Biostatistics in Practice Session 2: Quantitative and Inferential Issues II Youngju Pak Biostatistician 1

What we have learned in Session 1?  Basic Study Design  Parallel vs., Cross-over Designs?  Categorical vs., Quantitative Data? Why important?  Summarizing the data with graphs: Contingency Tables, Box Plots, Histogram, etc.  How to run MYSTAT 2

Today’s topics  Article : McCann, et al., Lancet 2007 Nov 3;370(9598):  Descritive Statistics vs. Inferential Statistics  Normal Distributions  Confidence Intervals & P-values  Correlations 3

McCann, et al., Lancet 2007 Nov 3;370(9598):  Food additives and hyperactive behaviour in 3-year- old and 8/9-year-old children in the community: a randomised, double-blinded, placebo-controlled trial.  Target population: 3-4, 8-9 years old children  Study design: randomized, double-blinded, controlled, crossover trial  Sample size: 153 (3 years), 144(8-9 years) in Southampton UK  Objective: test whether intake of artificial food color and additive (AFCA) affects childhood behavior

McCann, et al., Lancet 2007 Nov 3;370(9598):  Sampling: Stratified sampling based on SES in Southampton, UK  Baseline measure: 24h recall by the parent of the child’s pretrial diet  Group: Three groups, for 3 years old –mix A : 20 mg of food colorings + 45 mg sodium benzoate, which is a widely used food preservative –mix B : 30mg of food coloring + 45 mg sodium benzoate(current average daily consumption) –Placebo –For 8/9 years old: multiply these by 1.25  Cross-over Design  A participants receive one of 6 possible random sequences. In a separate study with N=20, no significant difference in looks and taste of drinks among three groups was found even though people ask about which diet type they got when they received placebo (65%) > mix B (52%) > mix A (40%) 5 T0 (baseline)Week 1Week 2Week 3Week 4Week 5Week 6 Randomize Typical DietWashout

McCann, et al., Lancet 2007 Nov 3;370(9598):  Outcomes: Global Hyper Activity(GHA) Score  Attention-Deficit Hyperactivity Disorder(ADHD) rating scale IV by teachers, scaled 1 – 5, higher number means more hyperactive  Weiss-Werry-Peters(WWP) hyperactivity scale by parents,  Classroom observation code,  Conners continuous performance test II (CPTII)  GHA to be aggregated from these four scores 6

Non-Completing or Non-Adhering Subjects Non-response bias? Societal effect vs. Scientific effect ? Efficacy vs. Effectiveness ?

Describing the sample 8

Describing the findings w/ descriptive statistics 9 What was your research question ? Did you get answer for that that research questions from this table? Why or Why not? GHA= (post –pre)/standard deviation (SD) for pre-scores

Describing the findings w/ inferential statistics 10

Describing the findings w/ Graphs using confidence intervals

Population Sample Sample estimate of population parameter Population parameter Sampling mechanism: random sample or convenience sample Confidence Interval for population parameter 12 The Life Cycle of a Research Study With Statistical Applications

So why use a sample?  Often the population is too large to obtain data  Saves time and money  All members of the population may be difficult to contact Parameter vs. Statistic  A parameter is a numerical description of a population characteristics e.g., μ (called as”mu:”): population mean, σ 2 (called as “sigma square”): population variance  A statistic is a numerical description of a sample characteristics e.g., m : sample mean, S 2 : sample variance

Branches of Statistics Descriptive statistics involves the organization, summarization, and presentation of the sample. e.g., sample means, sample standard deviations, histograms, box plots, etc. Inferential statistics involves using a sample to draw conclusions about a population. e.g., confidence intervals, p-values, etc.

3 questions that statisticians attempt to answer How should I collect my data ? - Study design, sample size, statistical power. How should I analyze and summarize the data that I’ve collected ? - displaying the data, descriptive statistics, statistical tests How accurate are my data summaries ? -Inferences: confidence intervals, p-values

Mean vs. Median (measure the central tendency) Mean –What most people think of as “average” –Easy to calculate –Easily distorted –Be cautious with SKEWED data –Calculate: sum of data / number of data points Median –Relatively easy to obtain –Not affected by extreme values so it is considered a “ROBUST” statistic –Calculate: Sort data If odd number points, the middle is the median Otherwise, the median is the average of the middle two numbers 16

Standard Deviation (SD) &Inter-Quartile Range(IRQ) (measuring the variability of the data ) Inter-Quartile Range (IQR)= 75th percentile (Q3) - 25th percentile(Q1), where 25% of the data <Q1, 75% of the data < Q3 SD is usually used for the normally distributed data (bellshape, symmetric around the mean) IQR is usually used when the data distribution is skewed. Range = Max -Min 17

Checking for the normality Symmetric. One peak. Roughly bell-shaped. No outliers. Many statistical tests assume outcome variable follow the normal distribution 18

Other properties of the normal distribution For bell-shaped distributions of data (“normally” distributed): ~ 68% of values are within mean ±1 SD ~ 95% of values are within mean ±2 SD “(Normal) Reference Range” ~ 99.7% of values are within mean ±3 SD 19

Histograms: Not OK for Typical Analyses Skewed Need to transform intensity to another scale, e.g. Log(intensity) Multi-Peak Need to summarize with percentiles, not mean. 20

Summary Statistics: Two quantitative Variables (Correlation) Always look at scatter plot. Correlation, r, ranges from -1 (perfect inverse relation) to +1 (perfect direct), Zero=no relation. Specific to the ranges of the two variables. Typically, cannot extrapolate to populations with other ranges. Measures association, not causation.. 21

Correlation Depends on Range of Data  Graph B contains only the points from graph A that are in the ellipse.  Correlation is reduced in graph B. Thus: correlation between two quantities may be quite different in different study populations.  Do not extrapolate BA 22

Confidence Interval (CI) How well your sample mean(m) reflects the true( or population) mean  How confident?  95%? A confidence interval (CI) is one of inferential statistics that estimate the true unknown parameter using interval scales. 23

Confidence Interval for Population Mean 95% Reference range or “Normal Range”, is sample mean ± 2(SD) _____________________________________ 95% Confidence interval (CI) for the (true, but unknown) mean for the entire population is sample mean ± 2(SD/√N) SD/√N is called “Std Error of the Mean” (SEM) 24

Confidence Interval: Case Study Confidence Interval: ± 1.99(1.04/√73) = ± 0.24 → to 0.10 Table 2 Normal Range: ± 1.99(1.04) = ± 2.07 → to Adjusted CI close to 25

P-values ! Used the evidence of contradiction to your null hypothesis (H 0 ) –e.g., H 0 : no difference in mean GHA scores among three different diet. Based on the statistical test –Eg., T test statistics = Signal / Noise – if Signal >> Noise  statistically significant Usually p < 0.05 called as “statistically significant” in favor of H a 26

Units and Independence Experiments may be designed such that each measurement does not give additional independent information. Many basic statistical methods require that measurements are “independent” for the analysis to be valid. In mathematics, two events are independent if and only if the occurrence of one event makes it neither more nor less probable that the other occurs. 27

Experimental Units in Case Study What is the experimental unit in this study? 1. School 2. Child 3. Parent 4. GHA score (results from three diets) Are all GHA scores(eg. 153 x 3 groups=459 GHA scores for 3-4 years old children) independent? The analysis MUST incorporate this possible correlation (clustering) if there exists.  eg., Mixed Model allowing for clustering due to schools. 28

Announcements Keys for HW1 and HW 2 will be posted on class website by Wednesday. Next session will be held in Oct 15 at RB-1 29