Lecture 2 - Karen Bandeen-Roche PDF

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Lecture Speaker: Karen Bandeen-Roche

Public health mandatory extra-departmental graduate course. Covers the bases for the role of quantitative methods in public health, including how to formulate scientific questions quantitatively, different types of data, properties characterizing hig...

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Lecture 2 Karen Bandeen-Roche Thursday, September 10, 2020

3:06 PM

Quantitative Measures Section A: Introduction, measurement scales, and data summary •

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Health begins all the way at the cellular level, then combine into physiology, organs and diseases, psycholgical functioning, behaviors, families and societies, all the way to the larger environment More recently we have seen an explosion of big data We have terminology to describe kinds of measurements which is called measurements scales - there are two types ○ Quantitative measurements: concept of amount; numerical § Discrete variables: those which have gaps, such as the number f births, the number of drinks per week, number of seizure episodes per month. Basically counts of things § Continuous Variables: numbers have no natural gaps but could occur at basically any fraction or decimal point, such as blood pressure, age at a given moment, weight, etc ○ Qualitative measurements: concept of attribute, categorical § Nominal scale: literally are categories or labels which have no natural order associated with them □ Binary or dichotomous: gender, alive or dead, □ Polychotomous or polytomous: marital status (married, divorced, single, dating) § Ordinal scale: ratings or preferences. Literal interpretable ordering such as satisfaction ratings, for example, I am completely dissatisfied, a little dissatisfied, neutral, somewhat satisfied, and very satisfied All of this matters because once one knows the measurement scale, this goes a long way towards determining what then is correct data display or data analysis method to use and ultimately by which to report one's d t

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data Notation ○ "Y", "X" are shorthand vairables that will be used and often we subscript these variables ○ Instead of "whether the 4th person enrolled gets lung cancer" we write Y4 ○ Instead of "wheather the /ith person enrolled gets lung cancer" we write Yi Measurement properties of data - preliminaries ○ "variation" refers to the differences among a set of measurements § Where does these differences come form, and why arnt all the measurments the same? ○ Natural versus measurment variation: § Natural variation -differences among persons (experimental units) in the "true" values of the variable of interest different people have different weights and there are lots of good reasons for that § Measurement variation (or error) has to do with differences between measured and true values Once we have a set of data in hand there are things we can do to summarize those data so as to give them easier interpretability - a first summary that we use is central tendency ○ Central tendency refers to values in a data set that either are in the middle or typical or somehow a good overall summary § The most common being mean or = center of mass § Median = middle observation § Mode = most frequent observation ○ Distribution is values relative to frequencies on the y-axis with which they occur Variability (dispersion) = how spread out the set of values are ○ Measures to summarize this = average of the squared differences of observations from the sample mean. Variance =

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Standard deviation is just the square root of the variance to put our measure of variability back on the scale at which we observed the data rather than the squared of those things

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We can create plots for visual display of data ○ Tallying ○ Ordering by hand ○ Stem and leaf plot (same idea of tallying except we keep track of all the actual numbers)

Section B: Boxplots - measurement accuracy and precision •

Box and whiskers plot or boxplot ○ To create the boxplot you start with the box § To do this you need the 3 quaritile or 75th percentile (it has 75% of the data at or below that value) § Similarly, the 1 quartile, the 25th percentile, has 25% at or below § In the middle there is the median - the 50th percentile, the one exactly in the middle § Then you find the fences - these are boundries which we can identify datapoints that are extreme or unusual - they are boundries we keep in our mind □ TOP ONE: Q3+1.5(Q3-Q1)

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BOTTOM ONE: Q1-1.5(Q3-Q1) ® We keep track of them because we mark any data beyond those boundries and classify them as outliars § Then you draw the lines out to the boundries What makes for a good measurment ○ Accuracy - we want our measurement to accurately asses its target. When that happens we call the measurement unbiased meaning that the mean or average is near the true value of whatever either that set of measurements or the truth for an individual person would be ○ Precicness - Basically meaning if we took the measurement again and again, it would reproduce at very close to the same value (reliable) § The same as saying that our measurement has low measurement variance or variability ○ If you put these 2 things together, a measure is accurate and precise, that’s saying that we are measuring what we calim we are measureing or what we aim to measure making it valid Bias: difference between the average (expected) value of measurement (variable) and the truth value that it targets (degree of inacuracy) ○ EXAMPLES: we are asking people about the amount of fat-rich food they eat, the average reported percent calories from fat will underestimate the true percentage and is therefor biased ○ If suicides are mistakenly attributed to accidents more often than vice versa, the number of suicides will underestimate the true number of self-inflicted deaths and is therefore biased ○ If the scale I use to weigh patients is miscalibrated, it will produce biased measurements of their weights Common sources of bias in public health ○ Miscalibration ○ Technical variation, people, kits (batch effects), lack of standarization ○ Cultural, contextual, or temporal difference ○ Selection bias (if measurement pertains to a population) Variance: variation among measurements about their average or mean value, even if that mean differs from the true targeted value (imprecision) ○ EXAMPLE: if residents are over reporting their calorie intake and under reporting their calorie intake, the reported percentage of calories from fat has measurment error or variation What sources of measurement variation may there be in the types of t th t t k ?

measurements that you take?: ○ Technical variation, people, kits, lack of standardization ○ Sloppy procedures ○ Crude measurement tools: imprecisely quantified, vague questions

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In science and stats, we continually balance bias and variance ○ It is easy to find measurments with small variance if you can tolerate large bias: estimate everyone's percent calories from fat by 30% then the variance =0 ○ A compromise measure - Mean squared error (MSE)= varience+bias (squared) ○ What constitute as high measurement variation requires a context § Clinical context § Coefficient of variation: standard deviaiton/mean □ Particularly useful when the variation increases in proportion to me □ Beware stock cutoffs: clinical and scientific context must guide inter

Section C: Reliability • Reliability has to do with reproducibility of different measures of the same quantity of ○ Low variation among the measures=high reliability •

Test-retest reliability: addresses variation among repeated measurements of a given characteristic on the same subject ○ For EXAMPLE if we take a pharmacy scale and step on it 10 times – how variable 10 weight readings?

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If we step on it and get 10 different readings is the variability of those readings i then the reliability of my scale is high

Inter-rater reliability: characterizes variation made by multiple assessors of a given characteristic on the same subject (compares multiple different people assessing the s thing) ○ EXAMPLE 10 different technicians measure my weight using a "doctor office" sca variable are the 10 weight readings Basic ideas - 2 specific measures of reliability ○ Intraclass correlation coefficient § Meant for at least numerical and preferably continuous measurements - w numbers have an actual meaning, and perhaps there are no gaps in betwe things, such as weight □ In this case we take M measurements of the same thing on n differe § ICC =

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Kappa § Designed for categorical measurments, 2 measures per person § We have labels of things and in particular when we take 2 measures per pe roughly, it gives the proportion agreement in those two repeated measures agreement by chance § Proportion agreement, net of agreement by chance

Validity •

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Imagine a scenario in which we can pretty precicely define what we want to measure b are at a state of science where no single gold standard method of measureing what we measure exist - that puts us in a situation in which validity becomes a very important consideration Formally, we call this sort of target of measurement a construct: a postulated attribute person that cannot be measured directly, but can be assessed using indirect measures ○ EXAMPLE: fraility of older adults - it is difficult to measure fraility older adults ○ To try to organize what we are trying to measure we break it down by health stat from a specific freestanding physiological mechanism § Disrupts energetic, muscle, nutrition § Signifies loss of resiliance in homeostatic regulations § Not only a secondayr manifestation of chronic disease § Also district from chronological age, disability or predisability, cognitive dys ○ The freestanding physiological mechanism is intervenable

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○ Putting this situation whithin the classic framework for assessing validation ○ 1ST step is to define precelsly what the construct that we aim to assess is ○ There are then 4 aspects of validity § Face validity - weather our measurment of what we seek to assess looks rig by eyeball § Content validity - whether we have chosen indirect measures, whether the span the whole construct domain - assessed by random selection and exper assessment § Criterion validity - whether our measure associates with other measuremen seek for it to if we have an effective measure - associaiton with a logical cor assess empirically § Construct valididty - assess whether our measures behave as we theoretica they should based on our definition in the first place - assess by experiment of fit, latent variable modles ○ SO REFERING BACK TO THE EXAMPLE of fraility in older people § For face valididty we would be worrie dif our fraility measure assess the lad look energetic as frail rather than those who look weak § Content valididity has to do wiith whether the elements of our measuer ass things that we hypothesize underlie frailty and manifest it. □ And so in the case of the physical frailty phenotype, the Y's are listed in t weight loss, exhaustion, low energy expenditure, slowness, and weaknes es/no variables. The overall frailty assessment then adds these up and d dividual as frail if they meet at least three of these criteria. And you can ey are chosen to reflect things like disrupted energy, disrupted muscle p utrition, and the like. § Criterion validity has to do with weather our measure coorilates with things th to in some sense. In geriatric context, we want measures of fraility to identify i who actually are at high risk of suffering adverse events subsequent to stressor § Construct validity has to do with whether we are identifying persons with a dys physiology. We could assess that using experiments to actually observe - wheth person returns more slowly to a baseline state following an oral glucose tolera which we measure their glucose to rise and then come back down □ This is the highest standard - it has to do with wheather our measures be predicted by the underlying theory haivng to do with the etiology or othe mechanisms □ We might want to assess whether a frail persons physiology actually see dysregulated relative to a non frail persons we can assess that by expeirm ○ Categorical measurements: in statistics, the basic display. In this case is a 2x2 table - a context we are tasking abut today a misclassification table in which we might display

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context we are tasking abut today a misclassification table in which we might display of disease yes or no or perhaps fraility, yes or no, against whatever our measure or o us. § The degree of concordance between true and test, or in this case discordance, us the assessment of measurement quality, wheather highly reliable, valid, or i misclassified, invalid, and potentially unreliable

ue status test tells ill provide this case,...