Στατιστικές Μέθοδοι στην Επιδημιολογία Επαναληπτικό μάθημα 22/2/2012

Chapter I Epidemiologic Research Επιδημιολογία: Η μελέτη της κατανομής των νοσημάτων ή των συμβαμάτων και των παραγόντων κινδύνου για αυτά, σε καθορισμένους πληθυσμούς και η εφαρμογή της μελέτης αυτής για τον έλεγχο των προβλημάτων υγείας Μεροληψία: Συστηματικό Σφάλμα Συγχητικοί παράγοντες: παράγοντες που επηρρεάζουν την έκβαση και σχετίζονται και με την έκθεση στον παράγοντα του οποίου την επίδραση μελετάμε. Μοναδική μέθοδος εξάλειψης της επίδρασης συγχητικών παραγόντων: Τυχαιοποίηση Αντιμετώπιση στο στάδιο της ανάλυσης: Μόνο δεδομένης της γνώσης όλων των συγχητικών παραγόντων και της καταγραφής των αντίστοιχων δεδομένων

Είδη μελετών Συγχρονικές (Cross-sectional) Ασθενών-Μαρτύρων (Case-Control) Κοορτής (Cohort) Τυχαιοποιημένες Κλινικές Δοκιμές (Randomized Clinical Trials)

Chapter II Measures of Health and Disease Επιπολασμός (Prevalence) Risk of having a disease: Odds of having the disease:

Επίπτωση (Incidence) Risk of getting the disease (Cumulative incidence) : Odds of getting the disease: Incidence Rate:

Prevalence vs. Incidence Consider a disease that takes a long time to cure, and that was spread widely in 2002, but whose spread was arrested in This disease will have a high prevalence and a high incidence in 2002; but in 2003 it will have a low incidence, although it will continue to have a high prevalence because it takes a long time to cure so the fraction of affected individuals remains high. In contrast, a disease that has a short duration may have a low prevalence and a high incidence. When the incidence is approximately constant for the duration of the disease, prevalence is approximately the product of disease incidence and average disease duration, so prevalence = incidence x duration. The importance of this equation is the relation between prevalence and incidence, for example when the incidence goes up then the prevalence must go up as well

Relative measures of Exposure Effect Risk Ratio Rate Ratio Odds Ratio ExposureNo exposure Diseaseaba+b No Diseasecdc+d a+c py1 b+d py2 N

Chapter III Rates of Disease Exposure +- No. of eventsD1D1 D0D0 Total time at riskY1Y1 Y0Y0 True rateλ1λ1 λ0λ0 Estimated rateR 1 =D 1 /Y 1 R 0 =D 0 /Y 0 95% error factorEF 1 =exp(1.96*D 1 -1/2 )EF 0 =exp(1.96*D 0 -1/2 ) Approximate C.I.(R 1 /EF 1, R 1 *EF 1 )(R 0 /EF 0, R 0 *EF 0 ) True RRθ=λ 1 /λ 0 Estimated RRRR=R 1 /R 0 95% error factorEF=exp{1.96*(1/D 1 +1/D 0 ) 1/2 } Approximate C.I.(RR/EF, RR*EF)

Έλεγχος Υπόθεσης Η 0 : True Rate Ratio R 1 /R 2 =1 H 1 : True Rate Ratio R 1 /R 2 ≠1 – Test (D 1 -E 1 ) 2 /V 1 Can have exposure with more than 2 levels… – Check for linear trend  compare Rate in each level with Rate in the previous one If trend, consider using variable as continuous

Confounding vs. Interaction Estimate the effect of exposure of interest within levels of suspected confounder Test for heterogeneity/effect modifier Η0: True Rate Ratio RR i =RR H1: True Rate Ratio RR i ≠RR για τουλάχιστον ένα i If effect of exposure same across levels of suspected confounder  confounder --- Present overall OR (e.g Mantel Haenszel, adjusted for the confounder) If effect of exposure different among levels of suspected confounder  effect modifier (Interaction) --- Present separate OR for each stratum Not adjusting for a confounding variable can result either on a more intense effect or a less intense effect of the exposure.

Chapter IV Poisson Regression Y~P(μ) τ. μ Υ: Αριθμός συμβαμάτων σε χρόνο t

β 0 : log rate in the absence of high energy β 1 : difference in the log rates between low energy and high energy patients

Incidence Rate in low energy: e β0 = e Incidence Rate in high energy: e β0+β1 = e Incidence Rate Ratio (IRR): e β0 +β1 /e β0 = e =0.52

Survival Analysis Time-to-event Data S(t): The probability of ‘Surviving’ beyond t h(t): Instantaneous hazard of experiencing the event on t. Major implication: Censoring

Kaplan-Meier Goal: Estimate S(t) Must take into account that the risk set is changing over time either due to censorings or events Then, S(t) is estimated as product of survival probabilities in each time point

Cox Regression Model λ(t)=λ 0 (t)e bx No assumption on the baseline hazard BUT: HR is assumed constant over time (PH) Extensions – Include interaction with time to allow for time- varying effect of a covariate. – Stratification to allow for different baseline hazard between the levels of a covariate. – Multiple records/patient to allow for change of exposure status.

Chapter VII Case-Control Studies Not appropriate for estimating odds of being a case. Number of cases and controls in the study is our choice! BUT: We can estimate relative measures of disease (e.g OR exposed/unexposed) – Retrospective approach: Ω 1 /Ω 0, the odds of having been exposed for a case/the odds of having been exposed for a control – Prospective approach: ω 1 /ω 0, the odds of an exposed individual is a case/the odds of an unexposed individual is a case

Logistic regression Για αύξηση του x j κατά 1 μονάδα Αν το x j είναι ψευδομεταβλητή για συγκεκριμένη κατηγορία κ κατηγορικής μεταβλητής το Odds Ratio αντιστοιχεί σε: Κατηγορία κ vs. Κατηγορία αναφοράς

If ω=Κ π/(1-π) odds of being a case in the specific case control study, K being the sampling fraction for cases and controls, this will cancel out in calculation of ratios!

Chapter VIII Matched Case-Control Studies To control for confounders Analyze using Conditional Logistic Regression β 0 is meaningless Main effects of matching not estimated, BUT their interaction with other variables CAN be studied – If matching variable confounder  gain efficiency – If matching variable associate with exposure only  Overmatching loss of efficiency

Chapter X Choice of Controls in Case-Control Studies What is your scientific question? What type of disease you study? What is the exposure of interest? ⇒ What relative measure of disease you need to estimate? Which group of controls will be suitable to provide you with least biased estimates?