Age-space-time models for mapping cancer mortality rates

Statistics in Medicine, 2016

Mortality counts are usually aggregated over age groups assuming similar effects of both time and region, yet the spatio-temporal evolution of cancer mortality rates may depend on changing age structures. In this paper, mortality rates are analyzed by region, time period and age group, and models including space-time, spaceage, and age-time interactions are considered. The integrated nested Laplace approximation method, known as INLA, is adopted for model fitting and inference in order to reduce computing time in comparison with Markov chain Monte Carlo (McMC) methods. The methodology provides full posterior distributions of the quantities of interest while avoiding complex simulation techniques. The proposed models are used to analyze prostate cancer mortality data in 50 Spanish provinces over the period 1986-2010. The results reveal a decline in mortality since the late 1990s, particularly in the age group [65, 70), probably because of the inclusion of the PSA (prostatespecific antigen) test and better treatment of early-stage disease. The decline is not clearly observed in the oldest age groups.

Joint modelling of space and time variation of the risk of disease is an important topic in descriptive epidemiology. Most of the proposals in this field deal with at most two time scales (age-period or age-cohort). We propose a hierarchical Bayesian model that can be used as a general framework to jointly study the evolution in time and the spatial pattern of the risk of disease. The rates are modelled as a function of purely spatial terms (local effects of risk factors that do not vary in time), time effects (on the three time axes: age, calendar period and birth cohort) and space-time interactions that describe area specific time patterns.

1999

Working papers of the Max Planck Institute for Demographic Research receive only limited review. Views or opinions expressed in working papers are attributable to the author(s) and do not necessarily reflect those of the Institute.

Stat Med

Our first paper reviewed methods for modelling variation in cancer incidence and mortality rates in terms of either period effects or cohort effects in the general multiplicative risk model. There we drew attention to the difficulty of attributing regular trends to either period or cohort ...

Biometrical Journal, 2008

The annual percent change (APC) has been used as a measure to describe the trend in the age-adjusted cancer incidence or mortality rate over relatively short time intervals. The yearly data on these age-adjusted rates are available from the Surveillance, Epidemiology, and End Results (SEER) Program of the National Cancer Institute. The traditional methods to estimate the APC is to fit a linear regression of logarithm of age-adjusted rates on time using the least squares method or the weighted least squares method, and use the estimate of the slope parameter to define the APC as the percent change in the rates between two consecutive years. For comparing the APC for two regions, one uses a t-test which assumes that the two datasets on the logarithm of the age-adjusted rates are independent and normally distributed with a common variance. Two modifications of this test, when there is an overlap between the two regions or between the time intervals for the two datasets have been recently developed. The first modification relaxes the assumption of the independence of the two datasets but still assumes the common variance. The second modification relaxes the assumption of the common variance also, but assumes that the variances of the age-adjusted rates are obtained using Poisson distributions for the mortality or incidence counts. In this paper, a unified approach to the problem of estimating the APC is undertaken by modeling the counts to follow an age-stratified Poisson regression model, and by deriving a corrected Z-test for testing the equality of two APCs. A simulation study is carried out to assess the performance of the test and an application of the test to compare the trends, for a selected number of cancer sites, for two overlapping regions and with varied degree of overlapping time intervals is presented.

Statistics in Medicine, 1994

To understand cancer aetiology better, epidemiologists often try to investigate the time trends in disease incidence with year of diagnosis (period) and birth cohort. Unfortunately, one cannot identify these factors uniquely in the usual regression model owing to a linear dependence between age, period and cohort, so that one requires additional information about the underlying biology of the disease. Carcinogenesis models provide one type of information that can result in a unique set of parameters for the effects of age, period and cohort. We use the multistage carcinogenesis model and its extensions to obtain a unique set of parameters for an age-period-cohort model of lung cancer trends of Connecticut males and females from 1935 to 1988. Some of these models d o not seem to provide a reasonable set of model parameters, but we found that a model that included second-order terms and a multistage mixture model both gave a good fit to the data and realistic parameter estimates.

BMC Cancer, 2014

Background: New disease mapping techniques widely used in small-area studies enable disease distribution patterns to be identified and have become extremely popular in the field of public health. This paper reports on trends in the geographical mortality patterns of the most frequent cancers in Spain, over a period of 20 years. Methods: We studied the municipal spatial pattern of stomach, colorectal, lung, breast, prostate and urinary bladder cancer mortality in Spain across four quinquennia, spanning the period 1989-2008. Case data were broken down by town (8073 municipalities), period and sex. Expected cases for each town were calculated using reference rates for each five-year period. For map plotting purposes, smoothed municipal relative risks were calculated using the conditional autoregressive model proposed by Besag, York and Mollié, with independent data for each quinquennium. We evaluated the presence of spatial patterns in maps on the basis of models, calculating the variance in relative risk corresponding to the structured spatial component and the unstructured component, as well as the proportion of variance explained by the structured spatial component.

BMC Public Health

Background: Ovarian cancer is a silent and largely asymptomatic cancer, leading to late diagnosis and worse prognosis. The late-stage detection and low survival rates, makes the study of the space-time evolution of ovarian cancer particularly relevant. In addition, research of this cancer in small areas (like provinces or counties) is still scarce. Methods: The study presented here covers all ovarian cancer deaths for women over 50 years of age in the provinces of Spain during the period 1989-2015. Spatio-temporal models have been fitted to smooth ovarian cancer mortality rates in age groups [50,60), [60,70), [70,80), and [80,+), borrowing information from spatial and temporal neighbours. Model fitting and inference has been carried out using the Integrated Nested Laplace Approximation (INLA) technique. Results: Large differences in ovarian cancer mortality among the age groups have been found, with higher mortality rates in the older age groups. Striking differences are observed between northern and southern Spain. The global temporal trends (by age group) reveal that the evolution of ovarian cancer over the whole of Spain has remained nearly constant since the early 2000s. Conclusion: Differences in ovarian cancer mortality exist among the Spanish provinces, years, and age groups. As the exact causes of ovarian cancer remain unknown, spatio-temporal analyses by age groups are essential to discover inequalities in ovarian cancer mortality. Women over 60 years of age should be the focus of follow-up studies as the mortality rates remain constant since 2002. High-mortality provinces should also be monitored to look for specific risk factors.

2010

An efficient computing procedure for estimating the age-specific hazard functions by the log-linear age-period-cohort (LLAPC) model is proposed. This procedure accounts for the influence of time period and birth cohort effects on the distribution of age-specific cancer incidence rates and estimates the hazard function for populations with different exposures to a given categorical risk factor. For these populations, the ratio of the corresponding age-specific hazard functions is proposed for use as a measure of relative hazard. This procedure was used for estimating the risks of lung cancer (LC) for populations living in different geographical areas. For this purpose, the LC incidence rates in white men and women, in three geographical areas (namely: San Francisco-Oakland, Connecticut and Detroit), collected from the SEER 9 database during 1975-2004, were utilized. It was found that in white men the averaged relative hazard (an average of the relative hazards over all ages) of LC in Connecticut vs. San Francisco-Oakland is 1.31 ± 0.02, while in Detroit vs. San Francisco-Oakland this averaged relative hazard is 1.53 ± 0.02. In white women, analogous hazards in Connecticut vs. San Francisco-Oakland and Detroit vs. San Francisco-Oakland are 1.22 ± 0.02 and 1.32 ± 0.02, correspondingly. The proposed computing procedure can be used for assessing hazard functions for other categorical risk factors, such as gender, race, lifestyle, diet, obesity, etc.

Biostatistics, 2010

There are many more strategies for early detection of cancer than can be evaluated with randomized trials. Consequently, model-projected outcomes under different strategies can be useful for developing cancer control policy provided that the projections are representative of the population. To project populationrepresentative disease progression outcomes and to demonstrate their value in assessing competing early detection strategies, we implement a model linking prostate-specific antigen (PSA) levels and prostate cancer progression and calibrate it to disease incidence in the US population. PSA growth is linear on the logarithmic scale with a higher slope after disease onset and with random effects on intercepts and slopes; parameters are estimated using data from the Prostate Cancer Prevention Trial. Disease onset, metastatic spread, and clinical detection are governed by hazard functions that depend on age or PSA levels; parameters are estimated by comparing projected incidence under observed screening and biopsy patterns with incidence observed in the Surveillance, Epidemiology, and End Results registries. We demonstrate implications of the model for policy development by projecting early detections, overdiagnoses, and mean lead times for PSA cutoffs 4.0 and 2.5 ng/mL and for screening ages 50-74 or 50-84. The calibrated model validates well, quantifies the tradeoffs involved across policies, and indicates that PSA screening with cutoff 4.0 ng/mL and screening ages 50-74 performs best in terms of overdiagnoses per early detection. The model produces representative outcomes for selected PSA screening policies and is shown to be useful for informing the development of sound cancer control policy.