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1.  ON IDENTIFIABILITY OF MIXTURES OF INDEPENDENT DISTRIBUTION LAWS*, **, *** 
We consider representations of a joint distribution law of a family of categorical random variables (i.e., a multivariate categorical variable) as a mixture of independent distribution laws (i.e. distribution laws according to which random variables are mutually independent). For infinite families of random variables, we describe a class of mixtures with identifiable mixing measure. This class is interesting from a practical point of view as well, as its structure clarifies principles of selecting a “good” finite family of random variables to be used in applied research. For finite families of random variables, the mixing measure is never identifiable; however, it always possesses a number of identifiable invariants, which provide substantial information regarding the distribution under consideration.
doi:10.1051/ps/2011166
PMCID: PMC4334394
Latent structure analysis; mixed distributions; identifiability; moment problem
2.  Morbidity risks among older adults with pre-existing age-related diseases 
Experimental gerontology  2013;48(12):1395-1401.
Multi-morbidity is common among older adults; however, for many aging-related diseases there is no information for U.S. elderly population on how earlier-manifested disease affects the risk of another disease manifested later during patient’s lifetime. Quantitative evaluation of risks of cancer and non-cancer diseases for older adults with pre-existing conditions is performed using the Surveillance, Epidemiology, and End Results (SEER) Registry data linked to the Medicare Files of Service Use (MFSU). Using the SEER-Medicare data containing individual records for 2,154,598 individuals, we empirically evaluated age patterns of incidence of age-associated diseases diagnosed after the onset of earlier manifested disease and compared these patterns with those in general population. Individual medical histories were reconstructed using information on diagnoses coded in MFSU, dates of medical services/procedures, and Medicare enrollment/disenrollment. More than threefold increase of subsequent diseases risk was observed for 15 disease pairs, majority of them were i) diseases of the same organ and/or system (e.g., Parkinson disease for patients with Alzheimer disease, HR=3.77, kidney cancer for patients with renal failure, HR=3.28) or ii) disease pairs with primary diseases being fast-progressive cancers (i.e., lung, kidney, and pancreas), e.g., ulcer (HR=4.68) and melanoma (HR=4.15) for patients with pancreatic cancer. Lower risk of subsequent disease was registered for 20 disease pairs, mostly among patients with Alzheimer’s or Parkinson’s disease, e.g., decreased lung cancer risk among patients with Alzheimer’s (HR=0.64) and Parkinson’s (HR=0.60) disease. Synergistic and antagonistic dependences in geriatric disease risks were observed among US elderly confirming known and detecting new associations of wide spectrum of age-associated diseases. The results can be used in optimization of screening, prevention and treatment strategies of chronic diseases among U.S. elderly population.
doi:10.1016/j.exger.2013.09.005
PMCID: PMC3895485  PMID: 24064264
Medicare; chronic disease onset; dependent risks; comorbidity; aging; geriatric disease
3.  Joint Analyses of Longitudinal and Time-to-Event Data in Research on Aging: Implications for Predicting Health and Survival 
Longitudinal data on aging, health, and longevity provide a wealth of information to investigate different aspects of the processes of aging and development of diseases leading to death. Statistical methods aimed at analyses of time-to-event data jointly with longitudinal measurements became known as the “joint models” (JM). An important point to consider in analyses of such data in the context of studies on aging, health, and longevity is how to incorporate knowledge and theories about mechanisms and regularities of aging-related changes that accumulate in the research field into respective analytic approaches. In the absence of specific observations of longitudinal dynamics of relevant biomarkers manifesting such mechanisms and regularities, traditional approaches have a rather limited utility to estimate respective parameters that can be meaningfully interpreted from the biological point of view. A conceptual analytic framework for these purposes, the stochastic process model of aging (SPM), has been recently developed in the biodemographic literature. It incorporates available knowledge about mechanisms of aging-related changes, which may be hidden in the individual longitudinal trajectories of physiological variables and this allows for analyzing their indirect impact on risks of diseases and death. Despite, essentially, serving similar purposes, JM and SPM developed in parallel in different disciplines with very limited cross-referencing. Although there were several publications separately reviewing these two approaches, there were no publications presenting both these approaches in some detail. Here, we overview both approaches jointly and provide some new modifications of SPM. We discuss the use of stochastic processes to capture biological variation and heterogeneity in longitudinal patterns and important and promising (but still largely underused) applications of JM and SPM to predictions of individual and population mortality and health-related outcomes.
doi:10.3389/fpubh.2014.00228
PMCID: PMC4222133  PMID: 25414844
forecasting; mortality; health; joint model; stochastic process model; aging; trajectory
4.  Recovery and Survival from Aging-Associated Diseases 
Experimental gerontology  2013;48(8):824-830.
Objectives
Considering disease incidence to be a main contributor to healthy lifespan of the US elderly population may lead to erroneous conclusions when recovery/long-term remission factors are underestimated. Using two Medicare-based population datasets, we investigated the properties of recovery from eleven age-related diseases.
Methods
Cohorts of patients who stopped visiting doctors during a five-year follow-up since disease onset were analyzed non-parametrically and using the Cox proportional hazard model resulted in estimated recovery and survival rates and evaluated the health state of recovered individuals by comparing their survival with non-recovered patients and the general population.
Results
Recovered individuals had lower death rates than non-recovered patients, therefore, patients who stopped visiting doctors are a healthier subcohort. However, they had higher death rates than in general population for all considered diseases, therefore the complete recovery does not occur.
Conclusion
Properties of recovery/long-term remission among the US population of older adults with chronic diseases were uncovered and evaluated. The results allow for a better quantifiable contribution of age-related diseases to healthy life expectancy and improving forecasts of health and mortality.
doi:10.1016/j.exger.2013.05.056
PMCID: PMC3723111  PMID: 23707929
Medicare; chronic disease onset; recovery/long-term remission; population-based analysis
5.  Time trends of incidence of age-associated diseases in the US elderly population: medicare-based analysis 
Age and Ageing  2013;42(4):494-500.
Objectives: time trends of age-adjusted incidence rates of 19 ageing-related diseases were evaluated for 1992–2005 period with the National Long Term Care Survey and the Surveillance, Epidemiology and End Results Registry data both linked to Medicare data (NLTCS-Medicare and SEER-Medicare, respectively).
Methods: the rates were calculated using individual medical histories (34,077 individuals from NLTCS-Medicare and 199,418 from SEER-Medicare) reconstructed using information on diagnoses coded in Medicare data, dates of medical services/procedures and Medicare enrolment/disenrolment.
Results: increases of incidence rates were dramatic for renal disease [the average annual percent change (APC) is 8.56%, 95% CI = 7.62, 9.50%], goiter (APC = 6.67%, 95% CI = 5, 90, 7, 44%), melanoma (APC = 6.15%, 95% CI = 4.31, 8.02%) and Alzheimer's disease (APC = 3.96%, 95% CI = 2.67, 5.26%), and less prominent for diabetes and lung cancer. Decreases of incidence rates were remarkable for angina pectoris (APC = −6.17%, 95% CI = −6.96, −5.38%); chronic obstructive pulmonary disease (APC = −5.14%, 95% CI = −6.78,−3.47%), and ulcer (APC = −5.82%, 95% CI = −6.77,−4.86%) and less dramatic for carcinomas of colon and prostate, stroke, hip fracture and asthma. Incidence rates of female breast carcinoma, myocardial infarction, Parkinson's disease and rheumatoid arthritis were almost stable. For most diseases, an excellent agreement was observed for incidence rates between NLTCS-Medicare and SEER-Medicare. A sensitivity analysis proved the stability of the evaluated time trends.
Conclusion: time trends of the incidence of diseases common in the US elderly population were evaluated. The results show dramatic increase in incidence rates of melanoma, goiter, chronic renal and Alzheimer's disease in 1992–2005. Besides specifying widely recognised time trends on age-associated diseases, new information was obtained for trends of asthma, ulcer and goiter among the older adults in the USA.
doi:10.1093/ageing/aft032
PMCID: PMC3684110  PMID: 23482353
Medicare; disease onset; time trends; comorbidity; age-associated disease; older people
6.  Long-term dynamics of death rates of emphysema, asthma, and pneumonia and improving air quality 
Background
The respiratory tract is a major target of exposure to air pollutants, and respiratory diseases are associated with both short- and long-term exposures. We hypothesized that improved air quality in North Carolina was associated with reduced rates of death from respiratory diseases in local populations.
Materials and methods
We analyzed the trends of emphysema, asthma, and pneumonia mortality and changes of the levels of ozone, sulfur dioxide (SO2), nitrogen dioxide (NO2), carbon monoxide (CO), and particulate matters (PM2.5 and PM10) using monthly data measurements from air-monitoring stations in North Carolina in 1993–2010. The log-linear model was used to evaluate associations between air-pollutant levels and age-adjusted death rates (per 100,000 of population) calculated for 5-year age-groups and for standard 2000 North Carolina population. The studied associations were adjusted by age group-specific smoking prevalence and seasonal fluctuations of disease-specific respiratory deaths.
Results
Decline in emphysema deaths was associated with decreasing levels of SO2 and CO in the air, decline in asthma deaths–with lower SO2, CO, and PM10 levels, and decline in pneumonia deaths–with lower levels of SO2. Sensitivity analyses were performed to study potential effects of the change from International Classification of Diseases (ICD)-9 to ICD-10 codes, the effects of air pollutants on mortality during summer and winter, the impact of approach when only the underlying causes of deaths were used, and when mortality and air-quality data were analyzed on the county level. In each case, the results of sensitivity analyses demonstrated stability. The importance of analysis of pneumonia as an underlying cause of death was also highlighted.
Conclusion
Significant associations were observed between decreasing death rates of emphysema, asthma, and pneumonia and decreases in levels of ambient air pollutants in North Carolina.
doi:10.2147/COPD.S59995
PMCID: PMC4075234  PMID: 25018627
chronic obstructive pulmonary disease; sulfur dioxide; carbon monoxide; nitrogen dioxide; particulate matter
7.  Variability in the Treatment of Elderly Patients with Stage IIIA (N2) Non-Small Cell Lung Cancer 
Introduction
We evaluated treatment patterns of elderly patients with stage IIIA(N2) non-small cell lung cancer (NSCLC).
Methods
The use of surgery, chemotherapy, and radiation for patients with stage IIIA(T1-T3N2M0) NSCLC in the Surveillance, Epidemiology, and End Results (SEER)-Medicare database from 2004–2007 was analyzed. Treatment variability was assessed using a multivariable logistic regression model that included treatment, patient, tumor, and census track variables. Overall survival (OS) was analyzed using the Kaplan-Meier approach and Cox proportional hazard models.
Results
The most common treatments for 2958 patients with stage IIIA(N2) NSCLC were radiation with chemotherapy (n=1065,36%), no treatment (n=534,18%), and radiation alone (n=383,13%). Surgery was used for 709 (24%) patients: 235 (8%) surgery alone; 40 (1%) surgery with radiation, 222 surgery with chemotherapy (8%), and 212 (7%) surgery, chemotherapy, and radiation. Younger age (p<0.0001), lower T-status (p<0.0001), female gender (p=0.04), and living in a census track with a higher median income (p=0.03) predicted surgery use. Older age (p<0.0001) was the only factor that predicted that patients did not get any therapy. The 3-year OS was 21.8±1.5% for all patients, 42.1±3.8% for patients that had surgery, and 15.4±1.5% for patients that didn’t have surgery. Increasing age, higher T-stage and Charlson Comorbidity index, and not having surgery, radiation, or chemotherapy were all risk factors for worse survival (all p-values<0.001).
Conclusions
Treatment of elderly patients with stage IIIA(N2) NSCLC is highly variable and varies not only with specific patient and tumor characteristics but also with regional income level.
doi:10.1097/JTO.0b013e31828916aa
PMCID: PMC3656972  PMID: 23571473
non-small cell; stage IIIA; surgery; elderly
8.  Modeling hematopoietic system response caused by chronic exposure to ionizing radiation 
Radiation and environmental biophysics  2011;50(2):10.1007/s00411-011-0351-3.
A new model of the hematopoietic system response in humans chronically exposed to ionizing radiation describes the dynamics of the hematopoietic stem cell compartment as well as the dynamics of each of the four blood cell types (lymphocytes, neutrophiles, erythrocytes, and platelets). The required model parameters were estimated based on available results of human and experimental animal studies. They include the steady-state number of hematopoietic stem cells and peripheral blood cell lines in an unexposed organism, amplification parameters for each blood line, parameters describing proliferation and apoptosis, parameters of feedback functions regulating the steady-state numbers, and characteristics of radiosensitivity related to cell death and non-lethal cell damage. The model predictions were tested using data on hematological measurements (e.g., blood counts) performed in 1950–1956 in the Techa River residents chronically exposed to ionizing radiation since 1949. The suggested model of hematopoiesis is capable of describing experimental findings in the Techa River Cohort, including: i) slopes of the dose-effect curves reflecting the inhibition of hematopoiesis due to chronic ionizing radiation, ii) delay in effect of chronic exposure and accumulated character of the effect, and iii) dose-rate patterns for different cytopenic states (e.g., leukopenia, thrombocytopenia).
doi:10.1007/s00411-011-0351-3
PMCID: PMC3830531  PMID: 21259022
9.  Modeling deterministic effects in hematopoietic system caused by chronic exposure to ionizing radiation in large human cohorts 
Health physics  2010;99(3):10.1097/HP.0b013e3181c61dc1.
A new model of the hematopoietic system for humans chronically exposed to ionizing radiation allows for quantitative description of the initial hematopoiesis inhibition and subsequent increase in the risks of late stochastic effects such as leukemia. This model describes the dynamics of the hematopoietic stem cell compartment as well as the dynamics of each of the three blood cell types (leukocytes, erythrocytes, and platelets). The model parameters are estimated from the results of other experiments. They include the steady-state numbers of hematopoietic stem cells and peripheral blood cell lines for an unexposed organism, amplification parameters for each blood cell line, parameters describing the proliferation and apoptosis, parameters of feedback functions regulating the steady-state numbers, and characteristics of radiosensitivity in respect to cell death and non-lethal cell damages. The dynamic model of hematopoiesis is applied to the data on subcohort of the Techa River residents with hematological measurements (e.g., blood counts) performed in 1950–1956 (which totals to about 3,500 exposed individuals). Among well-described effects observed in these data are the slope value of the dose-effect curves describing the hematopoietic inhibition and the dose rate patterns of the fractions of cytopenic states (e.g., leukopenia, thrombocytopenia). The model has been further generalized by inclusion of the component describing the risk of late stochastic effects. The risks of the development of late effects (such as leukemia) in population groups with specific patterns of early reactions in hematopoiesis (such as leukopenia induced by ionizing radiation) are investigated using simulation studies and compared to data.
doi:10.1097/HP.0b013e3181c61dc1
PMCID: PMC3830533  PMID: 20699693
Chronic radiation exposure; deterministic and stochastic effects; hematopoiesis; modeling
10.  Does surgery improve outcomes for esophageal squamous cell carcinoma? An analysis using the Surveillance Epidemiology, and End Results Registry from 1998 to 2008 
Background
We examined survival associated with locally advanced esophageal squamous cell cancer (SCC) to evaluate if treatment without surgery could be considered adequate.
Study design
Patients in the SEER registry with stage II–III SCC of the mid or distal esophagus from 1998–2008 were grouped by treatment with definitive radiation versus esophagectomy with or without radiation. Information on chemotherapy is not recorded in SEER. Tumor stage was defined as first clinical tumor stage in case of neo-adjuvant therapy and pathological report if no neo-adjuvant therapy was performed. Cancer specific (CSS) and overall survival (OS) were analyzed using the Kaplan-Meier approach and propensity-score adjusted Cox proportional hazard models.
Results
Of the 2,431 patients analyzed, there were 844 stage IIA (34.7%), 428 stage IIB (17.6%), 1,159 stage III (47.7%) patients. Most were treated with definitive radiation (n=1,426, 58.7%). Of the 1,005 (41.3%) patients who underwent surgery, 369 (36.7%) had preoperative radiation, 160 (15.9%) had postoperative radiation, and 476 (47.4%) had no radiation. Five-year survival was 17.9% for all patients, and 22.1%, 18.5%, and 14.5% for stages IIA, IIB, and stage III, respectively. Compared to treatment that included surgery, definitive radiation alone predicted worse propensity-score adjusted survival for all patients (CSS Hazard Ratio (HR) 1.48, p<0.001; OS HR 1.46, p<0.001) and for stage IIA, IIB, and III patients individually (all p-values ≤0.01). Compared to surgery alone, surgery with radiation predicted improved survival for stage III patients (CSS HR 0.62, p=0.001, OS HR 0.62, p<0.001) but not stage IIA or IIB (all p-values>0.18).
Conclusions
Esophagectomy is associated with improved survival for patients with locally advanced SCC and should be considered as an integral component of the treatment algorithm if feasible.
doi:10.1016/j.jamcollsurg.2012.07.006
PMCID: PMC3479433  PMID: 23084493
12.  What can we learn from the age- and race/ethnicity- specific rates of inflammatory breast carcinoma? 
Inflammatory Breast Carcinoma (IBC), the most aggressive type of breast tumor with unique clinicopathological presentation, is hypothesized to have distinct etiology with a socioeconomic status (SES) component. Using the Surveillance, Epidemiology and End Results (SEER) Program data for 2004–2007, we compare incidence rates of IBC to non-inflammatory locally advanced breast cancer (LABC) among racial/ethnic groups with different SES. The analysis includes women 20–84 years of age. To examine evidence for the distinct etiology of IBC, we analyzed age-distribution patterns of IBC and non-inflammatory LABC, using a mathematical carcinogenesis model. Based on the Collaborative Staging Extension codes, 2,942 incident IBC cases (codes 71 and 73) and 5,721 non-inflammatory LABC cases (codes 40–62) were identified during the four-year study period. Age-adjusted rates of IBC among non-Hispanic White and Hispanic women were similar (2.5/100,000 in both groups). Similar rates were also found in non-inflammatory LABC in these two groups (4.8/100,000 and 4.2/100,000, respectively). In African-American women, the IBC (3.91/100,000) and non-inflammatory LABC (8.47/100,000) rates were greater compared with other ethnic/racial sub-groups. However, the ratio of rates of IBC/non-inflammatory LABC was similar among all the racial/ethnic groups, suggesting that African-American women are susceptible to aggressive breast tumors in general but not specifically to IBC. The mathematical model successfully predicted the observed age-specific rates of both examined breast tumors and revealed distinct patterns. IBC rates increased until age 65 and then slightly decreased, whereas non-inflammatory LABC rates steadily increased throughout the entire age interval. The number of critical transition carcinogenesis stages (m-stages) predicted by the model were 6.3 and 8.5 for IBC and non-inflammatory LABC, respectively, supporting different etiologies of these breast tumors.
doi:10.1007/s10549-011-1719-4
PMCID: PMC3788601  PMID: 21850396
Epidemiology; Inflammatory breast cancer; Etiology
14.  Effect of the APOE Polymorphism and Age Trajectories of Physiological Variables on Mortality: Application of Genetic Stochastic Process Model of Aging 
Scientifica  2012;2012:568628.
We evaluated effects of the APOE polymorphism (carriers versus noncarriers of the e4 allele) and age trajectories of total cholesterol (CH) and diastolic blood pressure (DBP) on mortality risk in the Framingham Heart Study (original cohort). We found that long-lived carriers and noncarriers have different average age trajectories and long-lived individuals have consistently higher levels and less steep declines at old ages compared to short-lived individuals. We applied the stochastic process model of aging aimed at joint analyses of genetic and nongenetic subsamples of longitudinal data and estimated different aging-related characteristics for carriers and noncarriers which otherwise cannot be evaluated from data. We found that such characteristics differ in carriers and noncarriers: (1) carriers have better adaptive capacity than noncarriers in case of CH, whereas for DBP the opposite situation is observed; (2) mean allostatic trajectories are higher in carriers and they differ from “optimal” trajectories minimizing mortality risk; (3) noncarriers have lower baseline mortality rates at younger ages but they increase faster than those for carriers resulting in intersection at the oldest ages. Such observations strongly indicate the presence of a genetic component in respective aging-related mechanisms. Such differences may contribute to patterns of allele- and sex-specific mortality rates.
doi:10.6064/2012/568628
PMCID: PMC3653307  PMID: 23682334
15.  Age Patterns of Geriatric Disease Incidences in the U.S. Elderly Population: Medicare-Based Analysis 
Background/Objectives
To utilize the Medicare Files of Service Use (MFSU) to evaluate patterns in the incidence of aging-related diseases in the U.S. elderly population.
Design
Age-specific incidence rates of nineteen aging-related diseases were evaluated with the National Long Term Care Survey (NLTCS) and the Surveillance, Epidemiology, and End Results (SEER) Registry data both linked to MSUF (NLTCS-M and SEER-M, respectively), using a developed algorithm for individual date at onset evaluation.
Setting
A random sample from the entire U.S. elderly population (Medicare beneficiaries) was used in NLTCS, and 26% of U.S. population is covered by the SEER Registry data.
Participants
34,077 individuals from NLTCS-M and 2,154,598 from SEER-M.
Measurements
Individual medical histories were reconstructed using information on diagnoses coded in MFSU, dates of medical services/procedures, and Medicare enrollment/disenrollment.
Results
The majority of diseases (e.g., prostate cancer, asthma, diabetes) had a monotonic decline (or decline following short period of increase) in incidence with age. A monotonic increase of incidence with age with a subsequent leveling off and decline was observed for myocardial infarction, stroke, heart failure, ulcer, and Alzheimer’s disease. An inverted U-shaped age pattern was detected for lung and colon carcinomas, Parkinson’s disease, and renal failure. The results obtained from the NLTCS-M and SEER-M were in agreement (excluding an excess for circulatory diseases in the NLTCS-M). A sensitivity analysis proved the stability of the evaluated incidence rates.
Conclusion
The developed computational approaches applied to the nationally representative Medicare-based datasets allows reconstruction of age patterns of disease incidence in the U.S. elderly population at the national level with unprecedented statistical accuracy and stability with respect to systematic biases.
doi:10.1111/j.1532-5415.2011.03786.x
PMCID: PMC3288526  PMID: 22283485
Medicare; chronic disease onset; comorbidity
16.  How lifespan associated genes modulate aging changes: lessons from analysis of longitudinal data 
Background and Objective: The influence of genes on human lifespan is mediated by biological processes that characterize body's functioning. The age trajectories of these processes contain important information about mechanisms linking aging, health, and lifespan. The objective of this paper is to investigate regularities of aging changes in different groups of individuals, including individuals with different genetic background, as well as their connections with health and lifespan. Data and Method: To reach this objective we used longitudinal data on four physiological variables, information about health and lifespan collected in the Framingham Heart Study (FHS), data on longevity alleles detected in earlier study, as well as methods of statistical modeling. Results: We found that phenotypes of exceptional longevity and health are linked to distinct types of changes in physiological indices during aging. We also found that components of aging changes differ in groups of individuals with different genetic background. Conclusions: These results suggest that factors responsible for exceptional longevity and health are not necessary the same, and that postponing aging changes is associated with extreme longevity. The genetic factors which increase lifespan are associated with physiological changes typical of healthy and long-living individuals, smaller mortality risks from cancer and CVD and better estimates of adaptive capacity in statistical modeling. This indicates that extreme longevity and health related traits are likely to be less heterogeneous phenotypes than lifespan, and studying these phenotypes separately from lifespan may provide additional information about mechanisms of human aging and its relation to chronic diseases and lifespan.
doi:10.3389/fgene.2013.00003
PMCID: PMC3551204  PMID: 23346098
age trajectories; physiological variables; longevity genes; genetic dose; integrative genetic mortality model
17.  Trade-off in the effects of the apolipoprotein E polymorphism on the ages at onset of CVD and cancer influences human lifespan 
Aging cell  2011;10(3):533-541.
Summary
Progress in unraveling the genetic origins of healthy aging is tempered, in part, by a lack of replication of effects, which is often considered a signature of false positive findings. We convincingly demonstrate that the lack of genetic effects on an aging-related trait can be due to trade-offs in the gene action. We focus on the well-studied apolipoproetin E (APOE) e2/3/4 polymorphism and on lifespan and ages at onset of cardiovascular diseases (CVD) and cancer, using data on 3,924 participants of the Framingham Heart Study Offspring cohort. Kaplan-Meier estimates show that the e4 allele carriers live shorter lives than the non-e4 allele carriers (log rank=0.016). The adverse effect was attributed to the poor survival of the e4 homozygotes, whereas the effect of the common e3/4 genotype was insignificant. The e3/4 genotype, however, was antagonistically associated with onsets of those diseases predisposing to an earlier onset of CVD and a later onset of cancer compared to the non-e4 allele genotypes. This trade-off explains the lack of a significant effect of the e3/4 genotype on survival; adjustment for it in the Cox regression model makes the detrimental effect of the e4 allele highly significant (p=0.002). This trade-off is likely caused by the lipid-metabolism-related (for CVD) and non-related (for cancer) mechanisms. An evolutionary rationale suggests that genetic trade-offs should not be an exception in studies of aging-related traits. Deeper insights into biological mechanisms mediating gene action are critical for understanding the genetic regulation of a healthy lifespan and for personalizing medical care.
doi:10.1111/j.1474-9726.2011.00689.x
PMCID: PMC3094490  PMID: 21332925
Aging; Longevity regulation; mortality; trade-offs; disease; lifespan; genetics
18.  Evaluating the Number of Stages in Development of Squamous Cell and Adenocarcinomas across Cancer Sites Using Human Population-Based Cancer Modeling 
PLoS ONE  2012;7(5):e37430.
Background
Adenocarcinomas (ACs) and squamous cell carcinomas (SCCs) differ by clinical and molecular characteristics. We evaluated the characteristics of carcinogenesis by modeling the age patterns of incidence rates of ACs and SCCs of various organs to test whether these characteristics differed between cancer subtypes.
Methodology/Principal Findings
Histotype-specific incidence rates of 14 ACs and 12 SCCs from the SEER Registry (1973–2003) were analyzed by fitting several biologically motivated models to observed age patterns. A frailty model with the Weibull baseline was applied to each age pattern to provide the best fit for the majority of cancers. For each cancer, model parameters describing the underlying mechanisms of carcinogenesis including the number of stages occurring during an individual’s life and leading to cancer (m-stages) were estimated. For sensitivity analysis, the age-period-cohort model was incorporated into the carcinogenesis model to test the stability of the estimates. For the majority of studied cancers, the numbers of m-stages were similar within each group (i.e., AC and SCC). When cancers of the same organs were compared (i.e., lung, esophagus, and cervix uteri), the number of m-stages were more strongly associated with the AC/SCC subtype than with the organ: 9.79±0.09, 9.93±0.19 and 8.80±0.10 for lung, esophagus, and cervical ACs, compared to 11.41±0.10, 12.86±0.34 and 12.01±0.51 for SCCs of the respective organs (p<0.05 between subtypes). Most SCCs had more than ten m-stages while ACs had fewer than ten m-stages. The sensitivity analyses of the model parameters demonstrated the stability of the obtained estimates.
Conclusions/Significance
A model containing parameters capable of representing the number of stages of cancer development occurring during individual’s life was applied to the large population data on incidence of ACs and SCCs. The model revealed that the number of m-stages differed by cancer subtype being more strongly associated with ACs/SCCs histotype than with organ/site.
doi:10.1371/journal.pone.0037430
PMCID: PMC3358315  PMID: 22629394
19.  Evaluation of genotype-specific survival using joint analysis of genetic and non-genetic subsamples of longitudinal data 
Biogerontology  2010;12(2):157-166.
Small sample size of genetic data is often a limiting factor for desirable accuracy of estimated genetic effects on age-specific risks and survival. Longitudinal non-genetic data containing information on survival or disease onsets of study participants for whom the genetic data were not collected may provide an additional “reserve” for increasing the accuracy of respective estimates. We present a novel method for joint analyses of “genetic” (covering individuals for whom both genetic information and mortality/morbidity data are available) and “non-genetic” (covering individuals for whom only mortality/morbidity data were collected) subsamples of longitudinal data. Our simulation studies show substantial increase in the accuracy of estimates in such joint analyses compared to analyses based on genetic subsample alone. Application of this method to analysis of the effect of common apolipoprotein E (APOE) polymorphism on survival using combined genetic and non-genetic subsamples of the Framingham Heart Study original cohort data showed that female, but not male, carriers of the APOE e4 allele have significantly worse survival than non-carriers, whereas empirical analyses did not produce any significant results for either sex.
doi:10.1007/s10522-010-9316-1
PMCID: PMC3352324  PMID: 21193960
model; combining data; Framingham Heart Study; mortality; APOE; sex differences
20.  Exceptional Survivors Have Lower Age Trajectories of Blood Glucose: Lessons from Longitudinal Data 
Biogerontology  2009;11(3):257-265.
Exceptional survival results from complicated interplay between genetic and environmental factors. The effects of these factors on survival are mediated by the biological and physiological variables, which affect mortality risk. In this paper, we evaluated the role of blood glucose (BG) in exceptional survival using the Framingham Heart Study data for the main (FHS) and offspring (FHSO) cohorts. We found that: (i) the average cross-sectional age patterns of BG change over time; (ii) the values of BG level among the longest lived individuals in this study differ for different sub-cohorts; (iii) the longitudinal age patterns of BG differ from those of cross-sectional ones. We investigated mechanisms forming average age trajectories of BG in the FHS cohort. We found that the two curves: one, characterizing the average effects of allostatic adaptation, and another, minimizing mortality risk for any given age, play the central role in this process. We found that the average BG age trajectories for exceptional survivors are closer to the curve minimizing mortality risk than those of individuals having shorter life spans. We concluded that individuals whose age trajectories of BG are located around the curve minimizing chances of premature death at each given age have highest chances of reaching exceptional longevity.
doi:10.1007/s10522-009-9243-1
PMCID: PMC3351103  PMID: 19644762
mortality risk; stochastic process model of aging; allostatic adaptation; age-specific physiological norm; blood glucose; Framingham Heart Study
21.  Age trajectories of physiological indices in relation to healthy life course 
We analyzed relationship between the risk of onset of “unhealthy life” (defined as the onset of cancer, cardiovascular diseases, or diabetes) and longitudinal changes in body mass index, diastolic blood pressure, hematocrit, pulse pressure, pulse rate, and serum cholesterol in the Framingham Heart Study (original cohort) using the stochastic process model of human mortality and aging. The analyses demonstrate how decline in resistance to stresses and adaptive capacity accompanying human aging can be evaluated from longitudinal data. We showed how these components of the aging process, as well as deviation of the trajectories of physiological indices from those minimizing the risk at respective ages, can lead to an increase in the risk of onset of unhealthy life with age. The results indicate the presence of substantial gender difference in aging related decline in stress resistance and adaptive capacity, which can contribute to differences in the shape of the sex-specific patterns of incidence rates of aging related diseases.
doi:10.1016/j.mad.2011.01.001
PMCID: PMC3064744  PMID: 21262255
stress resistance; adaptive capacity; age-dynamics; physiological norm; Framingham Heart Study
22.  Transitional Probability-Based Model for HPV Clearance in HIV-1-Positive Adolescent Females 
PLoS ONE  2012;7(1):e30736.
Background
HIV-1-positive patients clear the human papillomavirus (HPV) infection less frequently than HIV-1-negative. Datasets for estimating HPV clearance probability often have irregular measurements of HPV status and risk factors. A new transitional probability-based model for estimation of probability of HPV clearance was developed to fully incorporate information on HIV-1-related clinical data, such as CD4 counts, HIV-1 viral load (VL), highly active antiretroviral therapy (HAART), and risk factors (measured quarterly), and HPV infection status (measured at 6-month intervals).
Methodology and Findings
Data from 266 HIV-1-positive and 134 at-risk HIV-1-negative adolescent females from the Reaching for Excellence in Adolescent Care and Health (REACH) cohort were used in this study. First, the associations were evaluated using the Cox proportional hazard model, and the variables that demonstrated significant effects on HPV clearance were included in transitional probability models. The new model established the efficacy of CD4 cell counts as a main clearance predictor for all type-specific HPV phylogenetic groups. The 3-month probability of HPV clearance in HIV-1-infected patients significantly increased with increasing CD4 counts for HPV16/16-like (p<0.001), HPV18/18-like (p<0.001), HPV56/56-like (p = 0.05), and low-risk HPV (p<0.001) phylogenetic groups, with the lowest probability found for HPV16/16-like infections (21.60±1.81% at CD4 level 200 cells/mm3, p<0.05; and 28.03±1.47% at CD4 level 500 cells/mm3). HIV-1 VL was a significant predictor for clearance of low-risk HPV infections (p<0.05). HAART (with protease inhibitor) was significant predictor of probability of HPV16 clearance (p<0.05). HPV16/16-like and HPV18/18-like groups showed heterogeneity (p<0.05) in terms of how CD4 counts, HIV VL, and HAART affected probability of clearance of each HPV infection.
Conclusions
This new model predicts the 3-month probability of HPV infection clearance based on CD4 cell counts and other HIV-1-related clinical measurements.
doi:10.1371/journal.pone.0030736
PMCID: PMC3265500  PMID: 22292027
23.  Effect of the APOE Polymorphism and Age Trajectories of Physiological Variables on Mortality: Application of Genetic Stochastic Process Model of Aging 
Scientifica  2012;2012:568628.
We evaluated effects of the APOE polymorphism (carriers versus noncarriers of the e4 allele) and age trajectories of total cholesterol (CH) and diastolic blood pressure (DBP) on mortality risk in the Framingham Heart Study (original cohort). We found that long-lived carriers and noncarriers have different average age trajectories and long-lived individuals have consistently higher levels and less steep declines at old ages compared to short-lived individuals. We applied the stochastic process model of aging aimed at joint analyses of genetic and nongenetic subsamples of longitudinal data and estimated different aging-related characteristics for carriers and noncarriers which otherwise cannot be evaluated from data. We found that such characteristics differ in carriers and noncarriers: (1) carriers have better adaptive capacity than noncarriers in case of CH, whereas for DBP the opposite situation is observed; (2) mean allostatic trajectories are higher in carriers and they differ from “optimal” trajectories minimizing mortality risk; (3) noncarriers have lower baseline mortality rates at younger ages but they increase faster than those for carriers resulting in intersection at the oldest ages. Such observations strongly indicate the presence of a genetic component in respective aging-related mechanisms. Such differences may contribute to patterns of allele- and sex-specific mortality rates.
doi:10.6064/2012/568628
PMCID: PMC3653307  PMID: 23682334
24.  Trade-Offs Between Cancer and Other Diseases: Do They Exist and Influence Longevity? 
Rejuvenation Research  2010;13(4):387-396.
Abstract
Relationships between aging, disease risks, and longevity are not yet well understood. For example, joint increases in cancer risk and total survival observed in many human populations and some experimental aging studies may be linked to a trade-off between cancer and aging as well as to the trade-off(s) between cancer and other diseases, and their relative impact is not clear. While the former trade-off (between cancer and aging) received broad attention in aging research, the latter one lacks respective studies, although its understanding is important for developing optimal strategies of increasing both longevity and healthy life span. In this paper, we explore the possibility of trade-offs between risks of cancer and selected major disorders. First, we review current literature suggesting that the trade-offs between cancer and other diseases may exist and be linked to the differential intensity of apoptosis. Then we select relevant disorders for the analysis (acute coronary heart disease [ACHD], stroke, asthma, and Alzheimer disease [AD]) and calculate the risk of cancer among individuals with each of these disorders, and vice versa, using the Framingham Study (5209 individuals) and the National Long Term Care Survey (NLTCS) (38,214 individuals) data. We found a reduction in cancer risk among old (80+) men with stroke and in risk of ACHD among men (50+) with cancer in the Framingham Study. We also found an increase in ACHD and stroke among individuals with cancer, and a reduction in cancer risk among women with AD in the NLTCS. The manifestation of trade-offs between risks of cancer and other diseases thus depended on sex, age, and study population. We discuss factors modulating the potential trade-offs between major disorders in populations, e.g., disease treatments. Further study is needed to clarify possible impact of such trade-offs on longevity.
doi:10.1089/rej.2009.0941
PMCID: PMC2959185  PMID: 20426618
25.  Cancer Risk and Behavioral Factors, Comorbidities, and Functional Status in the US Elderly Population 
ISRN Oncology  2011;2011:415790.
About 80% of all cancers are diagnosed in the elderly and up to 75% of cancers are associated with behavioral factors. An approach to estimate the contribution of various measurable factors, including behavior/lifestyle, to cancer risk in the US elderly population is presented. The nationally representative National Long-Term Care Survey (NLTCS) data were used for measuring functional status and behavioral factors in the US elderly population (65+), and Medicare Claims files linked to each person from the NLTCS were used for estimating cancer incidence. The associations (i.e., relative risks) of selected factors with risks of breast, prostate, lung and colon cancers were evaluated and discussed. Behavioral risk factors significantly affected cancer risks in the US elderly. The most influential of potentially preventable risk factors can be detected with this approach using NLTCS-Medicare linked dataset and for further deeper analyses employing other datasets with detailed risk factors description.
doi:10.5402/2011/415790
PMCID: PMC3197174  PMID: 22084731

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