preventative medicine PM - BS

8/13/2019 preventative medicine PM - BS

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Biostatistics: Hypothesis Testing 9/29/2011 9:56:00 AM

1. Describe the null and alternative hypotheses for a given studydesign.

Null hypothesis (H0) - the hypothesis to be tested, typically a statement

of "no difference/effect/association"; this is the hypothesis that is assumedtrue unless the test produces sufficient evidence to the contrary.

Alternative hypothesis (H1 or Ha) - the hypothesis that contradicts thenull hypothesis. The alternative hypothesis can be two-sided or one-sided;this should be decided before beginning analysis of the data. - Two- sided () : Used when study is interested in any deviation from thenull. More commonly used than one-sided.- One-sided () : Used if prior evidence or the nature of the studydirects the focus towards a deviation in just one direction. A one-sided testincreases the power to detect a significant effect in one direction, but doesnot account for deviations in the other direction at all. Thus, deciding to usea one-sided test requires careful consideration.OK: A newly developed drug is considerably cheaper than the optioncurrently on the market. The researcher may choose to utilize a one-tailedtest that will strongly detect if the new drug is LESS effective. The other tailneed not be addressed because being more effective or merely equally

effective are both fine, as the main positive point of the new drug in thiscase is its increased affordability.Not OK: A researcher wishes to demonstrate that a new drug is moreeffective than the current one, and chooses a one-tailed test in order tomaximize detection of improvement in the data. However, this approachwould fail to account for the possibility that the new drug is less effective.

2. Define and interpret p-values.

What the p-value is: The probability of observing a result/difference asextreme as, or more extreme than, those observed in the studied sample(s),assuming that the null hypothesis is true.What the p-value is NOT: The probability that the null hypothesis is true.(See #6 in the practice problem set for this lecture.)How do you obtain the p-value?


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After calculating the test statistic ( t or chi-squared), refer to a table orcomputer program that provides the corresponding p-value. Graphicallyspeaking, the p-value is the area under the t or chi-squared distributioncurve (probability density function) that lies beyond the calculated test

statistic.

(For more on interpretation of p-values, see objective #4 regardingstatistical significance.)

3. Recognize appropriate hypothesis tests for means. (i.e., continuousvariables)


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clinical setting), or it can be statistically insignificant but still have potentialfor clinical significance (ex., statistical insignificance was due to insufficientsample sizes; requires further investigation).

6. Recognize when proportions are appropriate summary statistics.

Proportions are useful when dealing with experiments with two outcomes (success vs. failure, yes vs. no, etc.). Sample proportion can be used toestimate population proportion (probability) of a given outcome.

7. Compute and interpret proportions and associated confidenceintervals.

(For equations used for calculation of the above, see handout or lectureslides.)

Interpretation of sample estimate of population proportion: We estimate thatX% of [the population in question] will have [outcome of interest]. or Theestimated probability of [outcome of interest] is X%.

Interpretation of 95% confidence interval ( z = 1.96) for proportions: We are

95% confident that the true proportion of [outcome of interest] in [thepopulation in question] is between [lower limit of confidence interval] and[upper limit of confidence interval].

8. Understand the two-by-two table format for displaying categoricaldata.


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Can test for association between variable A and variable B using 2 x 2 chi-squared test that compares observed values to the expected valuesassuming the variables are independent (i.e., assuming the null hypothesisof no association).

9. Distinguish between when to use a t-test and when to use a chi-squared test.

t-test: Use to compare continuous outcome variable between groups(involves means)

chi-squared test: Use to compare categorical outcome variable betweengroups (involves proportions)

10. Interpret p-values and statements of statistical significance forchi-squared tests.

Follow same guidelines of interpretation as for t-tests. (See objectives #2and #4.)


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Correlation and Power 9/29/2011 9:56:00 AM

1. Describe the advantages and disadvantages of contingencytable procedures versus correlation procedures for assessingassociations between continuous variables.

Contingency tables are easy to interpret, can be easily stratified, and haveno distributional assumptions. However, there may be some loss ofinformation due to arbitrary grouping.

Correlation procedures maintain the continuity of the data and model onevariable as a function of another, but they can only measure linearrelationship and are only useful with two continuous variables.

Contingency Table (2x2) Correlation and Regression

Advantage - Ease interpretation- No distributionassumptions- Easily stratify byother variables- Can calculate ORand RR

- Maintains continuityof data- Model one variableas fxn of another

Disadvantage - Arbitrary groupingof continuous (loss ofinformation)

- Only measures linearrelationships- Only useful whenboth variables arecontinuous

2. Understand a scatter plot for displaying the relationshipbetween two variables and use it to distinguish between positive,negative, and zero correlation.

When observing data in a scatter plot, the correlation can be represented bya linear regression or best fit line. The slope of that line is proportional to thecorrelation between the two variables.


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3. Interpret the correlation coefficient (r) and the coefficient ofdetermination (r squared)

The correlation coefficient is a representation of how linearly correlated twovariables are. It can range from -1 (perfectly negatively correlated) to +1(perfectly positively correlated). The coefficient of determination is thesquare of the correlation coefficient, and represents the percentage of thevariation that can be explained by the correlation.*This means that a certain amount of the range exists simply because of thecorrelation ie. the rise that must be present given the run *

4. Interpret p-values and statements of statistical significancewith regard to the correlation coefficient

A linear relationship between two variables cannot be considered statisticallysignificant without an accompanying p-value of adequate value.

5. Distinguish between possible conclusions that can be drawnfrom a correlation coefficient

Correlation does NOT imply causation. That is to say even if we observe astatistically significant correlation, it only implies that the relationshipbetween the variables MAY reflect a causal relationship. You must always beaware of extraneous variables. NO 2 exposure vs. FEV1 example.

6. Distinguish between a simple regression equation and amultiple regression equation

A simple regression equation takes a dependent variable(Y) and seeks toobserve its change against an independent variable (X). Think y=mx+bMultiple linear regression plots the dependent variable (Y) against multipleindependent variables (X1, X2, X3) An example is a plot of carotid intimia-media thickness against several factors including age, height, BMI etc.


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7. Use a regression equation to make predictions and understandwhen these predictions are validA regression equation can be used to make predictions by simply plugging inthe hypothetical "x" value and seeing what y value you get. This can only be

used within the confines of the study (domain of x values observed) asextrapolation is not possible because we don't know how the relationshipbetween the variables behaves beyond these values.

8. Interpret slope coefficients in a regression equationThe slope coefficient represents how much of a change in Y we expect to seefor a one unit increase in X.The y intercept represents the dependent variable (y) value when thedependent variable (x) is zero.

9. Contrast linear vs. logistic regression and simple vs multipleregressionmultiple regression covered in question 6Linear regression is exactly what we've been describing up until now.Logistic regression is actually the same thing except the dependent variablebasically turns into a dummy variable in that it has only two values: 0 and 1.Often 0 is not diseased where 1 is diseased. These are primarily used to

determine if X is a risk factor for Y.

10. understand the difference between type 1 and type 2 errorsA type 1 error is when we reject the null hypothesis when the null is in facttrue. =the probability of a type one error. alpha is AKA the significancelevelA type 2 error is when we should in fact reject the null, but we do not.=probability of a type 2 error, and 1 - is known as the power o f a study.Power is the chance of detecting a difference in treatments if the differencetruly exists.

11. Identity the information needed before an appropriate samplesize can be determined1. Determine whether this is a 1 or 2 sided hypothesisH


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2. Determine , the significance level 3. Determine the minimum difference in values you wish to detect

4. Determine the power level you want1- 5. Estimate the standard deviation of the data you will collectstd

12. Understand the concept of statistical power and the importanceof adequate sample size in testing hypotheses

Increasing sample size will always increase power, and power is the chanceyou will discover an effect if an effect truly exists. If you have a new drug,you are much more likely to determine if it truly works better than the olddrug if you test it on thousands of people instead of dozens.

13. recognize the effects on power and the needed sample size toachieve the same power when there are specific changes in thesignificance level, detectable difference, standard deviation of theoutcome, and sidedness of the alternative hypothesis.

When significance level increases, the power needed decreasesWhen the minimum detectable difference increase, the power neededdecreasesWhen the standard deviation decreases, the power needed decreasesIf the study is one sided, the power needed decreases


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Epidemiology 1 9/29/2011 9:56:00 AM

Epidemiology 1

Prevalence The proportion of people who have the disease at a given point in

time=(Diseased)/(Total Population)Example: There are 180 medical students in class today. 18 have cholera.Therefore, prevalence=18/180=0.1 of the population is sick

Units: number of sick people over total population

Cumulative Incidence The proportion of cases that develop over a specified period of time.Example: There are 180 medical students. In the next year, 36 developanality retentiveness. Therefore, the cumulative incidence of analityretentiveness is (36 new cases)/(180 total people)=0.2

Note: The study population at risk (denominator must be free of disease).Example: There are 180 medical students. 120 of them already have analityretentiveness. In the next year, 15 develop anality retentiveness. Therefore,the cumulative incidence of this population is (15 new cases)/(180-120students without disorder)=15/60=0.25.

Units: number of new cases over population without disorder over a certainamount of time.

Incidence Rate The rate at which individuals develop a disease in a population.

Person-time is the total amount of time all subjects contribute to the study.Example: 120 students are followed for 1 year, 30 students are followed for2 years, and 50 students are followed for 3 years. Therefore, total person-time=120(1 year)+30(2 years)+ 50(3 years)=330 person-years.

When calculating person-time, the people who get sick are considered tohave served only half the amount of time.


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Example: Let's say you a have a study spanning one year and 10 people getsick. On average, half of these people will have gotten sick before thehalfway point and half after so that they average out. So each person wouldhave contributed an average of 0.5 person-years. Therefore, total person-

time=10(0.5 years)=5 person-years.

Units: number of new cases over population without disorder over a certainamount of time or number of new cases per person-time

Mortality Rate A measure of the rate at which individuals in a population die over a specificamount of time.Example: 200 people are followed over the next year. 30 of them die.Mortality rate=30/200 person-years

Cause-Specific Rates The number of new events over a specified amount of time.Example: 180 medical students are followed over 2 years. 60 developcholera. The cause-specific rate is 60 new cases/[120(1 year)+60(0.5years)]=60/150 person-years.

Sex-Specific Rates Event rates within gender.Example: In a class of 180 medical students, 75 are women and 105 aremen. Over the next year, 10 women develop cholera and 20 men developcholera.Therefore: Sex-specific rate for women is 10/[65(1 year)+10(0.5years)]=10/70 person-years.Therefore: Sex-specific rate for men is 20/[85(1 year)+20(0.5years)]=20/95 person-years.

Race-Specific Rates Same as sex-specific rates but with race used instead of sex.

Case Fatality Rate (not an actual rate)The proportion of people who die from a specific disease.


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Example: There are 180 medical students. 50 develop anality retentiveness.40 die from it. The case fatality rate=40/50=0.8

Proportional Mortality

The proportion of deaths attributed to a specific cause.Example: A medical class had 100 deaths in 2008. 40 were caused byanality retentiveness. The proportional mortality of anality retentiveness in2008 = 40/100=40%.

Crude-Rates vs. Age-Adjusted Rates Crude rates measure the total amounts of death while age-adjusted ratesstratify by age.See PM 4-8. The age-adjusted rates for 1990 are lower than for 1960 butthe crude rate is higher. Simpson's Paradox!Annual Rate

Miscellaneous Incidence rates are more helpful when studying the etiology of the disease.An incidence rate could show a change in causative factors of the effect of apreventive program.

Prevalence is more helpful when planning public health programs. A changein prevalence could reflect a change in incidence rate, a change in duration,or a change in immigration/emigration rate of sick people.

Relationships Incidence Rate * Time = Cumulative IncidencePrevalence = Incidence Rate * Average Duration of Disease


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Study Designs 9/29/2011 9:56:00 AM

1. State the exposure - disease hypothesis when given a descriptionof a study.

Exposure (E) = the independent variable

Disease (D) = the dependent variable; may also be called outcome Basic hypothesis: If exposed, then disease. 2. Recognize possible explanations for an observed association; e.g.recognize that any association observed in a hypothesis-testingstudy might be causal, or due to chance, confounding, or bias.Questions to ask when evaluating possibilities besides causality:- Chance : What is the p-value and/or alpha-value? What is the probabilitythat the observed association could have occurred by pure chance whenthere is no actual relationship? Is it possible that we are rejecting the nullwhen it is true (type I error)?- Confounding : Are there other variables that could be in play besides E andD? What other factors might be connected to E? What else might cause orcontribute to D?- Bias (ex. selection bias, information bias) : Are there any issues with thestudy design (ex. sampling technique, reliability of reported data, etc.) thatmight affect the results?3. Describe the criteria used for judging whether an association is

causal.1. Temporal relationship E precedes onset of D2. Strength of association Stronger associations are more likely to becausal; look for a high, statistically significant relative risk (RR) value3. Dose-response relationship Strength of the association shows arelationship with the level/dose of exposure4. Consistency Same association is observed in multiple different types ofstudies and in different populations5. Biological plausibility Reasonable explanation for how E D;experimental evidence6. Consideration of alternate explanations Other possibilities (see objective#2) have been controlled for or otherwise ruled out7. Cessation of exposure rate of D decreases after E is eliminated/reduced;similar to dose-response relationship


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4. Understand the differences between descriptive and analyticstudies.Descriptive studies describe patterns of disease occurrence relative tocharacteristics of person, place, time; can be used to identify correlations

and formulate hypotheses, but do not have capacity to test them; do notexamine a specific exposure-disease association

Analytic studies focus on and test hypotheses regarding exposure-diseaseassociations*Note: Testing does not necessarily mean experimental or intervention studies (actively assigning E to subjects in order to observe results);observational studies are considered analytic too, in that they are alsodesigned to find evidence of causality for a particular E-D association- Cross-sectional studies could be considered either descriptive or analytic5. List the major types of descriptive studies, and describe theadvantages and limitations of descriptive study designs.

Type of DescriptiveStudy

Pros Cons

Case reports, case

series giveinformation on a single

patient or group of patients (usu. forunusual/rare conditions)PERSON

- Most basic type of

descriptive study easy, inexpensive- Early warning bringsattention to new/rareconditions- Can help generatehypotheses

- No comparison groups

cannot testhypotheses- Deals with single orsmall number of cases(which might beexceptions, not arepresentative sample),so limited

generalizabilityEcological studies(correlationalstudies) documentdisease occurrence inrelation to specific

- Also relatively easy,inexpensive; datausually already available- Can work with datathat is only

- No way to control forconfounding factors (ifgroup data on thesefactors is not available) cannot test


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population characteristics(measures of exposurefor population as a

whole, i.e. averages); Eand D data onpopulations, notindividuals (usu. basedon geographic regions)PLACE

available/possible toreport as a population-based measure (ex. airpollution in a given city)

- Can help identifypotential risk factors fora disease, generatehypotheses applicableto individuals

hypotheses- Beware of ecologicalfallacies cannotdistinguish in group

data whether individualswith disease were infact the ones who wereexposed, so unable toform an E Dconclusion

Studies of diseasefrequency examinechange in disease/deathfrequency with respectto personalcharacteristics (age,gender, race, etc.),location (geographicarea, city or rural, etc.),over timePERSON, PLACE, and

TIME

- Can help identifypotential exposures thatare causing differingdisease rates in specificpopulations, locations,or time periods;generate hypotheses

- Again, cannot testhypotheses from thesestudies alone

6. For each of the major types of descriptive and analytic studydesigns:(a) Describe in general terms the basic process for conducting thestudy(b) Distinguish between designs from a brief description.

Analytic Studies

Observational (Non-experimental; thethree Cs)

Cross-sectional : Take sample from specifiedpopulation, then ascertain both E and D status atsame time for each subject in sample.


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Cohort : First identify E or non-E status in subjectswithout D, then follow to observe onset of D. (Canbe retrospective if info on E status is obtained frompast records)

Case-control : First identify cases and non-casesof new/incident D, then ascertain E status (currentor past).

Intervention (Experimental)

Intervention : Randomly assign E to subjects,then observe effect on D. Can be E 1 vs. E 2 , or E vs.placebo/control.

For the types of descriptive studies, refer to first column of the table forobjective #5.


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Analytic Study Design 9/29/2011 9:56:00 AM

For each of the major epidemiologic study designs be able to:- Identify the type of study design from a brief description of the study- Recognize the major advantages and disadvantages inherent in the design- Recognize situations in which each would be the most appropriate study

design- Describe which measures of association are commonly used with eachdesignStudy

name

Pros Cons When

do you

use it

Measures

associated

with this

study

How is it

different

from the

other

studies?

Cross-

Sectional

-2 nd cheapest

and quick

-generates

hypotheses

-results can be

generalized to

the population

-temporality

bias

-prevalence bias

-selection bias

-hard to find

subjects with

rare exposures

or disease

-when

you dont

know time

or dont

have it

-when

you are

observing

a common

E and O in

a defined

population

-prevalence

-odds ratio

-relative

risks

-lack of time

variable

-no %s

(AR%,

PAR%)

-common E

and O

Cohort -no

temporality

issues

-no ethical

issues

-rare

exposures can

be followed

- its okay if we

get multiple

outcomes

-expensive

-not good for

rare disease

outcomes, but if

your exposure is

rare disease,

thats fine

-validity

(presence of

information bias,

confounding,

-when

you just

want

incidence

of O

-when E is

rare

-Absolute

Risk

-Relative

Risk

-AR%

-PAR%

You cant get

an odds ratio

-You can

control time!

(prospective

vs.

retrospective)


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-more robust

to selection

bias

-less likely

that resultswill bias our

study

-we can find

incidence

rates!

and loss to

follow-up can

screw things up)

-

nonparticipation:many will be

ineligible for a

rare disease

study, makes

the study

difficult to

generalize

Case-

Control

-cheapest

-rare diseases

can be studied

multiple

exposures can

be

investigated

simultaneously

-efficient

-OR can be

used to

estimate

relative risk

-validity

(information

bias, selection

bias, prevalence

bias,

confounding,

and temporal

relationship

bias)

-Odds Ratio

-AR%

-PAR%

- you cant get

relative risk.

At all.

Interven-

tion

-this can

prove

causality

-no temporal

bias

-no selection

bias

-multiple

outcomes can

be studied

-expensive

-not always

feasible

-not always

ethical

-outcomes can

be limited by

time, money,

etc.

-validity placebo

You

assign

exposure

and

monitor

through

time to

see

outcome

-incidence

rate

-relative risk

-AR and

AR%

-PAR and

PAR%

-you can

measure

incidence

rates (not

like case-

control)


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-incidence

rates can be

measured

directly

effect,

information bias,

loss to follow-

up,

noncompliance,confounding)

Describe the differences between cohort studies: specific exposure vs

general population cohort studies, and prospective vs retrospectivecohort studies.Specific exposure vs general populationSpecific exposure: subjects are chosen to represent a specific exposureGeneral population: subjects are chosen to represent the population, whichhas a wide range of exposuresWhats the difference: one exposure versus several Examples, which is which?You are chosen for a study that is interested in seeing if there is a relationbetween taking the MCAT and the average stress level of all currentgraduate school students (exposure: MCAT, disease: stress level) over thecourse of 4 years

You are chosen for a study that is interested in seeing if exposure tocadavers, hospitals, and libraries leads to the development of any stress-related diseasesProspective vs retrospectiveProspective: subjects are chosen who are exposed, and the investigatorfollows the cohort into the future to see if exposure leads to diseaseRetrospective: subjects are chosen who have already been exposed andshow disease

Whats the difference: one hasnt shown signs of disease yet and the otheralready hasExamples, which is which?You choose subjects for a study on lung cancer based on their exposure toasbestos before retirementYou choose subjects for a study on lung cancer based on their currentexposure to asbestos


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Explain the purpose, process, and effects of matching in a case-controlstudy.Purpose: to prevent confounders (the reason why we do anything instatistics, really)

Process: Pair control and exposed group based on matched control variables(ex. Age, race). But its tricky to match more than two controls Effect: By eliminating as many confounders as possible, you increase thechance that a relationship between exposure and disease are associated,and not due to chance (think back to t-tests)ExamplesA study of a new diabetes medications efficacy in lowering blood glucoselevels compared to the current markets top grossing diabetes medication isdone via case-control study. The control group and case group are all of thesame race, age, and sexYour turn!Describe the process of conducting and advantages of a nested case-controlstudy, and recognize examples from brief descriptions of studies.Nested case-control: when members of a cohort develop the disease ofinterest, you can select members from the cohort who have yet to get thedisease to be their controls. So basically you create a control group in acohort study

How we do this: we separate diseased from non-diseased. We match upthose with the dise ase to a control partner in the non -diseased group. Wethen look to the previous information weve gathered on the cohort membersto determine what the exposure was that brought about the diseaseExample: Nurse Health Study. If a group of nurses in this study cohortdeveloped alcoholism do to exposure to over 200 trauma cases per year, wecan attempt to prove this relation by making the non-alcoholic nurses thecontrol and the alcoholic nurses our exposed groupYour turn!Explain why an incidence rate ratio cannot be calculated directly in a case-control studyThe controls that we select for a study is only a small fraction of thepopulation that is not exposed.Explain why the odds ratio is a good estimator of the RR in a case-controlstudy.


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Odds ratio is a good estimator because of the nature of the case-controlstudy, which is looking at disease, aka outcome, measurement, and not theexposure measurement. (because we supposedly already know what theywere exposed to or exposed them to it)

Example: (whi ch is totally, not mine, its fromhttp://www.childrensmercy.org/stats/journal/oddsratio.asp and superbrilliant)Consider a case-control study of prostate cancer risk and male patternbalding. The goal of this research was to examine whether men with certainhair patterns were at greater risk of prostate cancer. In that study, roughlyequal numbers of prostate cancer patients and controls wereselected. Among the cancer patients, 72 out of 129 had either vertexor frontal baldness compared to 82 out of 139 among the controls (seetable below).

Cancer cases Controls Total

Balding 72 82 154 Hairy 55 57 112 Total 129 139 268 So you can estimate the probability of balding for cancer patients(72*57)/(82*55), but you cant calculate the probably of cancer for baldpatients.This is because we are looking for information on the outcome. There areplenty of bald people out there who dont have cancer, but that would be ahuge probability that is clearly not represented in the data we have here.So you would need additional information or a different type of researchdesign to estimate the relative risk of prostate cancer for patients withdifferent types of male pattern balding.You can always calculate and interpret the odds ratio in a casecontrol study as long as the outcome event is rare

Recognize the purpose for randomization in intervention studies.Ex: A study on 1 st grader s height growth wants to see the associationbetween drinking milk with increases in height. They plan to give the controlgroup one extra cup of water at lunch everyday, and the exposure group oneextra cup of milk at lunch everyday.
http://www.childrensmercy.org/stats/journal/oddsratio.asphttp://www.childrensmercy.org/stats/journal/oddsratio.asphttp://www.childrensmercy.org/stats/journal/oddsratio.asp


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The researchers notice that some of the children are definitely smaller thanthe othersand they worry that maybe the children arent getting enoughnutrition at homeSo they decide to put all the smaller children in the milk-drinking group

What could potentially happen to these smaller children that were notrandomly assigned to the exposure group? What could potentially happen tothe studys results as a whole? The small kids grow a lot the study claims that kids have dramatic heightgrowth when they drink milk everyone makes their kids drink milk manykids and parents are disappointed when they dont grow much The small kids dont grow much, they just get fat the study finds notenough information to associate milk and height, but they instead say thereis an association between weight gain and milk everyone stops their kidsfrom drinking milk many kids and parents are disappointed when theydont grow much And thats why you randomize your intervention studies.

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