S, Lash T. (2008) Modern Epidemiology (3rd edition). http://www.columbia.edu/cgi-bin/cul/resolve?clio8363805 • Hosmer DW, Lemeshow S (2013). Applied Logistic Regression (3rd edition). http://onlinelibrary.wiley.com/book/10.1002/9781118548387 • Hosmer DW, Lemeshow S (2008). Applied Survival Analysis. http://onlinelibrary.wiley.com/book/10.1002/9780470258019 SUPPLEMENTAL READING LIST (see last page of syllabus) • Contains recommended readings, additional textbook chapters and articles relevant to that week’s topic. PDFs of additional textbook and article readings will be provided on courseworks. SAS RESOURCE http://www.ats.ucla.edu/stat/sas/modules/ 5
– 3:50pm – Lectures: Hammer, 301 (except 9/25: P&S Amp 7) – Labs: Hammer LL106, LL107, LL108A/B, LL109A/B, LL110 • One lecture and one recitation / computer lab per session • We expect you to attend all lectures and labs 6
under Files & Resources – Slides will be saved as PDFs – They will be saved as one slide per page – However, you can print multiple slides per page by choosing this option on your computer (look for a “multiple pages” option in your print dialog box). • Slides will be posted the day before class 7
but will not be automatically released on CourseWorks. • The taped classes will only be available on a case by case basis if you need to miss a class due to illness, disability, or any other need for audio reinforcement. • Please contact Richard Teran ([email protected]) to request regular access or to access for a specific class. We are happy to accommodate. 8
Completion based • You will still receive a score for self- assessment • Please email/contact Dr. Genkinger and Richard Teran (rat2127) if you have not completed the assessment 9
homework assignments, each worth 4% • We drop the lowest grade • Homework due dates: • Released on CourseWorks • Due at the BEGINNING of class • No late homeworks will be accepted • If you know you will be late to class, send an email to your Lab TA and Dr. Genkinger • For all questions requiring calculations, use 4 decimal points during computations and round to two decimal points at the LAST step 10
– To encourage participation, track your understanding of concepts and to give students an opportunity to submit real-time feedback on concepts that remain unclear following lecture. – Your Poll Everywhere account will be linked to your Courseworks gradebook, therefore, your account must be associated with your Columbia email. – The program can be accessed via the PollEverywhere app or through the following website: pollev.com/Jeaninegenki547. *if you have any issues, please email Richard at [email protected] 12
15th –In class closed-book exam • Final – 30% of your grade –In class closed-book exam, December 10th –Take-home open-book exam • Received: Tuesday, December 3rd • Due: Thursday, December 12th by 12:00pm • Final exams should be submitted in person. • You will NEED a PENCIL and a CALCULATOR (no cell phones or internet devices permitted) 13
on any assignment (homework, quiz, exam) they must bring it to Dr. Genkinger to discuss. After review, the student will be notified about the re-grade decision. 14
discuss concepts and work through homework problems with classmates; however, the work you submit must be your own (e.g., in your own words, performing your own calculations, providing your own code and results). – It is in violation of the honor code to use answer keys from previous semesters to complete course assignments. Sharing of answer keys either directly or via internet upload is strictly prohibited in this class. **Anyone found to be in violation of these course procedures will be reported to OSA. 19
open book/open notes, but must be completed independently. You cannot discuss the quiz or work with classmates to complete the quiz. You may only discuss the content of the quiz with classmates after the quiz due date (i.e. after all students have completed the quiz). **Anyone found to be in violation of these course procedures will be reported to OSA. 20
– Unlike homeworks, for the final exam you may not discuss concepts or work through exam questions with classmates – you must complete the final exam alone. If you have any clarification questions after release of the final exam you may direct them to the TAs and the professor. **Anyone found to be in violation of these course procedures will be reported to OSA. 21
of Epidemiology is committed to creating an educational culture that encourages robust, open, and inclusive classroom environments. • Key to achieving this goal is to ensure that all students are included in the conversation and feel comfortable expressing themselves. • An inclusive classroom environment is undermined by microaggressions. 22
commonplace verbal, behavioral, and environmental indignities, frequently unintentional, that communicate hostile, derogatory, or negative sentiments about individuals on the basis of status characteristics such as race, ethnicity, gender, sexual-orientation, religion, disability, etc. • Those who commit a microaggression are usually unaware that they have demeaned another individual, but the consequences for those on the receiving end can be significant. • Microaggressions harm individuals by making them feel invalidated, isolated, diminished, and marginalized. They harm the learning environment by making it less inclusive, open and productive. • If you have observed or been the target of a microaggression from a classmate, TA, or faculty member, you are encouraged to bring it to their attention when it happens. 23
the role of epidemiology in public health • Define and compare Measures of Effect and Measures of Association • Discuss Relationships Among Measures • Introduce the Multivariable Model 25
research question: – Is circulating vitamin D concentration positively associated with CD4 count in an HIV+ population? – Does exposure to BPA increase your risk of obesity? – Does the HPV vaccine prevent oral cancers? • We want to answer does our exposure CAUSE our outcome…… 27
condition or characteristic that preceded the disease event and without which the disease event would not have occurred at all or would not have occurred until some later time” Rothman and Greenland (1998) 28
E D Component Cause Rothman’s Causal Pie Each Causal Pie = “Causal Mechanism” = “Sufficient Cause” Component Cause: event or condition that plays a necessary role in the occurrence of some cases of disease
C D E F F G H I J I II III • There are multiple mechanisms that cause any type of disease: 3 are illustrated here. • Each individual instance of disease will occur through a single sufficient cause. (A single pie) • What component is a necessary cause?
of one component cause prevents disease from occurring by that mechanism/pathway. • Therefore, it is unnecessary to know all of the component causes of a sufficient cause to prevent disease. 33 A E B C
a Testable Hypothesis Design and Conduct a Study • Randomized Trials, Cohort Studies, Case-Control Studies, Ecological Studies • Minimize Bias, Minimize Random Error, Collect Data on Confounding Variables
of a study that results in an incorrect estimate of an exposure’s effect on the frequency of disease • Random Error – Result from measurement errors and sampling variability (by chance) • Confounding variables – Other “third” variables associated with both exposure and disease that distort the estimate of an exposure’s effect on the risk/rate of disease 38 Causal inference in epidemiologic research
a Testable Hypothesis Design and Conduct a Study Analyze Data • Observe disease frequencies (risk, rate, prevalence) using comparisons, i.e. those exposed to causal factor vs. those unexposed to the casual factor • Calculate measures of association, i.e. RR and OR • Adjust for confounders
a Testable Hypothesis Design and Conduct a Study Analyze Data Interpretation of Results • How strong is the association between exposure and disease? • Assess study validity: How precise is the estimate of effect? Is association due to bias and/or unadjusted confounding variables?
cohort if unexposed A B C F D D Note: A, B, C, F, G and H are risk factors for disease Fact Contrary to fact 46 F G H B D D Unexposed cohort Unexposed cohort if exposed F G H B E D D
D2: Disease experience among exposed if remove exposure Absolute effects Relative effects A B C F D D Measure of Effect 49 Exposed cohort Exposed cohort if unexposed
Exposed Cohort 1 1 1 Doomed p1 2 1 0 Exposure is causal p2 3 0 1 Exposure is preventive p3 4 0 0 Immune p4 50 1 = gets disease, 0 = does not get disease p = proportion of types in the cohort Measure of Effect
= p2 Causal risk ratio = (p1 + p2 ) / p1 = (p1 + p2 ) / p1 Causal odds ratio = (p1 + p2 ) / (p4 ) (p1 ) / (p2 + p4 ) 55 What if exposure can only be causal? P3 has now dropped out of the equation as it is not possible
know about causal relationships and not just associations • First choice - What we want (but can’t have) - The counterfactual (or potential outcomes) • Second choice - What we want (and may get) - Exchangeability/comparability - Why RCTs are powerful • What do we have? 56
(or "comparability", as Miettinen and Cook called it). • The compared groups were said to be exchangeable with respect to an outcome measure if their outcomes would be the same whenever they were subjected to the identical exposure history. 57 Greenland, Robins, Epi Perspectives & Innovations 2009
• Confounding occurs when the rate difference as measured causal rate difference – true for ratio measures, average risks, incidence times, or prevalences 61
if and only if The incidence proportion for cohort 2 equals what cohort 1 would have experienced if exposure were absent 66 Measures of Association vs. Effect Odds ratio: = ൙ (p1 + p2 ) (p3 + p4 ) ൘ (q1 + q3 ) (q2 + q4 )
causal mechanism • amount of change in a population’s disease frequency caused by a specific factor • Absolute effects • differences in incidence rates, proportions, prevalences, or incidence times • Relative effects • ratios of these measures 68
the absolute number of cases that differ between exposure groups • Risk Ratios describe the relative increase between groups, strength of association for a given exposure • E.g., Smoking and CVD versus smoking and lung cancer 69
T 0 Causal risk difference A 1 N − A 0 N We’re now using Rothman notation! A = # of events T = time at risk N = total N at risk Causal Absolute Measures 70
0 T 0 = I 1 I 0 Causal risk ratio ൗ A 1 N ൗ A 0 N = A 1 A 0 = R 1 R 0 A = # of events T = time at risk N = total N at risk I = rate R = risk Causal Relative Measures 71
the estimated RR. RR = a/(a+b) c/(c+d) • Step 2: Take the natural log of this value. • Step 3: Compute the estimated standard error of the log-transformed RR as: SE[ln( RR)] = 1 a − 1 a + b + 1 c − 1 c + d • Step 4: Compute a 95% CI for ln RR: ln( RR) ± 1.96 SE[ln( RR)] = (l, u) • Step 5: Exponentiate the endpoints (l and u) of the above interval to obtain a 95% CI for RR. 72 D+ D- E+ a b E- c d
the estimated OR. OR = a/b c/d = ad bc • Step 2: Take the natural log of this value. • Step 3: Compute the estimated standard error of the log-transformed OR as: SE[ln( OR)] = 1 a + 1 b + 1 c + 1 d • Step 4: Compute a 95% CI for ln OR: ln( OR) ± 1.96 SE[ln( OR)] = (l, u) • Step 5: Exponentiate the endpoints (l and u) of the above interval to obtain a 95% CI for OR. 73 D+ D- E+ a b E- c d
R S = R 1 −R if R is small S ≈ 1, R S ≈ R but if S < 1 then R S > R So if R is small, incidence odds will approximate incidence proportion but it will always be an overestimate We are using Rothman notation!! A = # of events T = time at risk N = total N at risk I = rate R = risk S = survival
S0 = R1 S0 R0 S1 • Odds Ratio = Risk Ratio * Ratio of Survival Proportions • This is why the OR is always _________________ than RR Relationship between Causal Odds Ratio and Risk Ratio 75 We are using Rothman notation!! A = # of events T = time at risk N = total N at risk I = rate R = risk S = survival O = odds
N A1 A0 = R1 N R0 N A1 A0 = I1 T1 I0 T0 Relationship between Causal Risk Ratio and Rate Ratio Remember: R = A/N I = A/T Risk Ratio = Rate ratio * Ratio of person time A = # of events T = time at risk N = total N at risk R = risk I = rate 77 R1 R0 = R1 N R0 N = A1 A0 = I1 T1 I0 T0
of period I = R if equal f/u time and A happens before end I > R if unequal, need to know person-time for each individual 78 R Small R Large N 100 100 100 100 A 1 5 20 50 R .01 .05 .20 .50 S .99 .95 .80 .50 R/S .0101 .052 .25 1 N= total population at risk R = risk A = # with disease or outcome/event S = survival I = rate
leads to disease only in the presence of its causal partners • Thus, the strength of a risk factor’s effect in a given population depends on the prevalence of its causal partners in the population – If causal partners are rare, people in the population will rarely get the disease – If causal partners are common, people in the population will frequently get the disease 84
exposure patterns, who gets disease? What component causes are needed for disease? 87 A=Smoking B=Salty Food G=E Cadherin gene P(A)=30% P(B)=50% P(G)=10% G A B
Food G=E Cadherin gene P(A)=0.3 P(B)=0.5 P(G)=0.1 Simplified example: Stomach cancer 90 Risk factor pattern Population 1 (N=1000) A B G Disease? # people 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 0 1 1 0 0 0 0 Risk of stomach cancer for smoking D (disease) d (no disease) E (has A) e (no A) Risk ratio: Risk difference: 15 135 15 135 35 315 35 315
Food G=E Cadherin gene P(A)=0.1 P(B)=0.5 P(G)=0.1 Example 1 92 Risk factor pattern Population 2 (N=1000) A B G Disease? # people 1 1 1 1 5 1 1 0 1 45 1 0 1 1 5 1 0 0 0 45 0 1 1 1 45 0 1 0 0 405 0 0 1 1 45 0 0 0 0 405 Risk of stomach cancer for smoking D (disease) d (no disease) E (has A) e (no A) Risk ratio: Risk difference:
vary the prevalence of risk factor B (salt) – a causal partner of A. Let’s first say that in population 2 instead of 50%, 90% of the population had high salt consumption 93
a risk factor’s effect is population or context dependent 1. depends on the prevalence of its causal partners (not its own prevalence) in the population 2. If causal partners are common, people in the population will frequently get the disease and effects will appear stronger 3. If causal partners are rare, people in the population will rarely get the disease and estimates appear weaker 97 Population 1 Population 2 Example 1: vary Pr(A) P(A) 30% 10% P(B) 50% 50% RR 5.5 5.5 RD 0.45 0.45 Example 2: vary Pr(B), a causal partner of A P(A) 30% 30% P(B) 50% 90% RR 5.5 9.1 RD 0.45 0.81 Example 3: vary Pr(B), a causal partner of A P(A) 30% 30% P(B) 50% 10% RR 5.5 1.9 RD 0.45 0.09
a risk factors effect – is context dependent – depends on how rare or common its causal partners are from population to population • Discrepancies between study findings may be due to ‘true’ heterogeneity between different populations in which studies are conducted (i.e. we don’t expect results to perfectly replicate) – This idea of heterogeneity between studies/populations will come up again in lecture on effect modification and meta- and pooled analysis • Rothman: “Over a span of time, the strength of the effect of a given factor on disease occurrence may change because the prevalence of its causal complement [causal partners] in various mechanisms may also change, even if the causal mechanisms in which the factor and its cofactors act remain unchanged” p. 13, Modern Epidemiology 98
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