Log-linear Trend Research Articles

Sharks caught in the KwaZulu-Natal bather protection programme, South Africa. 14. The smooth hammerhead shark Sphyrna zygaena (Linnaeus)

The current study provides long-term catch-rate, biological and feeding data for smooth hammerhead sharks, Sphyrna zygaena, caught in South Africa’s KwaZulu-Natal bather protection programme. In total, 2 512 S. zygaena were caught in net installations between 1978 and 2014, and 72 S. zygaena were caught on drumlines between 2007 and 2014. There was no significant log-linear year trend in the net catch rate over time (slope = 0.0054, t = 1.808, p = 0.07). However, there was a significant temporal increase in mean size of the captured sharks (slope = 0.0012, t = 3.502, p < 0.001). A quasi-Poisson generalised additive mixed model showed that increasing latitude, winter months, colder sea temperatures and the deployment of drumlines all had a significant positive effect on the catch rate of sharks in nets. The size frequency of the catch was unimodal, with significantly more females caught in the nets and more males on the drumlines. The majority (93.1%) of all sharks caught were immature and measured between 80 and 120 cm precaudal length. Teleosts and cephalopods dominated the sharks’ diet in terms of all dietary indices. The prey species consumed indicate that immature S. zygaena are feeding primarily within the pelagic zone of shallow coastal habitats.

Anthropometric traits at military medical examinations associated with demographic family characteristics in Sardinia at the turn of twentieth century

Anthropometric traits observed during military medical examinations are excellent indicators of individual health and nutritional status, and more generally reflect historical socio-economic conditions. Historical demographers have shown little interest in the association of anthropometric traits with demographic family characteristics, except with sibship size according to the resource dilution hypothesis (RDH). In this study we present an analysis of both height and chest circumference of conscripts of Villagrande in Sardinia, Italy, born between 1853 and 1935. Among a total of 1499 conscripts who passed their first examination, height and chest circumference were recorded respectively for 1432 and 1253 conscripts. These traits were almost normally distributed around the average height of 157.60 cm and chest circumference of 81.89 cm. A multivariate regression analysis was performed using height or chest circumference as dependent variables and a set of demographic variables as potentially explanatory factors. The strongest explanatory power was observed for the year of birth indicating a significant secular increase, for conscript’s age at the first medical examination and the maternal age at conscript’s birth. The mortality rate under age five within the sibship shows a negative association with height only, whereas neither parity nor intergenesic intervals show any statistically significant impact. Finally, the relative birth index is associated with the chest circumference only, with larger values for conscripts born within the younger half of the sibship. Overall, our findings are consistent with the general statement that height and chest circumference are largely under genetic control although they may be partially modulated by the environmental and socio-economic conditions of the individual’s life. This study also aimed to test RDH. Although conscripts who were an only child may have had a slight increase in height and chest circumference, no significant negative linear or log-linear trend was detected for the two body parameters in respect of sibship size.

Non-detection of HC11N towards TMC-1: constraining the chemistry of large carbon-chain molecules

Bell et al. (1997) reported the first detection of the cyanopolyyne HC$_{11}$N toward the cold dark cloud TMC-1; no subsequent detections have been reported toward any source. Additional observations of cyanopolyynes and other carbon-chain molecules toward TMC-1 have shown a log-linear trend between molecule size and column density, and in an effort to further explore the underlying chemical processes driving this trend, we have analyzed GBT observations of HC$_9$N and HC$_{11}$N toward TMC-1. Although we find an HC$_9$N column density consistent with previous values, HC$_{11}$N is not detected and we derive an upper limit column density significantly below that reported in Bell et al. Using a state-of-the-art chemical model, we have investigated possible explanations of non-linearity in the column density trend. Despite updating the chemical model to better account for ion-dipole interactions, we are not able to explain the non-detection of HC$_{11}$N, and we interpret this as evidence of previously unknown carbon-chain chemistry. We propose that cyclization reactions may be responsible for the depleted HC$_{11}$N abundance, and that products of these cyclization reactions should be investigated as candidate interstellar molecules.

Use of explosives to investigate liquefaction resistance of aged sand deposits

Current methods of predicting liquefaction potential were largely developed using data from relatively young deposits or deposits that have been frequently disturbed (i.e., areas of high seismicity). While engineers recognize that these prediction methods are overly conservative for assessing liquefaction potential in geologically aged deposits, there is no widely accepted method for quantitatively accounting for age in these assessments. Because a major disturbance, such as an earthquake or explosion that causes liquefaction, resets a deposit's “geological age,” data from explosive compaction projects in aged deposits are used herein to provide information about both the aged and fresh deposits. A recent explosive compaction project performed in Griffin, IN, as well as four other explosive compaction projects, is used to develop an aging correction relationship for liquefaction resistance. Using a log-linear trend frequently proposed in previous studies, the method proposed herein predicts an approximate 20% gain in liquefaction resistance per time log cycle. The proposed relationship can be used directly if the time since deposition or last disturbance is known or in conjunction with the measured-to-estimated-velocity-ratio (MEVR) relationship proposed by Andrus et al. if the deposit's age is unknown.

Electroacoustic Process Study of Plasma Sparker Under Different Water Depth

The plasma sparker has been applied in oceanic high-resolution seismic exploration for decades. Normally it is towed on the water surface. This is suitable for shallow water, but if the water depth is great, the resolution will decrease dramatically, especially in the horizontal direction. This paper proposes the concept of a deep-towed plasma sparker and presents an experimental study of plasma sparker performance in terms of electric parameters, bubble behavior, and acoustic characteristics. The results show that hydrostatic pressure at a source depth ranging from 1 to 2000 m has a negligible influence on the electric parameters but a strong influence on bubble behavior, wherein both the maximum bubble radius and oscillation period are decreased. The collapse pulse vanishes when the source depth reaches 1000 m or deeper, and no bubble oscillation can be distinguished. The source level (evaluated by the expansion pulse) is also decreased as the source depth increases; moreover, the greater the discharge energy, the smaller the source level loss. The discharge energy per electrode should be greater than 20 J for the deep-towed plasma sparker, which can make the source level loss induced by hydrostatic pressure smaller than the transmission loss. The fast Fourier transform (FFT) results show that the dominant energy is around 20 kHz, which is mainly induced by the expansion pulse and its oscillation. According to the simulation results, the fundamental frequency of the acoustic waveform increases with source depth in accord with a log linear trend, and also reaches tens of kilohertz in deep water. So, before the development of deep-towed plasma sparker, a new technical solution will need to be developed to solve this problem.

The effects of phthalate restrictions on Turkey s footwear imports

This study analyzes the effects of a technical barrier to trade containing phthalate restrictions on Turkey’s imported footwear. To this end, a log-linear trend model is estimated to identify the value and quantity impacts on trade flows from the European Union (EU) and non-EU countries by using monthly data over the last decade. The results suggest that the policy measure has a promoting effect on the footwear import value of non-EU countries, while it does not matter for the import from EU countries. On the other hand, the impact of the measure on the import quantity cannot be observed from the regression results for EU and non-EU countries or both.

Assessment of Various Policy Regimes towards Agricultural Export Growth in Nigeria

The performance of the agricultural export in Nigeria has been decimally, declining from 75 percent in 1960 to 1.63 percent in 2010. In response to this scenario, this study assessed the performance of various policy regimes that managed the resources of Nigeria from 1961 to 2010. This is with the goal of identifying the regime that is the best in growing the agricultural export sector for recommendation. The study estimated the exponential trend of the agricultural export and analyzed such growth under different policy regimes. Time series data were used. Data analysis involved the use of exponential or log-linear trend. The result of the trend analysis showed that Nigeria’s agricultural export did not fare well under the policy regimes except during structural adjustment Original Research Article Udah et al.; AJAEES, 6(2): 94-101, 2015; Article no.AJAEES.2015.066 95 (1986 – 1994) and liberalization (1995 – 2010) where acceleration was recorded in the short run. However, structural adjustment policy regime manifested positive characteristics which indicated that it has the best structure, among other regimes, in growing Nigerian agricultural export. The study advocated for policy of accelerated investment in public goods that supports agricultural production and marketing. This policy could be made possible through instituting Agricultural Trust Fund (akin to Educational Trust Fund) where certain percentage of proceeds from oil is saved towards agricultural development. This can be used to fund human capital development in agriculture, rural infrastructure, irrigation and power supply. The study further recommended a revisit of the Bretton Woods supported Structural Adjustment Program (SAP) with caution.

Landslide inventories for climate impacts research in the European Alps

Landslides present a geomorphological hazard in Alpine regions, threatening life, infrastructure and property. Here we present the development of a new regional landslide inventory (RI) for the European Alps. This database provides a substantial temporal and spatial picture of landsliding in the Alps, with particular focus on the Swiss and French Alps. We use segmented models to evaluate recording bias in the temporal record. We use scaling relationships to calculate landslide area based on a given volume for similar types of landslide; with the result of this being that 9.5% of the landslides recorded in the RI now have area data recorded. These landslide area data are then used to examine the log–linear trend, which exists between landslide area and frequency in inventories. We show that this relationship is present for this historical dataset; however, none of the individual databases, nor a unification of these, contain a complete record with the small and larger landslides being recorded more consistently. The use of segmented models on the temporal distribution of landslides in the RI shows that the post-1970 portion of the database is more reliable, highlighted through an improved power–law relationship, although the frequency of medium sized landslides is still underestimated. We show that creating a unified database (RI) can increase the reliability of datasets and consistency in recording for the use by researchers for attribution and detection studies.

Perfluorooctanoic Acid Exposure and Thyroid Disease in Community and Worker Cohorts

Perfluorooctanoic acid (PFOA) was released from a mid-Ohio River Valley chemical plant, exposing the surrounding community to PFOA for >50 years, primarily through drinking water. Toxicological studies and some previous human studies have suggested that PFOA can disrupt thyroid homeostasis. We examined the association between PFOA and thyroid disease among community members and plant workers. Participants completed health surveys during 2008-2011. Yearly serum PFOA concentrations were estimated for each participant starting at birth or in 1952, whichever came later. We used Cox proportional hazard models, stratified by birth year, to assess adult thyroid disease hazard in relation to time-varying yearly or cumulative (sum of yearly estimates) estimated PFOA serum concentration, controlling for sex, race, education, smoking, and alcohol use. Of 32,254 participants, 3,633 reported functional thyroid disease (excluding neoplasms, congenital disease, nodules without functional changes, cysts, and unspecified type). Analyses were restricted to 2109 cases of functional thyroid disease with thyroid prescription medication use and validation through medical record review. In analyses starting at age 20 years or in 1952, thyroid disease hazard ratios across cumulative exposure quintiles were 1.00, 1.24, 1.27, 1.36, and 1.37 among women and 1.00, 1.12, 0.83, 1.01, and 1.05 among men (log-linear trend tests: P = 0.03 and P = 0.85, respectively); similar results were observed for yearly exposure. Associations were observed for hyperthyroidism and hypothyroidism among women. Some subanalyses also suggested an increased hazard of hypothyroidism among men. Higher PFOA exposure was associated with incident functional thyroid disease in this large cohort with high exposure.

Has the Rate of Reduction in Infant Mortality Increased in India Since the Launch of National Rural Health Mission? Analysis of Time Trends 2000-2009 with Projection to 2015.

National Rural Health Mission (NRHM) - India was launched in 2005 to tackle urban-rural health inequalities, especially in maternal and child health. We examined national and state level trends in Infant Mortality Rates (IMR) from 2000 through 2009 to: 1) assess whether the NRHM had increased the average annual reduction rate (AARR) of IMR 2) evaluate state-wise progress towards Millennium Development Goals (MDG4) and estimate required AARRs for 'off track' states. Log-linear regression models were applied to national and state IMR data collated from the Sample Registration System (SRS)-India to estimate average annual reduction rates and compare AAARs before and after introduction of NRHM. The log-linear trend of infant mortality rates was also projected forward to 2015. The infant mortality rate in rural India declined from 74 to 55/1000 live births between 2000 and 2009, with AARR of 3.0% (95% CI=2.6%-3.4%) and the urban-rural gap in infant mortality narrowed (p =0.036). However there was no evidence (p=0.49) that AARR in rural India increased post NRHM (3.4%, 95% CI 2.0-4.7%) compared to pre NRHM (2.8%, 95% CI 2.1%-3.5%). States varied widely in rates of infant mortality reduction. Projections of infant mortality rates suggested that only eight states might be on track to help India achieve MDG4 by 2015. Despite a narrowing urban-rural gap and high AARRs in some states, there was no evidence that the rate of reduction in infant mortality has increased in rural India post NRHM introduction. India appears unlikely to achieve child survival-related NRHM and millennium development goals. Government should revisit the child survival related NRHM strategies and ensure equitable access to health services. More robust monitoring and evaluation mechanisms must be inbuilt for following years.

Annual Survival of Double-Crested Cormorants from the Great Lakes, 1979–2006

Double-crested Cormorant (Phalacrocorax auritus) populations have rapidly increased in the Great Lakes and in wintering areas in the southeast USA since the mid-1970s, resulting in conflicts with humans. To increase understanding of their population biology, band-recovery models were used to estimate temporal trends in hatch year (HY), second year (SY), and after second year (ASY) survival of cormorants banded in the Great Lakes from 1979 to 2006. SY and ASY annual survival varied among years with no apparent trend. HY annual survival exhibited a negative log-linear trend. Lack of clear temporal patterns in SY and ASY survival suggested that increases in cormorant abundance subsequent to 1979 did not impact survival in these age-classes, whereas HY annual survival declined as abundance increased. In addition, issuance of depredation orders in 1998 and 2003 appeared to have a small negative effect on HY survival, but no clear effect on SY and ASY annual survival. The percentage of band returns reported from cormorant control operations generally increased over time, and greatly during the depredation orders. Mean ± SE annual survival from 1979 to 2006 was 0.446 ± 0.022 for HY, 0.835 ± 0.026 for SY, and 0.884 ± 0.020 for ASY individuals. Although increases in cormorant abundance did not appear to be related to increases in annual survival, the relatively high average annual survival rate of ASY cormorants may have been responsible for rapid population growth in the 1980s and 1990s in the Great Lakes.

Characterizing Vaccine-associated Risks Using Cubic Smoothing Splines

Estimating risks associated with the use of childhood vaccines is challenging. The authors propose a new approach for studying short-term vaccine-related risks. The method uses a cubic smoothing spline to flexibly estimate the daily risk of an event after vaccination. The predicted incidence rates from the spline regression are then compared with the expected rates under a log-linear trend that excludes the days surrounding vaccination. The 2 models are then used to estimate the excess cumulative incidence attributable to the vaccination during the 42-day period after vaccination. Confidence intervals are obtained using a model-based bootstrap procedure. The method is applied to a study of known effects (positive controls) and expected noneffects (negative controls) of the measles, mumps, and rubella and measles, mumps, rubella, and varicella vaccines among children who are 1 year of age. The splines revealed well-resolved spikes in fever, rash, and adenopathy diagnoses, with the maximum incidence occurring between 9 and 11 days after vaccination. For the negative control outcomes, the spline model yielded a predicted incidence more consistent with the modeled day-specific risks, although there was evidence of increased risk of diagnoses of congenital malformations after vaccination, possibly because of a "provider visit effect." The proposed approach may be useful for vaccine safety surveillance.

Short‐term cancer mortality projections: A comparative study of prediction methods

This paper provides a systematic comparison of cancer mortality and incidence projection methods used at major national health agencies. These methods include Poisson regression using an age-period-cohort model as well as a simple log-linear trend, a joinpoint technique, which accounts for sharp changes, autoregressive time series and state-space models. We assess and compare the reliability of these projection methods by using Canadian cancer mortality data for 12 cancer sites at both the national and regional levels. Cancer sites were chosen to provide a wide range of mortality frequencies. We explore specific techniques for small case counts and for overall national-level projections based on regional-level data. No single method is omnibus in terms of superior performance across a wide range of cancer sites and for all sizes of populations. However, the procedures based on age-period-cohort models used by the Association of the Nordic Cancer Registries tend to provide better performance than the other methods considered. The exception is when case counts are small, where the average of the observed counts over the recent 5-year period yields better predictions.

Output response of staple food crops in Nigerian agriculture (1990 – 2005)

This study examined the output response of staple food crops in Nigerian Agriculture from 1990 – 2005. Secondary data from the Central Bank of Nigeria statistical bulletin and those from the food and agriculture database as well as from the National Bureau of statistics were used for the analysis. The analysis include the exponential or log linear trend multiple regression. Output and time were all positive and significant atone percent. In the regression results, labour, fertilizer and land area cultivated were significant at various levels. However, land had a negative coefficient. The study recommended that the subsidy on fertilizer should be sustained in other to obtain the needed output from these staple crops. Educating farmers on the right use of fertilizer and extension agents trained and deployed to the rural areas will also be steps in the right direction.

Geostatistical Analyst for Deciding Optimal Interpolation Strategies for Delineating Compact Zones

Variability maps of Hydraulic conductivity (K) were generated by using geo statistical analyst extension of ARC GIS for delineating compact zones in a farm. In the initial exploratory spatial data analysis, K data for 0 - 15 and 15 - 30 cm soil layers showed spatial dependence, anisotropy, normality on log transformation and linear trend. Outliers present in both layers were also removed. In the next step, cross validation statistics of different combinations of kriging (Ordinary, simple and universal), data transformations (none and logarithmic) and trends (none and linear) were compared. Combination of no data transformation and linear trend removal was the best choice as it resulted in more accurate and unbiased prediction. It thus, confirmed that for generating prediction maps by kriging, data need not be normal. Ordinary kriging is appropriate when trend is linear. Among various available anisotropic semivariogram models, spherical model for 0 - 15 cm and tetra spherical model for 15 - 30 cm were found to be the best with major and minor ranges between 273 - 410 m and 98 - 213 m. The kriging was superior to other interpolation techniques as the slope of the best fit line of scatter plot of predicted vs. measured data points was more (0.76) in kriging than in inverse distance weighted interpolation (0.61) and global polynomial interpolation (0.56). In the generated prediction maps, areas where K was <12 cm?day–1 were delineated as compact zone. Hence, it can be concluded that geostatistical analyst is a complete package for preprocessing of data and for choosing the optimal interpolation strategies.

Are the declining trends in forest grouse populations due to changes in the forest age structure? A case study of Capercaillie in Finland

In Finland, Capercaillie ( Tetrao urogallus) populations have a history of serious decrease starting from the mid-20th century. The decline is temporally in line with the expansion of modern forestry practices that created major changes in the landscape. We used tetraonid route-censuses from 18 forestry board districts and Finnish forest inventories (data on forest stand structure) to analyze the decline in 1965–1988. We used information theoretical model selection to evaluate a set of log-linear second order autoregressive models, allowing for spatially correlated process errors. The average trend throughout the country corresponded to an annual decline of 4.01% (mean of local trends) ± 0.24% (SEM), parallel to a half-life of 17 years. The decline was surprisingly uniform throughout the country (SD = 1.01%) and most parsimoniously explained by a geographically constant log-linear trend. At the large scale of observation applied here, population trends could not be explained by the proportional increase of younger forest age classes (<40 years old and <80 years old, respectively). Our analysis does not support the hypothesis that the decline in Capercaillie numbers is due to changes in the forest age structure, but we cannot exclude the possibility that other factors behind the decline may have interacted with forestry in general. From a conservation point of view, we caution against over-emphasizing the role of forest age especially at large spatial scales, but leaning also on other research, we recommend that more management efforts would go into the preservation of the overall forest cover and the original physiognomy in single forest patches.

Filter-design and model-based analysis of trends and cycles in the presence of outliers and structural breaks

A large proportion of today’s econometric literature addresses the question of whether long run GDP follows a random walk or a log linear trend with one or more structural breaks. Much less attention is paid to the modelling of the long run trend and cycle component. In most studies, the trend is simply eliminated by taking first differences of the log of the series without considering the implications of this kind of trend removal for growth and cycles. Filter design and model-based approaches are used here to assess the long run trend and the cyclical component of Chile’s per capita GDP from 1820 to 2007. Careful attention is paid to outliers and trend breaks and how they influence the appraisal of the components. We show that filter and model-based approaches give comparable results if the filter and model parameters are not chosen mechanically but tailor-made for the time series to be investigated.

Comparison of the heterogeneity within bulk sediment humic substances from a stream and reservoir via selected operational descriptors

The heterogeneity within a bulk humic substances (HS) of two sediment HS from different sources (stream and reservoir) was compared using selected operational descriptors for ultrafiltration (UF) fractions. The operational descriptors investigated included the specific UV absorbance (SUVA), the C/N ratio, the ratio of humic-like/fulvic-like fluorescence (HLF/FLF), the humification index (HIX), the molecular weight (MW) and the organic carbon normalized pyrene binding coefficient ( K oc). The UF fractions exhibited a linear or a log-linear trend with respect to MW for most operational descriptors. The two sediment HS exhibited similar patterns in the fluorescence excitation–emission matrix (EEM). The trends among some operational descriptors of the UF fractions based on one HS source were not the same as those obtained from the other HS source. For the C/N ratio, HLF/FLF, and the pyrene binding reactivity, the UF fractions of the stream sediment HS had higher values than those of the reservoir sediment HS UF fractions. For SUVA and HIX, however, a single relationship was presented with MW irrespective of HS sources. This indicates that SUVA and HIX may be more related to MW of the sediment HS than to the chemical nature and/or the source. A common strong correlation between HLF/FLF and pyrene K oc was also observed for the UF fractions of the two HS, suggesting that HLF/FLF might serve as a good descriptor to predict the extent of pyrene binding independent of sediment source.

Use of seasonal climate information to predict coconut production in Sri Lanka

AbstractAccurate forecasting of annual national coconut production (ANCP) is important for national agricultural planning and negotiating forward contracts. Climate and the long‐term trends (attributed to ‘technology’) are major factors that determine ANCP. The effect of climate on ANCP of the following year was studied for the seven agro‐ecological regions (AER's) in the principal coconut growing areas for the period 19502002. Climate was studied based on seasons aggregated by the monsoon calendar and by quarters that are consistent with the agricultural calendar. The use of quarterly seasons explained more of the variability of ANCP than the use of monsoon based seasons. January–March rainfall in all AER's and July–September rainfall in the wetter regions are positively correlated with the ANCP (p &lt; 0.005). The technology effect was estimated using a log–linear trend model. The regression model integrates both climate and technology effects developed to predict ANCP with high fidelity (R2 = 0.94). The climate effect was estimated by regressing production data that had been de‐trended to remove the technology effects with quarterly rainfall in the year prior to harvest. The most significant predictors were found to be the quarterly rainfall from the AER's in the coconut growing regions that are designated as wet and intermediate. Representative rainfall from each quarter was used in a regression model with corrections for the technology effect. The correlation between observed and predicted values of the ANCP was 0.83 (p &lt; 0.001). The prediction of ANCP for 2003 and 2004 gave errors of only 6.5 and 7.0%. The estimated value of ANCP for 2005 is 2715 million nuts, which is 12% higher than the mean. The lead time of the prediction extends to 15 months but it may be extended with the use of seasonal climate forecasts to 24 months. Copyright © 2007 Royal Meteorological Society

Circulating Insulin-Like Growth Factor-I and Binding Protein-3 and the Risk of Breast Cancer

Four meta-analyses and literature reviews have concluded that a positive association exists between circulating levels of insulin-like growth factor-I (IGF-I) and IGF-binding protein-3 (IGFBP-3) and breast cancer risk for premenopausal but not postmenopausal women. Recently, a large prospective study reported an association with IGF-I and IGFBP-3 concentration for breast cancer diagnosed after, but not before, the age of 50 years; and in a large cohort of primarily premenopausal women, IGF-I and IGFBP-3 were not associated with breast cancer risk. We did a case-cohort study within the Melbourne Collaborative Cohort Study, which included a random sample of 1,901 women (subcohort) and 423 breast cancer cases diagnosed during a mean of 9.1 years of follow-up. IGF-I and IGFBP-3 concentrations were measured in plasma collected at baseline. The association between quartiles of IGF concentration and breast cancer risk was tested using a Cox model adjusted for known and potential confounders. The hazard ratio (HR) for breast cancer comparing the fourth with the first quartiles was 1.20 [95% confidence interval (95% CI), 0.87-1.65] for IGF-I and 1.09 (95% CI, 0.78-1.53) for IGFBP-3. Both associations varied with age: for IGF-I, the HRs for breast cancer comparing the fourth with the first quartiles were 0.60 (95% CI, 0.25-1.45) before age 50 and 1.61 (95% CI, 1.04-2.51) after age 60 (test for the log-linear trend of HR according to age, P = 0.05); for IGFBP-3, the HRs were 0.79 (95% CI, 0.34-1.83) before age 50 and 1.62 (95% CI, 1.03-2.55) after age 60 (test for log-linear trend, P = 0.08). IGF-I and IGFBP-3 were positively associated with breast cancer risk in older women but not in younger women. More prospective studies are needed to clarify the age dependence of the association between IGF-I and IGFBP-3 and breast cancer.