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Parametric modelling to predict survival time to first recurrence for breast cancer
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2003 Phys. Med. Biol. 48 L31 (http://iopscience.iop.org/0031-9155/48/12/101) View the table of contents for this issue, or go to the journal homepage for more
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INSTITUTE OF PHYSICS PUBLISHING
PHYSICS IN MEDICINE AND BIOLOGY
Phys. Med. Biol. 48 (2003) L31–L33
www.iop.org/Journals/pb
PII: S0031-9155(03)62199-8
LETTER TO THE EDITOR
Parametric modelling to predict survival time to first recurrence for breast cancer Received 15 April 2003 The Editor, Sir, Mould et al (2002) describe the methodology of parametric modelling using lognormal distributions for survival time to death. We have extended this work for breast cancer by studying survival time to first recurrence and, using the notation of Mould et al (2002), testing for lognormality for cases who experienced a recurrence. The breast cancer patients were treated at the Institut Curie 1981–1990 by a combination of conservative surgery and radiotherapy, and follow-up was available to 2002. We subgrouped our data, table 1, by disease stage T and by Broder’s histological stage SBR (Bloom and Richardson 1957). Stage T1 is defined as tumour size 2 cm and stage 2 by tumour size > 2 cm or 5 cm. SBR = 1 represent good prognosis and SBR = 3 poor prognosis. Table 1. Breast cancer patient subgroups. Cases with tumour size > 5 cm were excluded from the analysis. Patients who experienced a first recurrence Stage
Total no. of cases
Number
Percentage
T1 T2 SBR1 SBR2 SBR3
1375 781 730 1187 259
220 116 96 179 61
16.0 14.9 13.2 15.1 23.6
Our results are shown in table 2 for Phase 1 lognormality testing where it is seen that a good fit, P > 0.10, was obtained for all except the 96 cases in SBR1 subgroup. Phase 2 validation can now be studied for the standard lognormal model, SLN, of Mould et al (2002), for the four subgroups T1, T2, SBR2 and SBR3. Model stability improves if a value of the lognormal standard deviation, S, can be estimated a priori and for T1 and T2 the estimates in table 2 are very similar at 0.83 and 0.84. We conclude that the applications of lognormal modelling can be extended to include time to first recurrence and not only be limited to time to death. We would also like to emphasize, because this is not always initially realized even by statisticians, that parametric modelling of long-term survival rates from short-term data, as described by Mould et al (2002), is not modelling associated with multivariate analysis regression modelling, such as the Cox proportional hazards model. The lognormal distribution within the framework of a regression model is a different concept and has been described for breast cancer by Gore et al (1984), Chapman et al (1996) and McCready et al (2000). 0031-9155/03/120031+03$30.00
© 2003 IOP Publishing Ltd
Printed in the UK
L31
L32
Letter to the Editor
M = 4.163 S = 0.825
1.0
1.1
rec T1
0.05 0.9
0.1 0.2
S
0.3
0.6
0.7
0.8
0.01
3.9
4.0
4.1
4.2
4.3
4.4
M
Figure 1. Example of iso-P-value curves. The bold curve is for P = 0.05 and the black circle corresponds to the minimum chi-squared parameters for M and S, see the first line of table 2. These curves are for 220 breast cancer patients with stage T1 disease. The choice of such iso-P curves was because of their analogy with radiotherapy (RT) isodose curves. As an interesting anecdote, the idea for the original RT isodose curves was described by W V Mayneord (1929) of the Royal Cancer Hospital (later the Royal Marsden), London, in the following terms: ‘The points are joined which have the same dose per second; i.e. we have drawn "isodose" lines just as in The Times weather charts one may join the points having the same barometric pressure or temperature, and hence obtain "isobars" and "isotherms".’ Table 2. Phase 1 validation for the two-parameter lognormal model. Minimum chi-squared parameter estimates Parameter
No. of cases
M
S
P-value
T1 T2 SBR1 SBR2 SBR3
220 116 96 179 61
4.163 4.085 4.425 4.030 4.052
0.825 0.838 0.925 0.775 0.710
0.581 0.588 0.002 0.800 0.788
We end by stating that it is an improvement to use S-Plus as a programming language rather than Excel. Advantages of S-Plus include the possibilities of presentation of results such as iso-P curves, figure 1, similar in concept to isodose curves in radiotherapy treatment planning, and 3D PMS surfaces, figure 2. The iso-P curves clearly indicate the acceptable, P > 0.05, ranges of M (lognormal mean) and S and are useful for comparing results from different series. The PMS surfaces give a very good visual indication of the goodness of fit results.
Letter to the Editor
L33
0
0.2
0.4
P
0.6
0.8
1
rec T1
1.1 1
4.4
0.9
4.3
S
0.8
4.2
0.7
4 .1
M
4
M = 4.163 S = 0.825
Figure 2. Example of a 3D PMS surface for 200 stage T1 breast cancer patients.
Bernard Asselain, Yann De Rycke and Alexia Savignon, Biostatistiques, Institute Curie, 26, rue d’Ulm, 75231 Paris Cedex 05, France (E-mail:
[email protected]) Richard F Mould, 41, Ewhurst Avenue, South Croydon, Surrey CR2 0ED, UK (E-mail:
[email protected])
References Bloom H J G and Richardson W W 1957 Histological grading and prognosis in breast cancer Br. J. Cancer 11 359–77 Chapman J W, Hanna W, Kahn H J, Lickley H L A, Wall J, Fish E B and McCready D R 1996 Alternative multivariate modelling for time to local recurrence for breast cancer patients receiving a lumpectomy alone Surg. Oncol. 5 265–71 Gore S M, Pocock S J and Kerr G R 1984 Regression models and non-proportional hazards in the analysis of breast cancer survival Appl. Stat. 33 176–95 Mayneord W V 1929 The Physics of X-Ray Therapy (London: J & A Churchill) p 131 McCready D R, Chapman J W, Hanna W M, Kahn H J, Murray D, Fish E B, Trudeau M E, Andrulis I L and Lickley H L A 2000 Factors affecting distant disease-free survival for primary invasive breast cancer: use of a log-normal survival model Ann. Surg. Oncol. 7 416–26 Mould R F, Lederman M, Tai P and Wong J K M 2002 Methodology to predict long-term cancer survival from short-term data using Tobacco Cancer Risk and Absolute Cancer Cure models Phys. Med. Biol. 47 3893–924
