NEW ASTERISKS IN VERSION 2.0 OF ACTIVEPI

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1 NEW ASTERISKS IN VERSION 2.0 OF ACTIVEPI ASTERISK ADDED ON LESSON PAGE 3-1 after the second sentence under Clncal Trals Effcacy versus Effectveness versus Effcency The apprasal of a new or exstng healthcare nterventon or treatment modalty nvolves three steps (Detsky, 1995; Detsky & Nagle, 1990; Grmes & Schulz, Intally, effcacy (achevng ts stated clncal goal s demonstrated under optmal crcumstances n a prospectve randomzed controlled tral. Subsequently, effectveness (producng greater beneft than harm s assessed under ordnary crcumstances n the general populaton by way of a prospectve observatonal cohort study or an expermental communty nterventon tral. The effcency of the healthcare nterventon (the health status mprovement realzed for a gven amount of resources expended s then determned va a cost-effectveness analyss or cost-utlty analyss. Alternatvely, such an economc evaluaton can provde essental nsght nto the resources requred to delver the healthcare nterventon to a specfc populaton (Kocher & Henley, 2003 Detsky, A. S. (1995. Evdence of effectveness: evaluatng ts qualty. In F. A. Sloan (Ed., Valung health care: costs, benefts, and effectveness of pharmaceutcals and other medcal technologes (pp Cambrdge, UK: Cambrdge Unversty Press. Detsky, A. S., & Nagle, I. G. (1990. A Clncan Gude to Cost-Effectveness Analyss. Annals of Internal Medcne, 113(2, Grmes, D. A., & Schulz, K. F. (2002. An overvew of clncal research: the lay of the land. Lancet, 359(9300, Kocher, M. S., & Henley, M. B. (2003. It s money that matters: Decson analyss and cost-effectveness analyss. Clncal Orthopaedcs and Related Research(413,

2 ASTERISK ADDED ON LESSON PAGE 4-4 n actvty completed secton of expo #3 (Age- Adusment. (see errata lst The Indrect Method of Adustment and the SMR An ndrect (age- adusted rate s A weghted average of (age- specfc rates for a select standard populaton usng the dstrbuton of the study populaton as weghts. Typcally used when any of the (age- specfc rates n the study populaton are unavalable or unrelable. Needed for ndrect adustment: 1. Specfc rates for the selected standard populaton. 2. Dstrbuton for the study populaton across the same strata as those used n calculatng the specfc rates n the standard populaton. 3. Crude rate for the study populaton. 4. Crude rate for the standard populaton. The SMR (Standardzed Morbdty/Mortalty Rato s a rato measure defned by O/E the observed number (O of cases of dsease n the cohort dvded by the expected number (E; ths rato s usually multpled by 100. The expected number s calculated by applyng age-specfc standard dsease rates from a reference populaton (e.g., natonal rates to the age dstrbuton of the cohort. Calculatng a SMR: hypothetcal example Reference Populaton -- Study Cohort (natonal rates Age Observed cases n cohort Person -years Rate per 1,000 person-years Expected number of cases (O/E x Total Advantages of an SMR Used extensvely n occupatonal studes It s not necessary to dentfy, recrut, and follow-up an unexposed (reference group. (One can smply use avalable age-specfc natonal or state dsease rates. Natonal or state age-specfc dsease rates are stable because they are based on large populatons

3 Dsadvantages of an SMR May not be able to compare SMRs from dfferent cohorts (Resdual confoundng by age because the standard dsease rates are appled to cohorts wth dfferent age dstrbutons. The SMR (lke any summary measure may obscure age-specfc effects. (In the hypothetcal example, the effect n the age-group was about twce as hgh as the effect n the and the age group. ASTERISK ADDED ON LESSON PAGE 5-3 ust pror to the expo #3 under the headng Odds Rato Approxmaton n case control studes (see errata lst The EOR Estmates the RR n a Case-Cohort Study Wthout A Rare Dsease Assumpton The typcal formula for the EOR n case-control study: P(E EOR P(E D/[1 - P(E D /[1 - P(E D D In a case-cohort study, the controls are sampled from the orgnal (entre cohort, so the formula for the EOR n a case-cohort study can be modfed n the denomnator as follows: P(E D/[1- P(E D EOR P(E/[1- P(E From algebra, t then follows that the formula for the RR n a case-cohort study s: P(D E RR P(D E P(E D/P(E P(E D/P( E P(E D/[1- P(E D P(E/[1- P(E EOR P(E DP(D/P(E P(E DP(D/P( E P(E DP(E P(E DP(E

4 SECOND ASTERISK ADDED ON LESSON PAGE 5-3 ust after the astersk on The EOR Estmates the RR n a Case-Cohort Study wrtten pror to expo #3 under the headng Odds Rato Approxmaton n case control studes (see errata lst The followng statement needs to be wrtten on Lesson Page 5-3 pror to expo #3: We have used the rare dsease assumpton to ndcate when an odds rato n a follow-up study wll approxmate a rsk rato calculated for the same study. We now descrbe how the odds rato from a casecontrol study can also estmate a rsk rato. (See for a descrpton of how, n a case-cohort study, the EOR estmates the RR wthout the need for a rare dsease assumpton. Also, see for a descrpton of how, n a nested case-control study, the Mantel-Haenszel Odds Rato (mor, whch s descrbed on Lesson Page 14-5 n Lesson 14, estmates the rate rato (IDR wthout the need for a rare dsease assumpton. The Mantel-Haenszel Odds Rato (.e., mor Estmates the Rate Rato (.e., IDR n a Nested Case-Control Study Wthout A Rare Dsease Assumpton In a nested case-cohort study, the controls are determned usng densty samplng so that each control s matched to a correspondng case at the tme of case dagnoss. In other words, one or more controls are selected for each case from subects n the orgnal cohort who are stll at rsk at the tme a case s dentfed. Because a nested case-control study nvolves matchng, the typcal odds rato measure of effect that s used s determned by a stratfed analyss, n whch the strata are the matched case-control sets of subects correspondng to dstnct tmes at whch cases occur. We assume, wthout loss of generalty, n the dscusson that follows that n any short tme nterval t durng whch M ( 1 cases occur, R M controls, where R 1, are matched to the number of cases occurrng durng that same nterval. (Note: f the tme ntervals were short enough so that no more than one case could occur durng an nterval, and R 1, then the matchng process s called par matchng, and each stratum conssts of two subects, the casecontrol par that s dentfed at the tme of case dagnoss. If, n ths stuaton, R>1, the process s called R-to-1 matchng. (See Lesson Page 15-3 for detals on how to carry out the analyss of par-matched and R-to-1 matched case-control data. Gven m cases, the -th stratum ( 1, 2,, N can then be descrbed by the followng 2 2 table, where N denotes the number of equal sze non-overlappng tme ntervals t over the entre tme of a gven nested case-control study: Stratum (.e., -th matched par E Not E Total Case a b M a + b Control c d R M c + d T M (R + 1 In ths table: a # of exposed cases n the -th stratum b # of unexposed cases n the -th stratum c # of exposed controls n the -th stratum d # of unexposed controls n the -th stratum T total # of cases and controls enrolled durng the -th tme nterval t.

5 SECOND ASTERISK ADDED ON LESSON PAGE 5-3 contnued Note that f only 1 case occurs n a gven tme nterval and R1, then the row total s 1 for both cases and controls, and each row n the above 2 2 table wll have at least one zero cell frequency, so the odds rato OR a d b c s undefned for each. Consequently, the adusted measure of effect used to combne the nformaton over all strata cannot be a typcal weghted average of the OR, but, rather, s defned by the Mantel-Haenszel Odds Rato (mor as follows: mor 1 a b 1 where denotes the total number of case-control pars, and the sums n the numerator and denomnator, respectvely, consder only those tme ntervals t, 1, 2,, n whch at least one case occurs. Here, T M (R +1, where M and R M are the number of cases and controls, respectvely, that are enrolled durng the tme nterval t. We now provde a proof to show that the mor defned above, and condtonal on the number of subects T enrolled each day, approxmates the rate rato (.e., IDR that would have been obtaned f a cohort study that consdered person-tme of follow-up for persons n the cohort had been carred out nstead of a nested case-control study. The proof requres the followng addtonal assumpton: The IDR s constant throughout the entre perod of follow-up of the cohort under study,.e., IDR(t IR 1 (t / IR 0 (t IDR where t denotes any tme durng follow-up of the cohort IR 1 (t denotes the ncdence rate among exposed subects (E, at tme t and IR 0 (t denotes the ncdence rate among the unexposed subects (not E at tme t. (Note: The above assumpton s essentally equvalent to assumng a proportonal hazard assumpton n a survval analyss. Also, the proof depends on the followng theoretcal relatonshp (proof omtted here but descrbed at the end of the dscusson: If then E[ a 1 IDR, where E(X denotes the Expected Value of X, 1 E[ b

6 SECOND ASTERISK ADDED ON LESSON PAGE 5-3 contnued mor a 1 b 1 s a consstent estmator of IDR. (1 The proof now proceeds as follows: E[ a 1 1 E[ b E(a 1 snce E[ x N E(x and we treat T as constant 0 E(b 1 E(a E( 1 (2 E(b E( 1 snce the controls ( and are selected ndependently of the cases (a and b at tme t. For the cases, ncdence rates IR 1 ( t and IR 0 ( t can be expressed as follows: IR 1 (t E(a t and IR 0 (t E(b (t t where N 1 ( t and ( t are the number of exposed and unexposed, respectvely, stll at rsk at tme t ust pror to the start of tme nterval t. Thus, usng algebra, t follows that E(a IR 1 (t t and E(b IR 0 (t (t t For the controls, the expected values E( and E( are the expected frequences of exposed and unexposed controls, respectvely, out of the total controls at rsk at tme t, whch can be expressed as follows:

7 SECOND ASTERISK ADDED ON LESSON PAGE 5-3 contnued E( RM + (t and E( RM (t + (t. Substtutng the above expressons for E( a, E( b, E( and E( nto expresson (2, we obtan the followng: E(a E( 1 E(b E( [IR 1 (t t [(RM (t + (t N 1 (t [IR 0 (t (t t [(RM + (t 1 1 N 1 (t (t [IR 1 (t t [(RM N 1 (t + (t N 1 (t (t [IR 0 (t t [(RM N 1 (t + (t 1 N 1 (t (t [(IDRIR 0 (t t [(RM N 1 (t + (t 1 (t N 1 (t [IR 0 (t t [(RM N 1 (t + (t snce we have assumed a constant IDR at any tme t,.e., IDR IR 1 (t IR 0 (t for any tme t. It then follows from algebra that E(a E(d / T 1 E(b E(c 1 / T 1 N 1 (t (t [(IDRIR 0 (t t [(RM N 1 (t + (t 1 (t N 1 (t [IR 0 (t t [(RM N 1 (t + (t (3

8 SECOND ASTERISK ADDED ON LESSON PAGE 5-3 contnued 1 IDR 1 Thus, we have shown that N 1 (t (t [IR 0 (t t [(RM N 1 (t + (t (t N 1 (t [IR 0 (t t [(RM N 1 (t + (t E[ a d / T 1 IDR E[ b c / T 1 from whch we can conclude usng (1 above that mor 1 a IDR s a consstent estmator of IDR, b c 1 / T and ths result was obtaned wthout requrng a rare dsease assumpton. [Note: The above consstency argument follows because from (3 E[ a /T 1 E[ b /T 1 (IDRE[ 1 E[ 1 X X 1 1 IDR, N 1 (t (t where X b c /T IR 0 (t t [(RM N 1 (t + (t /T, so E[ 1 a d /T 1 p (IDRE[ 1 X 1 and E[ 1 b c /T 1 p from whch t follows that E[ 1 X, 1 E[ a d / T 1 E[ b c / T 1 p (IDRE[ 1 E[ 1 X X 1 1 IDR.

9 REPLACEMENT ASTERISK ON Calculatng Sample Sze for Clncal Trals and Cohort Studes AT THE BOTTOM OF LESSON PAGE 12-5 (see errata lst p p2 (RR + r/(r + 1 p (. 04(2 + 3/( ( (.05(.95(3 + 1 n [(.04(2 1 3 Thus, the sample sze (n needed to detect a rsk rato (RR of 2 at an α of.05 and a β of.20, when the expected rsk for exposed p 2 s.04 and the rato of unexposed to exposed subects (r s 3, s 312 exposed subects and unexposed subects. The above sample sze formula can also be used to determne the sample sze for estmatng a prevalence rato (.e., PR n a cross-sectonal study; smply substtute PR for RR n the formula.

10 REPLACEMENT ASTERISK ON Calculatng Sample Sze for Case-Control Studes AT THE BOTTOM OF LESSON PAGE 12-6 (see errata lst CALCULATING SAMPLE SIZE FOR CASE-CONTROL AND CROSS-SECTIONAL STUDIES In an astersk on the prevous lesson page (12-5, we descrbed a formula for determnng the sample sze (n for estmatng a rsk rato (RR n clncal trals and cohort studes. Ths formula also apples to sample sze calculatons for the prevalence rato (PR n cross-sectonal studes (.e., replace RR wth PR n the formula. We now descrbe and llustrate a varaton of the above-mentoned formula that can be used to determne the sample sze for estmaton of an odds rato (OR n case-control studes. As wth sample sze formula for RR, when consderng the OR nstead, the nvestgator must specfy values for the sgnvcance level α, the probablty of a Type II error β, and the extent of the departure of the study effect from the null effect,.e.,, nto an approprate formula to determne the requred sample sze. For case-control and cross-sectonal studes, the sample sze formula for detectng an odds rato (OR that dffers from the value of 1 by at least,.e., OR-1, s gven by the formula: p 2 ( p1 + rp /(r + 1 To use ths formula, one typcalloy specfes (a guess for p 2 and the OR to be detected, and then solves the OR formula for p 1 n terms of OR and p 2. (Note: f the sample szes are to be equal n the case and control groups, then r1. When r does not equal 1, the formula provdes the sample sze for the case group; to get the sample sze for the control group, use n r. To llustrate the calculaton of n, suppose α.05, β.20, OR2, and r3. Then and solvng for p 1 we obtan We then calculate p [ (.04/(

11 and fnally solve for n to yeld ( (.0492(.9508(3 + 1 [ n Thus, the sample sze (n to detect an odds rato (OR of 2 at an α of.05 and a β of.20, when the expected proporton of exposed among controls (p 2 s.04 and the rato of controls to cases (r s 3, s 360 cases and ,080 controls.