FORMULAS FROM EPIDEMIOLOGY KEPT SIMPLE (3e) Chapter 3: Epidemiologic Measures

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1 FOMULAS FOM EPIDEMIOLOGY KEPT SIMPLE (3e) Chater 3: Edemologc Measures Basc edemologc measures used to quantfy: frequency of occurrence the effect of an exosure the otental mact of an nterventon. Edemologc Measures Measures of dsease frequency Measures of assocaton ( Measures of Effect ) Measures of otental mact Incdence Prevalence Absolute measures of effect elatve measures of effect Attrbutable Fracton n exosed cases Attrbutable Fracton n the Poulaton Incdence roorton (Cumulatve Incdence, Incdence sk) Incdence rate (ncdence densty, hazard rate, ersontme rate) sk dfference (Incdence roorton dfference) sk ato (Incdence Proorton ato) Incdence odds ate Dfference (Incdence densty dfference) ate ato (Incdence densty rato) Prevalence Dfference Odds ato Page o

2 3. Measures of Dsease Frequency Incdence Proorton o. of onsets o. at rsk at begnnng of follow-u Also called rsk, average rsk, and cumulatve ncdence. Can be measured n cohorts (closed oulatons) only. equres follow-u of ndvduals. Incdence ate o. of onsets erson-tme Also called ncdence densty and average hazard. When dsease s rare (ncdence roorton < 5%), ncdence rate ncdence roorton. In cohorts (closed oulatons), t s best to sum ndvdual erson-tme longtudnally. It can also be estmated as Σerson-tme (average oulaton sze) (duraton of follow-u). Actuaral adjustments may be needed when the dsease outcome s not rare. In an oen oulatons, Σerson-tme (average oulaton sze) (duraton of follow-u). Examles of ncdence rates n oen oulatons nclude: brths Crude brth rate (er m) m md-year oulaton sze deaths Crude mortalty rate (er m) m md-year oulaton sze Infant mortalty rate (er m) deaths < year of age m lve brths Prevalence Proorton o. of cases o. of ndvduals n the study Also called ont revalence or just revalence. The concet of erod revalence should be avoded when ossble because t confuses the concets of ncdence and revalence (Elandt-Johnson & Johnson, 98). Prevalence deendence on the nflow and outflow of dsease accordng to ths formula Prevalence (ncdence rate) (average duraton of llness). Addtonal otes Termnology: The term rate s often used loosely, to refer to any of the above measures of dsease frequency (even though the only true rate s the ncdence densty rate Odds: Both revalence and ncdence roortons may be addressed n terms of odds. Let reresent the ncdence roorton or revalence roorton of dsease and o reresent the odds of dsease. Thus, odds o / ( ). eortng: To reort a rsk or rate er m, smly multly t by m. For examle, an ncdence roorton of.., er,. Un-cohort: To reort a rsk or rate as a uncohort, take ts recrocal and reort t as n uncohort. For examle, an ncdence roorton of.25 n or n Page 2 o

3 3.2 Measures of Assocaton (Measures of Effect) otaton and termnology: Concets aly to ncdence roortons, ncdence rates, and revalence roortons, all of whch wll be loosely called rates. Let reresent the rate or rsk of dsease n the exosed grou and let reresent the rate or rsk of dsease n the non-exosed grou. Absolute Measure of Effect (ate Dfference) elatve Measure of Effect (ate ato) D The relatve effect of an exosure can also catured by the SM (see secton on ate Adjustment) 2-by-2 Cross-Tabulaton D+ D Total E+ (Grou ) A B E (Grou ) A B M M For erson-tme data (ncdence rates/denstes) gnore cells B and B and let and reresent the erson-tme n grou and grou, resectvely. A A A / ates, ate ato, and ate Dfference:,,, and A / D ( A / ) ( A / ) (cohort and cross-sectonal data) AB Odds rato: O (ndeendent samles only; for matched-ars and tules data, see text) AB oundng: Basc measures should be reorted wth 2 or 3 sgnfcant dgt accuracy. Carry 4 or 5 sgnfcant dgts to derve a fnal answer that s accurate to 2 or 3 sgnfcant dgts, resectvely. 3.3 Measures of Potental Imact The attrbutable fracton n exosed cases AF, or equvalently, AF e e. The attrbutable fracton n the oulaton AF Equvalent, AF AF where e c c reresents roorton of oulaton cases that are exosed Page 3 o

4 3.4 ate Adjustment ( Standardzaton ) For unformty of language, the term rate wll be used to refer to any ncdence or revalence measure. Drect Standardzaton The drectly adjusted rate (a drect ) s a weghted average of strata-secfc rates wth weghts derved from a reference oulaton: a drect wr where w reresents the sze of strata of the reference oulaton r reresents rate n strata of the study oulaton. ote that catal letters denote values that come from the reference oulaton and lower case letters denote values the come from the study oulaton. Indrect Standardzaton Indrect standardzaton s based on the Standardzed Mortalty ato (SM) Observed SM Exected where Observed s the observed number of cases and Exected s the exected number of cases n the oulaton based on ths formula: Exected n where reresents the rate n strata of the reference oulaton and n reresents the number of eole strata of the study oulaton. The Exected n the oulaton can be understood n terms of the exected number of cases wthn strata, whch s: Exected n. Thus: Exected Exected. The SM s a oulaton-based relatve rsk estmate n whch reresents a oulaton n whch the observed rate equals the exected rate. Otonal: Use the SM to derve the ndrectly adjusted rate va ths formula: a ndrect (crude rate) SM Page 4 o

5 Chater : Screenng for Dsease eroducblty (Agreement) ater B ater A + + a b g c d g 2 f f 2 obs a+ d fg + fg 2 2 ex 2 κ obs ex ex Valdty (Senstvty, Secfcty, PVPT, PVT) Dsease + Dsease Total Test + TP FP Test F T TP + FP (those who test ostve) F + T (those who test negatve) Total TP + F (those wth dsease) FP + T (those w/out dsease) SE (TP) / (those wth dsease) [note: TP (SE)(TP + F)] (TP) / (TP + F) SPEC (T) / (those wthout dsease) (T) / (T + FP) [note: T (SPEC)(FP + T)] PVP (TP) / (those who test ostve) (TP) / (TP + FP) PV (T) / (those who test negatve) (T) / (T + F) True revalence (TP + F) / [also known as ror robablty ] Bayesan equvalents for PVP and PV are resented n the text. Page 5 o

6 TE COMMADMETS FO DEALIG WITH COFOUDIG Source: EPIB-6 McGll Unversty, Montreal, Canada htt:// foundng.df I. Always worry about confoundng n your research, esecally at the desgn/rotocol stage. Try to use desgn elements (e.g. randomzaton) that wll hel reduce otental confoundng. II. Pror to the study, revew the lterature and consder the underlyng causal mechansms (e.g. draw causal dagrams such as drected acyclc grahs [DAGs]). Then make sure you collect data on all otental confounders; otherwse you wll not be able to adjust for them n your analyses. III. Know your feld or collaborate wth an exert who does! Subject-matter knowledge s mortant to recognze (e.g. draw causal dagrams) and adjust for confoundng. IV. Use a ror and data-based methods to check f the otental confounders are ndeed confounders that should be adjusted for. V. Use stratfed analyses and multvarable methods to handle confoundng at the analyss stage. Choose the multvarate model that best suts the tye of data (e.g. dchotomous vs. contnuous) you collected and the desgn you emloyed (e.g. casecontrol vs. cohort). VI. Do not adjust for covarates that may be ntermedate causes (on the causal athway between the exosure and dsease). Do not adjust for covarates that may not be genune confounders. And beware of tme-varyng covarates that wll need secal aroaches. VII. Use matchng wth great cauton. Use analytc methods that are arorate for the desgn used; for examle, f matchng was done, use methods that take matchng nto account (e.g. condtonal logstc regresson, matched ars analyses). VIII. Always consder effect measure modfcaton, but erform and nterret subgrou analyses wth cauton. The subgrou analyss should be one of a small number of hyotheses tested, and the hyothess should recede rather than follow the analyss (.e. subgrous must be re-secfed). IX. Always remember that adjustment for confoundng can be nadequate due to resdual confoundng because of unmeasured confounders, msclassfcaton of confounders, and nadequate adjustment rocedures (e.g. model mssecfcaton, categorzaton of contnuous covarates). X. If conventonal methods rove to be nadequate, consder usng newer aroaches such as roensty scores, matched samlng, nstrumental varables and margnal Page 6 o

7 structural models. However, make sure you work wth statstcans who understand these new methods (not many do). When all else fals, ray! If rayer fals, consder changng rofessons!! Page 7 o