SMALL AREA CLUSTERING OF CASES OF PNEUMOCOCCAL BACTEREMIA.

Transcription

1 SMALL AREA CLUSTERING OF CASES OF PNEUMOCOCCAL BACTEREMIA. JP Metlay, MD, PhD T Smth, PhD N Kozum, PhD C Branas, PhD E Lautenbach, MD NO Fshman, MD PH Edelsten, MD Center for Health Equty Research and Promoton, VA Medcal Center, Departments of Medcne, Bostatstcs and Epdemology, Engneerng, and Pathology and Laboratory Medcne, Unversty of Pennsylvana, Phladelpha, PA ABSTRACT Background. Whle recent studes have dentfed the exstence of neghborhood-level factors that nfluence the carrage of S. pneumonae, no studes have extended ths observaton to determne whether substantal small area varaton exsts n the rsk of pneumococcal dsease. Methods. Data from populaton based survellance for bacteremc pneumococcal pneumona n the fve-county regon surroundng Phladelpha was analyzed for the exstence of geographc clusterng of cases of pneumococcal bacterema. Detecton of case clusters was accomplshed usng a spatal analytc method and confrmed wth a second, dstnct method.. Results. Over the perod , there were 608 cases of pneumococcal bacterema, of whch 538 cases were geocoded. Case cluster analyss usng both analytc methods demonstrated the exstence of geographcally dstnct clusters wthn the regon. The dentfcaton of clusters of pneumococcal dsease was not explaned by the racal or age dstrbuton of the underlyng populaton. Conclusons. Cases of pneumococcal bacterema demonstrate geographc clusterng not accounted for by the underlyng densty and race-age dstrbuton of the populaton. The dentfcaton of neghborhood-level factors underlyng ths clusterng may have mportant mplcatons for efforts to control pneumococcal dsease and other respratory pathogens. Key Words: pneumococcal nfectons, small-area analyss, geographc nformaton systems

2 INTRODUCTION Streptococcus pneumonae s a major cause of morbdty and mortalty, responsble for a spectrum of dseases rangng from otts meda to menngts. One of the more severe forms of pneumococcal nfecton s pneumococcal bacterema, whch contnues to have a hgh mortalty rate n adults despte the development of multple effectve antmcrobals. Thus, targetng of preventon strateges, partcularly for hgh rsk populatons, remans a major publc health approach to reducng pneumococcal morbdty and mortalty. Pror research has emphaszed that ndvdual level factors strongly nfluence the rsk of pneumococcal dsease, ncludng extremes of age, socoeconomc status, mmunosuppresson, and chronc heart and lung dseases.(1-6) However, an mportant parallel lne of research has begun to uncover communtylevel factors that may nfluence the rsk of transmsson of pneumococcal bactera, potentally sheddng lght on mportant preventon strateges.(7) It s well known that nvasve pneumococcal dsease rsk vares wdely on a global scale.(8) To some extent, large-area geographc varaton lkely reflects clmatc ssues that are also observed n analyzng season trends n pneumococcal dsease, leadng to ncreased nfecton durng perods of ncreased transmsson of respratory vruses that facltate pneumococcal nfecton.(9) However, whether pneumococcal dsease rsk vares over small geographc areas s less well known. The dentfcaton of such small area varaton n dsease rsk could ultmately shed lght on other envronmental factors, such as housng condtons and socal nteractons that nfluence pneumococcal dsease rsk and could reveal preventon strateges for the future. Most studes of small area varaton n pneumococcal dsease rsk have utlzed exstng geographc boundares to calculate dsease rsk per unt area or analyze communty-level rsk factors.(1, 7, 10) However, these boundares may have very lttle relatonshp to the socal and envronmental structures that nfluence pneumococal dsease transmsson. In contrast, the present methods of hot spot analyss allow small area varaton n dsease rsk to be studed wthout utlzng any assumptons about exstng geographc boundares. Such approaches may thus provde substantally greater nsght nto the exstence of small area varatons n dsease rsk that can shed lght on communty-level factors promotng or mpedng pneumococcal dsease transmsson. Moreover, such approaches permt adjustment for types of populaton heterogenety that may underle some of the observed small area varaton n dsease rsk. The ams of ths study were: 1) to examne the geographc dstrbuton of nvasve pneumococcal dsease n a fve county regon of Pennsylvana to determne whether geographc clusters of dsease exst and 2) to analyze the extent to whch such case clusterng can be explaned by characterstcs of the underlyng populaton. MATERIALS AND METHODS Study populaton Ths study was conducted wthn the fve-county regon surroundng Phladelpha, PA: Bucks, Chester, Delaware, Montgomery, and Phladelpha countes. The adult populaton (age 18 years) of ths regon s 2,881,132 (US Census 2000). At the start of the survellance perod, there were 46 acute care hosptals servng ths regon. Of these, 43 hosptals partcpated n ths study. Two of the remanng three hosptals were small hosptals outsde Phladelpha county that 2

3 were closed to external studes and one was a larger academc hosptal that was unable to partcpate (but was projected to account for < 2 percent of all cases n the regon). Subjects For populaton survellance, the case defnton was restrcted to adults 18 years wth at least one blood culture drawn wthn 48 hours of hosptal admsson wth growth of S. pneumonae; resdence n one of the fve countes; and confrmaton n our laboratory that the bacteral solate was S. pneumonae (see below). Cases were further restrcted based on physcan reports to those cases wth radographc evdence of an acute respratory nfecton. These restrcton crtera reflected the ams of the parent study to explore rsk factors and outcomes for adults wth bacteremc pneumococcal pneumona. Excluson crtera for the case-control study ncluded evdence of bacteral menngts (CSF growth of S. pneumonae or CSF fndngs compatble wth bacteral menngts) or hosptalzaton wthn 10 days precedng the ndex hosptalzaton. Cases were dentfed by mcrobology laboratory personnel at each partcpatng hosptal. Valdaton of ths survellance system was establshed by comparng the number of cases dentfed by the research team to the total number of pneumococcal bacterema cases reported to the Phladelpha Health Department under a mandatory reportng system n The study survellance system dentfed 97% of the cases reported to the Phladelpha Health Department (all of the non-dentfed cases came from one of the non-partcpatng hosptals). Whenever laboratory personnel dentfed a blood culture wth growth of S. pneumonae, research staff contacted the physcan of record to determne subject elgblty. Elgble subjects (or proxes n cases of mental ncompetence or death) were then approached for study enrollment at a tme determned by the treatng physcan (typcally after hosptal dscharge). Subjects were maled nformatonal study materals and then contacted by phone to provde consent for study partcpaton and complete a telephone ntervew. Ths study was approved by the nsttutonal revew board at the Unversty of Pennsylvana and each of the partcpatng hosptals. Mcrobologcal data collecton Pneumococcal blood solates were transported to a central laboratory at the Hosptal of the Unversty of Pennsylvana for analyss. Isolates were re-dentfed to confrm that they were pneumococc on the bass of colony morphology and hemolytc actvty, Gram stan appearance, catalase reacton, ble solublty, and optochn susceptblty. (11) Spatal cluster analyses The resdental addresses of all subjects n the study were geocoded (that s, assgned geographcal coordnates) usng ArcVew 9.0 (ESRI) software and the StreetMaps USA reference database. Two dstnct methods of spatal cluster analyss were employed. Frst the exstence of resdental address data allowed ndvdual case locatons to be analyzed as a pont pattern. Here a varant of the pont cluster analyss of Rushton and Lolons (1996) was employed,(12) n whch a grd of reference ponts was constructed over the regon at about one half mle on center. To test for clusterng at varous scales, a range of rad, d, were selected, and approxmate crcular regons, R, about each grd pont,, were constructed by ncludng all cty blocks wthn centrod dstance d of pont. Ths allowed exact block-level census data to be used for 3

4 the analyss. The smplest null hypothess consdered for testng purposes was that each resdent n the total regon, R, s equally lkely to be a case (refnements of ths hypothess are consdered n the next secton). If the total populatons n R and R are denoted by n and n, respectvely, then under ths hypothess, the probablty that a randomly sampled case occurs n R s smply, p = n/ n. Hence f the total case counts n R and R are denoted by c and c, respectvely, and f ndvdual cases are assumed to be statstcally ndependent events, then the probablty of observng c cases n R gven c cases n R s gven by the Bnomal probablty (1) c! c Pc ( c) = p (1 p) c!( c c)! c c The approprate p-value, P, for a (one sded) test of clusterng at s thus smply the probablty of observng as many cases as c under ths null hypothess,.e., c (2) P = P( k c) k= c Ths procedure was programmed n Matlab, and grds of p-values were computed for a range of selected rad. Results presented here are lmted to the use of a radus of one half mle, whch produced the most vsually coherent group of clusters. A pror, we defned a meanngful cluster of cases as one whch ncluded at least 5 cases wthn the half mle radus snce smaller values generated substantally larger numbers of clusters due to the overall rarty of nvasve pneumococcal nfecton. One shortcomng of the above procedure s that the dentfcaton of cluster sze s somewhat ad hoc n that t s based largely on a vsual nspecton of the plotted results for selected rad. However there s a second well known method of regonal cluster analyss due to Besag and Newell (1991) that seeks to determne a sngle most sgnfcant clusterng of regons.(13) As a senstvty analyss to examne the robustness of our fndngs, we chose to construct a verson of Besag-Newell at the census tract level. The basc dea s to start wth a gven census tract and to test for sgnfcant clusterng n ths tract n the same manner as above, where the relevant regon s now tract, denoted by R 0. But rather than stoppng here, one can then grow a larger regon by adjonng to tract the adjacent tract j 1 closest to n centrod dstance. For ths larger regon, say R 1 wth total populaton, n 1 = n + nj, and case 1 count, c 1 = c + cj, one may agan test for clusterng by settng p / 1 1 = n 1 n, and replacng p and c n (1) above wth p 1 and c 1, respectvely. If the resultng p-value n (2) s denoted by P 1, then by successvely adjonng closest tracts to the exstng cluster, one can produce a set of p- values, { Pj : j = 0,1,.., J}, for a sequence of successvely larger clusters, j = 0,1,.., J, where P 0 s the orgnal p-value for tract alone. The most sgnfcant -cluster s then taken to be the cluster R Rj wth the lowest p-value, P Pj = mn{ Pk : k = 1,.., J}. Hence the most sgnfcant cluster n R s then taken to be the smallest of these, namely the mnmum p-value cluster for that tract * wth 4

5 (3) P* = mn P Adjustment for populaton heterogenety Because pneumococcal dsease rsk s known to vary wth specfc ndvdual level characterstcs, t was necessary to account for heterogenety n the dstrbuton of these characterstcs n order to elmnate these factors as explanatons for any observed small area varaton n dsease rsk. To account for populaton heterogenety wth respect to rsk of bacteremc pneumococcal pneumona, t s necessary to refne the smple null hypothess of homogeneous rsk used above. Here the expected case rates for varous populaton subgroups at the cty-block level (as subgroups of ether the one half mle rad appled for the pont cluster analyss or census tracts used for the Besag-Newell approach) were estmated usng absolute annual ncdence rates of nvasve pneumococcal dsease for populaton subgroups n 2002 provded by the Centers for Dsease Control through ther Actve Bacteral Core Survellance system.(14) Whle these absolute rates apply to all nvasve pneumococcal dsease (ncludng non-pneumona assocated cases), the underlyng assumpton was that the relatve rates would be the same for populaton subgroups when restrcted to cases of bacteremc pneumococcal pneumona. The underlyng sze of the subgroup populatons wthn each cty-block were estmated usng 2000 Census data. In partcular, f the populaton, n b, of block b s parttoned nto relevant subpopulatons, ( nbk : k = 1,.., K) wth nb = Σknbk, and f the reported annual ncdence rate for nvasve pneumococcal dsease n subpopulaton k s denoted by r k, then the total number of cases expected n block b s gven by K (4) eb = rn k= 1 k bk Hence the correspondng rsk-adjusted null hypothess s smply that the probablty, p, of observng a randomly sampled case n regon R s now proportonal to the number of cases, e = e, expected n that regon,.e., Σb R b (5) p e = = er e b b R ( e b ) j j b R Ths refnement nto subpopulatons was carred out n two stages. Frst the populaton was parttoned by race, usng only whte and black (snce only fve cases dd not self-dentfy nto one of these two groups). The pont cluster analyss n (1) and (2) was then carred out usng (4) and (5) for these 2 subpopulatons. Next, ths classfcaton was further stratfed by age, usng fve age groups as reported n the CDC data on populaton rates of dsease (18-34, 35-49, 50-64, 65-79, 80 years).(14) The above analyss was then repeated for ths partton nto 10 subpopulatons. Of note, ths approach s lmted to explorng those ndvdual level characterstcs that are avalable both n terms of known expected populaton rates of dsease and n terms of dstrbuton n the populaton. Moreover, smultaneous analyss of multple ndvdual level factors requres knowledge of jont dsease rsks. In effect, these constrants resulted n our focusng only on adjustng for ndvdual effects of age, race and age/race n the cluster analyses. 5

6 For all pont analyses, the fgures dsplay the calculated p-value grds and do not reflect the actual pont locatons of any observed cases. In partcular, each dot on the map s a grd pont that s wthn half a mle of at least fve cases, and for whch ths cluster of cases s sgnfcant n the p-value range shown. For the Besag-Newall calculaton, the fgure reflects the census aggregatons of consecutvely larger p values. RESULTS Case dentfcaton Over the perod Aprl 1, 2002 through March 31, 2004, we dentfed a total of 608 adult cases of bacteremc pneumococcal pneumona n the 5 county regon surroundng Phladelpha (Bucks, Chester, Delaware, Montgomery and Phladelpha countes). The overall adult populaton annual rsk of dsease was 10.6 per 100,000. Of 608 total subjects, 545 had some geographcal nformaton about ther resdence (geocodng canddates). Out of the 545 canddates, 4 canddates provded only cty or county nformaton (one subject n each of Bucks, Chester, Montgomery, and Phladelpha countes). These 4 cases were subsequently removed from the analyss. Among the remanng 541 wth complete address nformaton, 3 addresses (two n Phladelpha county and one n Bucks county) could not be geocoded due to non-exstent nformaton and were also removed from the analyss. The fnal dataset, therefore, conssted of 538 total subjects of whch, by county, 63 were from Bucks, 42 from Chester, 78 from Delaware, 105 from Montgomery and 250 from Phladelpha Countes. Cluster analyss under homogeneous populaton rsk Fgure 1 dsplays the ntal cluster analyss applyng a half-mle radus as the bandwdth. Of note, multple approaches varyng the bandwdth faled to detect any sgnfcant clusters outsde of Phladelpha County. Therefore, all subsequent analyses focused on Phladelpha County alone. The overall hot spot analyss dentfed several regons wth sgnfcant geographc clusters over the two year observaton perod. In order to confrm the exstence of multple clusters, we analyzed the same data usng a second hot spot detecton technque, specfcally the Besag Newell method, sequentally removng clusters from the analyss as they were dentfed. In ths method, the four most sgnfcant clusters are dentfed (Fgure 4) n locatons that concde wth four clusters dentfed n the frst method (Fgure 1), confrmng the exstence of multple dscrete hot spots. Cluster analyss under heterogeneous populaton rsk The analyses above all examned the underlyng adult populaton dstrbuton under the assumpton of homogeneous rsk. Of note, the patents located n the observed geographc clusters were almost all self-dentfed as black. Thus, t was natural to ask whether ths cluster could be accounted for by the underlyng race dstrbuton n the regon. To answer ths queston, the above pont cluster analyss was repeated generatng expected case dstrbutons based on block-level counts of blacks and whtes separately. The results n Fgure 2 show that whle all clusters are somewhat less sgnfcant than before, the most sgnfcant clusters n Fgure 1 reman. Ths s partly due to the fact that whle these clusters are mostly black, there are other communtes n the regon wth dense black populatons but wth relatve few cases. Ths 6

7 analyss was repeated usng the Besag-Newell procedure at the tract level, and produced essentally the same results (not shown) as the pont-cluster analyss. Next, the degree of underlyng populaton heterogenety was further refned by ncludng age/race categores (wth fve age categores and two race categores yeldng a total of 10 subgroups) (Fgure 3). Here the sgnfcance levels agan seem to be reduced to some degree; but the most sgnfcant clusters n Fgures 1 and 2 reman. Agan, a Besag-Newell analyss for ths case produced essentally the same results (not shown) and added further confrmaton to these fndngs. DISCUSSION Our analyses demonstrate that the ncdence of nvasve pneumococcal dsease exhbts sgnfcant geographc heterogenety over small areas. Ths geographc heterogenety s not fully explaned by selected ndvdual level demographc factors that are known to modfy the rsk of pneumococcal nfecton. In addton, the specfc locaton of dsease clusters was confrmed by a second analytc approach. Pror studes on pneumococcal dsease have emphaszed ndvdual level heterogenety n dsease rsk. On a more global scale, t s well establshed that certan populatons experence above average dsease rsk.(8) However, t s not clear whether such elevated rsk reflects endogenous characterstcs of nhabtants of these regons or exogeneous envronmental factors that medate dsease rsk. It s well establshed that pneumococcal dsease dsplays seasonal and clmatc varaton,(9) whch may be an mportant consderaton n nterpretng global and natonal patterns of pneumococcal dsease. However, small area varatons n dsease rsk are unlkely to reflect varaton n clmatc factors. More lkely, f these results are confrmed, the exstence of pneumococcal dsease clusters suggests that small area varaton n communty characterstcs nfluence the spread of pneumococcal bactera among hosts n an area. Such relevant factors could nclude the structure of housng and shared lvng spaces and, especally, the relatonshp of day care centers and schools wthn a communty. Pror research confrms that as the proporton of chldren n a communty attendng day care ncreases, the probablty of pneumococcal carrage ncreases among both attendees and non-attendees of the day care centers.(7) Our results expand on ths observaton by ndcatng that rsk of nvasve dsease can vary across communtes n a small geographc regon. It s possble that as the densty of pneumococcal carrage ncreases wthn a small area, the ncdence of nvasve pneumococcal dsease ncreases proportonately. One lmtaton of ths study s that we were able to control for only a small number of potental endogenous characterstcs of patents that could nfluence the observed geographc dstrbuton of dsease. For the approaches adopted n ths study, we were lmted to explorng only those factors for whch expected populaton rates were known and for whch dstrbutons of the characterstcs were known n the source populaton. Thus, we could not explore the mpact of the dstrbuton of clncal factors (e.g., chronc heart and lung dsease) or socal factors (e.g., day care center utlzaton) on the observed small area heterogenety.. A second lmtaton s that we can not elmnate the possblty that the observed geographc heterogenety reflects heterogeneous dstrbuton of pneumococcal clones wth varable nvasve potental. Thus, the ntroducton of a partcularly vrulent clone n one communty may lead to a hgher observed case rate n that area due to the chance ntroducton of 7

8 that clone. Smlar outbreaks have been observed n more closed envronments. In ths regard, t s notable that only two percent of all patents n ths study were nursng home resdents at the tme of nfecton and only two patents were resdents n the same nursng home n Phladelpha, makng t unlkely that outbreaks n closed envronments explan our results(data not shown). Future work wll specfcally examne molecular heterogenety of solates to dstngush mechansms of clonal spread from other communty-level factors that nfluence dsease transmsson. In summary, we have observed sgnfcant geographc clusters for bacteremc pneumococcal pneumona wthn a sngle urban regon, a level of small area varaton n pneumococcal dsease rsk not prevously observed. Such clusters may provde mportant opportuntes for dentfyng communty-level factors that modfy dsease transmsson rsk such factors could ultmately be valuable for desgnng publc health nterventons n the face of emergng pathogens. Moreover, better understandng of the mult-level nature of pneumococcal dsease rsk may play an mportant role n targetng lmted resources to the hghest rsk populatons. REFERENCES 1. Chen FM, Breman RF, Farley M, Plkayts B, Deaver K, Cetron MS. Geocodng and lnkng data from populaton-based survellance and the US Census to evaluate the mpact of medan household ncome on the epdemology of nvasve Streptococcus pneumonae nfectons. Am J Epdemol 1998;148(12): Nuort JP, Butler JC, Farley MM, et al. Cgarette smokng and nvasve pneumococcal dsease. Actve Bacteral Core Survellance Team. N Engl J Med 2000;342(10): Flce GA, Darby CP, Fraser DW. Pneumococcal bacterema n Charleston County, South Carolna. Am J Epdemol 1980;112(6): Breman RF, Spka JS, Navarro VJ, Darden PM, Darby CP. Pneumococcal bacterema n Charleston County, South Carolna. A decade later. Arch Intern Med 1990;150(7): Lpsky BA, Boyko EJ, Inu TS, Koepsell TD. Rsk factors for acqurng pneumococcal nfectons. Arch Intern Med 1986;146(11): Talbot TR, Hartert TV, Mtchel E et al. Asthma as a rsk factor for nvasve pneumococcal dsease. N Engl J Med 2005;352(20): Huang SS, Fnkelsten JA, Lpstch M. Modelng communty- and ndvdual-level effects of chld-care center attendance on pneumococcal carrage. Cln Infect Ds 2005;40(9): Fedson DS, Scott JA. The burden of pneumococcal dsease among adults n developed and developng countres: what s and s not known. Vaccne 1999;17 Suppl 1:S Talbot TR, Poehlng KA, Hartert TV, et al. Seasonalty of nvasve pneumococcal dsease: temporal relaton to documented nfluenza and respratory syncytal vral crculaton. Am J Med 2005;118(3):

9 10. Huang SS, Fnkelsten JA, Rfas-Shman SL, Klenman K, Platt R. Communty-level predctors of pneumococcal carrage and resstance n young chldren. Am J Epdemol 2004;159(7): Koneman E, Allen S, Janda W, Schreckenberger P, Wnn Jr. W. Color atlas and textbook of dagnostc mcrobology. 5th ed. Phladelpha: Lppncott-Raven; Rushton G, Lolons P. Exploratory spatal analyss of brth defect rates n an urban populaton. Statstcs n Medcne 1996;15: Besag J, Newell J. The detecton of clusters n rare dseases. Journal of the Royal Statstcal Socety, Seres A. 1991;154: Flannery B, Schrag S, Bennett NM, et al. Impact of chldhood vaccnaton on racal dspartes n nvasve Streptococcus pneumonae nfectons. JAMA 2004;291(18):

10 P-Values Fgure 1. Pont locaton cluster analyss under an assumpton of homogeneous adult populaton rsk. The fgure depcts the Phladelpha county regon. A grd of 0.5 mle dmensons s overlad on the fgure and we calculate the p values assocated wth each cluster analyss at each grd ntersecton. The analyss s conducted for 0.5 mle rad, excludng clusters wth < 5 cases wthn the crcle. Of note, the locaton of the plotted p values does not represent actual case locatons. P-values > 0.1 are not plotted on the map. 10

11 P-Values Fgure 2. Pont locaton cluster analyss adjustng for the black and whte adult populaton dstrbuton n Phladelpha. The fgure depcts the Phladelpha county regon. A grd of 0.5 mle dmensons s overlad on the fgure and we calculate the p values assocated wth each cluster analyss at each grd ntersecton. The cluster analyss adjusts for the underlyng black and whte adult populaton dstrbuton from the Census data and apples absolute race specfc rates of dsease based on CDC natonal survellance data from The analyss s conducted for 0.5 mle rad, excludng clusters wth < 5 cases wthn the crcle. Of note, the locaton of the plotted p values does not represent actual case locatons. P values > 0.1 are not plotted on the map. 11

12 P-Values Fgure 3. Pont locaton cluster analyss adjustng for the underlyng age and racal dstrbuton of the populaton. The fgure depcts the Phladelpha county regon. A grd of 0.5 mle dmensons s overlad on the fgure and we calculate the p values assocated wth each cluster analyss at each grd ntersecton. The cluster analyss adjusts for the underlyng black and whte adult populaton dstrbuton n age strata avalable from the Census data and apples absolute age by race specfc rates of dsease based on CDC natonal survellance data from The analyss s conducted for 0.5 mle rad, excludng clusters wth < 5 cases wthn the crcle. Of note, the locaton of the plotted p values does not represent actual case locatons. P values > 0.1 are not plotted on the map. 12

13 Legend Pop_Cluster_1_ Pop_Cluster_2_ Pop_Cluster_3_ Pop_Cluster_4_ Fgure 4. Besag Newell cluster analyss under an assumpton of homogenous adult populaton rsk. The fgure depcts the Phladelpha county regon. Cluster analyss s conducted at the census tract level, examnng all possble combnatons of contguous census tracts to dentfy the clusters wth the lowest probablty of observaton under an assumpton of homogenous rsk n the populaton. As each cluster s dentfed, t s removed from subsequent analyses. In ths fgure, the four clusters wth the lowest probablty of observaton are depcted. The p values assocated wth each cluster are as follows: Populaton_Cluster_1 (p= ), Populaton_Cluster_2 (p= ), Populaton_Cluster_3 (p= ), Populaton_Cluster_4 (p=.00088). Note, the sequental removal procedure does not guarantee that each successve cluster has a larger p value than the precedng cluster hence, the p value for the thrd dentfed cluster s slghtly smaller than the p value for the second dentfed cluster. The analyss excludes clusters wth < 5 cases per combnaton of census tracts. 13