Chldhood Cancer Survvor Sudy Analyss Concep Proposal 1. Tle: Inverse probably censored weghng (IPCW) o adjus for selecon bas and drop ou n he conex of CCSS analyses 2. Workng group and nvesgaors: Epdemology/Bosascs Workng Group Chongzh D cd@fhcrc.org 206-667-2093 Wendy Lesenrng wlesenr@fhcrc.org 206-667-4374 Kayla Sraon ksraon@fhcrc.org 206-667-7293 Toana Kawashma kawash@fhcrc.org 206-667-7697 Kr Ness kr.ness@sjude.org 901-595-5157 Yuaka Yasu yyasu@ualbera.ca 780-492-4220 Greg Armsrong greg.armsrong@sjude.org 901-495-5892 Ann Merens ann.merens@choa.org 404-785-0691 Aaron McDonald aaron.mcdonald@sjude.org Les Robson les.robson@sjude.org 901-495-5817 3. Background and raonale The Chldhood Cancer Survvor Sudy (CCSS) quered parcpans wh a baselne and several follow-up (we focus on Follow-up 2000, 2003 and 2007 here) quesonnares. As n mos longudnal cohor sudes, here s non-parcpaon a each follow-up quesonnare. Ths may be problemac as dfferenal non-parcpaon, by eher an exposure of neres or a poenal confounder of he assocaon beween he exposure and he oucome of neres, has he poenal o nroduce bas no he esmae of he assocaon beween he exposure and he oucome. Tha s, s unlkely ha he responden cohor members a a gven quesonnare, hose who remaned n he cohor and who compleed he quesonnare, are a represenave sample of he orgnal populaon of neres. Mos analyses n he CCSS have smply omed ndvduals who dd no complee a parcular quesonnare, cng dfferenal non-parcpaon as a poenal lmaon of he sudy. Invesgaors have ndcaed ha dfferenal non-parcpaon may generae based resuls, bu have no quanfed hs poenal bas. Because he cohor connues o age, and because parcpaon declnes gradually over me, s mporan o quanfy hs poenal bas so ha we have a conssen mechansm o examne bas when conducng analyses and wrng manuscrps. Ths concep proposes an nvesgaon o examne poenal bas due o non-parcpaon n he CCSS.
4. Goal We wan o undersand whch characerscs of survvors are assocaed wh nonparcpaon and o wha degree non-parcpaon a follow-up quesonnares are nfluencng analyses (.e. assocaons beween rsk facors and oucomes). If here s an mpac, we wan o adjus for hs ype of selecon bas n fuure analyss, f possble. 5. Analyss framework We plan o conduc analyses usng nverse probably censored weghng (IPCW) mehodology. Ths mehod can be used for mos of he analyses oulned below. When he oucome of neres s from a follow-up quesonnare and he exposures (rsk facors) are from baselne (e.g., dabees a FU 2003 vs. BMI a baselne), we may also explore he augmened IPCW (AIPCW) mehod. When he daa are avalable, he laer mehodology can provde asympocally more effcen esmaes han he former. Analyses for hree follow-ups wll be conduced separaely, each compared o he baselne populaon. In he followng, we use FU2000 as an example, and mehods for FU2003 and FU2007 are he same. IPCW: Inversely wegh regresson analyses by he probably of parcpaon (deermned based on a logsc regresson model for probably of parcpaon gven pas hsory covaraes and oucomes), effecvely nflaes he mpac of underrepresened subjecs, so we can observe assocaons ha would have been observed f all subjecs had sayed n he sudy, assumng he models are correcly specfed. Key references for hs mehodology are: Robns JM, Ronzky A, Zhao LP. Analyss of semparamerc regresson models for repeaed oucomes n he presence of mssng daa. Journal of he Amercan Sascal Assocaon 1995; 90:106 121. Robns JM. Margnal srucural models versus srucural nesed models as ools for causal nference. In Sascal Models n Epdemology: The Envronmen and Clncal Trals, Halloran ME, Berry D (eds). IMA Volume 116, Sprnger-Verlag: New York, 1999; 95 134. Robns JM, Hernan MA, Brumback B. Margnal srucural models and causal nference n epdemology. Epdemology 2000; 11:550 560. Mahemacally,he models are represened as follows: Le Y be he oucome a FU1, X be covaraes (FU1 and/or baselne) for he oucome model, Z be covaraes (baselne) for he mssng mechansm model, R be he mssng ndcaor (R =1 when Y s observed and R =0 f Y s mssng).
Then he probably of mssngness a FU1 can be modeled usng logsc regresson exp( γ 0 + Z γ ) π = P( R = 1 Z ) =, 1+ exp( γ + Z γ ) where he oucome s assumed o follow a generalzed lnear model 1 µ = E ( Y X ) = g ( β0 + X 0 β ), g s a lnk funcon, for nsance deny for connuous oucome and log for bnary oucome. The IPCW esmaon s equvalen o solvng he followng esmang equaons n = 1 R π µ V β 1 ( Y µ ) = 0,where V = var(y ), whch uses nformaon from complee cases only, and gnores nformaon from ncomplee cases. The sandard errors for regresson coeffcens need o be correced by he sandwch varance esmaors. In IPCW analyss, assumng he logsc model for R (.e., facors nfluence log odds of R lnearly) could be quesoned as may or may no approxmae he underlyng mssngness mechansm. Therefore, we wll conduc some sensvy analyss wh respec o he logsc model for mssngness. We wll also consder he possbly of usng nonparamerc models f needed. Augmened IPCW (AIPCW): To mprove effcency, he augmened IPCW mehod (see 4-5) adds an augmenaon erm o he IPCW esmang equaon. Ths mehod nroduces he augmenaon erm for non-parcpans, n conras o IPCW, whch gnores observaons from non-parcpans. However, hs mehod requres ha covaraes for oucome model X are avalable for boh respondens and non-respondens. Thus, Augmened IPCW s applcable n CCSS only f rsk facors are observed a baselne. The mahemacal formula for AIPCW esmang equaon s gven by n n R µ 1 R V ( Y µ ) + (1 ) h( X ) = 0 π β π = 1 = 1 where h s a funcon of X. The augmened erm ncorporaes nformaon from ncomplee cases, and hus poenally mproves effcency compared o IPCW esmaes. The gan n effcency depends on he choce of he funcon h. In pracce, one can choose some smple funconal forms for h (see 4-5).
In addon o possble effcency gans, anoher advanage of AIPCW s ha s doubly robus, n he sense ha yelds conssen resuls f eher he mssngness mechansm or he oucome regresson model s correcly specfed. Algorhm for mplemenaon: 1. Calculae probably weghs: Among subjecs who parcpaed a baselne, and who were elgble (.e alve and elgble) for he relevan FU quesonnare, f a logsc regresson model o predc parcpaon a ha quesonnare, usng covaraes from baselne ha are key predcors of parcpaon (Z defne hese as he se we ve currenly denfed n our parcpaon models) and hose ha are any baselne versons of he curren oucome (D) and rsk facor of neres (E) (f he exac quesons are no avalable, we ry o use any smlar nformaon avalable). Resuls of hs modelng process wll be summarzed o descrbe facors assocaed wh parcpaon a each quesonnare. Calculae predced probables from hs model call hese P. 2. Calculae sablzed versons of probably weghs: A sablzng calculaon nvolves fng he same predcon model as above, bu only wh E as he covarae. Calculae predced probables from hs model call hese S. Then calculae sablzed weghs = SW = S/P. 3. F weghed logsc regresson usng 1/P as weghs: Among subjecs who responded o FU quesonnare of neres, f a logsc regresson model wh D as he oucome, and wh E as he covarae of neres and any oher approprae adjusmen covaraes for ha oucome (would probably do boh unvarae w/ E as well as mulvarae). A samplng wegh of 1/P should be ncorporaed n hs analyss (double check wheher SAS auomacally akes he nverse of P when usng weghs, or wheher you need o gve 1/P. Use robus varances. 4. F weghed logsc regresson usng sablzed weghs: F he same model as above wh sablzed weghs, SW = S/P, nsead of 1/P. Correc sandard errors by sandwch esmaors. 5. F an unweghed verson of he logsc regresson for comparson. Use he same model(s) as above n (3), bu whou any samplng weghs. Repor ORs for E for he hree models, 1) weghed w/ P, 2) weghed wh SW and 3) unweghed.
Proposed Oucome / Rsk facor combnaons o look a, along wh relevan covaraes for probably wegh predcon model. Covaraes for: Quesonnare Oucome (D) Key Rsk Facor (E) Probably wegh Model (1,2) FU 2003 Dabees* BMI (FU 2003) BMI(base), Dabees(base), oher RF from parcpaon model (Z) FU 2007 Dabees* BMI (FU 2007) BMI(base), Dabees(base), oher RF from parcpaon model (Z) Assocaon Models (3, 4, 5, 6) BMI(FU 2003), oher RF from parcpaon model (X) BMI(FU 2007), oher RF from parcpaon model (X) FU 2003 Pan (E21) BSI (scored from FU 2003 G) hree subscales depresson, somazaon, anxey (dchoomzed) BSI (base - J16 J37), RF from parcpaon model (Z) BSI (FU 2003), RF from parcpaon model (X) FU 2003 SF-36 Physcal funcon and General healh subscales Age (FU 2003) Age (Base), Healh a base (N15), RF from parcpaon model (Z) Age (FU 2003), RF from parcpaon model (X) * Use defnon used by Yuaka s group ** We wll also consder analyses wh reamen as a covarae. However, he use of reamen s somewha problemac snce here s a dfferen mssng daa suaon here (mssng covaraes, n conras o mssng oucomes n oher proposed analyses). Yuaka Yasu s group s workng on mssng reamen ssue usng a mulple mpuaon mehodology and as ha daa becomes avalable, we wll evaluae ncorporang he mulply mpued daa no some reamen relaed hypoheses.
Table 1: Saus a each follow-up Baselne FU 2000 FU 2003 FU 2007 Parcpan Non- Parcpan Dead Inelgble Toal
Table 2 Dsrbuon of covaraes a each follow-up or for MRAF avalably Baselne elgble FU 2000 elgble FU 2003 elgble FU 2007 elgble Parcpans Parcpans Parcpans Parcpans Nonparcpans Nonparcpans Nonparcpans Nonparcpans Gender Race Baselne age Dagnoss Age of dagnoss
Table 3: ORs beween parcpaon and subjec characerscs Baselne FU 2000 FU 2003 FU 2007 OR (95% CI) OR (95% CI) OR (95% CI) OR (95% CI) Gender Race Baselne age Dagnoss Age of dagnoss Table 4: ORs beween oucomes and key rsk facors, unadjused and adjused Quesonnare Oucome Key rsk facor ORs (95% CIs) FU 2003 Dabees BMI FU 2003 Dabees BMI (base)? FU 2003 Pan BSI FU 2003 Pan BSI (base)? FU 2003 SF-36 Age Naïve IPCW IPCW (sablzed)
6. References 1. Robns JM, Ronzky A, Zhao LP. Analyss of semparamerc regresson models for repeaed oucomes n he presence of mssng daa. Journal of he Amercan Sascal Assocaon 1995; 90:106 121. 2. Robns JM. Margnal srucural models versus srucural nesed models as ools for causal nference. In Sascal Models n Epdemology: The Envronmen and Clncal Trals, Halloran ME, Berry D (eds). IMA Volume 116, Sprnger-Verlag: New York, 1999; 95 134. 2. Robns JM, Hernan MA, Brumback B. Margnal srucural models and causal nference n epdemology. Epdemology 2000; 11:550 560. 3. Scharfsen DO, Ronzky A, Robns JM. (1999). Adjusng for non-gnorable drop-ou usng semparamerc non-response models. Journal of he Amercan Sascal Assocaon, 94:1096-1120. 4. Ronzky A, Robns JM, Scharfsen D. (1999). Semparamerc regresson for repeaed oucomes wh nongnorable nonresponse. Journal of he Amercan Sascal Assocaon, 93(444):1321-1339.