slcompose zif-inf zif-inf zif00208 zif6523-08a$sl
<XXzif002086523XX>
<zdoi;10.1097/INF.0b013e318159833e>
<zkeybdr;disk;pj>
<zjs;Original Studies>
<zjss;Original Studies>
<iflww><artno;INF200912>
<zpit;FLA>
<zmlcopy;28;2;February;2008;000>
<px;;1>Papillomatosis<pa>
<px;;2>Hawkes et al<pa>
<<sh>>Original Studies
<<title>>Time Course of Juvenile Onset Recurrent Respiratory Papillomatosis Caused by
Human Papillomavirus
<<aut>><bx;1><zfn>Michael <zsn>Hawkes, <zdeg>MD,*<zaffr;*><zcorr><ba>
<bx;1><zfn>Paolo <zsn>Campisi, <zdeg>MD,†<zaffr;†><ba> <bx;1><zfn>Rubeena
<zsn>Zafar, <zdeg>MBBS,*<zaffr;*><ba> <bx;1><zfn>Xerxes <zsn>Punthakee,
<zdeg>MD,†<zaffr;†><ba> <bx;1><zfn>Annie <zsn>Dupuis, <zdeg>PhD,‡<zaffr;‡><ba>
<bx;1><zfn>Vito <zsn>Forte, <zdeg>MD,†<zaffr;†><ba> and <bx;1><zfn>Elizabeth Lee
<zsn>Ford-Jones, <zdeg>MD*<zaffr;*><ba>
<<abs>><foot;fnu;10>Background:<mc>With the recent licensure of a new quadrivalent
vaccine, many diseases caused by human papillomavirus (HPV) can now be prevented, including
recurrent respiratory papillomatosis (RRP). The purpose of this study was to describe the burden
and time course of juvenile onset RRP.
<mc>Methods:<mc>A retrospective chart review was conducted of children with airway
papillomatosis at the Hospital for Sick Children in Toronto, Canada, between 1994 and 2004.
Statistical methods included descriptive statistics of the cohort, a repeated events survival model,
and nonlinear modeling equations to describe the time course of illness.
<mc>Results:<mc>Nine hundred twenty-six surgical procedures in 67 patients were identified
through a review of surgical records. The median age at diagnosis was 3.2 years (range, 0.1-14.8
years) and the most common presenting symptom was hoarseness (75%). Adjuvant
pharmacologic therapy (interferon or cidofovir) was used in 13 cases (19%). HPV types 6 or 11
were identified most commonly as the etiologic agent. Nonlinear modeling equations
(exponential and quadratic) fit the observed data well, and were superior to linear models.
Repeated events survival analysis identified significant prognostic variables: surgeon, adjuvant
therapy, and anatomic score. A decision rule is presented that allows the time to next surgery to
be predicted based on the previous surgery and the anatomic score.
<mc>Conclusions:<mc>Most patients have a decelerating rate of debulking surgeries over time,
well described by our nonlinear modeling equations. Factors affecting the time course of RRP
include: intersurgeon variability, the extent and severity of papillomas at the time of
laryngoscopy, and the use of adjuvant medical therapies.
<<key>>Key Words:<med> human papillomavirus, recurrent respiratory papillomatosis,
mathematical modeling<ziss>
<<texf>><zdci;H>uman papillomavirus (HPV) is the most common sexually transmitted
disease, affecting 70% of sexually active women worldwide.<zref>1<zrefx> Children born to
infected women can develop recurrent respiratory papillomatosis (RRP), which causes marked
physical and emotional suffering because of the need for repeated invasive surgical debridement
of the airway, sometimes for many years. Recently, intensive research has yielded vaccines that
offer hope for the prevention and treatment of HPV-related diseases<zref>1,2<zrefx>; however,
the impact of these vaccines on RRP will be difficult to interpret without a thorough
understanding of the progression of RRP with time. A detailed study of the time course of RRP
in children, as well as patient- and surgery-specific factors that affect the progression of airway
papillomata, was therefore undertaken.
<mc>It is commonly accepted that children acquire HPV (usually types 6 and 11) at the time of
birth by aspiration of contaminated vaginal secretions into the upper airway.<zref>3<zrefx>
Juvenile onset RRP presents at a mean age of 4 years, most commonly with symptoms of
hoarseness or an abnormal cry.<zref>4<zrefx> Life threatening airway obstruction, respiratory
distress, and stridor may also occur at presentation or later in the disease course.<zref>5<zrefx>
There is a high degree of morbidity related to the need for repeated surgical procedures to debulk
papillomata, which encroach on the airway and laryngeal structures as they expand. Rarely,
papillomata may disseminate to cause distal airway or pulmonary parenchymal disease, or may
undergo malignant transformation.<zref>6<zrefx> The prevalence of juvenile onset RRP is 1.72.6 per 100,000 children in the United States, where at least $110 million annually is spent on
direct medical costs.<zref>4<zrefx>
<mc>The mainstay of treatment for RRP is repeated surgical debulking; other therapies are
considered adjuvant to surgery and may have a role in decreasing the number of procedures
needed. Current medical as well as newer immunologic interventions for RRP are unlikely to
permanently eradicate virus or papillomata from the airway and their impact will be measurable
in terms of a decreased total number or rate of surgeries with time. However, the time course of
RRP has not been accurately described in previous reports, which generally assume a linear
pattern (static frequency) despite evidence that the rate of surgeries decreases over
time.<zref>7<zrefx> Furthermore, multiple patient- and surgery-specific variables likely
influence the frequency of surgeries but have not been extensively studied in previous reports.
We describe the time course of RRP using nonlinear mathematical modeling equations and
identify prognostic variables using repeated events survival analysis to refine our current concept
of the temporal progression of RRP. Finally, we propose a decision rule to assist clinicians in
planning the timing of future surgical interventions, based on our findings.
<<hd1>>MATERIALS AND METHODS
<<texp>>Surgical records at the Hospital for Sick Children in Toronto, Canada, between 1994
and 2004 were searched using the keyword papilloma. Our institution is a tertiary pediatric care
center that receives referrals to the pediatric otolaryngology service from Ontario and
surrounding provinces. Ninety-nine cases were identified. Charts were retrospectively reviewed,
and patients were included in this series if they underwent at least 1 surgery for papillomatosis
involving the respiratory tract. Patient data were gathered using a standardized data collection
form including information on demographics, birth history, symptoms at initial presentation,
comorbidities, family data, surgical procedures, complications, use of adjuvant therapies, and
identification of HPV.
<mc>HPV identification on surgical pathology specimens was performed by in situ
hybridization with a commercially available kit (Enzo Diagnostics Inc. Framingham, NY).
Briefly, biotinylated DNA probes were annealed to de-paraffinized fixed tissue sections. Three
separate DNA probe mixtures (types 6 and 11; types 16 and 18; types 31, 33, and 51) allowed
identification of the virus and classification into 1 of 3 groups 6/11, 16/18, or 31/33/51, although
the specific virus type was not generally elucidated.
<mc>Data were collected on the extent and severity of respiratory lesions using a previously
published and validated anatomic scoring system.<zref>3<zrefx> Based on the chart description,
lesions were ranked from 0 (none) to 3 (severe) at 29 anatomic sites in the respiratory tract, for a
total possible score of 87.
<mc>Descriptive statistics (median, range) were computed using Microsoft Excel and SPSS 14.0
statistical software. Repeated events survival analysis was used to explore the effect of surgery
and patient-specific covariates on time to next surgery using SAS software (version 9.1.3). We
used mathematical modeling to describe the time course of illness (number of surgeries as a
function of time) for patients who underwent at least 5 surgeries (n = 46). Nonlinear modeling
equations (exponential and quadratic) were conceived based on the observation that surgery rate
tends to decrease with time. The modeling equations were fit to the data for individual patients
using SPSS software (minimizing the sum of square of residuals by an iterative procedure). The
nonlinear modeling equations were compared with a linear modeling equation of the same data
and the nonlinear model was accepted if the fit was significantly improved (P [lt]
0.05).<zref>8<zrefx> Residual plots were inspected visually to verify assumptions of regression
analyses.
<<hd1>>RESULTS
<<texp>>A search of surgical records (keyword papilloma) between 1994 and 2004 at the
Hospital for Sick Children in Toronto, Canada, revealed 99 patients. Thirty-two cases were
excluded because the papilloma occurred outside the respiratory tract.
<mc>Sixty-seven patients underwent a total of 926 surgical procedures. The median number of
surgeries per patient was 9 (range, 1-60). Patient charts documented follow-up for a median
period of 3.0 years (range, 0-15.5) years. The total observation period was 279 patient-years.
Table 1<pick;t1;0> shows summary statistics (percentage, median, range) for the variables
specific to each patient.
<mc>The median age at diagnosis was 3.2 years (range, 0.1-14.8 years). At presentation, the
most commonly reported symptom was hoarseness (52 patients, 78%). A history of maternal
condylomata was documented in 5 cases (8%). At the time of first surgery, 43 patients (64%) had
lesions only at the level of the larynx, 9 patients had lesions at the larynx and below, 5 at the
larynx and above, and 2 above and below the larynx. Lesions were tested for HPV DNA in 27
cases (40%) by in situ hybridization. HPV DNA was detected in lesions from 21 patients (78%
of specimens tested). HPV types 6 or 11 were found most commonly (19 patients, 90% of
positive specimens). Adjuvant medical therapy was used in 13 patients (19%), including
subcutaneous interferon alone (8 patients), interferon plus intralesional cidofovir (2 patients),
interferon plus intravenous cidofovir (1 patient), intravenous cidofovir alone (1 patient), and
indole-3-carbinol (1 patient).
<mc>Table 2<pick;t2;0> shows the variables specific to the surgical procedures. We sought to
determine which among the host of surgery-specific variables significantly influenced the time to
next surgery using repeated events survival analysis. In models with time dependent covariates
controlling for the age of the patient, increased time to next surgery was associated with longer
time since diagnosis (P [lt] 0.0001), smaller number of previous surgeries (P [lt] 0.0001),
surgeon 3 (P [lt] 0.0001), lower anatomic score (P [lt] 0.0001) or severity score (P [lt] 0.0001),
and use of adjuvant medical therapy (P = 0.0001).
<<hd5>>Nonlinear Modeling Equations.<mc>Although previous studies have assumed a
constant rate of surgical debulking procedures with time,<zref>5,9-11<zrefx> we and
others<zref>7<zrefx> have observed that the surgery rate tends to decrease with time. Two
nonlinear modeling equations were therefore developed to describe the time course of surgeries.
First, an exponential modeling equation was conceived based on the observation that the mean
annual number of surgeries for the cohort decelerated by approximately 12% per year (Fig.
1<pick;f1;0>). The exponential modeling equation (derivation in Appendix 1, online only) has 2
parameters: r0, representing the initial surgery rate; and k, a time constant (larger values of k
indicate a more rapid decrease in the surgery rate over time) (Fig. 2<pick;f2;0>). Second, a
quadratic modeling equation was developed assuming a fixed incremental increase in the interval
between consecutive surgeries (derivation in Appendix 2, online only). These nonlinear models
were fit to the observational data for the 46 patients in our series who underwent 5 surgeries or
more.
<mc>The modeling equations fit the data with remarkable success (Fig. 3<pick;f3;0>): the R2
value (ratio of variability accounted for by the model to the total variability of the data) was a
median of 0.989 (range, 0.708-0.999) for the exponential model and median 0.984 (range, 0.6170.998) for the quadratic model. Compared with a best fit linear model (which assumes a constant
surgery rate with time), both nonlinear modeling equations were superior (P [lt] 0.05) in 29 cases
(63%), and were no better than the linear model in 17 cases (37%).<zref>8<zrefx> Among the
patients with a nonlinear time course, the surgery rate decelerated in 27 cases and accelerated in
2 cases. Comparing the exponential and the quadratic models, the fit (value of R2) of the
exponential model was superior in 26 cases (90% of nonlinear cases). Therefore, the exponential
modeling equation was favored and used in subsequent analysis.
<<hd5>>Decision Rule for Surgical Interval.<mc>We observed intersurgeon variability in the
interval between surgeries, yet recognize the importance of optimizing the surgery interval to
minimize morbidity related to excessive surgeries (if surgery performed too early) as well as
delayed treatment of airway papillomata (if surgery performed too late). Therefore, we sought to
develop a clinically useful rule for predicting the time to next surgery. Derivation of this
simplified rule is given in Appendix 3 (online only). The time to next surgery is predicted from
the previous surgical interval and the observed anatomic score. Using our retrospective data, this
decision rule achieved statistical significance (regression P [lt] 0.001) as a statistical model for
the prediction of the time to next surgery.
<<eq>><mx>
<<texf>>where:
<mc>i = surgery number [lsqb]i = 1,2,3,…,n[rsqb]
<mc>ti = time interval from surgery i to surgery i +1
<mc>ci = anatomic score at the time of surgery i
<mc>a, constant
<<hd1>>DISCUSSION
<<texp>>Here we show that RRP frequently follows a nonlinear time course, with a decelerating
rate of surgeries with time. Intersurgeon variability, the extent and severity of lesions at the time
of laryngoscopy, and the use of adjuvant medical therapies affect the interval between surgeries,
variables which will be important to control in future interventional trials for this disease. We
present a decision rule to assist surgeons in planning the time to next surgery based on our
findings.
<mc>This study, involving 67 patients, is among the largest series from a single center. Patient
characteristics were similar to other published juvenile onset RRP cohorts.<zref>3,4,7<zrefx>
<mc>Adjuvant medical therapy was used in fewer patients (19%) in our study than in the U.S.
series, where rates of 48%<zref>4<zrefx> and 30%<zref>3<zrefx> were reported. As in our
series, interferon was used most commonly,<zref>4<zrefx> followed by intralesional cidofovir.
Variability in clinical practice may be attributed to a lack of clear evidence from quality clinical
trials of lasting benefit of adjuvant medical therapies.<zref>12<zrefx> We observed that the use
of adjuvant medical therapy was associated with a longer time to next surgery. This is consistent
with 2 randomized clinical trials of interferon plus surgical debridement compared with surgery
alone that found that the rate of progression of lesions and the severity of lesions was decreased
during administration of interferon.<zref>13-15<zrefx> Sustained remission was documented in
one of these trials<zref>16<zrefx> but not in the other.<zref>15<zrefx>
<mc>The surgery frequency, a marker of morbidity in RRP,<zref>4<zrefx> is usually
determined by the surgeon at the time of laryngoscopy and debulking. The decision of when to
perform the subsequent procedure is a human estimate of the time for lesions to progress to a
clinically significant size and extent, and is likely based on a number of factors including the age
of the patient, the anatomic distribution and severity of disease observed, and the previous rate of
progression. We observed a significant effect of the surgeon on the time to next surgery. Surgeon
3 tended to have more protracted intervals between surgeries in a survival analysis with repeated
events (HR = 0.72, P [lt] 0.0001) compared with the other 4 surgeons at our institution.1 This
surgeon performed more procedures than other surgeons in this series (42% of all procedures)
but the anatomic scores were not significantly different for operations performed by this surgeon
compared with others (P = 0.150). This variability between surgeons suggests that there is a
significant subjective element involved in the decision about when to perform the next debulking
surgery. Therefore, it will be important for future interventional trials that use the surgical
frequency as an outcome measure to be blinded to the intervention arm, unlike a recently
published open-label clinical trial.<zref>10<zrefx> Furthermore, this variability highlights the
need for uniform criteria or decision rules to assist in planning the timing of surgical
interventions.
<mc>The anatomic score used in this study was that of Wiatrak et al,<zref>3<zrefx> but was
assigned retrospectively based on the chart record. A higher anatomic score predicted a shorter
time to next surgery in the survival analysis with repeated events (P [lt] 0.0001), as expected
because more extensive and severe disease would influence the surgeon’s decision to return for
earlier debulking, or would progress more quickly to symptomatic partial airway obstruction.
This has been observed in another study, where the time to next surgery decreased by 4 days for
every additional point on an anatomic severity score.<zref>17<zrefx>
<mc>Nonlinear modeling equations were developed based on the observation that the frequency
of surgical debulking tends to decrease with time. Compared with a linear model, both modeling
equations were of superior fit<zref>8<zrefx> in 63% of patients and equivalent in 37%. Their
success in modeling the observed time course of individual patients is notable because previous
studies have generally assumed a linear time course, representing the surgical frequency as a
fixed average annual rate.<zref>5,9-11<zrefx> Furthermore, at least 1 previous interventional
study drew conclusions about the efficacy of a vaccine based on a decrease in the surgical
interventions after therapeutic vaccination.<zref>10<zrefx> Our results indicate that the rate of
surgeries decreases with time in the majority of patients, raising the possibility that the observed
change in surgery rate in this study was not a result of vaccination but of the natural history of
the disease.
<mc>Our modeling equations demonstrated that 27 patients (59%) had a decelerating rate of
surgeries with time, 17 (37%) had a constant surgery rate, and 2 (4.3%) had an accelerating
surgery rate. Similar figures were found in a Danish study, where 67% of patients had a
decelerating surgery rate and 33% had a constant or accelerating rate.<zref>7<zrefx>
<mc>This analysis is noteworthy as a novel approach to patient data with repeated events with
time (in this case, repeated surgeries). Using nonlinear modeling to describe the cumulative
number of surgeries as a function of time allowed a more accurate representation of the
longitudinal activity of the disease. This approach may prove useful in future comparative trials
of RRP and may have general applicability to studies involving repeated events with time.
1
Please spell out “HR.”
<mc>Conceptually, airway debulking surgery is indicated above a “threshold” size and extent of
papillomata. Based on this reasoning, we propose a simplified decision rule to assist surgeons in
deciding the time to next surgery, based on the previous surgery interval and the anatomic score
observed (derivation in Appendix 3, online only). Although multiple variables (age, time since
diagnosis, surgeon, anatomic severity score, and the use of adjuvant medical therapy) influence
the interval between surgeries, these are relatively constant for a given patient at a given time,
allowing the subsequent surgery interval to be estimated from the previous surgical interval, with
adjustment for the observed severity (anatomic score). The decision rule achieved statistical
significance (P [lt] 0.001) as a model of our retrospective data, but will require prospective
validation before it can be applied in clinical practice.
<mc>The rate of surgical intervention as a surrogate measure of disease activity has some
inherent strengths and weaknesses. It is an accurate reflection of patient morbidity due to
surgery, but may not exactly mirror the biologic growth characteristics of papillomata, due to
human and other factors (as illustrated by intersurgeon variability in our series). The
retrospective design is an inherent weakness of this observational study, as illustrated by gaps in
the chart record for some of the variables investigated, such as the virus type (only 40% of
patients were tested). Because of special challenges posed by the data set (repeated events,
multiple confounding variables, some patient-specific, others surgery-specific, variable time of
follow-up), multiple statistical methods were used to approach the analysis. Further validation of
the mathematical models derived and applied to our retrospective data set will require them to be
tested against new data from different patient cohorts.
<mc>Future directions for this research include the anticipated creation of a Canada-wide
consortium of pediatric otolaryngologists who treat children with RRP. Because of the relatively
small number of referral centers (13 tertiary care institutions nationwide), population-based
incidence data could be collected, which will be important for monitoring the impact of the
preventative HPV vaccine that may soon be widely implemented. Furthermore, given universal
access to health care in Canada, such a network would be ideal for the study and uniform
implementation of treatment strategies for RRP, including therapeutic vaccination.
<<hdr>>REFERENCES
<<ref>><ens>1.<ens><ix>Villa LL, Costa RL, Petta CA, et al. Prophylactic quadrivalent human
papillomavirus (types 6, 11, 16, and 18) L1 virus-like particle vaccine in young women: a
randomised double-blind placebo-controlled multicentre phase II efficacy trial. Lancet Oncol.
2005;6:271-278.
<mc><ens>2.<ens><ix>Zawisza J. FDA Licenses New Vaccine for Prevention of Cervical
Cancer and Other Diseases in Females Caused by Human Papillomavirus. Washington, DC:
Food and Drug Administration; 2006.
<mc><ens>3.<ens><ix>Wiatrak BJ, Wiatrak DW, Broker TR, Lewis L. Recurrent respiratory
papillomatosis: a longitudinal study comparing severity associated with human papilloma viral
types 6 and 11 and other risk factors in a large pediatric population. Laryngoscope. 2004;114:123.
<mc><ens>4.<ens><ix>Reeves WC, Ruparelia SS, Swanson KI, Derkay CS, Marcus A, Unger
ER. National registry for juvenile-onset recurrent respiratory papillomatosis. Arch Otolaryngol
Head Neck Surg. 2003;129:976-982.
<mc><ens>5.<ens><ix>Armstrong LR, Derkay CS, Reeves WC. Initial results from the national
registry for juvenile-onset recurrent respiratory papillomatosis. RRP Task Force. Arch
Otolaryngol Head Neck Surg. 1999;125:743-748.
<mc><ens>6.<ens><ix>Silver RD, Rimell FL, Adams GL, Derkay CS, Hester R. Diagnosis and
management of pulmonary metastasis from recurrent respiratory papillomatosis. Otolaryngol
Head Neck Surg. 2003;129:622-629.
<mc><ens>7.<ens><ix>Silverberg MJ, Thorsen P, Lindeberg H, Ahdieh-Grant L, Shah KV.
Clinical course of recurrent respiratory papillomatosis in Danish children. Arch Otolaryngol
Head Neck Surg. 2004;130:711-716.
<mc><ens>8.<ens><ix>Motulsky H. Comparing the Fits of Two Models. Vol. 2006. 2003.2
<mc><ens>9.<ens><ix>Rimell FL, Shoemaker DL, Pou AM, Jordan JA, Post JC, Ehrlich GD.
Pediatric respiratory papillomatosis: prognostic role of viral typing and cofactors. Laryngoscope.
1997;107:915-918.
<mc>10.<ens><ix>Derkay CS, Smith RJ, McClay J, et al. HspE7 treatment of pediatric
recurrent respiratory papillomatosis: final results of an open-label trial. Ann Otol Rhinol
Laryngol. 2005;114:730-737.
<mc>11.<ens><ix>Soldatski IL, Onufrieva EK, Steklov AM, Schepin NV. Tracheal, bronchial,
and pulmonary papillomatosis in children. Laryngoscope. 2005;115:1848-1854.
<mc>12.<ens><ix>Chadha NK, James AL. Adjuvant antiviral therapy for recurrent respiratory
papillomatosis. Cochrane Database Syst Rev. 2005;19:CD005053.
<mc>13.<ens><ix>Kashima H, Leventhal B, Clark K, et al. Interferon alfa-n1 (Wellferon) in
juvenile onset recurrent respiratory papillomatosis: results of a randomized study in twelve
collaborative institutions. Laryngoscope. 1988;98:334-340.
<mc>14.<ens><ix>Leventhal BG, Kashima HK, Weck PW, et al. Randomized surgical adjuvant
trial of interferon alfa-n1 in recurrent papillomatosis. Arch Otolaryngol Head Neck Surg.
1988;114:1163-1169.
<mc>15.<ens><ix>Healy GB, Gelber RD, Trowbridge AL, Grundfast KM, Ruben RJ, Price KN.
Treatment of recurrent respiratory papillomatosis with human leukocyte interferon. Results of a
multicenter randomized clinical trial. N Engl J Med. 1988;319:401-407.
2
Please provide the publisher and place of publication for Reference 8.
<mc>16.<ens><ix>Leventhal BG, Kashima HK, Mounts P, et al. Long-term response of
recurrent respiratory papillomatosis to treatment with lymphoblastoid interferon alfa-N1.
Papilloma Study Group. N Engl J Med. 1991;325:613-617.
<mc>17.<ens><ix>Derkay CS, Hester RP, Burke B, Carron J, Lawson L. Analysis of a staging
assessment system for prediction of surgical interval in recurrent respiratory papillomatosis. Int J
Pediatr Otorhinolaryngol. 2004;68:1493-1498.
<</PICK;f1;;;block>>FIGURE 1.<med> For the entire cohort, the mean annual surgery rate
decreased from approximately 5 per year in the first year after diagnosis, by 12% per year. With
time, the mean number of surgeries is derived from a decreasing number of patients, owing to
different lengths of observation periods. The decreasing surgery rate with time (a fixed
percentage change in the annual surgery rate was assumed), was the basis of the exponential
nonlinear modeling equation (Appendix 1, online only).</.>
<</PICK;f2;;;block>>FIGURE 2.<med> The stepwise progression of the cumulative number of
surgeries with time is well described by the exponential nonlinear modeling equation for this
selected patient. In contrast, the assumption of a constant surgery rate with time (linear modeling
equation) fits the observed data poorly.</.>
<</PICK;f3;;;block>>FIGURE 3.<med> Selected patients’ time courses of surgeries with time.
Panel 1: 3 selected patients of similar age at diagnosis underwent very different courses of
illness, with 1 patient undergoing a total of 60 surgeries over a 15-year period (heavy line). Panel
2: A minority of patients had a linear time course (constant rate of surgeries), as illustrated by the
3 selected cases. Panel 3: The exponential modeling equation parameter r0 represents the initial
surgery rate. A steeper initial slope corresponds to a higher value of r0. Panel 4: The exponential
modeling equation parameter k (related to the percent change in the annual surgery rate) reflects
the degree of curvature of the patient’s time course. Patients with a rapidly decelerating surgery
rate have a higher magnitude of the parameter k (heavy line). When k = 0, the time course is
linear (constant surgery rate).</.>
<</FOOT;fnu>><<altfoot>>Accepted for publication August 27, 2007.
<mc>From the <zaff;*>*Division of Infectious Diseases, <zaff;†>†Department of
Otolaryngology, Head and Neck Surgery, and <zaff;‡>‡Population Health Sciences, Hospital for
Sick Children, Toronto, ON, Canada.3
<mc><zsupp>Merck provided funding for the chart review and for presentation of results at an
international conference.
<mc><zcor>Address for correspondence: Michael Hawkes, MD, Division of Infectious
Diseases, Hospital for Sick Children, 555 University Ave., Toronto, ON, Canada M5G 1X8. Email: michael.hawkes@utoronto.ca.<cpy></.>
3
Please verify that the affiliations are complete and accurate as given.