similar decreases in local tumor control are calculated for treatment protraction and for...

ELSEVIER

l Clinical Investigation

Int. J. Radintion Oncology Rid. Phys.. Vol. JIJ. I\io. 2. pp. 3 19.-.729, 1998 Copyright 0 I’)98 klscvier Science Inc

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SIMILAR DECREASES IN LOCAL TUMOR CONTROL ARE CALCULATED FOR TREATMENT PROTRACTION AND FOR INTERRUPTIONS IN THE

RADIOTHERAPY OF CARCINOMA OF THE LARYNX IN FOUR CENTERS

CHRIS ROBERTSON, PH.D.,* A. GERALD ROBERTSON, F.R.C.P.,’ JOLYON H. HENDRY, D23~..‘~ STEPHEN A. ROBERTS, PH.D.,’ NICHOLAS J. SLEVIN, F.R.C.R..’ WILLIAM B. DUNCAN.’

R. HUGH MACDOUGALL,’ GILLIAN R. KERR,’ B. O’SULLIVAN, F.R.C.P.1: AND

THOMAS J. KEANE, F.R.C.P.C.#

*Division of Epidemiology and Biostatistics, European Institute of Oncology, via Ripamonti 435, 20141 Milano. Italy: ‘Beatson Oncology Center, Western Infirmary, West Glasgow Hospitals University Trust. Glasgow. GI I 6NT, Scotland; *Christie CRC Research

Center, Christie Hospital NHS Trust, Manchester. M20 4BX, England; “Department of Clinical Oncology, University of Edinburgh. Western General Hospital, Edinburgh. EH4 2XU, Scotland; %Department of Radiation Oncology, Princess Margaret Hospital. Toronto.

Canada: and #Division of Radiation Oncology. British Columbia Cancer Agency, Vancouver, Canadrl. VSZ 4Eh

Purpose: Data on patients with cancer of the larynx are analyzed using statistical models to estimate the effect ofln the treatment time on the local control of the tumor. Methods and Materials: Patients from four centers, -burgh, Glasgow, Manchester, and Toronto, with carcinoma of the larynx and treated by radiotherapy were followed up and the disease-free period recorded. In all centers the end point was control of the primary tumor after irradiation alone. The local control rates at 22 years, PC, were analyzed by log linear models, and Cox proportional hazard models were used to model the disease-free period. Results: T stage, nodal involvement, and site of the tumor were important determinants of the disease-free interval, as was the radiation schedule used. Elongation of the treatment time by 1 day, or a gap of 1 day, was associated with a decrease in PC of 0.68% per day for PC = 0.80, with a 95% con&knee interval of (0.28,1.08)%. An increase of 5 days was associated with a 3.5% reduction in PC from 0.80 to 0.77. At PC = 0.60 an increase of 5 days was associated with an 7.9% decrease in PC. The time factor in the Linear Quadratic model, y/a. was estimated as 0.89 Gyklay, 95% confidence interval (0.35, 1.43) Gy/day. Conclusions: Any gaps (public holidays are the majority) ln the treatment schedule have the same deleterious effect on the disease free period as an increase in the prescribed treatment time. For a schedule, where dose and fraction number are specified, any gap in treatment is potentially damaging. 0 1998 Elsevier Science Inc.

Linear quadratic model, Time effects, Gap length, Carcinoma of the larynx.

INTRODUCTION

Acute mucosal radiation reactions arising in the head and neck can be extremely distressing to patients receiving radiotherapy. In an effort to minimize these reactions, some centers have tried a policy of giving patients a break during the course of treatment (17, 21). Other reasons for inter- rupting patient treatment include most importantly public holidays, machine servicing, transport failure, and machine breakdowns. Over the past 15 years analysis of treatment outcome for various patient groups from centers in North America and Europe have shown that unplanned interruption of treatment resulting in the prolongation of the treatment time reduces the chances of a laryngeal cancer patient achieving local control and, hence, cure. Maciejewski et al.

(13-15) in Poland, Barton et al. (1) in Toronto, and a number of other groups have analyzed their own data and

Fowler and Lindstrom (7). Fowler and Chapel1 (6). and Bentzen (2) have carried out overviews of the studies. The conclusion is that a break in treatment of about a week is associated with an absolute reduction in local control rates of IO-12%; hence, a break of 1 day may reduce the control rate by around 1.4%.

Also, some recent analyses of hospital records of patients treated in different overall times for carcinoma of the larynx, using linear quadratic modeling have focused on the estimation of the time factor for tumor control expressed as the extra dose per additional day of overall treatment time to maintain the same level of tumor control. About 0.6-0.7 Gylday, using 2 Gy fractions, was required to maintain the same level of tumor control after a lag period of about 3-4 weeks (10, 13, 18, 19, 20, 22, 26).

The above analyses focused on the overall length of --- -. -_---.-

Reprint requests to: Dr. Chris Robertson, Division of Epidemi- ology and Biostatistics. European Institute of Oncology, via Ri-

pamonti 435. 20010 Milano. Italy. Accepted for publication 18 August 1097.

320 I. J. Radiation Oncology 0 Biology l Physics Volume 40, Number 2, 1998

treatment time and did not specifically consider unplanned gaps. In the present analysis the effect of unplanned gaps have been specifically estimated, independently of the planned treatment. In this way, the effect of the prescribed schedules can be assessed together with independent information on the effect of unplanned gaps in the therapy. The aim of the study was to see whether the time factor for unplanned gaps was the same as that for the additional dose required to give the same level of local control for longer prescribed overall treatment times, i.e., is the loss of local control/time factor for, say, 55 Gy in 4 weeks given actually in 5 weeks (with 1 week gap), compensated by the 5 Gy extra prescribed dose for an overall treatment time of 5 weeks (total 60 Gy with no gaps)?

In this article we have analyzed data from four treatment centers, Edinburgh, Glasgow, Manchester, all UK, and To- ronto, Canada, each of which have different treatment practices. In Edinburgh the most common therapy was 52.5 Gy in 20 fractions over 28 days, in Glasgow it was 60 Gy in 25 or 30 fractions over 35 or 42 days, respectively, in Manchester it was 55 Gy in 16 fractions over 21 days, while in Toronto it was 50 Gy in 20 fractions over 28 days. These centers give a wide spread of schedules and provide suffi- cient patients to be able to estimate the effects of unplanned gaps. Also, it is important to test the homogeneity of the effect of unplanned gaps over the four centers and different stages of disease.

DATASETS

Manchester The Manchester and Toronto data are described else-

where (1, 10, 22). In Manchester, 495 cases of T2 and T3 cancers treated between 1971 and 1984 at the Christie Hospital were studied and who were followed up until tumor recurrence or for at least 2 years if well; patients without a recurrence and with a follow-up of less than 2 full years were excluded. Out of a possible 602 patients, 107 did not have a 2-year follow-up, leaving 495 patients for study. Cases with nodal recurrence before larynx recurrence were not censored out. Information is also available on site, total dose, number of fractions and treatment time. Forty-three patients were node positive. Overall treatment time was calculated by calendar subtraction and the dose was expressed uniformly as a mid point dose of the central axis.

Toronto The data from Toronto were also available for patients

followed up for at least 2 years (10). All patients treated at the Princess Margaret Hospital between 1960 and 1982 were available and 1001 satisfied the entry criteria to the study, which were the same as in Manchester (22). Infor- mation was available on exactly the same variables as for Manchester. The treatment techniques varied considerably over the 22 years of data collection leading to a wide variety in the total doses dispensed and the fractionation schedules used. There were also a large number of interruptions to the

treatment from a variety of causes. Data on the number of patients who were not followed up for at least 2 years are not available.

Edinburgh The Edinburgh data came from the Western General

Hospital and contained full information on 383 patients, including treatment, recurrence and follow-up dates (5). Most patients were in Stage Tl or T2 and there were 6 in situ patients. Few [28] had any nodal involvement, only 12 had subglottic cancer. For the analysis of the local control rates a subset of 334 patients with squamous cell carcinoma in the glottis or supraglottis only were selected to resemble the Manchester and Toronto data as closely as possible. Local recurrence was defined as a primary relapse in the larynx. This includes patients who died from cancer of the larynx. Nodal or metastatic recurrence was not considered as a failure of local control unless there was also a recurrence in the larynx. Thirty patients who died within 2 years, but where the cause of death was not related to cancer of the larynx were not included in the analysis of local control at 2 or more years. Patients who had a local recurrence after 2 years from treatment were classified as a lack of local control. This same definition of local control was used in the Toronto and Manchester data. There were 22 patients with nodal relapse but no primary relapse, of whom 11 experi- enced the nodal relapse within 2 years. In common with Manchester these patients were not censored. There were also 23 node-positive patients included.

Glasgow The Glasgow data used were slightly different from those

reported in the analysis of Robertson et al. (20). The main reason is the different end point as the definition of local control was changed to coincide with that used in the previous Manchester and Toronto analysis. There were 910 patients with laryngeal tumors treated at the Western Infir- mary between 1958 and 1977. The treatment schedule cho- sen depended upon Clinician preference, whether or not the patients were entered into the British Institute of Radiology fractionation trial, and whether or not the Clinician in charge wanted to give a break in the middle of treatment to minimize the acute reactions. After 1968 all patients were treated on a linear accelerator, using 4-6 MV photons. The field arrangement was a parallel pair-two lateral wedged fields-minimal field size 5 X 5 cm. Sixty-six percent of patients had a beam directed shell constructed prior to treatment; the remainder were treated by a free-hand setup. The dose distribution throughout the volume varied by no more than 25%. Patients who were treated prior to 1968 were irradiated on a cobalt machine or a linear accelerator, using 4-6 MV photons. The treatment setup was a parallel pair of two lateral wedged fields and 12% had a beam directed shell. The dose distribution in these patients was 18%.

Only patients with a poor, moderately, or well-differen- tiated histology were included. The cancer was also only in

Local tumor control l C. ROBERTSON. et rd. 321

the glottis or supraglottis. Patients with cancer both in the glottis and in another site were excluded. There were 45 node-positive patients included. Patients treated on the cobalt machine were also excluded. A total of 479 patients satisfied these criteria. As in Edinburgh, local recurrence was defined as either death from cancer of the larynx or a primary relapse in the larynx at any time after treatment. There were 84 patients who were not followed up for at least 2 years from the beginning of treatment who had to be excluded from the ~2 year local control analysis, leaving a total of 395 patients.

The same definition of local control was used in all four centers. Our definition has been used in previous investiga- tions (I 0, 22). This choice was made to ensure compatabil- ity of the new data with the data included from previous studies. The result of this procedure will be to have slightly lower local control rates relative to a definition of local control at exactly 2 years, and slightly higher rates relative to those at later times, for example, exactly 5 years. In this analysis the comparisons are all made between groups of patients using the same end points, and these comparisons should be valid whatever precise definition of local control is used,

METHODS AND MATERIALS

The analysis is based on the same model as used previously for three of the datasets (10, 20. 22) but in a slightly more general setting. The Linear Quadratic model with the addition of treatment time relating the probability of local control, PC.. to the treatment schedule is:

ln( -In(P,)) = ln(M,) - N(ad + pd’) + y,T

= p - aD - @Dd + y,T. (1)

where N is the number of fractions, d is the dose per fraction, T is the total treatment time, and D is the total dose. The parameters of the model, which have to be estimated are p, the intercept term, which is related to the effective clonogen number per tumor M,. (Y and p estimate the linear and quadratic effects of dose, respectively, and yt is the rate of increase in ln(M,,) with time. The model is a generalized linear model based on a Poisson distribution (4), for the number of clonogenic cells remaining after radiotherapy (13. 20).

To assess the effect of gap length on the probability of local control we replaced the total treatment time, T, in Model [l] by the sum of the planned treatment time plus any gaps so that:

ln( -ln(P,)) = k - aD - /3Dd + yf + yRG. (2)

where G is the gap length, in days, and P is the planned treatment time. Parameters were also included to control for the T stage. site of the tumor, and the treatment center both as contributions to the p term in the models and through

their influence on (Y, p, and the y terms. In models 1 I ] and [2] the variables were centered around their midpoints: dose was centered on 54 Gy, the number of fractions. N, on 20. Time, T, and P, on 28 days and the gap length. G, on 0. These figures correspond closely to the means for Edin- burgh. With this centering exp(-exp(p)} represents the probability of local control for a patient on a 54-20-28 schedule with no gap in treatment. Significance tests were based on the differences of deviances which follow a x2 distribution in large samples ( 16).

In models [l] and [2] it is important to note the parameters associated with the effect of dose, D or Dd. have a negative sign, whereas those associated with time, r, planned time, P, and gaps, G, have positive signs. This means that if the estimates of (Y and /3 in models [ 1 ] and [2 I are positive then increasing the dose is associated with an increase in the local control rates. If the esttmated coefficients of T or G are positive then increasing the variable is associated with a reduction in the local control rates.

In model [I], the extra dose, in Gy, required per day to counteract the effect of protracting the treatment time is given by yj(a! + pd) when the fraction size is kept constant and the number of fractions is increased. The extra dose per day is given by yi(a + 2pd) when the number of fractions is kept constant and the dose per fraction is increased. as happens in some of the shorter schedules. The maximum time factor applicable using very small fractions is y,/n.

As there is complete information on the length of the local control period for two centers, Edinburgh and Glas- gow, a survival analysis could be carried out to estimate the effect of the gap length on the hazard of a local f’ailure. The disease free curves were estimated using the Kaplan Meier method (121, and the log rank test (8) was used to test for differences in these curves. The Cox proportional hazards regression model (3) was used to estimate the effect of the treatment time and gap length on the hazard of a local recurrence. adjusting for the effects of other treatment and tumor variables.

We modeled the hazard of a failure of local control and were interested in estimating the efiects of the treatment time on this hazard. Essentially the hazard, denoted /r(r), is the instantaneous probability of a failure of local control at a specified time, conditional on local control up to that time point. The Cox Proportional Hazards model can be written as

ln(h(t)) = ln(h,(t)) - aD - /3Dd 4 yrT.

where h,(t) is the baseline hazard associated with patients treated with 54 Gy in 20 fractions over 28 days. This model can equally well be written as a model for the survival function, S(t). which is the probability of having local control for at least time f.

322 I. .I. Radiation Oncology l Biology l Physics Volume 40, Number 2, 1998

Table 1. Number of patients and local control rates have been different. There is evidence for this in the differ- (at 2 years or more) by stage and center ent distributions of T stage in the four centers.

Tl T2 T3 T4 - -

n % n % n % II %

Glottis Edinburgh Glasgow Manchester Toronto

Supraglottis Edinburgh Glasgow Manchester Toronto

135 91 81 76 40 55 4 25 220 78 47 66 25 40 7 0 NA NA 231 84 121 59 NA NA

1 0 324 69 145 50 85 42

16 69 24 67 18 22 16 38 48 56 12 67 8 0 28 29

NA NA 59 78 84 60 NA NA 139 75 63 78 45 53 199 53

NA-Not available.

where S,(t) is the survivor function for the baseline group. From this model y,la will also give the increase in dose, in Gy, required to compensate for an increase of 1 day in the treatment.

If the estimated coefficients of dose, D and Dd, in the Cox model are negative then this is associated with an increase in the hazard of a failure of local control; if they are positive, then the hazard decreases. For all other terms a positive estimate is associated with an increase in the hazard.

All the statistical analysis was carried out using Splus, version 3.3 (24).

RESULTS

A summary of the number of patients in different stages analyzed from the four centers, together with their local control rates is given in Table 1. Toronto supplies the most patients to the analysis with Edinburgh the fewest. Manchester patients included were either T2 or T3, whereas the other three centers had included all four T stages. Of the 140 Tl patients in Toronto 139 had cancer in the supraglottis. Manchester and Toronto had 28% and 44% patients with cancer in the supraglottis, respectively, while in Edinburgh and Glasgow the percentages were 22% and 24%, respectively. For stage T2, the local control rates in the glottis were higher in Manchester than in the other centers. Glas- gow and Toronto had relatively low local control rates in the glottis and the local control rates in the supraglottis were lower in Glasgow and Edinburgh. It is not known what percentage of the Toronto patients were node positive but in Manchester, Edinburgh, and Glasgow the percentages were 8, 7, and ll%, respectively. Thirty-three of the node-positive Glasgow patients had the primary tumor in the supraglottis. Although local control rates have been provided as part of the summary statistics of these data we do not consider it correct to make direct comparisons of disease control by center as the groups of patients from each of the centers are very different, as are the treatment schedules. Furthermore, the selection of patients for radiotherapy may

In Manchester the doses ranged from 42.5 Gy to 66.2 Gy, with modes at 52.5 Gy (20% of patients) and 55 Gy (69% of patients). In Toronto, the doses ranged from 40 Gy to 71.6 Gy, with modes at 50 Gy (40% of patients), 55 Gy (20%), 52.4 Gy (4%), 60 Gy (4%). In Edinburgh the range was from 40.0 Gy to 57.5 Gy, with peaks at 52.5 Gy (48%), 55 Gy (16%), and 56 Gy (6%). In Glasgow the range was from 40 Gy to 66.5 Gy, with peaks at 60 Gy (54%) and 54 Gy (6%). Thus, the total doses were higher in Glasgow, and the distribution was less variable in Manchester.

The distributions of the treatment times are presented in Fig. 1. In Manchester the treatment times ranged from 9 to 42 days, but 77% of patients were treated in their standard short time of 21 days. The treatment times in Toronto ranged from 14 to 84 days. The major peak was at 28 and 29 days with 19% of patients on each day. There was another smaller peak at 35 days with 8% of patients. There was considerable variation about these peaks. There was a small range of treatment times in Edinburgh of 26 to 37 days with 61% of patients completing treatment in 28 days. In Glasgow, the length of treatment ranged from 19 days to 73 days, with peaks around 35 and 42 days. There was considerable variation about these peaks. Thus, Glasgow used longer treatment times on average, at 5 and 6 weeks, with much less clustering on specific days compared to the other three centers. Manchester had the shortest standard times at 3 weeks, with Toronto and Edinburgh at 4 weeks.

In Manchester, the number of fractions varied from as little as 8, for a few patients with concomitant medical illnesses, up to 32 for other patients but 89% of patients received the standard schedule in that center of 16 fractions. In Toronto, the majority of patients received 20 fractions (55%) and the distribution ranged from 10 to 33 fractions. There was another peak at 24 fractions with 20% of patients. All of the Edinburgh patients were treated in 20 fractions. In Glasgow, the number of fractions ranged from 12 to 42 with peaks at 25 (23%) and 30 (35%). The different numbers of fractions in the four centers reflect the differing patterns of treatment times.

The differences in the distributions of the treatment variables and the tumor characteristics over the datasets has implications for the analysis. Notably, information about Tl patients will be obtained primarily from Edinburgh and Glasgow, while information about T4 patients will come from Toronto in the main. Also, the effects of dose, time, and fraction may be confounded to some extent by other differences between the four centers.

Assessment of treatment gaps The treatment patterns of all patients were investigated

with a view to establishing those patients who had a gap in their treatment. This could be done exactly with the Edin- burgh data as details of treatment gaps were recorded. No such information was available at the other three sites.

In Edinburgh all patients received 20 fractions at five

Local tumor control l C. ROBERTSON, et ul

Edinburgh Glasgow

w _ d

9 R 0 ,l-, 1 I 20 40 60 00

Treatment Time, in days

Manchester Toronto

20 40 60 80

Treatment Time, in days

20 40 60 80 20 40 60 80

Treatment Time, in days Treatment Time, in days

Fig. 1. Distributions of treatment times in the four centers.

fractions per week. Thus, the treatment for a patient would be complete within 26 days if treatment began on a Monday and ended on a Friday. For treatments beginning on a Tuesday to Friday the planned length of treatment would be 28 days. Consequently, anyone with a treatment time of 29 days or greater had a gap in the treatment in addition to conventional weekend gaps.

Five fractions per week were the standard for most patients at the other three centers. In Glasgow, there were a number of patients on schedules with three fractions per week. The common schedules in Glasgow were 25 fractions in 35 days, 30 fractions in 42 days, 18 fractions in 42 days, 15 fractions in 35 days. Inspection of the data showed that, for example, a 25 fraction treatment over 5 weeks was expected to last 35 days (or 33 if it began on a Monday), a 20 fraction treatment over 4 weeks was expected to last 28 days (or 26 if treatment began on a Monday). For this reason the convention was adopted that a 30 fraction treatment would be completed within 40-42 days if there were no gaps, and a 25 fraction treatment would be completed in 33-35 days. This takes into account the differences caused by starting a schedule on a Monday as opposed to any other day of the week. If anything, this is likely to underestimate the effect of a gap as a number of patients with a gap of 1 or 2 days whose treatment began on a Monday would have been recorded as completing their treatment on time.

In Manchester. most patients were on a schedule of 16

fractions, which would be completed within 22 days if there were no gaps at all. There were also a number of patients with 30 fractions. These would be completed in 39-42 days, depending on the start day. There were very few patients with gaps in their treatment in Manchester. In Toronto, there were commonly 20, 24, 26, or 30 fractions, which would be completed within 25-28. 3 l-34, 36. or 39-42 days, respectively.

Using only these fraction numbers, 15, 16. l&20,24,25. and, 30, a total of 148 patients out of the 2225 in the combined database could not be. used. These patients were excluded because they were not on a common fractionation scheme and it was not possible to deduce the planned treatment time. The main areas of data loss were in Glasgow and Toronto. These two centers had the greatest variability in treatment practise with the use of nonstandard fraction numbers and doses.

Having established the planned maximum length of time for the treatment of the patient it was possible to work out the length of any gaps in the treatment by subtraction from the observed treatment time. Consequently, the gap length is more correctly described as the excess treatment time over the estimated treatment time based upon five, or three fractions per week. In the Edinburgh dataset there was some information about the reason for the gap and unplanned gaps could be detected. This was not the case with the other centers.

Volume 40, Number 2, 1998 324 I. J. Radiation Oncology l Biology l Physics

Table 2. Distribution of gap length

Gap (Days) All four centers Edinburgh Glasgow

0

2 3 4-6 7-13 14-3.5 Early Total

1249 398 143 48 79 69 30 61

2077

230 42 62

9 33

6

0 383

341 111 41 21 35 33 41 52

675

Early-this category denotes patients whose treatment for the number of fractions given appeared to have been completed before it was scheduled to do so. For example, a patient scheduled to have 25 fractions whose planned treatment time would be 33 to 35 days but whose actual treatment time was 29 days.

The distribution of gap length is presented in Table 2 separately for all four centers. There were 61 patients whose treatment for the number of fractions given appeared to have been completed in a very short time, between 4 and 9 days earlier than they could have been given using five (or three) daily fractions per week. These are denoted “early” in the table and were omitted from the analysis. Most of the gaps were only 1, 2, or 3 days, but there were a number of patients with long gaps in the treatment.

MODELING LOCAL CONTROL RATES AT 2, OR MORE, YEARS

The estimates for the linear models [l] and [2] were based on a total of 2225-148-61 = 2016 patients who did not apparently complete treatment early and who were on one of the recognized fractions numbers 115, 16, l&20,24, 25, 301. The parameter estimates for stage, center, and site are the differences from the baseline category. Thus, for T-stage the estimates are differences relative to Tl, for center the differences are relative to Edinburgh, and for site they are relative to the glottis. In this analysis knowledge of the dose and number of fractions effectively fixes the schedule, as all but 71 patients were on five fractions per week. There was no evidence of nonlinearity or of quadratic effects with time. The parameter estimates for T stage, site, center, and dose are remarkably consistent in models [l] and [2]. This means the effect of these variables on local control is not influenced significantly by how the time effects are measured.

As the estimated coefficients of T2, T3, and T4 were all positive, this means that the local control rates were lower in stages T2, T3, and T4, compared to stage Tl. The site of the cancer within the larynx had an effect on local control as its estimated parameter was significantly different from zero. There was poorer local control in the supraglottis relative to the glottis. Adjusting for the different tumor mixes and treatment practices there was some marginal evidence of different local control rates in the four centers, p = 0.054, with slightly lower local control rates in Glas-

gow relative to the other three centers. With regard to the estimates of the treatment effects in Table 3, the exclusion of center differences from the model had no influence on the estimated effect of treatment time. Only the linear effect of dose (a) was affected with a reduction from 0.033 to 0.023 Gy- ‘. This suggests that the center differences would not affect the estimation of the effect of treatment time or gap length.

In model [l] there was no evidence of any significant variation in the estimates of LY, /3, and yt over the centers, stages, or sites. This was investigated in two ways. One, by formally testing for interactions in the pooled data, and two, by fitting model [l] separately in each center, stage and site, and inspecting the confidence intervals of the parameters. The estimated value of the quadratic dose term was a = 0.361 X lo-’ Gy-‘, with a standard error of 0.314 X 10e2 Gye2. There was no evidence that /3 was significantly different from zero (X2 = 1.36 on lu!! with a p-value of 0.24). Consequently, the quadratic dose term Dd was omitted from models [l] and [2] and the estimates in Table 3 are based on this model, with common values for cr and 3/t over the centers, sites and stages.

The parameters associated with stage T2, T3, and T4 are all positive and significantly greater than zero, which means that, as expected, ln(A4,) tended to increase with tumor

Table 3. Parameter estimates for models local control rates (at 2 years or more)

Model 1 Model 2

Estimate Std. error Estimate Std. error

Intercept* Tl T2 T3 T4 Edinburgh Glasgow Manchester Toronto Glottis Supraglottis Dose, cy(Gy-‘) Time, y,(d- ‘) Planned Time,

y,(d- ‘1 Gap length

ye(d- ‘1

-1.760 0.141 -2.747 0.388 0 - 0 - 0.483 0.134 0.483 0.135 1.252 0.135 1.252 0.135 1.195 0.144 1.196 0.145 0 - 0 - 0.299 0.166 0.297 0.173

-0.114 0.158 -0.112 0.163 -0.070 0.131 -0.072 0.136

0 - 0 - 0.183 0.089 0.183 0.089 0.039 0.014 0.039 0.016 0.035 0.008 -

- - 0.035 0.012

- - 0.035 0.010

* The intercept is the value of In(&) for Edinburgh, Tl, glottis, receiving 54 Gy in 20 fractions in 28 days. The other intercept terms, T stage, center, and site, are differences from this. Thus, the term for Stage T2 gives the amount by which ln(ln(P,)) is higher in T2 patients compared to Tl patients; the term for Glasgow gives the amount by which ln(ln(P,)) is higher in patients treated in Glasgow compared to patients treated in Edinburgh.; the term for Supraglottis gives the amount by which ln(ln(P,)) is higher in patients with supraglottic cancer compared to patients with glottic cancer. The coefficients of dose time, planned time, and gap length all give the amount by which ln(ln(P,)) changes for a unit increase in these variables according to the specification of the model.

Local tumor control l C. ROBERTSON. et al. 3.3

Table 4. Parameter estimates of models of local control rates (at 2 years or more) in Edinburgh, p = 0

Edinburgh estimate Std. error

Intercept * -2.371 0.259 Tl 0 T2 0.826 0.312 T.3 1.825 0.307 T4 1.640 0.419 Glottis 0 - Supraglottis 0.791 0.244 Dose. cr (Gy ’ ) 0.088 0.062 Time, y,(d- ‘) 0.085 0.049

* The intercept is the value of In(&) for Tl, glottis, receiving 54 Gy in 20 fractions in 28 days. The other intercept terms, T stage and site, are differences from this.

stage. The maximal time factor was estimated as 0.89 Gy/ day, with a 95% symmetric confidence interval of (0.35, 1.43) Gylday.

The parameter estimates for Model [2] are also presented in Table 3, and they show that the estimated effect of a gap of one day is of the same magnitude as the effect of an elongation of the treatment time by 1 day.

In this analysis there was no evidence that there was any statistically significant difference in the estimates of (II or y, or y, among the four T stages (p = 0.54). The estimates of (Y, 95% confidence intervals in parenthesis, for the different T stages were, in units of Gyy’, Tl: -0.0094 (-0.0816, 0.0627). T2: 0.0504 (-0.0115, 0.1123), T3: 0.0484 (-0.0053,0.1021), and T4: 0.0456 (-0.0020,0.0932). The estimates for stages T2, T3, and T4 are similar and larger than for Tl. However, the confidence intervals for (Y in these four stages are wide and all overlap considerably. This relatively low precision is also reflected in the fact that the confidence intervals all span zero, in this stratified analysis, whereas in the pooled analysis of all four T stages it does not. As the estimates of (Y or y,, or 7, are not significantly different among the four T stages the pooled analysis, using ail the data, is valid.

In the Edinburgh data the presence or absence of gaps in the treatment were recorded, as opposed to inferred in the other three centers. Consequently, we refitted model [l], without the Dd term, using only the Edinburgh data. It is not possible to use Model [2] as all patients had a planned treatment time of 28 days and so there is a linear relation- ship between the gap length and the total treatment time- G = T - 28. The effect of treatment time, Table 4, is of the same order but tends to be higher than the figures obtained from all four centers. The maximal time factor, ~JLY, is estimated as 0.96 Gy/day with a 95% confidence interval of (-0.7, 2.6) Gy/day.

The estimated local control rates were lower in Glasgow even when allowing for T stage, site, and treatment parameters (Table 3). One possibility for this is the use of a Beam Directed Shell (BDS). A shell is now standard practice in all four centers but the Glasgow data span a much larger time range than those in Manchester and Edinburgh, and about

half of the patients were not treated with a BDS. Also, in Toronto, a beam-directed shell was fairly standard from 1974 onwards but patients treated before then did not have a shell fitted.

With the Glasgow data only, it is possible to investigate if there is any influence of a BDS on the effect of an elongation of the treatment time. There was no significant difference in the effect of the treatment parameters in Model [2] between those patients who had a BDS and those who had not, p = 0.12. The only significant influence of the use of a BDS was that the effect of T Stage was different among those who had a BDS compared to those who did not. p ~2 0.032. Among those with no BDS there was no difference between the local control rates for the four T stages. whereas in patients who had a BDS fitted there was higher local control in Stage Tl, relative to those T 1 cases with no BDS, and decreasing local control rates with increasing T stage [see also (20)]. As no significant effect of BDS was found on the estimated effect of cr. /3, or yp y,,. y, this analysis supports the view that including non-BDS cases in the main analysis in Table 3 does not significantly influence the estimation of the treatment effects and the effect of treatment time and gap length in particular. As Tl and T3 patients treated without a BDS have poorer local control rates than those treated with a BDS (Table 4). then this may contribute to the lower local control rates in Glasgow. T3 and T4 patients treated without a BDS have a better prognosis, but there are few of such patients in the Glasgow data.

In Glasgow the estimated values, standard errors in parenthesis, of the treatment variables are i? :-, 0.047(0.038) Gy-‘, b = 0.01 l(O.007) Gy-.‘, TZ = 0.060(0.0191 days .I. The yja ratio is 1.26 Gy/day. 95% confidence interval (-0.6, 3.1) Gy/day. which is comparable with Edinburgh and the four centers data, albeit with a very n,ide confidence interval. In Model [2] the effect of planned time and gap length are similar.

SURVIVAL ANALYSIS

In the previous section we modeled P,., the probability of local control 2 years after treatment, where all recurrences at later than 2 years were treated as if they had occurred at 2 years. In Edinburgh and Glasgow, the complete history of patients following treatment was available and can be used to ascertain the effect of gaps of the full disease-free period. In this analysis the hazard of a failure of local control was modeled and the effects of gaps in the treatment on this hazard were estimated The hazard. denoted k(r). is the instantaneous probability of a failure of local control at a specified time, conditional on local control up to that time point.

Edinburgh

In these data it was possible to carry out a full survival analysis of the effect of gaps as complete follow-up histo- ries were available for individual patients. The distribution of gap length is presented in Table 2. and 6 I % of patients

326 I. J. Radiation Oncology l Biology l Physics

Disease Free Curves by Gap Length (Edinburgh)

1

0 20 40 s4l SO 100 120

Months slnce bagInnIng aftmatment

Fig. 2. Disease-free curves in Edinburgh. Solid line: No gap; dotted line: l-day gap; dotted and dashed line: 2-day gap; dashed line: gaps of 3 days or more.

completed their treatment with no gaps. The Kaplan-Meier curves representing the effect of gap length are presented in Fig. 2. Only in situ and nonsquamous cell carcinoma patients were excluded. This left 375 out of the 383 patients. There was no evidence that gaps had any significant effect on the length of time a patient was disease free. The log rank statistic was 4.5 on 3 degrees of freedom with a p-value of 0.21.

When taking into account T stage, site, nodal involvement, and dose using the Cox proportional hazards model, the estimated effect of an increase of one day in the treatment time was to increase the hazard of a primary recurrence by a factor of 1.06 with a 95% confidence interval of (0.957, 1.18), (Table 5). The confidence interval is wide, which means that the effect is not precisely estimated, and it also spans 1, indicating no effect. The only suggestion of an effect of gap length comes from the group of patients with the longest gaps, (Fig. 2), but the number of recurrences was so small that there is little precision in the estimated effect. ~JCY was estimated as 0.63 Gylday (95% confidence interval -0.54, 1.8 1). As has already been noted it was not possible with the Edinburgh data to include treatment time, T, and gap length G in the same model, as

Table 5. Edinburgh: Cox model parameter estimates for the effect of the specified variables on the hazard

of a failure of local control

Estimate Std. error

Tl 0 - T2 0.835 0.313 T3 and T4 1.625 0.307 No nodes 0 - Nodes 0.592 0.302 Glottis 0 - Supraglottis 0.604 0.241 Dose, a(Gy-‘) 0.100 0.063 Time, ‘yr (D-‘) 0.062 0.054

Volume 40, Number 2, 1998

Disease Free Curves by Gap Length (Glasgow)

0 50 100 150 200

Months. since Lqinnirg of treatment

Fig. 3. Disease-free cnrves in Glasgow. Solid line: no gap; dotted line: l-day gap; dotted and dashed line: 2-day gap; dashed line: gaps of 3-6 days; dashed and twice dotted line: gaps of 7 days or more.

they are linearly related. Also, as all patients received exactly 20 fractions and similar total doses, there is such a high correlation between D and Dd that both could not be included in the model.

Glasgow The full Glasgow dataset, with 910 patients was more

extensive than that from Edinburgh, but was not as well defined in terms of the gaps in the treatments. The common fraction numbers were 15, 18,20,24,25,26, and 30 and the maximum associated treatment times were 35, 42, 35, 34, 36, and 42 days, respectively. Using these definitions there were 760 patients available. The remaining 150 were on other fraction numbers that were not recognized as being common prescribed treatments, which meant that it was not possible to deduce the planned treatment time. The Glasgow data were more varied and contained some recurring patients and some who were treated with a 250 kV source, all of whom were omitted from this analysis, and so there were a maximum of 675 patients. These data have a great variety of patient characteristics that need to be accounted for in the model.

The distributions of the gap lengths are presented in Table 2. Compared to the Edinburgh data, there was much more variation in the length of the gaps.

With a simple survival analysis of the reduced data there was evidence that longer gaps in treatment were associated with a shorter disease free interval. All patients with treatment completed before the maximal time were omitted, as in the Modeling Local Control Rates section. The curves are presented in Fig. 3, with a log rank test p-value of 2.2 X 10-4. This shows that long gaps in treatment are associated with a shorter disease-free interval compared to no gap.

The estimates of the Cox Regression parameters are presented in Table 6. It was necessary to incorporate effects for nodal involvement, histology and site. Of these, only

Local tumor control l C. ROBERTSON, er ~1. 32:

Table 6. Glasgow: Cox model parameter estimates for the effect of the specified variables on the hazard of

a failure of local control

Estimate Std. error Estimate

Std. error

TI T2 T7 and T4 No nodes Nodes Glottis only Glottis plus Supraglottis Subglottis Site unknown Dose. a(Gy ‘) Dd. PcGy -‘) Time, y,(d ‘) Planned time,

y,,(d’ ‘1 Gap length.

y,(d - ’ )

All eligible patients 0 - 0 0.162 0.212 0.143 0.846 0.190 0.820 0 - 0 0.973 0.187 0.976 0 - 0 0.689 0.205 0.709 0.374 0.120 0.370 I.074 0.304 I.071 0.153 0.605 0.115 0.030 0.016 0.02 1 0.001 0.003 0.002 0.018 0.009

0.002

0.022

0.212 0.192

0.187

0.205 0.120 0.304 0.607 0.018 0.004

0.019

0.010

Node-negative patients only, treatment effects adjusted for T-stage and site

Dose, cx(Gy ' ) 0.045 0.024 0.044 0.024 Dd, P(G) ‘) 0.001 0.004 0.001 0.004 Time, y,(d ‘J 0.038 0.012 - Planned time.

y,,W ’ ) - 0.033 0.023 Gap length.

Y,Jd ’ ) - 0.039 0.013

histology did not prove to be significantly associated with the hazard of recurrence. There was no evidence that the parameters (Y, p. or yt. y,,, y, varied over the different levels of stage. site. nodal involvement. or histology. In these data the effect of an increase of I day in the treatment time was to increase the log hazard by 0.018 (st. error. 0.009), with a p-value of 0.046. The yJc~ estimate is 0.59 Gy/day, with 95% confidence interval (-0.09. 1.28).

When looking at planned treatment time and gap length we find the latter was apparently the more influential variable, (Table 6). These results are not totally consistent with the information from the 12 year local control data, (Table 3), where similar effects of planned time and gap length were noted. The reason for this is that there is a much broader spectrum of patients. In particular. there were 72 node-positive patients. Among the node-negative cases there was evidence that the effect of a gap and planned treatment time were of similar magnitude, (Table 6).

There was no evidence of any nonlinear trends in the effects of dose, fraction, or gap length; nor was there any evidence of nonproportional hazard effects.

DISCUSSION

The values of the parameters calculated using overall treatment time are very similar to those reported previously

using the individual datasets (10, 20, 22). There is evidence from the log linear model of the data in all four centers that the length of gap in the treatment has an important effect on the proportion of patients who are disease free after 2 years. This evidence is strongest in the two centers with the greatest variability in treatment patterns. namely Glasgow and Toronto. The other two centers do not provide contra- dictory evidence, and the magnitude and sign of the esti- mators are consistent over the different center% and T stages.

This analysis has shown small but important reductions in the probability of local control at ~2 years associated with increased length in treatment. From these results one would conclude that for a specified schedule. where dose and fraction number are specified, any gap is potentrally damaging. There is little observed difference in the local control rates in Table 2 for gaps of 0, 1, or 2 days, and most of the information on the trends in Tables 4-6 comes frotn the longer gaps. It has also been demonstrated that after adjusting for fraction number and time, increased doses tend to be associated with greater local control.

Although the survival analysis of the disease-free period for the Edinburgh data did not produce any evrdence for the effect of a gap. the results did not contradict the modeling results. One reason for the difference is that there in less statistical power with a survival analysis than with a log linear model. Secondly, the Edinburgh data are so free from

variability. especially in fraction number. that there 15 little statistical power to detect any effect in these data. This is the case both in the log linear models and in the survival analysis. In the recent analysis of the Edinburgh data (5). significant effects of long gaps were noted on the disease- free period. The reason for the disparity in the results is that a different end point was used in (5). They included nodal relapses as a failure of local control of radiotherapy, whereas we do not as such data were not available in ;rII four centers.

The Glasgow data are much better for detecting the effect of a gap, as there are many more patients with gaps in the treatment. There is good evidence here that long treatment times are associated with poorer survival. Strictly. thi% is not evidence that it is the long times themselves that cause the poorer disease-free survival as elongation of’ the treatment time may occur because of other factors that arc related to a poor outcome. However. it has been noted that \imilar time factors are obtained from datasets whether selection bias was minimized or not (19).

Also. there is some evidence in the data that longer gaps occur in patients with poorer prognosis. OVLY al1 760 patients in Glasgow receiving one of the recogniz.ed fractions. the average gap length in TI patients was 0.X days. whereas for stages T2. T3, and T4 it was 1.2. 3.0. and 4.0 days, respectively. Also. a similar pattern exists in the sne and nodal involvement. Node-negative patients have shorter- gaps on average than node-positive patients, and there are longer gaps. on average, in the glottis plus subglottis. glottis plus supraglottis. and supraglottis-alone patients relative to those patients with a cancer solely in the glottis. In addition.

328 I. J. Radiation Oncology l Biology 0 Physics Volume 40, Number 2, 1998

there was poorer local control in the supraglottis relative to the glottis in the total dataset, a feature not detected in the previous analysis of the Manchester and Toronto data (10). In the present analysis these confounding effects were con- trolled for, and the relatively poorer local control with long treatment times was still evident.

ter-specific treatment practices. However, our study covers a wide range of dose and fractionation schedules, which was one of the parameter areas where the effects of the selection bias were not considered as severe (25).

In as much as the results from Edinburgh contribute to the gap analysis, they at least are consistent with the Glasgow findings. In Glasgow, the effect of an increase of 1 day in the gap length is to multiply the hazard by an estimated effect of 1.02, 95% confidence interval (1.00, 1.04). These are comparable with the interval estimate obtained from Edinburgh of (0.96, 1.18).

The loss to follow-up in the modeling of the 2-year local control rates is about 18% of eligible patients in Manchester and Glasgow (in Toronto, it is likely to be of the same order of magnitude), but only 8% in Edinburgh. There is no problem with loss to follow-up in Edinburgh, but there may be more of a problem in the other centers. The loss to follow-up will obviously create a bias in the investigation of gap length if those individuals lost to follow up have a different distribution of gap length compared to those who were followed up. This was checked in Glasgow, and there is no evidence of any discrepancy; 52% of those who were followed up had no gap, compared to 59% of those who were lost to follow-up. Furthermore, the reason for the survival analysis is partly as a check on the modeling of the 2-year local control rates, precisely because of the possible bias as a result of loss to follow-up. The similar results obtained in the survival analysis compared to the ~2 year local control model suggest that there is not much bias as a result of the loss to follow-up in this analysis.

This analysis has shown that unplanned gaps in the treatment schedule have the same deleterious effect on the disease-free period as does an increase in the prescribed treatment time. Within the model used for the analysis the percentage reduction in the local control rates with an increase in the treatment time depend upon the local control rate. Elongation of the treatment time by 1 day was associated with a decrease in PC of 0.68% per day for P, = 0.80, with a 95% confidence interval of (0.28, l.OS)%. An increase of 5 days was associated with a 3.5% reduction in PC from 0.80 to 0.77. At P, = 0.60 an increase of 5 days was associated with an 7.9% decrease in PC. These figures are applicable over all stages, sites, and centers, as there was no significant differences in the estimates of -yt in the different stages, sites, and centers. In Stage Tl tumors one is expect- ing a local control probability of 0.8, whereas in Stage T3 this may only be 0.5-0.6 (Table 1). Thus, the percentage decrease in local control is greater in Stage T3 compared to Tl, and so a clinician must be even more vigilant in ensur- ing that the planned overall time is not allowed to be extended unnecessarily in advanced tumors.

The time factor in the Linear Quadratic model, yJa, was estimated as 0.89, 95% confidence interval (0.35, 1.43) Gy/day. The figure previously quoted for yJcr at Manchester (22), 0.63 (0.42, 1.08) Gy/day, tends to be lower and has a narrower confidence interval. Although there are more ob- servations here, the model is more complex as it has 10 parameters as opposed to the 3 in the model in Slevin et al. (22). This contributes to the wider confidence intervals for the parameter values.

This analysis has not taken into account the position of the gap, or gaps, in the radiotherapy schedule, as such information was not available in all centers. Current evidence on gap position is conflicting (9,23). However, a gap in the first part of radiotherapy or a gap near the end both may result in the same amount of treatment prolongation (1 l), and hence, both are likely to be important. The present model uses the latter information and does not distinguish gap position.

Data that are collected retrospectively are often subject to unmeasured effects of selection bias (2, 25). As with any retrospective data, we cannot claim that our data are free of any of the selection bias associated with clinician and cen-

Methods to compensate for the detrimental effect of treatment interruptions recently have been compared (11). Using the same mathematical model as employed here with appropriate parameter values, it was concluded that methods that avoided changes in overall treatment time and dose per fraction were preferable. For example, if there was a 1 day gap in the treatment it was better to treat at the weekend or to give two fractions on the day after the 1 day gap as opposed to extending the treatment time or changing the dose.

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similar decreases in local tumor control are calculated for treatment protraction and for...

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