Zero-Inflated Statistical Model for Breast Cancer Progression
Date Issued
2014
Date
2014
Author(s)
Tsau, Huei-Shian
Abstract
Background
Contextual factors for predicting the risk of breast cancer have evolved with time in parallel with the growth of breast cancer screening with mammography. The tendency of having small, node negative, well differentiation have created a statistical thorny issue excess zeros (under-dispersion) in the language of the survival of breast cancer for breast cancer patients and over-detection in the language of theory of mass screening for underlying women.
Objectives
By using this Swedish screened cohort data, the objectives of this thesis are to
(1) assess independent or interactive effect of mammographic appearance and triple negative breast tumour on the risk for breast cancer death making allowance for three conventional tumour attributes and also histological tumour attributes using Bayesian approach;
(2) develop a series of count model and zero-inflated model to evaluate the effect of the spread of lymph nodes, tumour size, and triple negative marker on the count part and histological grade and focality on the zero part for the risk of breast cancer death;
(3) develop the zero-inflated and zero-hurdle multi-state Markov models with respects to dedifferentiation and also the change of focality of breast tumour for over-detection resulting from mass screening.
Materials and Methods
The study subjects were derived from a consecutive series of patients diagnosed with breast cancer at Falun Central Hospital of Dalarna County in Sweden. The Dalarna county was the place of the W-county trial, one of the Swedish Two-county randomized controlled trial from 1977 to 1986. Breast cancer service screening program has been offered after the trial until now. Information on IHC markers and histological tumour distribution was collected.
A retrospective cohort of 498 patients diagnosed with breast cancer at Falun Central Hospital, Sweden between 1996 and 1998 was enrolled for the assessment of independent or interactive effect of mammographic appearance and triple negative breast tumour on the risk for breast cancer death making allowance for three conventional tumour attributes and also histological tumour distribution. This cohort together with prior information on conventional tumour attributes and mammographic appearance from 1968 to 1995 was formed by Bayesian method and was followed until the end of 2011 to ascertain breast cancer death.
Zero-inflated models (ZIP) for the count of advanced stage of three conventional tumour attributes and for breast cancer death, were used to evaluate the effect of triple negative or other IHC markers on the counts of three tumour attributes and breast cancer death.
A series of zero-inflated and zero-hurdle multi-state Markov models were developed for the elucidation of disease temporal natural history for breast cancer, and for further consideration of disease in terms of different histological grade, and histological tumour distribution (unifocal, multifocal and diffuse).
Results
After adjusting for tumour size, node status, grade, and mammographic appearance, triple-negative still remained statistically significant for the risk of breast cancer death using non-informative prior (aHR=2.54, 95% CI: 1.21-5.19) and using informative prior(aHR=1.95, 95% CI: 1.06-3.52).
The effect of triple-negative on breast cancer was statically significant on breast cancer death (3.05 (95% CI:1.69-5.52)) after adjusting conventional tumor attributes in the count part and the focality in the zero-inflated part was significant(β=1.28, P=0.013),indicating the zero-inflated probabilities of unifocality was 0.6340.
In the zero-inflated four-state Markov model, the estimated annual pre-clinical incidence rate of progressive PCDP and non-progressive PCDP with adjustment for sensitivity were 2.01 (95% CI: 1.78-2.25) and 0.032 (95% CI: 0.013- 0.051) per thousand. The proportion of zero-hurdle estimated from the zero-hurdle four-state model was around 14.19% (95% CI: 5.83%-22.56%). Computer simulation based on the four-state Markov model estimated the number of screen to detect one over-detected case (NSO) was the lowest at first screen equal to 1070 and then increased to 39526 at the seven round screen with annual screening regime. The NSO decreased with longer inter-screening interval.
As far as histological grade is concerned, the zero-inflated six-state Markov model suggests around 25% breast tumour was inherited from poor differentiation at the inception of tumour carcinogenesis. The sensitivity for detecting histological grade 1/2 was 62% (95% CI: 51%-73%). The estimated proportion of zero-hurdle was 6.11% (95% CI: 1.64%-22.82%) based on the zero-hurdle six-state model. The trends of NSO with round of screening and interval of screening were similar to that from four-state model. The computer simulation based on six-state zero-inflated Markov model further shows the reduction of breast cancer with histological grade 3 was 27% (RR=0.73, 0.65-0.82) for annual regime, 22% (RR=0.78, 0.70-0.87) for biennial regime, and 18% (RR=0.82, 0.73-0.91) for triennial regime compared with the control group.
For mutifocal and diffuse type, the reduction of such cases was 19% (RR=0.81, 95% CI: 0.73-0.89) for annual regime, 14% (RR=0.86, 95% CI:0.78-0.95) for biennial regime, and 11% (RR=0.89, 95% CI: 0.80-0.98) for triennial regime compared with the control group.
Conclusions
While evaluating the effect of triple negative breast tumour on the prognosis of breast cancer from breast cancer patients and elucidating disease progression of breast cancer from data on breast cancer screening with mammography, excess zeros and over-detection should be evaluated. By using the proposed zero-inflated count model, triple negative breast tumour made contribution to the risk of counts while unifoical versus multi-focal/diffuse type account for true zeros, very low risk group. The zero-inflated and zero-hurdle multi-state Markov models with histological grade and focality by considering the sensitivity were further developed to solve a thorny issue of over-detection that is regarded as a harm in mass screening for breast cancer. We found over-detection is not serious about this Swedish data.
Subjects
乳癌
貝氏分析方法
零-膨脹模型
過度偵測
疾病自然史
零膨脹多階段馬可夫模型
零閾值多階段馬可夫模型
SDGs
Type
thesis
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