Estimation of Hazard Functions in the Log-Linear Age-Period-Cohort Model: Application to Lung Cancer Risk Associated with Geographical Area

Abstract

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.

Meilleur pronostic des sujets de 45ans et moins, atteints de cancer du poumon, lié au bon état général et au stade TNM plus faible (étude rétrospective et comparative)

“…Avec 34 000 nouveaux cas estimés en 2009 en France, le cancer du poumon représente la deuxième cause de cancer chez les hommes et la troisième cause de cancer chez les femmes [3,4]. En dehors du tabagisme, l'augmentation de l'âge s'associe à une augmentation de la fréquence du CBP [5]. Les patients « âgés » de plus de 70 ans ont la particularité d'avoir de nombreuses co-morbidités et une faible tolérance à la chimiothérapie [6].…”

Weibull-like Model of Cancer Development in Aging

“…To estimate the values of a cancer hazard function in aging, the recently proposed method can be utilized 4,10. This method allows one to correct the observed age-specific incidence rates I ( t ) for time period and cohort effects.…”

“…In practice, the observed values of I ( t ) are presented as I i , j , c ( t i ), where t i is a given age interval, j —a time period interval of observation and c —indicates a given categorical risk factor (for example, gender, race, etc .). The procedure allows one: (i) to separate the problem of estimating the time period and birth cohort coefficients from the problem of estimating the unknown hazard function; (ii) to resolve the identifiability problem by an assumption that neighboring cohorts almost equally influence the I i , j , c ( t i ) and by anchoring the time period and birth cohort effects to the selected time period and cohort; and (iii) after obtaining the time period and birth cohort coefficients, to estimate values of the hazard function, $h_c^{*}false(t_{i}false)$, and their standard errors, SE i , in each age interval, t i 4,10. Here and below estimates of statistical parameters as well as hazard function values are designated by asterisk (*).…”

“…According to these mathematical functions, the cancer risk should monotonically increase with aging. However, recent analyses of data collected in the SEER database showed that,9 after an initial increase, the cancer hazard functions in aging have turnover and even fall at the end of the lifetime 10. To model such behavior of the cancer hazards, beta-like functions have been utilized 11–13.…”

Extension of Cox Proportional Hazard Model for Estimation of Interrelated Age-period-Cohort Effects on Cancer Survival

“…In this paper we introduce a simple, computationally effective method to solve this identifiability problem. The proposed solution of this problem is analogous to one that we recently utilized for accounting APC effects on cancer incidence rates 10,11…”