Case Study: Lead Exposure in Children

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1 Case Study: Lead Exposure in Children Instructions for Lab # 3 Statistics Probability and Statistical Inference DUE DATE: Upload on Sakai on July 22 Lab Objective The purpose of the lab is to help you pull together what you have learned about univariate and bivariate graphical and numerical summaries in the context of a case study. The lab will also demonstrate that in these few weeks you have acquired most of the statistical tools that form the basis of a published scholarly work. Lab Procedures Before coming to lab, read the paper by Landrigan et al. (1975) Neuropsychological dysfunction in children with chronic low-level lead absorption, The Lancet, March, 29, pp The Lancet is one of the leading journals in medical science. In this lab, you will have access to the data presented in this paper. While this paper was published in 1975, it still has an impact today. The topic of lead exposure in children remains under investigation and new research results appear in the news almost every month. The topic is studied by interdisciplinary teams of medical personnel, epidemiologists, social scientists, environmentalists, and policy makers. Open the data file lead.dta by clicking on the link on the course website. A description of all the variables names in the data set (often called a Code Book) can be found at the end of this lab. The variable in the data set for the blood group has three categories. The researchers suggest that two categories (below 40mg and above 40mg) are adequate. So, let s make a new variable that recodes the variable group to a binary variable high_group that is equal to 1 if it s high, and 0 if it s low (tabulate group to see the categories). One option is to use the generate command with if-statements. However, here we will introduce a new command: recode varlist rule rule..., generate(newvar) where varlist is a list of one more variables to recode, the option generate(newvar) allows a new variable to be created, and the most common forms for rule are:

2 Stats Case Study: Lead Exposure in Children rule Example Meaning # = # 3 = 1 recoded to 1 # # = # 2. = 9 2 and. recoded to 9 #/# = # 1/5 = 4 1 through 5 recoded to 4 So, in order to create our new variable high_group, we need to change values of 1 to 0 and values of 2 and 3 to 1, and use the generate option. You should be able to code that up easily with the above table as a guide. Once you are done, perform a two-way tabulate on group and high_group to make sure that it was successful. Data Analysis Tip: Variables that take on only the values of 0 and 1 are called binary, dummy or indicator variables. They are immensely useful in programming. Of special interest, Stata interprets values of 0 as FALSE and values of 1 as TRUE. In this sense, you can shortcut some notation. If you want to only look at the age, sex and group of high blood pressure individuals, you can simply type list age sex group if high_group, rather than having to type list age sex group if high_group==1. Use this with prudence (i.e., make sure that the variable is a true dummy, especially make sure there are no missing values). Data Analysis Tip: Stata allows you to easily change the label of a variable: label variable varname [ label ]. Questions: 1. This question is based on your reading of the article. You do not need to use Stata for Question 1. (a) What are the experimental units (the subjects)? (b) What is the treatment variable? What is the name of one of the response variables? (c) Is this an observational study or a randomized experiment? (Note: most of the background characteristics in Table 1 are pretty similar in the lead and control groups, except for age. A one year difference could have a large impact on mental and physical abilities for children of young ages.) 2. (a) NOT HANDED IN: The main analysis compares mean performance IQ scores (W.I.S.C. + W.P.P.S.I.) for the high lead and low lead groups. Let s make sure we get the same results when we analyze the data. Do the means and standard deviations for performance IQs (see code book at end of lab for the variable name) for the high and low groups match the means and SDs reported in the paper? How do these look graphically? Data Analysis Tip: Use the by varname: prefix before the summarize and graph box varname, over(varname) commands.

3 Stats Case Study: Lead Exposure in Children (b) HANDED IN: In any analysis, it is important to check whether the means and SDs are strongly influenced by individual data points. For Stata s box plot, the box contains observations in the Inter-Quartile Range (IQR), aka the 25th and 75th percentiles. The lines extend an additional 1.5*IQR. The low lead group has three outliers on performance IQ, and the high lead group has one outlier on performance IQ. Exclude these four observations and compare the means and SDs to those in part 2a. Are any of the changes big enough that the authors should have mentioned the effect of the outliers in their article? Report the two new means and SDs as part of your answer, as well as a three-sentence-maximum explanation. Perform computations for Question 3 and all later questions with all data points; do not exclude anything. 3. A comparison of means and standard deviations might be inadequate. For example, suppose one group has a right-skewed distribution, and the other group has a left-skewed distribution. Just reporting means and standard deviations does not inform the reader about such structure. Compare the distributions of performance IQ of the high and low lead groups. Describe any differences between the two groups distributions of performance IQ: compare locations of most of the data, the spreads of the distributions, and whether there are outliers. Write at most three sentences. Reminder: Box plots are useful for side-by-side comparisons. 4. The authors chose to categorize blood lead level rather than use it as a continuous variable. Is there a strong linear relationship between performance IQ and the blood lead level in 1972 measured on a continuous scale? Data Analysis Tip: Researchers sometimes categorize continuous variables to simplify analyses. However, when there are strong linear relationships, categorization sacrifices information and can lead to inaccurate results. Implicitly, disecting blood levels at 40mg assumes that the average performance IQ of all kids in the population with blood levels below 40 equals some constant, i.e., their average performance IQ does not depend on the actual blood levels. When categorizing, be sure to have a valid scientific rationale for choosing the end points of the categories. 5. Older kids typically have faster reflexes than younger kids. Hence, when comparing fingerwrist tapping speeds for the high and low lead groups, we want to make sure the two groups have similar distributions of ages. Age is in funky units (e.g., 1011 means 10 years and 11 months), so I created a new variable with age in months, Agemo. Compare the distributions of age in months for the high and low lead groups. Based on your comparisons, could the groups average finger-wrist tapping speeds (or some other outcome variable) reflect effects of age differences? Explain in at most three sentences. 6. One of the key analyses is a regression of finger-wrist tapping speed on age in months (bottom right corner of page 710). Let s replicate their regression and check its validity. The Stata

4 Stats Case Study: Lead Exposure in Children command for regression analysis is very straightforward: regress depvar indepvars, options. where depvar is the dependent or left-hand-side variable and indpevars are the independent or right-hand-side-variables. Use the by varname: prefix or the if modifier to create separate regressions for different groups. (a) NOT HANDED IN. You should get very similar results as those in the paper. If not, you did something wrong! (b) HANDED IN. Create and examine a scatter plot. Are there any patterns (e.g., curvilinear relationships) that cause you to worry about the validity of the regression lines as a way to summarize the trends in the data? Or, do the regression lines do a reasonable job of fitting the data? Justify your answer in at most three sentences. 7. For this question, assume any patterns you noticed in Part 6 result by random chance, so that the regression model reasonably fits the data. On page 711, Landrigan et al. state, To adjust these data for age, a regression of dominant-hand finger-wrist tap data against age was plotted for each group (see figure); the slopes of the resulting lines are nearly parallel. (a) NOT HANDED IN. Verify that the regression lines are nearly parallel. Parallel regression lines have the same slopes with possibly different intercepts. (b) HANDED IN: Since the lines are parallel, what is the difference in predicted average tapping speed between a kid in the low lead group and a kid of the same age in the high lead group? Assume the kids in question have ages within the range of ages in the data. (c) HANDED IN: If the lines were not parallel, describe (in two sentences) how the answer you got in part (b) might not be correct for all ages.

5 Stats Case Study: Lead Exposure in Children Code Book for lead.dta Variable Description DEMOGRAPHICS ID person ID number area Residence on Aug = 0-1 miles from smelter 2= miles 3= miles age 1011=10 years, 11 months sex 1=male 2=female IQ TEST RESULTS info information subtest in WISC and WPPSI comp comprehension subtest in WISC and WPPSI ar arithmetic subtest in WISC and WPPSI ds digit span subtest(wisc) and sentence completion(wppsi) vraw raw score/verbal IQ pc picture completion subtest in WISC and WPPSI bd block design subtest in WISC and WPPSI oa object assembly subtest(wisc), animal house subtest(wppsi) cod coding subtest(wisc), geometric design subtest(wppsi) praw raw/score performance subtest hhindex Hollingshead index of social status iqv verbal IQ iqp performance IQ iqf full scale IQ (not sum or average of IQV and IQP) typeiq Type of IQ test 1=WISC (usually given to children GT 5 years) 2=WPPSI (usually given to children LE 5 years of age) group blood level group 1= blood lead levels below 40 micrograms/100ml in both 1972/1973 2= blood lead levels GE to 40 micrograms/100ml in both 1972/1973 or GE 40 micrograms/100ml in 1973 alone (3 cases only) 3= blood lead levels GE to 40 micrograms/100ml in 1972 and LT 40 in 1973 ld72 blood lead values in 1972 (micrograms/100ml) MISSING=99 ld73 blood lead values in 1973 (micrograms/100ml) frst2yrs did child live for 1st 2 years within 1 mile of smelter totyrs total number of years spent within 4.1 miles of smelter

6 Stats Case Study: Lead Exposure in Children Variable Description SYMPTOM DATA (AS REPORTED BY PARENTS) 1=Yes, 2=No pica colic clumsiness iritability convulsions NEUROLOGICAL TEST DATA Note: MISSING DATA ( -1 or 99). tapsright # of taps for right hand in the 2 plate tapping test (#taps in one 10 second trial) tapsleft # of taps for left hand in the 2 plate tapping test (#taps in one 10 second trial) reactionright visual reaction time right hand (milliseconds) reactionleft visual reaction time left hand (milliseconds) auditoryright auditory reaction time right hand (milliseconds) auditoryleft auditory reaction time left hand (milliseconds) fingerright finger wrist tapping test right hand (taps in one 10 second trial) fingerleft finger wrist tapping test left hand (taps in one 10 second trial) wwps Werry Weiss Peters Scale for hyperactivity 0=no activity.... 4=severely hyperactive (parent reports)