ESTIMATION PROCEDURES USED TO PRODUCE WEEKLY FLU STATISTICS FROM THE HEALTH INTERVIEW SURVEY James T. Massey, Gail S. Pe, Walt R. Simmns Natinal Center fr Health Statistics. INTRODUCTION In April 97, the United States Cngress apprpriated $35 millin fr a natinal immunizatin prgram against the A /New Jersey r "Swine Flu." The Center fr Disease Cntrl (CDC) was charged with the respnsibility f develping a cmprehensive immunizatin delivery system with the assessment f the cverage f the vaccinatin prgram, as well as the surveillance f flu cases. Missing frm CDC's surveillance systems was a system thrugh which natinal estimates culd be made frm a natinal prbability sample r a full census. Althugh CDC's basic systems culd prvide partial infrmatin fr the entire cuntry, they culd nt prvide sufficient data fr prductin f estimates that culd be assessed fr precisin. CDC therefre, requested the Natinal Center fr Health Statistics (NCHS) t cllect influenza activity data in the Health Interview Survey (HIS). In the Health Interview Survey a prbability sample f husehlds representing the civilian, nninstitutinalized U.S. ppulatin is interviewed each week. Interviewing is dne cntinuusly n a weekly sample f abut 800 husehlds. In respnse t CDC's need a supplemental set f questins n influenza influenza vaccinatins was added t the regular HIS interview questinnaire in the last week f September 97. In the regular HIS prcessing prcedures, the time between the data cllectin publicatin f the results is generally at least ne year. Because f the dem fr timely data n influenza cases vaccinatins the HIS implemented a rapid reprting system in which estimates f influenza -like illnesses; bed days due t such illnesses; all types f influenza, including swine flu, vaccinatins were published weekly three weeks after the week fr which the estimates were made nly ne week after the data were cllected. The HIS sample is designed s that tabulatins can be prvided fr each f fur majr gegraphic regins, fr large metrplitan areas, fr urban rural sectrs f the United States. The sample is als designed s that husehlds interviewed each week represent thse in the target ppulatin that the weekly samples are additive ver time. A rapid reprting system was used ne ther time in the histry f the HIS, that was during the 957-58 influenza epidemic. At that time, weekly reprts als were issued. The weekly reprts fr 977 were cntinued thrugh April, the estimates presented were prvisinal. Final estimates will be published after several mnths f extensive data prcessing in which medical cding is cmpleted many errr cnsistency checks are made n the data. The HIS weekly estimates were nt part f CDC's systems fr detecting early utbreaks f influenza. Because f the natinal scpe f the data, lcal utbreaks f influenza -like illness pssibly were undetected. Hwever, when used in cnjunctin with ther surces f infrmatin within the CDC surveillance system, the HIS data culd cnfirm r deny early inferences regarding the spread f this disease its effect.. STATISTICAL METHODS Several estimatin prcedures were cnsidered by NCHS fr estimating the weekly number f flu cases, the number f bed -days due t flu, the number f all types f flu shts swine flu shts. The tw mst prminent estimatrs are described belw alng with sme f their prperties. Since the HIS uses a tw -week reference perid t cllect data n the incidence f acute cnditins a tw -week reference perid was als chsen fr the influenza supplement. That is, during each week f interviewing a flu case is enumerated if its nset ccurred during the tw weeks preceding the interview week, a bed -day is enumerated if it ccurred during the tw weeks prir t the interview week, a flu sht is enumerated if it were received in the tw weeks prir t the interview week. Thus, fr each week i f interest the fllwing tw independent estimates can be made fr the number, saki X., f flu cases, bed -days, r flu shts. a: - the estimate fr the "last week" btained frm interview week (i+l), ß: - the estimate fr "week befre" btained frm interview week (i +). The first estimatr f Xi cnsidered was used during the 957-58 flu epidemic t estimate the incidence f acute upper respiratry cnditins is given by X7 = (a: + ßi) The estimatr, X, is unbiased, if ne assumes that the variance f X7 is cnstant frm week t week, then the variance f X7 is given by _ The secnd estimatr t be cnsidered is given by Xi + ai + + (Ui 578
where - + is the average weekly estimate btained frm interview week (i +l). The estimatr Xí is a weighted average f fur weekly estimates btained frm interview weeks (i +l) ( +). Since the estimatr cntains infrmatin frm the week n either side f the week f interest a smthing effect results. The expected value f Xí is given by E(Xi) = Xi + Xi - + Xi +l -Xi. The bias f X; is given by the secnd term n the right h side f the abve equatin. In mst situatins (especially if a linear trend is present) this bias will be small. The nly time when this bias might be mre than a few percentage pints is at the maxima r minima pints f a trend. Anther imprtant feature f the estimatr X:, hwever, is that it can be frmed using the tw -week average estimates Ui Uí +l desn't require the frmatin f tw separate weekly estimates fr each week f interviewing. Operatinally, this feature reduces the number f weekly tabulatins in half. Fr this reasn the estimatr Xí was selected fr making ur weekly estimates. The difference between incidence fr adjacent weeks is estimated by Xi - Xi- the variance f d: can be shwn t be 0, Il+r ai L Again, assuming that the variance f the weekly statistics remains cnstant frm week t week, the variance f X; can be expressed as equal t = a X.. The variance f can als be shwn t be, ( -r ), thus, r = Xi Xi, Xi Xi, Xi This crrelatin is intuitively bvius since where r is the crrelatin between the -, a. incidence f "last week" the "week befre" frm a single week's sample. Fr mst acute cnditins the crrelatin is assumed t be small, althugh the crrelatin will be higher fr very cntagius diseases. The assumptin f equal weekly variances shuld hld unless Xi changes cnsiderably frm week t week. It shuld als be nted that the weekly statistics Ui +l are independent since they are btained frm independent weekly samples. Cmparing the variances f X;' X;, < X7 fr rß,, a: <. -, Using the data n the number f flu cases fr the 975-7 flu seasn (the last quarter f 975 plus the first quarter f 97) the crrelatin cef- ficient, rß, was estimated t be apprxi- -, a, mately 0.75. Thus, fr flu cases the variance f Xi is apprximately 3 percent smaller than the variance f X. Based n a mean squared errr criteria there is little t chse between X: is used t frm ne half f bth the estimatrs Xí X' i The weekly estimates can be summed t frm aggregates such that fr N weeks XS Xí + X + + X. The variance f Xs, assuming equal weekly vari- ances, is given by...+ = N + = (N-) Xi + + The relative stard errr f X' can be written s as N N Fr NCHS's weekly publicatins VX, is further apprximated by VXi where is the relative stard errr f Xí 579
is defined as a. Estimating Sampling Variance There are several alternative methds fr apprximating the sampling variance f X; three such methds which are described belw were cmpared. If the weekly statistics are reasnably stable frm week t week with n apparent trend, then a simple estimate f can be made using any tw cnsecutive weekly estimates f X.. Fr a single week i, the estimated sampling variance is given by - - +) the relative stard errr is given by U: i - +. v + + By summing ver k weeks a mre stable estimate f can be btained such that where v X. = U kc- (k-) j= k U Uj. - U A secnd methd f apprximating a), uses least squares regressin t fit three cónsequtive values f lks at the deviatin abut the regressin line t estimate mre stable estimate is again btained by averaging a series f estimates. This methd is satisfactry fr linear trends but tends t ver estimate the sampling variance when there are changes in directin in the trend. The apprximatin is given by k - (k (Uj -Uj + s, s, Xi j = + ) Yet anther methd f estimating the variance f the weekly statistics is t cmpute a simple rm sample variance estimate inflate by a design factr. The design factr represents the increase r decrease in precisin due t deviatins frm a simple rm sample design such as A stratificatin clustering. Fr the HIS the design factr has been shwn t be arund tw. Using this assumptin estimates f variances were calculated fr the number f flu cases cmpared t the estimates btained using the secnd methd f apprximatin presented abve. The results are presented belw in terms f percent relative stard errr (PRSE) which is the stard errr f an estimate divided by the estimate itself multiplied by 00. Size f Estimate (In thuss) Methd 3 (Simple Rm Sample) Methd (Regressin) 500 9 000 8 500 5 3000 3 3 000 0 5000 0 9 000 9 8 The verall average values f the percent relative stard errrs fr the number f flu cases bed days shwn in NCHS's weekly flu publicatin were btained using data frm the 975 flu seasn (September t March) then reverified using the first weeks f the 97 flu seasn. The PRSE fr the weekly estimate f flu shts was nt available in 975 was apprximated using the 97 data. The first tw methds presented in this sectin were used t estimate the PRSE's the methds were fund t be quite cmparable The average weekly PRSE is abut fr flu cases 0 fr bed days flu shts.. Weighting Pst -Stratificatin Up t this pint it has been assumed that the average weekly estimates, Uí, have already been calculated. The first step in the weekly estimatin prcedure is t calculate Uí. This is dne by weighting the weekly sample data. Except fr minr adjustments due t nnrespnse subsampling the HIS sample is self - weighting (each sample persn has the same prbability f selectin in the natinal sample). Fr weekly estimatin each sample persn is assigned the same prbability f selectin. One final pst - stratificatin adjustment is required, hwever, t adjust each week's sample t the same natinal ppulatin. Since each week's sample is a rm sample, the distributin f sample persns will vary frm week t week by age race an adjustment t the ppulatin distributin will imprve the precisin f the weekly estimates. The ppulatin distributin is btained frm the Bureau f the Census adjustments are made each week fr ten age -race grups. If yjk = ttal number f sample persns in the jkth age -race cell reprted during interview week (i +l), zjk = ttal number f flu cases, bed days, r flu shts in the jkth age -race cell 580
reprted during interview week (i +l), = ppulatin cntrl (Census value) fr jkth age -race cell fr week i, then the average weekly estimate Uí btained frm interview week (i +l) is given by = z Yjkfyjk. jk The U:.are.-then. -used t calculate the their sampling errrs. 3. RESULTS ' Figure belw shws the weekly estimates f flu -like illness fr September 0, 97 thrugh April 7, 977 Figure cntains the estimates f bed days due t flu fr the same time perid. The curves are similar t nes fr the last several years. The relative smthness f the curves further indicates the stability f the estimatrs which were emplyed in the rapid reprting system. The table belw gives the actual weekly estimates fr the variables f interest.. CONCLUSION reprting system was a success. Reliable weekly estimates were published nly ne week after the data were cllected nly three weeks after the reference week. It wuld have been impssible t implement such a system after the detectin f an epidemic because f the rapidity with which such a virus spreads thrughut the entire cuntry. The influenza supplement will prvide health data analysts. -. planners with_ext.ensive infrmat.in :n.the crrelates f influenza. Amng the :.many that may be are the relatin- 'ships amng ther health demgraphic characteristics (btained in the main interview) influenza, as well as the effect f influenza symptms n limitatin f usual activity (such as wrk lss). Additinally, the characteristics f persns wh btained flu vaccinatins as ppsed t thse wh did nt the timing f the vaccinatin in relatin t the cntractin f an upper respiratry illness may be studied. REFERENCES Pe, Gail S. Massey, James T., "Estimating Influenza Cases Vaccinatins by Means f Weekly Rapid Reprting System," Public Health Reprts, 9 N. (977), 99-30. Althugh there was, frtunately, n epidemic f Swine Flu this year we felt that the HIS rapid 0 Figure. Weekly Estimates f Flu -Like Illnesses in the United States 8 975-7 97-77 I I I I II I July Aug. 'Sept. Oct. Nv. Dec. Jan. Feb. Mar. Apr. 58
Figure. Weekly Estimates f Average Number f Persns in Bed Each Day Because f Flu -Like Illness in the United States 5 975-7 97-77 5 3 3 July Aug. Sept. Oct. Nv. Dec. Jan. Feb. Mar. Apr. Weekly Estimates f Flu -Like Illnesses, Average Number f Persns in Bed Each Day, Flu Shts: United States, 97-77 Week Flu -like illness Average number f persns in bed each day because f flu -like illness All types f flu shts Each week Cumulative since September 0 Each week Swine flu shts Cumulative since September 0 Numbe in thuss September 0-, 97,70 9 38 38 September 7- Octber 3, 97,90 39,30,788 Octber - 0,97,5 57,8 3,,00,8 Octber -7, 97,57 59 3,9,80,378,0 Octber 8 -, 97,39 89,737,57,0 8,00 Octber 53, 97,0 3 5,,9,3,9 Nvember - 7,97,880 0 5,580,9 5,09 7,73 Nvember 8-,97,39 5,79 8,998,39,0 Nvember 5., 97,93 70 5,379 3,377 5,5 9,58 Nvember.8, 97,77 700,0 38,78 3,9 33,79 Nvember 9- December 5, 97,7 573,8,0 3,97 37,5 December -, 97,857 789, 5,,3 39,5 December 3-9, 97,83 753,35,57,03 0,575 December 0-, 97,07 3 December 7,97 - January,977,03 3 January 3-9, 977, 5 January 0-,977,57 January 73, 977,7 5 January -30, 977,938 95 January 3- February, 977 3,,05 February 7.3, 977 3,7,38.February 0, 977,50,597 February.7, 977..._,333,57 February 8-March, 3,90,99 March 7-3, 977,308 99 March.0, 977,90 778 March -7, 977,55 88 March 8 -April 3, 977,3 89 April.0, 977, 77 April -7, 977,38 5 *Figure des nt meet stards f precisin. NOTE: Even thugh the suspensin f the Public Health Service immunizatin prgram was lifted n February 7, 977, estimates f flu shts are nt shwn after the week ending December 9, 97. 58