Survival analysis of acute myocardial infarction patients using non-parametric and parametric approaches

In this paper, an investigation about the survival pattern of acute myocardial infarction patients was explored, using non-parametric and parametric modeling strategies. Median survival time and their associated confidence intervals are often used to summarize the survival pattern of a group of patients in clinical data with failure- time end points. Although there is an extensive literature on this topic but to the best of our knowledge no study exists which compare the survival pattern of AMI patients using the non-parametric and parametric modeling strategies. Life table estimation of cumulative survival function of AMI patients stratified by age and marital status show a poor prognosis for older and married patients respectively. The estimated median survival time of overall AMI patients by clinical life table method is 3.31(95% confidence interval, 2.80-3.82) years. Probability plotting and Anderson-Darling goodness of fit test were used to compare the theoretical distributions viz. Weibull and Gamma distributions. Among these, the Weibull distribution is found to be the best fit to the observed data. The median survival time of overall AMI patients using Weibull distribution is 2.45(95% confidence interval, 1.87-3.03) years. Knowledge of median survival time will enable the physicians to develop strategies for preventive cardiology so that survival time of new AMI patients could be improved. Also it can be considered as a baseline for further studies

Trend in BMI z-score among Private Schools’ Students in Delhi using Multiple Imputation for Growth Curve Model

Objective: The aim of the study is to assess the trend in mean BMI z-score among private schools’ students from their anthropometric records when there were missing values in the outcome. Methodology: The anthropometric measurements of student from class 1 to 12 were taken from the records of two private schools in Delhi, India from 2005 to 2010. These records comprise of an unbalanced longitudinal data that is not all the students had measurements recorded at each year. The trend in mean BMI z-score was estimated through growth curve model. Prior to that, missing values of BMI z-score were imputed through multiple imputation using the same model. A complete case analysis was also performed after excluding missing values to compare the results with those obtained from analysis of multiply imputed data. Results: The mean BMI z-score among school student significantly decreased over time in imputed data (β= -0.2030, se=0.0889, p=0.0232) after adjusting age, gender, class and school. Complete case analysis also shows a decrease in mean BMI z-score though it was not statistically significant (β= -0.2861, se=0.0987, p=0.065). Conclusions: The estimates obtained from multiple imputation analysis were better than those of complete data after excluding missing values in terms of lower standard errors. We showed that anthropometric measurements from schools records can be used to monitor the weight status of children and adolescents and multiple imputation using growth curve model can be useful while analyzing such dat

A Multistate Markov Model Based on CD4 Cell Count for HIV/AIDS Patients on Antiretroviral Therapy (ART)

Abstract: The main purpose of this study is to assess the impact of Antiretroviral Therapy (ART) by using a multistate Markov model to estimate transition intensities and transition probabilities among various states (transient as well as absorbing) of the AIDS patients. A total of 580 AIDS patients were included in this study who are undergoing Antiretroviral Therapy treatment in the ART centre in New Delhi during the period of April 2004 to April 2011. The patients are classified in different states on the basis of their available CD4 cell counts. The authors also estimated the mean sojourn time and total length of stay in each state before absorption, and also examined the effects of explanatory variables (i.e Age, Sex, Mode of transmission) on the rates of transition using Cox's proportional hazard model

An Application of Gamma Generalized Linear Model for Estimation of Survival Function of Diabetic Nephropathy Patients

Diabetic nephropathy (DN) is a generic term referring to deleterious effect on renal structure and/or function caused by diabetes mellitus. World Health Organization estimates that diabetes affects more than 170 million people worldwide and this number may rise to 370 million by 2030. The rate of rise in Serum Creatinine (SrCr) is a well-accepted marker for the progression of Diabetic Nephropathy (DN). In this paper, survival functions of type 2 diabetic patients with renal complication are estimated. Firstly, most appropriate distribution for duration of diabetes is selected through minimum Akaike Information Criterion value, Gamma distribution is found to be an appropriate model. Secondly, the parameters estimates of the selected distribution are obtained by fitting a Generalized Linear Model (GLM), with duration of diabetes as the response variable and predictors as SrCr and number of successes (number of times SrCr values exceed its normal range (1.4 mg/dl)). These covariates are linked with the response variable using two different link functions namely log and reciprocal links. Using the estimates of parameters obtained from generalized linear regression analysis, survival functions for different durations under both the links are estimated. Further we compared the estimated survival functions under both the links with Kaplan Meier (KM) estimates graphically. Findings suggested that the Kaplan Meier estimate and Gamma distribution under both links provided a close estimate of survival functions. Median survival time is 16.3 years and 16.8 years obtained from KM method and Gamma GLM respectively

Bayesian Formulation of Time-Dependent Carrier-Borne Epidemic Model with a Single Carrier

In this paper, the time dependent carrier-borne epidemic model defined by Weiss in 1965 has been adopted into a Bayesian framework for the estimation of its parameters. A complete methodological structure has been proposed for estimating the relative infection rate and probability of survival of k out of m susceptibles after time t from the start of the epidemic. The methodology has been proposed assuming a single carrier to simplify the study of the behavioral validity of the fitted Bayesian model with respect to time and relative infection rate. Further, the proposed model has been implemented on two real data sets- the typhoid epidemic data from Zermatt in Switzerland and the Covid-19 epidemic data from Kerala in India. Results show that the proposed methodology produces reliable predictions which are consistent with those of the maximum likelihood estimates and with expected epidemiological patterns

A Correlation Technique to Reduce the Number of Predictors to Estimate the Survival Time of HIV/ AIDS Patients on ART

Till now, many research papers have been published which aims to estimate the survivle time of the HIV/AIDS patients taking into consideration all the predictors viz, Age, Sex, CD4, MOT, Smoking, Weight, HB, Coinfection, Time, BMI, Location Status, Marital Status, Drug etc, although all the predictors need not to be included in the model. Since some of the predictors may be correlated/ associated and may have some influence on the outcome variable, therefore, instead of taking both the significantly correlated/ associated predictors, we may take only one of the two. In this way, we may be able to reduce the number of predictors without affecting the estimated survival time. In this paper we have tried to reduce the number of predictors by determining the highly positively correlated predictors and then evaluating the effect of correlation/ association on the survival time of HIV/AIDS patients. These predictors that we have considered in the starting are Age, Sex, State, Smoking, Alcohol, Drugs, Opportunistic Infections (OI), Living Status (LS), Occupation (OC), Marital Status (MS) and Spouse for the data collected from 2004 to 2014 of AIDS patients in an ART center of Delhi, India. We have performed one – way ANOVA to test the association between a quantitative and a categorical variable and Chi-square test to test between two categorical variables. To select one of the two highly correlated/ associated predictors, a suitable model is fitted keeping one predictor independent at a time and other dependent and the model having the smaller AIC is considered and the independent variable in the model is included in the modified model. The fitted models are logistic, linear and multinomial logistic depending on the type of the independent variable to be fitted. Then the true model (having all the predictors) and the modified model (with reduced number of predictors) are compared on the basis of their AICs and the model having minimum AIC is chosen. In this way we could reduce the number of predictors by almost 50% without affecting the estimated survival time with a reduced standard error

Estimation of survival times of HIV-1 infected children for doubly and interval censored data

International studies have established the association of antiretroviral (ARV) therapy and survival in HIV-infected patients. Our study was carried out to confirm the influence of ARV therapy on survival in a group of vertically transmitted HIV-1 infected children. We employed Turnbull’s methods based on double censoring (1974) and interval censoring (1976) to estimate the survival time distribution for children receiving and not receiving ARV therapy. It was noted that children undergoing ARV therapy had a longer survival than those not under treatment. In our study group, children under treatment survived for 15 years with a probability of almost 95% while children not under treatment had a survival of 11 years with a probability of 75%. Further, the estimates of survival times as obtained by the interval censoring mechanism were found to be more precise than those obtained by the double censoring mechanism. We even utilized imputation approach which showed that the width of the band of estimates was narrower for interval censored data as compared to double censored data

Examining the Effect of Reduction of Predictors Affecting the Survival Time of HIV/ AIDS Patients using a Multiple Correlation/ Association Technique

The main objective of this paper is to reduce the number of predictors using multiple correlation/ association while estimating the survival of HIV/AIDS. MANOVA is used to test the association when we have two or more continuous predictors and two or more categorical predictors. Also, log-linear models are used to test the joint independence of two or more predictors. The survival times are estimated using AFTM. It is observed that the estimated survival times are not affected by the reduction of predictors from 11 to 4. Also, the estimates so obtained are more efficient as they have reduced standard error. Results of the proposed reduction method were also compared with the results of the two existing variable reduction methods, viz, LASSO and Net- Elastic method

On the estimation of survival time of cardio-vascular disease patients with random number of myocardial infarctions using parametric and semi-parametric methods

Cardiovascular disease (CVD) is the leading cause of mortality in developing countries.  CVD  studies that involve the recording  of  two  or  more distinct and well-defined  myocardial infarctions (MI) occurring  over  time  in   the  same  patient  give rise to recurrent  event  data. In  recent  years  a  variety  of  fruitful   statistical   methods    have  been proposed for the analysis of recurrent events  in  medical  areas. The  present  article  is  concerned  with   the  estimation   of   the  survival  time   of    CVD   patients,  in   the  presence   of   recurrent    myocardial infarctions followed  by  a  terminal event    death, under    three    different   possibilities,  i.e., the inter-event times between heart attacks follow gamma distribution,    the  number   of    heart attacks for   an individual   occur   with  time   independent   constant   intensity   λ ,  which   is    varying   across   individuals,   and  the hazard  rates  for   the   recurrent heart attacks  vary  from  different  attacks  for  the  same  individual. Cox's proportional hazard model has also been applied to study the effect of age at the time of first MI  and the number of MI's experienced by the patient, on the survival time of CVD patients. Prior to that proportionality assumption has been tested. The methods  are   applied  to  a CVD  patients data    set  obtained  from  Dr.Ram  Manohar  Lohia  (R.M.L)  Hospital,   Delhi. The major advantage  of   developing   models    for  estimating the survival time of CVD patients is that the  treatment comparisons  can  be  designed so  that  the  expected   survival time of new CVD patients   can  be   predicted   and   improved  after the first MI. Also it can be used as a baseline for further studies