Biostatistics. Donna Kritz-Silverstein, Ph.D. Professor Department of Family & Preventive Medicine University of California, San Diego

Transcription

1 Biostatistics Donna Kritz-Silverstein, Ph.D. Professor Department of Family & Preventive Medicine University of California, San Diego (858)

2 Introduction Overview of statistical techniques Includes most major types of statistical analyses needed to analyze your data Focus Practical considerations Applied data analysis

3 Importance Why is it important to understand research methods & statistics? Advances the body of scientific knowledge & skills Gives you the ability to evaluate research New treatments New techniques New products Lay literature / articles from patients

4 Scientific Method Research Question (identifying problem) Examples: Do babies bottle-fed for a longer period of time have more tooth decay at age 5? Will use of a particular brand of toothpaste get teeth whiter than other brands? What factors predict better oral health practices in children?

5 Scientific Method Hypothesis testing The researcher s prediction Null vs. Alternate hypothesis H o = null hypothesis (no differences bet gps) H 1 = alternate hypothesis (predicts a difference bet. groups)

6 Scientific Method Hypothesis testing H o = there will be no differences in tooth decay at age 5 by length of time bottle fed H 1 = children bottle fed for a longer duration will have more tooth decay at age 5

7 Hypothesis testing error Decision Null Hypothesis True False Reject Type I error Correct Accept Correct Type II error Type I error - H o is rejected when it s in fact true; ie, there really is no difference (ex. clinical trial of new drug, H o : new drug = old drug; Type I error -conclude new drug is better when it really isn t Type II error- Accept a false H o - conclude H o is true & no difference when there really is a difference. (ex. concluded old drug= new drug when new drug is better

8 Scientific Method Literature Review Identify similar studies (also get insights into statistical approach) Evaluate measures & questionnaires Validity - does scale look like it measures what it purports to measure Reliability Internal consistency Stability over time Inter-rater reliability

9 Deciding who to study Population- entire group (all 5 year olds in San Diego) Considerations Feasibility (can it be done?) Time (How long will it take?) Cost (and practical considerations -study staff)

10 Deciding Who to Study Sample = subset of the entire group Considerations Representativeness (sample to population?) Size (larger is better) Pilot (feasibility) study

11 Sampling Strategies 1. Random Sampling-each member of the population has = chance of being included 2. Stratified sampling- taking subdivision of pop w/ a particular characteristic

12 Sampling Strategies (cont.) 3. Systematic Sampling- including individuals in systematic way (every nth person, even SSN) 4. Convenience Sampling- using those most readily available as subjects

13 Study Design Observational study No manipulation of variables Experimenter doesn t change anything Examples: case study, cohort studies

14 Study Design Experimental Study- Randomly divide sample into Experimental group -gets intervention/treatment Control group- no intervention/placebo; reference group for comparison

15 Common Types of Studies Case study Report on 1 person Observational-Describes unusual case/rare disease Case-Control study Like experiment but subjects placed in group by whether or not they have a disease Compare cases w/disease vs no disease controls Problem with bias

16 Types of Studies Clinical Trial Experimental study Test new treatment vs. control (or est tx) Double blind Randomized Controlled

17 Types of Studies Retrospective Collect data from past (medical records, hx) Prospective/Longitudinal Follow participants from baseline to future Involves 2 measures of same factor Can see change in time Cross-sectional All data comes from 1 point in time Can see associations (not causality)

18 Variables Variable = Any characteristic that can vary Examples: Height, weight, age, behaviors, attitudes, presence of specific disease, clinical measurements

19 Variables Independent Variable = Variable that is changing or manipulated Dependent Variable = Outcome variable

20 Variables Any variable can serve as the IV in one study, and the DV or outcome in another Examples: Does use of fluoride prevent tooth decay? IV=fluoride DV=caries Does parents education level predict use of fluoride in children? IV=education DV=fluoride

21 Variables Confounders / Covariates Associated w/ both independent & dependent variables (eg., age in study of diabetes & AD) Variables that can affect or bias observed results ( Lurking variables )

22 Types of Data Discrete data Categorical data Has limited set of values May be qualitative Examples: eye color, blood type, gender, presence/absence of diseases, yes/no data

23 Types of Data Continuous data Has values that range along a continuum Quantitative Examples: age, body mass index, blood pressure, # teeth Can always take continuous data & convert to categories

24 Scales of Measurement Nominal scales Named categories No particular order (1 isn t any more than another) Examples: eye color, hair color, gender

25 Scales of Measurement Ordinal scales Ordered categories Distance between categories is unequal Examples: 1 st place, 2 nd place, 3 rd place; rate heath compared to others better, the same, worse; mild, mod, severe perio disease

26 Scales of Measurement Interval scales Equal distance between data points No true zero Examples: Fahrenheit temperature (distance 10 & 20 =distance 20 & 30 )

27 Scales of Measurement Ratio scales Equal intervals between data points Has true zero Best type of scale Examples: blood pressure, # teeth

28 Scales of Measurement Order of scales Nominal Ordinal Interval Ratio Each successive scale has all characteristics of the previous one

29 Data Analysis Statistics = describes & presents collected data in a meaningful way 2 types of statistics Descriptive statistics = describes the sample, summarizes who is in sample Inferential Statistics = infer things about population based on sample

30 Descriptive statistics Measures of central tendency Mean Median Mode

31 Descriptive statistics Measures of central tendency Mean = average = x N Where x=scores; N=total sample size Scores: Mean= 645 =

32 Descriptive statistics Mean - properties Very sensitive to small variations in scores Outliers (extreme values) can cause large changes in the mean; won t give accurate picture of the population (eg., exam scores) More powerful statistics use means

33 Descriptive statistics Measures of central tendency Median = middle score, 50 th percentile -Put into numerical order, middle score; if 2 middle scores, median= average of the two Scores: Mean= 645 = Median=

34 Descriptive statistics Median Advantages Not as sensitive to outliers Use for describing a variable where there are many outliers (eg., income) Disadvantages Statistics not as powerful

35 Descriptive statistics Measures of central tendency Mode = Most frequently occurring score Scores: Mean= 645 = Median= Mode=

36 Descriptive statistics Mode- properties Distributions can have 1 mode Bimodal distribution- distribution with 2 different peaks 2 distinct values that measurements center around example: heights of men & women Distributions can have no mode all measures=frequency

37 Descriptive statistics Measures of dispersion Another way to describe the sample Shows how far scores are scattered around the mean Distributions Range Variance Standard deviation

38 Distributions Normal distribution Bell shaped Most data points fall in middle, w/ few very small & few very large values Mean, Median & Mode all occur at the same score

39 Distributions Normal distribution Mean, Median & Mode all occur at the same score Symmetrical each half=mirror image exactly half the scores occur above and half below mean

40 Distributions Skewed to Right looks like bell curve w/ longer tail on right and mound pushed to left Most data points fall to left of middle & more very small than very large values

41 Distributions Skewed to Right Mean > median Positively skewed large extremes pull mean the tail (extremes high values) Median remains closer to center of the distribution Ex: income, CRP

42 Distributions Skewed to Left looks like a bell curve w/ a longer tail on left & mound pushed to right Most data points fall to right of middle, & there are more very large than very small values

43 Distributions Skewed to Left Mean < median Negatively skewed large extremes pull mean the tail (extremes are low values) Median remains closer to center of the distribution Ex: Hormone assays

44 Distributions What if you have a skewed distribution? Most statistics assume normality Fairly robust to violation of assumptions But may not get accurate results if very skewed Data transformations-logs Pulls in extremes Problem-logged values not clinically useful Do statistics on logged values & p based on logs, but report unlogged means Compare results of stats w/unlogged values

45 Descriptive statistics Measures of dispersion Describes the sample Shows scatter of scores around mean Distributions Range Variance Standard deviation

46 Range Range lowest to highest score/value Use for continuous variables Normally distributed, presenting mean Example: age ranged from months years in practice ranged from 1-25

47 Range Interquartile range (IQR) Use w/ continuous data Skewed data & presenting median Divide sample into quartiles IQR = 75 th 25 th quartile Tells where most values are located

48 Descriptive statistics Measures of dispersion Describes the sample Shows scatter of scores around mean Distributions Range Variance Standard deviation

49 Variance Shows dispersion (spread) of data points around mean The further away the data points are from the mean, the greater the variance

50 Variance Might think the variance = average difference of each score from the mean, summed together & by total # data points or (x mean) N but, If normal distribution, then # data pts above mean = # data pts below mean averaging the difference of each score from the mean=0

51 Variance Average squared deviation from the mean Computational formula: Variance = (x mean) 2 N-1 Where = sum of; x = each score N=sample size or # values *Note, formula above is for sample variance; to get population variance, use N

52 Variance Example: Community research project of teenaged mothers & their knowledge of baby bottle tooth decay 12 teen mothers in study group Give survey to assess their knowledge & score it

53 Variance Mother Score(%) (x-48) Mean= 580=48.3% variance= 4 30 Median=45% = mode=45% Range= variance= (x-mean) N = 580 = 2518

54 Descriptive statistics Measures of dispersion Describes the sample Shows scatter of scores around mean Distributions Range Variance Standard deviation

55 Standard Deviation Average deviation from the mean, ignoring the sign of the difference The further away data points are from the mean, the greater the SD

56 Standard Deviation Computed as sq root of variance = SD=sqrt (x mean) 2 N-1 For population, use N; for sample, use N-1 w/ large sample, difference bet N or N-1 is negligible

57 Standard Deviation Mother Score(%) (x-48) Mean= 580=48.3% variance= 4 30 Median=45% = mode=45% Range= SD=sqrt = variance= (x-mean) N SD=sqrt variance 484 = 580 = 2518

58 Standard Deviation SD useful to compare sets of data w/ the same mean but a different range Example: two data sets Set A=15, 15, 15, 14, 16 Set B=2, 7, 14, 22, 30 Mean A = 15 Mean B=15 SD=sqrt 2/4=0.7 SD=sqrt 508/4=11.3 Low SD= values are not spread High SD= values very spread out Set B-more spread out

59 Standard Deviation Normal Distribution 68% within ±1 SD of the mean 95% within ±2 SD of the mean 99% within ±3 SD of the mean Skewed Distribution Eliminate scores >3 SD above or below mean

60 Data Display for Descriptive Statistics Bar graphs Used to display nominal or ordinal data that are discrete in nature Display can be horizontal Score Test scores on Baby Bottle Tooth D ecay Participant #

61 Data Display for Descriptive Statistics Bar graphs Data display can be vertical Bilat Hyst CRP IL-6 Cortisol intact

62 Data Display for Descriptive Statistics Histogram Used to display interval or ratio scaled variables that are continuous Bars have = width and touch each other indicating data are on a continuum Age (months)

63 Data Display for Descriptive Statistics Frequency polygon Used to display interval or ratio scaled variables that are continuous in nature Dots are connected Use instead of histogram

64 Questions???? Thank You!