POTH 612A Quantitative Analysis Dr. Nancy Mayo

© Nancy E. Mayo A Framework for Asking Questions Population Exposure (Level 1) Comparison Level 2 OutcomeTimePECOT

© Nancy E. Mayo PECOT Format In people with _____________________________________________ ______________ Does suboptimal level of factor 1 _____________________________________________ _____________________________________________ In Comparison to optimal level of factor 1 _____________________________________________ __________________________ Affect (outcomes) _____________________________________________ _____________________________________________ At Time ____________________________________

© Nancy E. Mayo Types of Questions About hypotheses Is treatment A better than treatment B? Answer: Yes or No About parameters What is the extent to which treatment A improves outcome in comparison to treatment B? Answer: A number / value (parameter)

Research is about relationships Links one variable or factor to another One is thought or supposed (hypothesized) to be the “cause” of the second variable Example: Risk factors for falls

Your Job When reading an article (later doing your own research) IDENTIFY THESE VARIABLES IDENTIFY WHAT SCALE THEY ARE MEASURED ON

What tables should I find in an article Table 1 – basic characteristics sample Table 2 – outcomes / exposures Table 3 - answer the main question –Relationship between exposure and outcome Table 4 – interesting subgroup

Fall yesFall no Foot problem +480 (24% of the column) 717 (20.1%) of column 1197 Foot problem P of falls for foot probmel / 1197 = 0.4 Prob of falls for foot problem / 4373 = 0.35 Risk of falls / foot problem relative to risk of falls / no foot problem = 0.4 / 0.35 = 1.14

Prevalence and Risk Factors for Falls in an Older Community-Dwelling Population What type of study is this? Study of prevalence Study of factors What is prevalence? –N of people with condition / All people in study Incidence = N of people who develop the outcome / N of people starting the study Both require a time frame In Falls study, time frame is 90 days after assessment So they estimated a period prevalence

Measurement Outcome: fall (yes or no) in 90 days following assessment –Binary Exposure: many – some continuous (age) some categorical Analysis: Logistic regression

TABLE 1: WHAT HAVE THEY PRESENTED

Characteristic No Falls (n = 3573) n (%) or M ± SE Falls (n = 1997) n (%) or M ± SEp Value Age (years)76.4 ± ± 0.24<.001 Gender (female)2088 (58.4)1192 (58.9).19 Cognitive Performance2.15 ± ± ADL impairment4.54 ± ± 0.05<.001 Foot problems717 (20.1)480 (24.0)<.001 Gait problems1893 (53.0)1454 (72.8)<.001 Fear of falling1525 (42.7)1152 (57.7)<.001 Visual impairment1595 (44.6)964 (48.3).005 Wandering98 (2.7)148 (7.4)<.001 Alzheimer's disease136 (3.8)78 (3.9).45 CHF562 (17.3)342 (18.7).12 Depression1960 (54.9)1370 (68.6)<.001 Diabetes mellitus623 (19.2)379 (20.7).09 Parkinsonism228 (6.4)158 (7.9).04 Peripheral artery597 (18.4)352 (19.3).24 Urinary incontinence1087 (30.4)657 (32.9).03 Environmental hazards1486 (41.6)1097 (54.9)<.001

N and % of people with falls according to risk factor staus Risk Factor +Risk Factor -RR (95% CI) Foot problems480 (40)1517 (35%1.14 Gait problems Xx x

Age, probability that faller and non fallers differed by age Falls = age Age = falls (yes or no) Does age depend on falls Does exposure depend on outcome E│O

What is the age range? What is the standard error?

Standard Normal Distribution Showing the proportion of the population that lies within 1, 2 and 3 SD (Wikipedia)

Measures Theoretical range: 0 to 36

ADL

Table 1 Proportion of Fallers (non-fallers) who were women –2088 women / 3573 fallers (women and men) This is the prevalence of exposure giving outcome (P E | Fall) Is this what you want to know? Is this the question? NO The question relates to the probability of having a fall, given exposure (P FALL | E )

Lets make a table P E | Fall+ = 1454 / 1997 = 72.8% P E | Fall- = 1893 / 3573 = 53.0% But, what we really want is ….. P FALL | E+ = 1454 / 3347 = 43.4% P FALL | E- = 543 / 2223 = 24.4% Risk ratio or Relative risk = 1.78 Risk of Fall | E Risk of Fall | E ExposureFall NOFall YESTotal Gait problems NO Gait problems YES

Lets Look at Table 2 Presented are the odds ratios –(approximately equivalent to risk ratio when the outcome is rare <15% prevalence) Parameter arising from statistical programs for logistic regression Gait problems OR 2.13 Our friend the 95% CI: 1.81–2.51 RR was 1.78 close to the adjusted OR of 2.13 Adjustment was for age, sex and significant variables in Table 2 OR > RR when outcome is prevalent

Adjustment Adjustment mathematically makes the two groups equal on the adjustment variables to find the independent effect of the variable under study Eg. People are given average age

95% CI for Risk Factors for Falls % CI that include 1.0 indicate no effect 95% CI that exclude 1.0 indicate an effect Ratio could be 1 = no effect Increased risk of fallDecreased risk of fall

What else can we learn from this paper?

Odds ratios and 95% confidence intervals of significant risk factor interactions for falling. Cesari M et al. J Gerontol A Biol Sci Med Sci 2002;57:M722- M726 The Gerontological Society of America

Odds ratios and 95% confidence intervals of significant risk factor interactions for falling. Cesari M et al. J Gerontol A Biol Sci Med Sci 2002;57:M722- M726 The Gerontological Society of America

Odds ratios and 95% confidence intervals of significant risk factor interactions for falling. Cesari M et al. J Gerontol A Biol Sci Med Sci 2002;57:M722- M726 The Gerontological Society of America

Odds ratios and 95% confidence intervals of significant risk factor interactions for falling. Cesari M et al. J Gerontol A Biol Sci Med Sci 2002;57:M722- M726 The Gerontological Society of America Wandering NoYes Gait NO11.34 Gait Yes2.25?

Odds ratios and 95% confidence intervals of significant risk factor interactions for falling. Cesari M et al. J Gerontol A Biol Sci Med Sci 2002;57:M722- M726 The Gerontological Society of America Environmental Hazards NoYes Depression Depression+2.08?

Odds ratios and 95% confidence intervals of significant risk factor interactions for falling. Cesari M et al. J Gerontol A Biol Sci Med Sci 2002;57:M722- M726 The Gerontological Society of America Environmental Hazards NoYes Wandering Wandering +2.49?

What have we learned so far? Descriptive stats –Understand distribution by looking at SD Correlation –Strength of linear relationship –% variance explained r 2 Statistics for Inference –On means (t-test) –On proportions (chi-square)

Inference on Proportions Chi square test (1 df) ExposureFall NOFall YESTotal Gait problems NO Gait problems YES Df = n rows * n columns so with a 2X2 table there is 1 df Given we would always know how many people were exposed and how many had the outcome (the margins) all we need to know is 1 of the cells and the rest are derived from that (1 df)

Chi to Normal As the number of df increases the distribution approaches a normal distribution Some of the computer programs for comparing 2 proportions use the normal distribution (F distribution) rather than Chi.

As df increase closer to normal normal

K by k table Total A B C D E F G H

Beyond Chi-square Tells you that there is an association Does not tell you where it is or how strong it is Need to calculate relative risks or odds ratios

Useful Websites ml mlhttp://math.hws.edu/javamath/

On to Regression Last class we will look at regression Look a paper Kuspinar et al. Predicting Exercise Capacity Through Submaximal Fitness Tests in Persons With Multiple Sclerosis