Gurprit Grover

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.

Multiple imputation of censored survival data in the presence of missing covariates using restricted mean survival time

Missing covariates data with censored outcomes put a challenge in the analysis of clinical data especially in small sample settings. Multiple imputation (MI) techniques are popularly used to impute missing covariates and the data are then analyzed through methods that can handle censoring. However, techniques based on MI are available to impute censored data also but they are not much in practice. In the present study, we applied a method based on multiple imputation by chained equations to impute missing values of covariates and also to impute censored outcomes using restricted survival time in small sample settings. The complete data were then analyzed using linear regression models. Simulation studies and a real example of CHD data show that the present method produced better estimates and lower standard errors when applied on the data having missing covariate values and censored outcomes than the analysis of the data having censored outcome but excluding cases with missing covariates or the analysis when cases with missing covariate values and censored outcomes were excluded from the data (complete case analysis).

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.

Estimation of Survivorship Function Based on Doubly Censored Data with Application to HIV/AIDS

Left censoring concept has been defined in different ways in statistical applications. Turnbull (1974) defines it in a particular way. Whereas in recent literature, especially in epidemiological studies, it has been defined in another way. This difference between the two approaches is the main reason that despite simplicity, Turnbull method cannot be applicable in all cases of doubly censored data. In this article we present a modified Turnbull method for analysis of doubly censored data adequate with recent definition. Comparison has been done with other statistical methods, including imputation estimator, full likelihood-based and conditional likelihood-based approach using Iranian HIV data.

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.

Multiple imputation for gamma outcome variable using generalized linear model

ABSTRACT We used a proper multiple imputation (MI) through Gibbs sampling approach to impute missing values of a gamma distributed outcome variable which were missing at random, using generalized linear model (GLM) with identity link function. The missing values of the outcome variable were multiply imputed using GLM and then the complete data sets obtained after MI were analysed through GLM again for the estimation purpose. We examined the performance of the proposed technique through a simulation study with the data sets having four moderate and large proportions of missing values, 10%, 20%, 30% and 50%. We also applied this technique on a real life data and compared the results with those obtained by applying GLM only on observed cases. The results showed that the proposed technique gave better results for moderate proportions of missing values.

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 data

On the assessment of various factors effecting the improvement in CD4 count of aids patients undergoing antiretroviral therapy using generalized Poisson regression

An important marker for identifying the progression of human immunodeficiency virus (HIV) infection in an individual is the CD4 cell count. Antiretroviral therapy (ART) is a treatment for HIV/AIDS (AIDS, acquired immune-deficiency syndrome) which prolongs and improves the lives of patients by improving the CD4 cell count and strengthen the immune system. This strengthening of the immune system in terms of CD4 count, not only depends on various biological factors, but also other behavioral factors. Previous studies have shown the effect of CD4 count on the mortality, but nobody has attempted to study the factors which are likely to influence the improvement in CD4 count of patients diagnosed of AIDS and undergoing ART. In this paper, we use Poisson regression model (GPR) for exploring the effect of various socio-demographic covariates such as age, gender, geographical location, and drug usage on the improvement in the CD4 count of AIDS patients. However, if the CD4 count data suffers from under or overdispersion, we use GPR model and compare it with negative binomial distribution. Finally, the model is applied for the analysis of data on patients undergoing the ART in the Ram Manohar Lohia Hospital, Delhi, India. The data exhibited overdispersion and hence, GPR model provided the best fit.