks randomly assign units to treatment groups using a mechanism entirely immune to biases of those involved in the experiment Confounding cont Characteristics of Outcome Measurement gtllt The placebo effect is the notion that the belief of the subject that they are being treated improves their outcome even if the treatment is not effective A placebo or active control reduces the placebo effect Single blinding or keeping the subjects in the dark regarding treatment assignment reduces the effect of patients7 biases due to the placebo effect or beliefs about Which active treatment is better Double blinding or keeping both the subjects and the experimenters in the dark regarding treatment as signment additionally reduces the effect of experi menters7 biases due to beliefs about Which treatment is better Choosing Random Numbers 0 ln a sequence of random numbers Each number is equally likely Each number is unrelated to the other members in the sequence the numbers are independent 0 Do you believe you can generate a list of random numbers 0 Generate random numbers using MlNlTAB Select Calc gt Make patterned data gt Simple set of numbers 0 Randomly select units using MlNlTAB Select Calc gt Random data gt Sample from columns Is this difference due to chance With good experimental design we have two choices for why we nd a difference between treatment and control groups 1 The treatment makes a difference 2 Chance Without enough evidence we cant tell the difference between the two Consider an experiment to test if coffee is poisonous 0 Design Randomly assign one subject to drink nothing but coffee Randomly assign one subject to drink nothing but tea 0 Outcome Time until death We replicate an experiment to reduce the variability due to chance With a larger sample size we gain more information about the distribution of the responses for the different treatment groups 10 Elements of 21 Well Designed Experiment 1 Control the effects of lurking variables by using a control group or comparing two active treatments blocking blind ing and randomizing 2 Repeat each treatment on many units to reduce the chance variation in the results The Hierarchy of Evidence for ef cacy 1 Systematic reviews of randomized controlled trials 2 Randomized controlled trial 3 Trials Without randomization 4 Observational studies 5 Anecdotal evidence 6 Opinion 11 Learn More About Experimental Design Take STAT 641 Design and Analysis of Experiments Offered in Winter and Spring 12 Observational Data Efficacy and Effectiveness There are two methods commonly used to assess efficacy 1 Matching Similar to blocking in experiments reduce the effect of lurking variables by matching units based on poten tial lurking variables or variables related to lurking variables 0 Case control study design 0 Propensity score analysis 0 Regression analysis 2 Imitation Randomization Similar to randomization in experiments reduce the effect of lurking variables by incorpo rating an explanatory variable that is independent of outcome Within treatment groups 0 lnstrumental variable analysis If you can control lurking variables observational studies tend to be better for assessing effectiveness because recruitment into the study is more broad 13 Observational Data and Population Characteristics Observational data may be used to estimate population charac teristics Examples 0 The American College of Cardiology can use its lCD reg istry to nd the average age of pacemaker batteries 0 An insurance company may use a database of insurance claims to nd the mean if its paid claim value for last year c A public health researcher may use the National Ambulatory Health Care Survey to nd the proportion of poor children who received at least one free samples of medication in 2004 The challenge here is to sample units from the population that as a group are representative of the population of interest 14 Selection Bias o A sample is not representative of the population of interest if sampled units are systematically different from unsampled units Voluntary sampling designs allow subjects to select themselves into the sample Systematic differences causes selection bias 0 We reduce selection bias using the same tools as experimental design Blocking is now called strati cation Randomization is used to assign units to the sample 15 Strati cation and Randomization 0 Simple Random Sampling is a method in which each possible sample has the same probability of being selected Example A researcher wants to know about the pro portion of doctors that distribute free samples of prescrip tion medication She purchases a list of doctors from the AMA uses MlNlTAB to randomly select 200 of these and mails each of these a survey about free samples 0 Strati ed Random Sampling is a method in which the population is divided into groups and a simple random sam ple is taken from each group Example The researcher believes that different kinds of doctors may distribute free samples at different rates She strati es divides her list of doctors into groups based on doctor specialty randomly selects 50 from each list and mails each of these her survey 16 Remarks o Strati cation and simple random sampling may be conducted iteratively to form a complex sample 0 lt is not necessary for all units to have the same chance of being selected as long as they have a known chance of being selected 0 ll all the units in a population are included in the sample then you have a census 17 We still aren t representative Limitations of Random Sampling o Undercoverage is when the entire population is not eli gible77 for sampling due to the list used for sampling 0 Nonresponse is when variables can not be measured for some units selected for the sample Another worry to mention 0 Response bias is when variables are measured inaccurately 18 The Great Debate Do You Need A Good Sampling Design o If you are estimating a population Characteristic population mean median proportion there is no debate that good sam pling is key o If you are estimating relationships between variables many statisticians believe the sampling scheme is unimportant as long as you implement a thoughtful analysis Some disagree 19 Learn More About Sampling STAT 451 Statistical Foundations of Survey Research Offered Spring 2009 may move next year 0 Core requirement for the Undergraduate Minor in Survey Re search Contact Dr Gerald Kosicki kosicki1osuedu o Elective for the Undergraduate Minor in Statistics Contact Dr Mike Fligner mafstatosuedu STAT 651 Survey Sampling Methods Offered Winter 0 Core requirement for the Graduate lnterdisciplinary Special ization in Survey Research Contact Dr Gerald Kosicki kosicki1osuedu 20 Summary 0 Experiments Prevent confounding by gtllt Balancing variables using blocking and random ization gtllt Comparing treatments using placebo active con trol or more than one active treatment gtllt Blinding units and experimenters lncrease the distinction between treatment effect and chance by replicating the experiment 21 Summary o Observational Studies Used to estimate treatment effects or relationships be tween variables gtllt Control confounding by balancing lurking variables us ing matching or imitation randomization Used to estimate population characteristics gtllt Prevent selection bias by Stratifying the population by variables related to the characteristics of interest Randomly selecting units from the population strata With known probability of selection gtllt Try to avoid Undercoverage Nonresponse and Re sponse bias 22
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