Adjusted Estimates for Time-to-Event Endpoints

Transcription

1 Adjusted Estmates for Tme-to-Event Endponts Barry E. Storer 1, Ted A. Gooley 1, Mchael P. Jones 2 1 Fred Hutchnson Cancer Research Center 2 Unversty of Iowa Phone: FAX: bstorer@fhcrc.org Abstract In the analyss of retrospectve data or when nterpretng results from a sngle-arm phase II clncal tral relatve to hstorcal data, t s often of nterest to show plots summarzng tme-to-event outcomes comparng treatment groups. If the groups beng compared are mbalanced wth respect to factors nown to nfluence outcome, these plots can be msleadng and seemngly ncompatble wth results obtaned from a regresson model that accounts for these mbalances. We consder ways n whch covarate nformaton can be used to obtan adjusted curves for tme-to-event outcomes. We frst revew a common model-based method and then suggest another model-based approach that s not as relant on model assumptons. Fnally, an approach that s partally model free s suggested. Each method s appled to an example from hematopoetc cell transplantaton. Keywords: Cox regresson, Kaplan-Meer, adjusted survval, cumulatve ncdence 1

2 1. Introducton In the evaluaton of tme-to-event data derved from phase II clncal trals or retrospectve studes n hematopoetc cell transplantaton (HCT), Cox regresson s typcally used to quantfy the dfference n outcome between two groups. Regresson analyss allows one to adjust for potental mbalances n characterstcs assocated wth outcome that mght partally explan the dfference (or lac thereof) between the groups beng compared. In addton to an estmate of the dfference n outcome as derved from the regresson model, t s often desrable to provde a graphcal llustraton of the dfference. The most common tool for ths purpose s the Kaplan-Meer estmate for survval endponts, and cumulatve ncdence estmate for endponts wth competng rss; however, nether of these estmates consders nformaton from covarates that may be mbalanced among the groups, thereby leadng to curves that may not reflect the dfferences among the groups as measured by the regresson model. A method to generate adjusted curves would therefore be desrable. Secton 2 provdes an example from HCT data and motvates the problem. Secton 3 descrbes a relatvely standard model-based approach, whch llustrates the ftted model but falls short of achevng what we would consder to represent adjusted survval curves. We then suggest a smple alternatve that better accommodates the noton of adjustment, though stll requrng some model assumptons. Secton 4 proposes a method that s less dependent on the model assumptons requred of the methods summarzed n Secton 3, and s extended to provde adjusted cumulatve ncdence estmates n Secton Example from HCT As an llustraton of the problem we present an example from a retrospectve data analyss that sought to compare outcomes after HCT followng the use of nonmyeloablatve condtonng to outcomes followng conventonal myeloablatve condtonng n 220 patents wth B-cell malgnances [non-hodgn lymphoma (NHL), chronc lymphocytc leuema (CLL), and Hodgn lymphoma (HL)], as reported prevously (Sorror et al. 2008). Ths comparson s complcated by a number of factors, chef among them the fact that nonmyeloablatve condtonng s generally offered only to older patents and to patents wth pre-exstng comorbdty, who are generally consdered to be unsutable for transplant wth myeloablatve condtonng regmens. There are also dfferences between these patent populatons wth respect to other factors that could nfluence outcome, ncludng the dagnoss beng treated, the use of moblzed perpheral blood (PBSC) versus bone marrow 2

3 (BM) as a source of stem cells, and the use of matched sblng versus msmatched or unrelated donor grafts. Shown n Fgure 1 are (unadjusted) Kaplan-Meer estmates of overall survval for the two condtonng groups. Table 1 summarzes the characterstcs of the two condtonng groups plus the results from proportonal hazards models relatng these factors to overall mortalty and non-relapse mortalty (NRM), whch s defned as any death occurrng n the absence of recurrence or progresson of malgnancy. As can be seen from ths table, patents recevng nonmyeloablatve condtonng are more lely to possess some factors that are assocated wth ncreased mortalty when compared to patents recevng myeloablatve condtonng. Although not all factors were assocated wth outcome n unvarate analyss, they were consdered as possble adjustment factors based on pror consderatons and the possblty that an assocaton was obscured by confoundng factors. The results from an unadjusted Cox regresson model show a modestly reduced hazard of mortalty assocated wth nonmyeloablatve condtonng relatve to myeloablatve condtonng [HR=0.77, 95% CI , p=0.20], as also evdenced by the curves n Fgure 1. However, the HR for overall mortalty adjusted for the factors n Table 1 suggests a much larger dfference between the condtonng groups than s vsually apparent [HR=0.50, 95% CI ), p=0.008]. Gven ths, there s a need for some type of adjustment to the curves shown n Fgure 1 so that the adjusted curves better reflect the assocaton measured by the regresson model. In the next two sectons, we dscuss several approaches to adjustment. 3. Model-based Approaches We frst ntroduce some notaton that wll be used throughout. Suppose we have K groups of nterest, wth sample sze n each group denoted n, and sets of labels of the ndvduals wthn each group, denoted M, = 1,..., K. Each ndvdual has a vector of addtonal covarates, z, that may be related to overall survval or to some cause-specfc hazard of nterest. The Cox proportonal hazards model assumes that the hazard of falure assocated wth a set of covarates z s defned by 3

4 λ( t z) = λ0( t) exp( z β ) (1) where λ ( ) s an arbtrary and unspecfed baselne hazard functon, and β s a vector of 0 t unnown regresson parameters. Based on ths model, the estmated survval for a partcular set of covarates z s gven by exp( z ˆ β ) [ Sˆ ( t ] Sˆ( t z) = (2) 0 ) where Sˆ ( t) = exp[ Λˆ ( )] s derved from any standard estmate of the cumulatve 0 0 t baselne hazard functon (Kalbflesch and Prentce 1980; Breslow 1974), and βˆ s the vector of estmated coeffcents from the Cox model. Under ths model, one can use equaton (2) to generate an estmate of survval for any specfed set of covarates. For the current example, a standard approach to llustratng the effect of the condtonng regmen adjusted for the other covarates, would be to ft a proportonal hazards model ncorporatng all of the covarates n Table 1 plus an ndcator of condtonng group. Then (2) would be plotted for two z vectors dfferng only by the presence or absence of the ndcator for condtonng, for example by usng the covarates= opton n the SAS baselne statement wthn the phreg procedure. For the factors lsted n Table 1, one could assgn the average value for patents n the myeloablatve group, yeldng the survval estmates n Fgure 2. In our vew, the adjusted curves that result from ths model-based approach have some shortcomngs. Frst, the overall shape of the unadjusted Kaplan-Meer curves s not mantaned. Ths s due to the fact that the adjusted curves from (2) are derved from a pooled estmate of the common baselne hazard functon, wth the separaton between curves dctated by the model-based hazard rato estmate. Even f the proportonal hazards model s completely correct, the jump ponts of the adjusted curves wll not match those of the unadjusted curves, because the jump ponts reflect deaths wthn ether group. Whle these curves accurately llustrate the ftted model, we beleve they are too far removed from the unadjusted Kaplan-Meer curves to conform to the conventonal noton of adjustment. 4

5 We propose a relatvely smple adjustment method whch results n jump ponts for the adjusted curve only when a death occurs wthn that group, so that the adjusted curve mantans ts overall shape, although there s stll dependence on a model-based hazard rato comparng the two groups. To mplement the method one frst chooses one of the K groups as the reference group, and then selects a tme pont t A as a pont of reference for adjustment. Ideally ths pont s well along the tme axs to the rght, but before the pont where excessvely large jumps may occur due to small numbers of patents at rs. In a settng wth two groups, suppose we choose M 1 as the reference group, S ˆ1 ( t ) and S ( t) denote the unadjusted Kaplan-Meer curves for M 1 and M 2, respectvely, andπˆ s the estmated adjusted hazard rato comparng M 2 to M 1. If S ( ) denotes the adjusted curve for M 2, then we requre ths curve to satsfy 2 t ˆ2 2 A 1 t ˆ A ˆ π S ( t ) = [ S ( )], (3) that s, at tme t A we want the survval estmate for the adjusted curve for group 2 and the survval estmate for the reference group1 to be n accordance wth the adjusted hazard rato πˆ. One way to modfy S ( t) to acheve ths condton s to mae a proportonate adjustment to ˆ2 the falure probablty that yelds the desred relatonshp at t A and then apply that to the entre curve, so that S ( t) = 1 ( m / m )(1 Sˆ ( )), (4) t ˆ 2 1 t A where ˆ π m = (1 [ S ( )] ) and m = 1 Sˆ ( t )). Although ths adjustment method s 2 ( 2 A based on the survval estmates at a sngle pont n tme, t produces reasonable results n many cases, although t s of course somewhat dependent on the choce of t A. Also, f S ( t) becomes small and the adjustment rato / m 2 m2 s large, then S ( ) can be < 0. In ˆ2 ths case the proportonate adjustment could be based on the survval probablty at t A, rather than the falure probablty. 2 t 5

6 Another alternatve to (4) that avods ths possblty s to solve for π to satsfy the relaton π [ ˆ ( t )] [ ˆ A S1( t A ˆ π S 2 = )]. That s, π s the effectve hazard rato that would need to be appled to S ( t) n order to acheve the desred survval probablty at t A, and s easly ˆ2 solved as ˆ ( )]/ log[ ˆ π = ˆ π log[ S t S ( t )], wth then S =. 1 A 2 A π 2 ( t) [ Sˆ 2( t)] In the example at hand we tae t A to be 6 years, snce t represents a pont relatvely far along n tme yet short of where the curves become obvously unstable due to small numbers at rs, and agan wsh to use the myeloablatve group as the reference group. We 5 2 = have ˆ1 (6) = 0. S , and snce πˆ = 0.5 we want S (6) = , so that the adjusted falure probablty m = Snce S ˆ2 (6) = 0., the unadjusted falure probablty at t A s m 2 = 0.527, and S ( ) s constructed by mutplyng the falure 2 t probablty n group 2 by a factor of 0.368/0.527 = at all ponts n tme. The adjusted curve accordng to (4) s shown n Fgure 3. The alternate adjusted curve s obtaned by usng an effectve hazard rato π = 0.5 log(0.399) / log(0.473) = appled to S ( t). The resultng curve s very smlar to (4) except n the tal. ˆ2 As noted above, a drawbac to ths smple approach s the need to choose the tmepont t A. If the survval curves are based on groups wth large sample szes, and the rs sets do not get too small (< 10 patents per group, say), then the method s not partcularly senstve to the choce of tme. When the sample szes are small, or there s clear non-proportonalty of hazards, then the choce of t A becomes problematc and one should consder the method descrbed below. 4. Partally Model-free Approach Although the methods descrbed above produce adjusted curves that retan the same appearance as the unadjusted curves, they rely on a model-based estmate of the hazard rato, ncludng the assumpton of proportonal hazards between the groups of nterest. They are also subject to some arbtrarness n the choce of the adjustment tme t A. The method descrbed below maes no modelng assumptons about the factor of nterest, though t depends on modelng the hazards assocated wth the covarates to be adjusted for. 6

7 Usng the notaton above, a stratfed proportonal hazards model for ths settng s defned by allowng the baselne hazard functon to vary for each group, wth other covarates modulatng ths hazard n a way that s common to all strata, as defned by λ ( t) = λ0 ( t) exp( z β ), = 1,..., K. (5) Although n prncple one or more components of β can be allowed to vary across strata, n the present context t maes lttle sense to tal about adjustment unless t s presumed that the observed survval dfferences among the K groups are attrbutable to mbalances n covarates, not to dfferences n covarate effects. Gven estmates of the λ 0 and β, a standard estmate of the survval functon for a member of group, wth arbtrary covarate vector z, s gven by Sˆ ( t z) = exp{ Λˆ ( t) exp( z ˆ)}, = 1,..., K (6) 0 β ˆ 0 where Λ ( t) s any standard estmator of the cumulatve baselne hazard functon for group n the context of a stratfed proportonal hazards model (Kalbflesch and Prentce 1980). Now defne a reference group of n A ndvduals wth a specfed set of covarates that wll consttute a common pont of adjustment; the set of labels for the ndvduals n ths group s denoted M A. In general we expect that M A would n fact be the same as one of the exstng groups M, and mostly lely the reference group used n Cox regresson analyss, but ths s not essental and M A could nstead represent some other defned populaton. The adjusted survval functon estmate for the th group s smply the average of the estmated survval functons that would be obtaned by applyng (6) to each of the covarate vectors of the ndvduals n M A = ( t) na 1 M A S Sˆ ( t z ), = 1,..., K. (7) Ths approach to adjustment s somewhat smlar to adjustment procedures descrbed by Mauch (1982) and Chang et al. (1982); however, ther methods used an unstratfed proportonal hazards model ncorporatng the group varable as a covarate. Thus, le the standard approach descrbed n Secton 3, the adjusted curves are constraned to have the 7

8 same shape (whch matches none of the unadjusted curves) and have a constant relatonshp determned by the ftted model. Gal and Byar (1986) consdered use of the stratfed proportonal hazards model for what they called drect adjustment of survval curves, due to the smlarty to the concept of drect standardzaton n epdemology. The use of the stratfed proportonal hazards model frees the adjustment process of an unnecessary proportonal hazards assumpton for the groups of nterest. The shape and jump ponts of the adjusted survval curves wll match those of the correspondng unadjusted Kaplan- Meer survval curves, and are free to cross. Zhang et al. (2007) also dscuss the stratfed approach. In fact, f M A = U M, = 1,..., K (.e., the adjustment set comprses the entre dataset) then (7) s equvalent to ther estmator (3). We apply ths approach to the data assocated wth the above example, wth the resultng curves shown n Fgure 4, wth M A correspondng to the group recevng myeloablatve condtonng. The adjusted curves now yeld the hypothetcal survval curves that would result f the patent characterstcs of both groups had been that of the group recevng myeloablatve condtonng. The adjusted curve for the latter group, as should be expected, s very close to the orgnal curve. In fact, the vsble separaton observed here s larger than that typcally seen when a group s adjusted to tself. The method s easly mplemented n SAS and we provde the requste code n the Appendx. A SAS macro that computes both estmates and standard errors when M A comprses the entre dataset can be found n Zhang et al. (2007). 5. Adjusted Cumulatve Incdence Estmates In the transplant settng, t s also common to mae comparsons of cause-specfc hazards (for example, relapse and non-relapse mortalty) and to graphcally llustrate dfferences among groups wth the use of cumulatve ncdence curves. The same ssues of adjustment arse when groups are mbalanced wth respect to factors whch may nfluence the causespecfc hazards of nterest, as would be true for the stuaton n Table 1. Suppose that j ndexes the J types of events, let t denote the event or censorng tmes for each ndvdual, and let δ = j ndcate that the event that occurred at t was of type j, wth δ = 0 ndcatng that t s a censorng tme. Then, the estmated cumulatve ncdence functon for the j th type of event n the th group may be wrtten as 8

9 j j j I ˆ 0 ( t) Sˆ ( t ) [1 Sˆ ( t ) / Sˆ ( t )], = 1,... K, j = 1,..., J (8) = M : t t, δ = j (Kalbflesch and Prentce 1980) where the Sˆ 0 ( t) are the Kaplan-Meer estmates of eventfree overall survval wthn the th group, and the S ˆ j ( t), j = 1,..., J are the Kaplan-Meer estmates of cause-specfc survval,.e., the estmates obtaned by censorng for other event types except j. In general the latter are not nterpretable, and are used here only as a devce for computng the adjusted curves. The expresson n bracets n (8) s an emprcal estmate wthn group of the condtonal probablty of a falure of type j at t, more commonly wrtten as an expresson le d j (t )/n(t ) (that s, the number of events of type j at t dvded by the number of subjects stll at rs at t ); however, we have re-expressed ths quantty by the equvalent representaton usng the cause-specfc survvor functons. The adjusted estmator of the cumulatve ncdence functon follows mmedately by substtutng the comparable adjusted estmator (7) for each of the Sˆ j ( t) n (8), yeldng I j ( t) = M : t t, δ = j S 0 ( t ) [1 S j ( t ) / S j ( t )], = 1,... K, j = 1,..., J (9) For example, 0 ( t) s the adjusted verson of event-free overall survval, computed usng S (7). We assume that each of the adjusted components of (9) s adjusted for the same set of covarates, although of course the covarates may have dfferent assocatons wth each of the cause-specfc hazards and wth event-free survval. The choce of the covarates to adjust for wll depend on the partcular cumulatve ncdence estmates that are of nterest. An alternatve formulaton of (9), more n the sprt of (7), would frst calculate ndvdual estmates of cumulatve ncdence assocated wth each covarate vector z n M A and then average these estmates, as defned by j I I ( t z ) j = A ( t) n 1 j where I ( t z ) l M : t t, δ = Sˆ = l l j M A 0 ( t l z ) [1 Sˆ j ( t l z ) / Sˆ j ( t l z )] (10) and the Sˆ j ( t z) are derved from stratfed overall and cause-specfc proportonal hazards models, as n (6). The adjusted estmators (9) and (10) are generally very close, but the computatonal algorthm for (9) s more straghtforward and the one whch we recommend. 9

10 Although we fnd the procedures gve sensble results, nether strctly satsfes the relaton 0 J j 1 S ( t) = = I ( t), whch would be true of the unadjusted estmates (8). In most cases, j 1 however, the dfference s neglgble except possbly n the far rght tal of the curves. Fgure 5 llustrates the same data as used above, except that now we show curves for the cumulatve ncdence of non-relapse mortalty, whch accounts for 62 of the 114 total deaths. The adjustment factors are the same as for overall mortalty, and agan M A represents the group recevng myeloablatve condtonng. The adjusted curve for the myeloablatve group closely tracs the unadjusted curve, as should be expected. Although the unadjusted curves are consstent wth a lower rate of non-relapse mortalty for the nonmyeloablatve group [HR=0.65, 95% CI , p=0.10], the cumulatve ncdence adjusted to the covarate characterstcs of the myeloablatve group s notably lower than the unadjusted curve and better reflects the adjusted analyss [HR=0.28, 95% CI , p=0.0003]. 6. Dscusson We have descrbed several methods to obtan adjusted curves that summarze the probablty of falure for tme-to-event endponts that commonly occur n HCT. Other than the frst of these methods (based drectly on the Cox proportonal hazards model), each has the desrable feature that the adjusted curves change only wth falures wthn the relevant group, and the adjusted curves also mantan the shape that s seen n the approprate unadjusted curve. Regardless of the method used, t should be emphaszed repeatedly that the adjusted curve s not real, s dependent on model assumptons, and s not n any way a surrogate for a properly desgned prospectve comparson. We recommend that the unadjusted estmates always be shown for comparson, ether n the same or a separate fgure. We argue, however, that the adjusted curves do mae sense and vsually provde a better reflecton of the estmated dfferences among groups compared to use of the unadjusted curves. There are lely other reasonable methods that would yeld results that ntutvely mae sense as well. The methods n Secton 3 provde smlar results, at least for the example consdered. The method n Secton 4 maes fewer model assumptons, and s not dependent on the choce of a tme pont to anchor the adjustment. We also show how t can be extended to provde adjusted estmates of cumulatve ncdence curves. Because of the general relatonshp 10

11 between cumulatve ncdence and cause-specfc survval functons seen n (8), the methods n Secton 3 could also be adapted to provde adjusted cumulatve ncdence estmates. We have not evaluated the propertes of such a procedure, however. Whle the model-based estmates dffer a bt from the partally model-free estmates (and from each other), t s dffcult to say that one s correct and another ncorrect snce, as emphaszed above, the adjusted estmates are not real. For the partcular example consdered, however, all methods resulted n adjusted curves that seem reasonable representatons of the group dfferences as measured by the regresson model. In our experence, ths has held true for other data sets as well, although n certan stuatons the estmates can dffer by a far amount n the tals, whch s not unexpected. Gven that the partally model-free approach requres the fewest assumptons, we prefer ts use over the π other methods. The model-based approach that s derved from S 2 ( t) = [ Sˆ 2 ( t)] s very easy to mplement, however, and would appear to be a reasonable approach as well. Acnowledgements Ths wor was supported n part by grants from the Natonal Insttutes of Health, CA and CA We wsh to than our clncal colleagues at the Fred Hutchnson Cancer Research Center and the Unversty of Iowa for motvatng our nterest n ths problem and provdng the opportunty to evaluate the wor n a real world settng. 11

12 erences Breslow NE (1974): Covarance analyss of censored survval data. Bometrcs 30, pp Chang IM, Gelman R, and Pagano M (1982): Corrected group prognostc curves and summary statstcs. J. Chron. Ds. 35, Gal MH and Byar DP ((1986): Varance calculatons for drect adjusted survval curves, wth applcatons to testng for no treatement effect. Bometrcal J. 28, Kalbflesch JD and Prentce RL (1980): The statstcal analyss of falure tme data. John Wley, New Yor. Mauch RW (1982): Adjusted survval curve estmaton usng covarates. J Chron Ds 35, Sorror ML, Storer BE, Maloney DG, Sandmaer BM, Martn PJ, and Storb R (2008): Outcomes after allogenec hematopoetc cell transplantaton wth nonmyeloablatve or myeloablatve condtonng regmens for treatment of lymphoma and chronc lymphocytc leuema. Blood 111, Zhang X, Loberza FR, Klen JP, and Zhang MJ (2007): A SAS macro for estmaton of drect adjusted survval curves based on a stratfed Cox regresson model. Comput. Meth. Prog. Bomed. 88,

13 Appendx SAS code for calculatng adjusted Kaplan-Meer estmate accordng to (7). * generc data setup; data a; * grp stratfcaton varable (eg 1=reference, 2=current); * daysur survval tme; * delsur falure ndcator; * z1-z5 covarates to adjust for; * defne reference covarate set as group 1; data ref; set a; f grp eq 1; * ft stratfed Cox model, wth covarate adjustment; * estsurv s estmated survval for each member of reference set; proc phreg noprnt data=a; strata grp; model daysur*delsur(0)=z1 z2 z3 z4 z5; baselne out=b covarates=ref survval=estsurv/method=emp nomean; * average across the ndvduals n reference set at each tme; * adjm s the adjusted Kaplan-Meer estmate; proc sort data=b; by grp daysur; proc unvarate noprnt data=b; by grp daysur; var estsurv; output out=c mean=adjm; 13

14 Fg 1 Kaplan-Meer estmates of overall survval from aretrospectve study n HCT. The gray curve represents the probablty of survval for patents who receved a nonmyeloablatve condtonng regmen, and the blac curve represents the same for patents who receved a myeloablatve regmen. Tc mars represent censored observatons. Fg 2 Kaplan-Meer estmates and adjusted estmates of overall survval from a retrospectve study n HCT. Sold curves represent the unadjusted (Kaplan-Meer) survval estmates for the two groups, dashed lnes represent the adjusted estmates as determned from the approprate Cox regresson model. Tc mars on the Kaplan-Meer curves represent censored observatons. Fg 3 Kaplan-Meer estmates and adjusted estmates of overall survval from a retrospectve study n HCT. Sold curves represent the unadjusted (Kaplan-Meer) estmates for the two groups, dashed lnes represent the adjusted estmates from two dfferent methods for the nonmyeloablatve group. The frst dashed curve s obtaned by proportonately changng the falure probablty at each tme; the second dashed curve s obtaned by exponentatng the unadjusted curve to the approprate power as detaled n Secton 3. Tc mars on the Kaplan-Meer curves represent censored observatons. Fg 4 Kaplan-Meer estmates and adjusted estmates of overall survval from a retrospectve study n HCT. Sold curves represent the unadjusted (Kaplan-Meer) survval estmates for the two groups; dashed lnes represent the adjusted estmates obtaned from the partally model-free approach detaled n Secton 4. Fg 5 Cumulatve ncdence estmates and adjusted estmates of non-relapse mortalty from a retrospectve study n HCT. Sold curves represent the unadjusted (cumulatve ncdence) non-relapse mortalty estmates for the two groups, dashed lnes represent the adjusted estmates obtaned from the partally model-free approach detaled n Secton 5. 14

15 Fgure 1 15

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17 Fgure 3 17

18 Fgure 4 18

19 Fgure 5 19

20 Table 1. Dstrbuton of potental rs factors and ther unvarate assocaton wth overall mortalty and non-relapse mortalty from a Cox regresson model. Ablatve (n=68) Non- Ablatve (n=152) Overall mortalty (114 events) Non-relapse mortalty (62 events) % % HR (95% CI) HR (95% CI) Dagnoss NHL CLL HL ( ) 0.88 ( ) 0.62 ( ) 0.69 ( ) HCT-CI 0 1, ( ) 2.30 ( ) 2.05 ( ) 2.99 ( ) Donor Sblng Other ( ) 1.07 ( ) Source PBSC BM ( ) 0.72 ( ) Age < ( ) 1.45 ( ) Pror regmens 0-2 3, ( ) 0.74 ( ) 1.44 ( ) 0.52 ( ) Resstant Dsease No Yes ( ) 1.39 ( ) Abbrevatons: NHL, non-hodgn lymphoma; CLL, chronc lymphocytc leuema; HL, Hodgn lymphoma; HCT-CI, hematopoetc cell transplant comorbdty ndex; BM, bone marrow; PBSC, perpheral blood stem cells. 20