Asymptotic Interval Estimation of Some Cause-Specific Mortality Risk Measures in Epidemiologic Studies

The present paper describes the algebraic and statistical relationships between the population-based mortality risk measures, the Standardized Mortality Ratio (SMR) and the Standardized Risk Ratio (SRR), and their respective proportional mortality-based counterparts, the internally and externally Standardized Proportional Mortality Ratios (SPMR, S_ePMR). The paper shows, how under some reasonable assumptions, asymptotically precise inferences about population-based risk measures can be made from studies of proportional mortality. Through application of the asymptotic multivariate normal approximation to the multinomial distribution, shortest confidence intervals for the relative SMR (RSMR) involving the corresponding SPMR are constructed for any cause of death. This same technique is also used to construct asymptotic prediction intervals about the cause-specific S_ePMR which, with high probability, contains the corresponding relative SRR (RSRR). The utility of the proportional mortality measures SPMR and S_ePMR as estimators of the corresponding cause-specific risks RSMR and RSRR in occupational epidemiologic research is empirically evaluated using data from two recent occupational cohort studies. Asymptotic Bonferroni type simultaneous inferential techniques are also developed for these measures which facilitate the assessment of overall risk in the presence of several competing factors.     

International Society of Chronobiology: Membership Information

Most variables of interest in laboratory medicine show predictable changes with several frequencies in the span of time investigated. The waveform of such nonsinusoidal rhythms can be well described by the use of multiple components rhythmometry, a method that allows fitting a linear model with several cosine functions. The method, originally described for analysis of longitudinal time series, is here extended to allow analysis of hybrid data (time series sampled from a group of subjects, each represented by an individual series). Given k individual series, we can fit the same linear model with m different frequencies (harmonics or not from one fundamental period) to each series. This fit will provide estimations for 2m + 1 parameters, namely, the amplitude and acrophase of each component, as well as the rhythm-adjusted mean. Assuming that the set of parameters obtained for each individual is a random sample from a multivariate normal population, the corresponding population parameter estimates can be based on the means of estimates obtained from individuals in the sample. Their confidence intervals depend on the variability among individual parameter estimates. The vari-ance-covariance matrix can then be estimated on the basis of the sample covariances. Confidence intervals for the rhythm-adjusted mean, as well as for the amplitude-acrophase pair, of each component can then be computed using the estimated covariance matrix. The p-values for testing the zero-amplitude assumption for each component, as well as for the global model, can finally be derived using those confidence intervals and the t and F distributions. The method, validated by a simulation study and illustrated by an example of modeling the circadian variation of heart rate, represents a new step in the development of statistical procedures in chronobiology.     

Vegetation and landscape connectivity control wildfire intervals in unmanaged semi‐arid shrublands and woodlands in Australia

Aim The aim of this study was to determine how spatial variation in vegetation type and landscape connectivity influence fire intervals in a semi‐arid landscape with low relief and complex mosaics of woodland and shrubland vegetation. Location Our study focused on a 15,500‐km² area of relatively undisturbed and unmanaged land in south‐western Australia, referred to as the Lake Johnston region. Methods We modelled fire‐interval data from a 67‐year (1940–2006) digital fire history database using a two‐parameter Weibull function, and tested for the effects of vegetation type and landscape connectivity on estimates of the length of fire intervals (Weibull parameter b) and the dependence of fire intervals on fuel age (Weibull parameter c). Results Vegetation type and landscape connectivity significantly influenced fire interval probability distributions. Fire intervals in shrublands (dense low shrub assemblage) were typically shorter (b = 46 years) and more dependent on fuel age (c = 2.33) than most other vegetation types, while fire intervals in open eucalypt woodlands were much longer (b = 405 years) and were less dependent on fuel age (c = 1.36) than in shrub‐dominated vegetation types. Areas adjacent to or surrounded by salt lakes burnt less frequently (b = 319 years) and fire intervals were less dependent on fuel age (c = 1.48) compared with more exposed areas (e.g. b < 101 years, c > 1.68). Fire intervals in thickets (dense tall shrub assemblage) were longer (b = 101 years) than would be expected from fuel loads, most likely because they were protected from fire by surrounding fuel‐limited woodlands. Main conclusions Fire intervals in south‐western Australia are strongly influenced by spatial variation in vegetation (fuel structure) and landscape connectivity. The importance of fuel structure as a control of fire intervals in south‐western Australia contrasts with other landscapes, where topographical gradients or climatic influences may override the effects of underlying vegetation. We found that, regardless of low relief, topographical features such as large salt lake systems limited the connectivity and spread of fire among landscape units in an analogous manner to lakes or mountainous features elsewhere.     

Diminished Confidence Levels in the Interval Estimation of an Unknown Regressor in Model I of Linear Regression

For the model y=β₀ + β₁ x + e (model I of linear regression) in the literature confidence estimators of an unknown position x₀ are given at which either the expectation of y is given (see FIELLER, 1944; FINNEY, 1952), or realizations of y are given (see GRAYBILL, 1961). These confidence regions with level 1—α need not be intervals. The occurrence of interval shape is a random event. Its probability is equal to the power of the t test for the examination of the hypothesis H: β₁ = 0. The papers mentioned above claim to provide confidence intervals with level 1 ? α. But because of the restriction of (1 —α)—confidence regions to intervals the true confidence probability is the conditional probability W_c: W_c = P (the confidence region covers x₀| the region has interval shape). Here this conditional probability is shown to be less than 1 —α. Evidence on the possible deviations from 1 —α has been obtained by simulations.     

Approximate Confidence Intervals for Contrasts in the Balanced Three Factor Mixed Model

When conducting a statistical analysis of data from a designed experiment, an investigator is often interested in confidence intervals for contrasts of the fixed effects. If the analysis involves a mixed linear model, exact confidence intervals for contrasts of the fixed effects are not always available. In such cases, confidence intervals with approximate coverage probabilities must be used. As will be shown, this problem may be generalized to that of constructing a confidence interval for the parameter μ, where X is a normal random variable with mean μ and variance ∑ a_qθ_q, where a₁…,a_Q are known constants, U_q = n_qS/θ_q is a chi-squared random variable with n_q degrees of freedom, for each q = 1,…, Q, and X,U₁,…, U_Q are mutually independent. In this paper, we consider the case where Q = 3 and a₃ ≤0.     

Sexual selection has minimal impact on effective population sizes in species with high rates of random offspring mortality: An empirical demonstration using fitness distributions

The effective population size (N_e) is a fundamental parameter in population genetics that influences the rate of loss of genetic diversity. Sexual selection has the potential to reduce N_e by causing the sex‐specific distributions of individuals that successfully reproduce to diverge. To empirically estimate the effect of sexual selection on N_e, we obtained fitness distributions for males and females from an outbred, laboratory‐adapted population of Drosophila melanogaster. We observed strong sexual selection in this population (the variance in male reproductive success was ～14 times higher than that for females), but found that sexual selection had only a modest effect on N_e, which was 75% of the census size. This occurs because the substantial random offspring mortality in this population diminishes the effects of sexual selection on N_e, a result that necessarily applies to other high fecundity species. The inclusion of this random offspring mortality creates a scaling effect that reduces the variance/mean ratios for male and female reproductive success and causes them to converge. Our results demonstrate that measuring reproductive success without considering offspring mortality can underestimate N_e and overestimate the genetic consequences of sexual selection. Similarly, comparing genetic diversity among different genomic components may fail to detect strong sexual selection.     

Confidence Intervals on Ratios of Variance Components for the Unbalanced Two Factor Nested Model

The model considered in this article is the two-factor nested unbalanced variance component model: for p = 1, 2, …, P; q = 1, 2, …, Q_p; and r = 1, 2, …, R_pq. The random variables Y_pqr are observable. The constant μ is an unknown parameter, and A_p, B_pq and C_pqr are (unobservable) normal and independently distributed random variables with zero means and finite variances σ²_A, σ²_B, and σ²_C, respectively. Approximate confidence intervals on ?_A and ?_B using unweighted means are derived, where The performance of these approximate confidence intervals are evaluated using computer simulation. The simulated results indicate that these proposed confidence intervals perform satisfactorily and can be used in applied problems.     

IFN-γ+874 A/T polymorphism and cancer risk: an updated analysis based on 32 case-control studies

IFN-γ is a T-helper 1 cytokine and plays important roles in modulating almost all the immune responses, such as hematopoiesis, T-cell differentiation, antiproliferative, antiviral, and antitumor activities. A single nucleotide polymorphism (+874A/T) which is located in the first intron of the human IFN-γ gene can putatively influence the secretion of IFN-γ. Results from previous studies on the association of +874A/T polymorphism with different cancer types remained contradictory. In order to derive a more precise estimation of the relationship, a meta-analysis was performed by searching PubMed, Embase, CNKI, and Chinese Biomedicine Database. Thirty two studies including 4524 cases and 5684 controls were collected for IFN-γ + 874 A/T polymorphism. Summary odds ratios (OR) and corresponding 95% confidence intervals (CIs) for IFN-γ polymorphism and cancer were estimated using fixed- and random-effects models when appropriate. Overall, no evidence indicated that individuals carrying TT or AT genotypes had significantly increased cancer risk when compared with AA genotype carriers. However, stratified analysis by cancer types indicated a significantly increased risk of breast cancer (TT vs AA: OR = 1.58, 95% CI = 1.10–2.27, P_{heterogeneity} = 0.26; TT vs AT/AA: OR = 1.53, 95%CI = 1.14–2.06, P_{heterogeneity} = 0.19). Moreover, significantly elevated risks were observed in African and European populations when population is concerned. Interestingly, when stratified separately by population-based studies and hospital-based studies, significantly elevated risk was found among population-based studies. This meta-analysis suggests that the IFN-γ + 874 T allele is a low-penetrant risk factor for cancer development.     

Characterisation of the distribution of individual response times in bacterial infection of plants

The distribution of time of visible response to infection was followed after inoculation of Pseudomonas syringae pv. syringae onto the flowers of pear cv. Williams, Pseudomonas syringae pv. phaseolicola into the leaves of bean cvs Borlotto di Vigevano and Saluggia, Corynebacterium michiganense subsp. michiganense into the stem of tomato cvs Fiorentina and C 1402 and Agrobacterium sp. biovar 3 into the stem of sunflower cv. Egnazia at a dosage of either 0.5–32 times the median effective dose (ED₅₀) or 1–64 ED₅₀. The distribution contracted and the median response time decreased as the dose of inoculum was increased for each host-pathogen combination. Modified Weibull regressions with shape parameter 1< c < 2.5 gave a highly significant fit to the observed distributions of individual response times in all dose groups and host-pathogen combinations.     

Pairwise Comparisons Using Trimmed Means or M-Estimators when Working with Dependent Groups

For J dependent groups, let θ_j, j = 1, …, J, be some measure of location associated with the jth group. A common goal is computing confidence intervals for the pairwise differences, θ_j — θ_k, j < k, such that the simultaneous probability coverage is 1 — α. If means are used, it is well known that slight departures from normality (as measured by the Kolmogorov distance) toward a heavy-tailed distribution can substantially inflate the standard error of the sample mean, which in turn can result in relatively low power. Also, when distributions differ in shape, or when sampling from skewed distributions with relatively light tails, practical problems arise when the goal is to obtain confidence intervals with simultaneous probability coverage reasonably close to the nominal level. Extant theoretical and simulation results suggest replacing means with trimmed means. The Tukey-McLaughlin method is easily adapted to the problem at hand via the Bonferroni inequality, but this paper illustrates that practical concerns remain. Here, the main result is that the percentile t bootstrap method, used in conjunction with trimmed means, gives improved probability coverage and substantially better power. A method based on a one-step M-estimator is also considered but found to be less satisfactory.     

Inference on Risk Rates Based on Mortality Data Under Censoring and Competing Risks Using Parametric Models

In this paper we consider the competing risks model where the risks may not be independent. We assume both fixed and random censoring. The random censoring mechanism could have either a parametric or a non-parametric form. The life distributions and the parametric censoring distribution considered are exponential or Weibull. The expressions for the asymptotic confidence intervals for various parameters of interest under different models, using the estimated Fisher information matrix and parametric bootstrap techniques have been derived. Monte Carlo simulation studies for some of these cases have been carried out.     

The association between three AXIN2 variants and cancer risk

Plenty of epidemiological studies have assessed the effects of AXIN2 polymorphisms on the risk of developing cancer, but the available results were somewhat inconclusive. Odds ratios (ORs) with 95% confidence intervals (CIs) were utilized to investigate the relationship between three AXIN2 variants (rs2240308 C/T, rs1133683 C/T, and rs4791171 A/G) and overall cancer susceptibility. In silico tools were undertaken to investigate the correlation of AXIN2 expression with cancer risk and survival time. Furthermore, we explored the serum expression of AXIN2 by enzyme-linked immunosorbent assay. A total of 4167 cancer patients and 3515 control subjects were evaluated. The overall results demonstrated that there was no major association of these polymorphisms on cancer risk. However, stratified analysis by cancer type showed evidence that rs2240308 C/T polymorphism had a lower risk in lung cancer (OR, 0.76; 95% CI, 0.63-0.92; P_{heterogeneity} = 0.865) and prostate cancer (OR, 0.54; 95% CI, 0.35-0.84; P_{heterogeneity} = 0.088) by heterozygote comparison. Similar results were indicated in Asian descendants and population-based studies. In silico analysis showed evidence that AXIN2 expressions in lung cancer and prostate cancer were lower than that in normal counterpart. High expression of AXIN2 may have longer overall survival time than low expression group for lung cancer participants. In addition, individuals who were CC/TC carriers had a higher serum expression level than TT carriers. In conclusion, this pooled analysis suggested that AXIN2 rs2240308 C/T variant may decrease both lung and prostate cancer susceptibility, particularly in Asian descendants and population-based studies. Future large scale and well-designed research are required to validate these effects in more detail.     

Density effect, self-thinning and size distribution in Pinus densiflora Sieb. et Zucc. stands

The competition-density (C-D) effect for given times and self-thinning over time in even-aged, natural, pure stands of Pinus densiflora Sieb. et Zucc. were analyzed with the reciprocal equation of the C-D effect in self-thinning stands, and the equation describing the time-trajectory of mean stem volume and stand density. The C-D effect and self-thinning were consistently well explained by the two equations. Differences in mean stem volume and in stand density among the stands tended to merge with increasing stand age. The self-thinning line with a slope of approximately –3/2 was reached by the higher density stand prior to the medium and lower density stands. The skewness of tree height distribution showed positive values, which means that the distribution is more or less L-shaped, and in addition the skewness decreased with increasing mean tree height, which indicates that smaller trees died as the stands grew. This trend is consistent with the asymmetric (one-sided) competition hypothesis that self-thinning is driven by competition for light. The tree height distribution was analyzed using the Weibull distribution. The location parameter h _min of the Weibull distribution increased with increasing stand age, and the scale parameter a tended to increase slightly with increasing stand age. The range of the shape parameter b of the Weibull distribution corresponded to that of the skewness.     

Simultaneous Statistical Inference Concerning the Standardized Mortality Ratios (SMB) of Several Strata in an Epidemiologic Study

In the present paper, simultaneous prediction intervals are constructed for some mortality measures involving real data in a recent retrospective epidemiologic study of a cohort of man-made mineral fiber workers. The object is to compare a test population with a standard population in which the workers are exposed to several levels (say K) of a suspected carcinogen and the number of deaths in the K exposure groups are recorded. The SMR is chosen as a mortality measure for this comparison. If the total number of deaths d. in the entire study is known, the number of deaths in the various strata become dependent random variables. Using univariate statistical procedures to test the significance of the individual SMR's is inappropriate and may give misleading conclusions. The present paper shows how to test the simultaneous statistical significance of the SMR's of the K exposure groups, i.e., to test the simultaneous null hypothesis H_o : E(SMR₁) = E(SMR₂) =…E(SMR_k) = 100. If the null hypothesis H_o is rejected, it is shown how to identify the SMR (or the SMR's) which contributed to the rejection of H_o. The power function of such a test is also constructed for some simple and useful alternative hypotheses.     

A Lagrangian Gamma Distribution of the Second Kind

The distribution of the time T for the occurrence of the rth event is derived in a linear function Poisson process, which belongs to a recently introduced family of distributions (JANARDAN and RAO, 1981), called Lagrangian distributions of the second kind (LD₂). In analogy with the ordinary Poisson process, the distribution of the random variable T has been termed the Lagrangian Gamma distribution of the second kind (LG₂); several of its properties and special cases are studied. The frequency function is graphed for some parameter values.     

Sharp simultaneous confidence intervals for the means of selected populations with application to microarray data analysis

Summary Simultaneous inference for a large number, N, of parameters is a challenge. In some situations, such as microarray experiments, researchers are only interested in making inference for the K parameters corresponding to the K most extreme estimates. Hence it seems important to construct simultaneous confidence intervals for these K parameters. The naïve simultaneous confidence intervals for the K means (applied directly without taking into account the selection) have low coverage probabilities. We take an empirical Bayes approach (or an approach based on the random effect model) to construct simultaneous confidence intervals with good coverage probabilities. For N= 10,000 and K= 100, typical for microarray data, our confidence intervals could be 77% shorter than the naïve K‐dimensional simultaneous intervals.     

A Mixed Model for Binary Data: The Modified X2-test

In this paper, a statistical model for clinical trials is presented for the special situation that a varying and unstructered number of binary responses is obtained from each subject. The assumptions of the model are the following: 1.) For each subject there is a (constant) individual Bernoulli parameter determining the distribution of the binary responses of this subject. 2.) The Bernoulli parameters associated with the subjects are realizations of independent random variables with distributions P_g in treatment group g(g = 1, 2, …, G). 3.) Given the value of the Bernoulli parameter, the observations are stochastically independent within each subject. Under these assumptions, a test statistic is derived to test the hypothesis H₀:E(P₁) = E(P₂) = … = E(P_G). It is proven and demonstrated by simulations, that the test statistic asymptotically (i.e. for a large number of subjects) follows the X²-distribution.     

Analytical Quantile Solution for the S‐distribution,Random Number Generation and Statistical Data Modeling

The selection of a specific statistical distribution as a model for describing the population behavior of a given variable is seldom a simple problem. One strategy consists in testing different distributions (normal, lognormal, Weibull, etc.), and selecting the one providing the best fit to the observed data and being the most parsimonious. Alternatively, one can make a choice based on theoretical arguments and simply fit the corresponding parameters to the observed data. In either case, different distributions can give similar results and provide almost equivalent models for a given data set. Model selection can be more complicated when the goal is to describe a trend in the distribution of a given variable. In those cases, changes in shape and skewness are difficult to represent by a single distributional form. As an alternative to the use of complicated families of distributions as models for data, the S‐distribution [Voit, E. O. (1992) Biom. J. 7 , 855–878] provides a highly flexible mathematical form in which the density is defined as a function of the cumulative. S‐distributions can accurately approximate many known continuous and unimodal distributions, preserving the well known limit relationships between them. Besides representing well‐known distributions, S‐distributions provide an infinity of new possibilities that do not correspond with known classical distributions. Although the utility and performance of this general form has been clearly proved in different applications, its definition as a differential equation is a potential drawback for some problems. In this paper we obtain an analytical solution for the quantile equation that highly simplifies the use of S‐distributions. We show the utility of this solution in different applications. After classifying the different qualitative behaviors of the S‐distribution in parameter space, we show how to obtain different S‐distributions that accomplish specific constraints. One of the most interesting cases is the possibility of obtaining distributions that acomplish P(X ≤ X_c) = 0. Then, we demonstrate that the quantile solution facilitates the use of S‐distributions in Monte‐Carlo experiments through the generation of random samples. Finally, we show how to fit an S‐distribution to actual data, so that the resulting distribution can be used as a statistical model for them.     

Seedling dynamics of <Emphasis Type="Italic">Acer mono</Emphasis> and <Emphasis Type="Italic">Fagus crenata</Emphasis>: an environmental filter limiting their adult distributions

Spatial pattern of a biotic population may change over time as its component individuals grow or die out, but whether this is the case for desert annual plants is largely unknown. Here we examined seasonal changes in spatial patterns of two annuals, Eriogonum abertianum and Haplopappus gracilis, in initial (winter) and final (summer) densities. The density was measured as the number of individuals from 384 permanent quadrats (each 0.5 m × 0.5 m) in the Chihuahuan Desert near Portal, Arizona, USA. We used three probability distributions (binomial, Poisson, and negative binomial or NB) that represent three basic spatial patterns (regular, random, and clumped) to fit the observed frequency distributions of densities of the two annuals. Both species showed clear clumped patterns as characterized by the NB and had similar inverse J-shaped frequency distribution curves in two density categories. Also, both species displayed a reduced degree of aggregation from winter to summer after the spring drought (massive die-off), as indicated by the increased k-parameter of the NB and decreased values of another NB parameter p, variance/mean ratio, Lloyd’s Index of Patchiness, and David and Moore’s Index of Clumping. Further, we hypothesized that while the NB (i.e., Poisson-logarithmic) well fits the distribution of individuals per quadrat, its components, the Poisson and logarithmic, may describe the distributions of clumps per quadrat and of individuals per clump, respectively. We thus obtained the means and variances for (1) individuals per quadrat, (2) clumps per quadrat, and (3) individuals per clump. The results showed that the decrease of the density from winter to summer for each plant resulted from the decrease of individuals per clump, rather than from the decrease of clumps per quadrat. The great similarities between the two annuals indicate that our observed temporal changes in spatial patterns may be common among desert annual plants.     

Effect of point substitutions in the <Emphasis Type="Italic">MnSOD,GPX1</Emphasis>, and <Emphasis Type="Italic">GSTP1</Emphasis> genes on the risk of familial and sporadic breast cancers in residents of Altai Krai

The frequencies of the polymorphic gene variants MnSOD Ala₉Val, GPX1 Pro₁₉₈Leu, and GSTP1 Ile₁₀₅Val were estimated in female residents of Altai krai with breast cancer. The frequency distributions of the genotypes for all genes studied in both patients and control subjects fit the Hardy-Weinberg equilibrium. The estimated frequencies of the genotypes for the studied genes in the control group did not differ from those earlier reported for Caucasoid women living in Europe. The T (rs1050450) allele of the GPX1 gene was demonstrated to protect against sporadic breast cancer (OR = 0.74 (95% CI = 0.58−0.94), p = 0.012). Carriers of the genotype combination MnSOD CC + GPX1 CC were found to have a 1.6 times higher risk of sporadic breast cancer compared to the control group (OR = 1.59 (1.05−2.41), p = 0.0258). The polymorphic loci GSTP1 (rs1695) and MnSOD (rs4880) were not found to be significantly associated with the risk of familial or sporadic breast cancer.