On estimation for accelerated failure time models with small or rare event survival data.

BACKGROUND: Separation or monotone likelihood may exist in fitting process of the accelerated failure time (AFT) model using maximum likelihood approach when sample size is small and/or rate of censoring is high (rare event) or there is at least one strong covariate in the model, resulting in infinite estimates of at least one regression coefficient. METHODS: This paper investigated the properties of the maximum likelihood estimator (MLE) of the regression parameters of the AFT models for small sample and/or rare-event situation and addressed the problems by introducing a penalized likelihood approach. The penalized likelihood function and the corresponding score equation is derived by adding a penalty term to the existing likelihood function, which was originally proposed by Firth (Biometrika, 1993) for the exponential family models. Further, a post-hoc adjustment of intercept and scale parameters is discussed keeping them out of penalization to ensure accurate prediction of survival probability. The penalized method was illustrated for the widely used log-location-scale family models such as Weibull, Log-normal and Log-logistic distributions and compared the models and methods uisng an extensive simulation study. RESULTS: The simulation study, performed separately for each of the log-location-scale models, showed that Firth's penalized likelihood succeeded to solve the problem of separation and achieve convergence, providing finite estimates of the regression coefficients, which are not often possible by the MLE. Furthermore, the proposed penalized method showed substantial improvement over MLE by providing smaller amount of bias, mean squared error (MSE), narrower confidence interval and reasonably accurate prediction of survival probabilities. The methods are illustrated using prostate cancer data with existence of separation, and results supported the simulation findings. CONCLUSION: When sample size is small (≤ 50) or event is rare (i.e., censoring proportion is high) and/or there is any evidence of separation in the data, we recommend to use Firth's penalized likelihood method for fitting AFT model.

Bio-inspired Analytical Heuristics to Study Pine Wilt Disease Model.

This paper portrays the dynamics of pine wilt disease. The specific formula for reproduction number is accomplished. Global behavior is completely demonstrated on the basis of the basic reproduction number [Formula: see text]. The disease-free equilibrium is globally asymptotically stable for [Formula: see text] and in such a case, the endemic equilibrium does not exist. If [Formula: see text] exceeds one, the disease persists and the unique endemic equilibrium is globally asymptotically stable. Global stability of disease-free equilibrium is proved using a Lyapunov function. A graph-theoretic approach is applied to show the global stability of the unique endemic equilibrium. Sensitivity analysis has been established and control strategies have been designed on the basis of sensitivity analysis.

Impact of eNOS 27-bp VNTR (4b/a) gene polymorphism with the risk of Systemic Lupus Erythematosus in south Indian subjects.

OBJECTIVE: Endothelial nitric oxide synthase (eNOS) is constitutively expressed by vascular endothelium including glomerular endothelium. Functional polymorphisms, -786T>C (rs2070744) promoter variant, 27 bp VNTR (4b/a) in intron 4 and 894G>T (rs1799983) exon variant of eNOS are known to alter the eNOS expression and activity leading to altered NO levels and contribute to the development of vascular and renal disease risk. Thus it might have a role in SLE risk and development of glomerulonephritis. Hence, the present study is aimed to investigate the role of eNOS polymorphisms in South Indian SLE patients. METHODS: Five hundred and four subjects (219 SLE cases and 285 controls) were included in the present case-control study. Genotyping was done using polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) for -786T>C and 894G>T SNPs. Another, 4a4b variable number of tandem repeat polymorphism was genotyped using direct PCR method using primer pairs flanking the 27 bp direct repeat region in intron 4 of eNOS gene. RESULTS: Our analysis revealed that intron 4 27 bp VNTR genotype frequency differ significantly between the SLE patients and controls (OR: 1.73, 95% CI %:1.18-2.54, P = 0.004). Further, "a allele" frequency was significantly higher in SLE patients as compared to the controls (20 vs. 13.8%) (OR: 1.56, 95%CI: 1.11-2.18, P = 0.01). However, promoter polymorphism -786T>C and missense variant 894G>T were not significantly different between the SLE cases and controls (OR: 0.92, 95%CI: 0.64-1.33, P = 0.7 and OR: 1.4, 95%CI: 0.95-2.06, P = 0.095 respectively). Furthermore, no association was found between any of the three polymorphisms with lupus nephritis phenotype. Increased plasma nitrate levels were observed in SLE patients (36.79 ±â€¯2.83 µM/L) as compared to healthy controls (28.53 ±â€¯1.94 µM/L) (P = 0.01). In addition, the genotype-based simulations have indicated that combined effect of eNOS polymorphisms contribute to 30.5% variability in NO production. CONCLUSION: Results of the present study indicate that 27-bp VNTR polymorphism in intron 4 of eNOS gene polymorphism may be the significant risk factor for SLE in south Indian subjects.