Determinants of waiting time to third pregnancy using censored linear regression

The intervals between pregnancies have important effects on fertility and maternal and infant health outcomes. This study uses linear regression with censored observation to assess the determinants of the waiting time to third pregnancy. The analysis is applied to data from the Second Malaysian Family Life Survey consisting of 1172 women who had their second delivery ending in a live birth. Contraceptive use, age of the woman, duration of breast-feeding, length of previous pregnancy interval and education of the woman all affect the waiting time to third pregnancy significantly.     

Segmented linear regression models applied to the analysis of data from a cross-sectional growth experiment

Several different methods of analysis are applied to data consisting of weight measurements, taken at specified post-treatment times, of harvested thyroids from rats given one of four treatments. Previous studies of this type of data indicated that the growth is initially rapid, and that a second phase of less rapid growth is followed by a final phase in which little additional growth occurs. The data are further characterized by increasing variance through time. The primary purpose of the analysis is to study the effect of the treatments at the end of the study period. One-way analysis of variance tests among groups are performed on each day, but the results are not particularly helpful. However, results from two-way analyses of variance (over subsets of days and groups) are consistent with the three phase model and accordingly indicate significant group differences during each. Finally, maximum likelihood methods are used to fit a three part segmented linear regression model.     

Using linear and non-linear regression to fit biochemical data

For biochemists or chemists the most common form of data analysis is likely to be regression analysis. This is a technique to find the ‘best’ values for various experimental parameters; defined as those values which, when used in an appropriate equation, result in the minimum deviation of the calculated results from the experimental data. Despite the widespread application of regression analysis, the basis of the technique and the underlying assumptions are often poorly understood or appreciated. This article describes the basics of linear and non-linear regression, the role of ‘weighting’ and the potential pitfalls of such analyses.     

Prediction of body volume by a stepwise linear regression technique

Body volume and 35 anthropometric measurements were obtained from 88 active soldiers using standard techniques. These anthropometric measurements were examined for their possible relationships to body volume using stepwise linear regression analysis. Four measurements (Body weight, anterior thigh skinfold thickness, subscapular skinfold thickness and suprailiac skinfold thickness) accounted for 99.7% of the variation in body volume and the introduction of each of these measurements in the equation was significant. The regression equation for predicting body volume from these 4 anthropometric measurements had a multiple correlation coefficient of 0.9987 (P less than 0.001). Body weight alone was correlated with body volume to the extent of 0.9966. An attempt has therefore been made to develop a multiple linear regression equation without incorporation of body weight in the regression analysis. Nine measurements were selected by stepwise linear regression analysis for predicting body volume. These nine measurements accounted for 97.1% of the variation in body volume. These equations have been validated on another small sample of 22 soldiers. The analysis has also revealed that a direct regression of body density from the anthropometric variables gives more accurate results than when estimated body volumes are utilized for calculating body density.     

Comparison of logistic regression and linear regression in modeling percentage data

Percentage is widely used to describe different results in food microbiology, e.g., probability of microbial growth, percent inactivated, and percent of positive samples. Four sets of percentage data, percent-growth-positive, germination extent, probability for one cell to grow, and maximum fraction of positive tubes, were obtained from our own experiments and the literature. These data were modeled using linear and logistic regression. Five methods were used to compare the goodness of fit of the two models: percentage of predictions closer to observations, range of the differences (predicted value minus observed value), deviation of the model, linear regression between the observed and predicted values, and bias and accuracy factors. Logistic regression was a better predictor of at least 78% of the observations in all four data sets. In all cases, the deviation of logistic models was much smaller. The linear correlation between observations and logistic predictions was always stronger. Validation (accomplished using part of one data set) also demonstrated that the logistic model was more accurate in predicting new data points. Bias and accuracy factors were found to be less informative when evaluating models developed for percentage data, since neither of these indices can compare predictions at zero. Model simplification for the logistic model was demonstrated with one data set. The simplified model was as powerful in making predictions as the full linear model, and it also gave clearer insight in determining the key experimental factors.     

A semiparametric model for regression analysis of interval-censored failure time data

Left-, right-, and interval-censored response time data arise in a variety of settings, including the analyses of data from laboratory animal carcinogenicity experiments, clinical trials, and longitudinal studies. For such incomplete data, the usual regression techniques such as the Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-220) proportional hazards model are inapplicable. In this paper, we present a method for regression analysis which accommodates interval-censored data. We present applications of this methodology to data sets from a study of breast cancer patients who were followed for cosmetic response to therapy, a small animal tumorigenicity study, and a clinical trial.     

Mean time to resolution of gene duplication

The mean time to resolution of gene duplication (T_r) is studied in this paper under the double null recessive (DNR) and haplo-insufficient (HI) models within the same analytical and simulation framework. We show that when population size is not too small (more precisely Nμ > 0.1), T_r for unlinked duplication is usually larger than that for linked and T_r for unlinked duplication under the HI model might be greatly prolonged, which were consistent with previous observations. Furthermore, by analytical approach we here indicate the primary underlying mechanism is that the frequency of the original (or wild-type) chromosomal haplotype of the linked duplication decreases nearly exponential to zero with time while that of the unlinked decreases quickly to an quasi-equilibrium; and this phenomenon is particularly profound under the HI model, because the quasi-equilibrium frequency of the original chromosomal haplotype (x₀) under the HI model is higher than that under the DNR model. These results suggest that recombination and HI model might jointly contribute to the marked prolongation of T_r even in a modest population. The prolonged T_r and higher quasi-equilibrium frequency of the original allele at both duplicated loci might have offered more opportunities for the emergence of novel genes.     

Semiparametric regression analysis of interval-censored data

We propose a semiparametric approach to the proportional hazards regression analysis of interval-censored data. An EM algorithm based on an approximate likelihood leads to an M-step that involves maximizing a standard Cox partial likelihood to estimate regression coefficients and then using the Breslow estimator for the unknown baseline hazards. The E-step takes a particularly simple form because all incomplete data appear as linear terms in the complete-data log likelihood. The algorithm of Turnbull (1976, Journal of the Royal Statistical Society, Series B 38, 290-295) is used to determine times at which the hazard can take positive mass. We found multiple imputation to yield an easily computed variance estimate that appears to be more reliable than asymptotic methods with small to moderately sized data sets. In the right-censored survival setting, the approach reduces to the standard Cox proportional hazards analysis, while the algorithm reduces to the one suggested by Clayton and Cuzick (1985, Applied Statistics 34, 148-156). The method is illustrated on data from the breast cancer cosmetics trial, previously analyzed by Finkelstein (1986, Biometrics 42, 845-854) and several subsequent authors.     

Multikink quantile regression for longitudinal data with application to progesterone data analysis

Motivated by investigating the relationship between progesterone and the days in a menstrual cycle in a longitudinal study, we propose a multikink quantile regression model for longitudinal data analysis. It relaxes the linearity condition and assumes different regression forms in different regions of the domain of the threshold covariate. In this paper, we first propose a multikink quantile regression for longitudinal data. Two estimation procedures are proposed to estimate the regression coefficients and the kink points locations: one is a computationally efficient profile estimator under the working independence framework while the other one considers the within-subject correlations by using the unbiased generalized estimation equation approach. The selection consistency of the number of kink points and the asymptotic normality of two proposed estimators are established. Second, we construct a rank score test based on partial subgradients for the existence of the kink effect in longitudinal studies. Both the null distribution and the local alternative distribution of the test statistic have been derived. Simulation studies show that the proposed methods have excellent finite sample performance. In the application to the longitudinal progesterone data, we identify two kink points in the progesterone curves over different quantiles and observe that the progesterone level remains stable before the day of ovulation, then increases quickly in 5 to 6 days after ovulation and then changes to stable again or drops slightly.     

使用SPSS线性回归实现通径分析的方法

由于通径分析可以将因变量与自变量的相互影响(相关系数)分解为直接影响(通径系数)和间接影响(间接通径系数),因此在遗传学等领域受到广泛的重视。目前在软件实现方法上,一方面缺乏必要的正态性检验,另一方面通径系数及间接相关系数计算步骤过于繁琐,限制通径分析的教学和使用。在应用中,我们注意到通过SPSS的线性回归"Linear"程序可以一次性获得计算通径系数的全部数据,从而简化通径分析的步骤。