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

A Double Truncated Binomial Model to Assess Psychiatric Health through Brief Psychiatric Rating Scale: When is Intervention Useful?

A double truncated binomial distribution model with ‘u’ classes truncated on left and ‘v’ classes truncated on right is introduced. Its characteristics, namely, generating functions; and the measures of skewness and kurtosis have been obtained. The unknown parameter has been estimated using the method of maximum likelihood and the method of moments. The confidence interval of the estimate has been obtained through Fisher’s information matrix. The model is applied on cross sectional data obtained through Brief Psychiatric Rating Scale (BPRS) administered on a group of school going adolescent students; and the above-mentioned characteristics have been evaluated. An expert, on the basis of the BPRS score values, suggested an intervention program. The BPRS scores of the students who could be administered the intervention program lied in a range (which was above the lowest and below the highest possible values) suggested by the expert. Whereas the complete data suggested the average number of problem areas is four (which was not in consonance with the observations given by the expert), the double truncated model suggested the number of such areas as five which was consistent with the observations made by the expert. This establishes the usefulness of double truncated models in such scenarios

An application of ordinal regression to extract social dysfunction levels through behavioral problems

Psychological problems are complex in nature and accurate identification of these problems is important. For the identification of psychological problems, one of the preliminary tools is the use of interviews/questionnaires. Questionnaires are preferred over interviews if the group under study is large. A strengths and difficulties questionnaire (SDQ) is one of the most widely used and powerful questionnaires to identify behavioral problems and distresses being faced by the respondents, affecting their day-to-day lives (responsible for social dysfunction). This study was held on college/university students in India, with the objective of examining if the extent of social dysfunction as measured by an impact score can be extracted from behavioral problems which are the components of the difficulty score of SDQ. Two surveys were conducted during the COVID-19 pandemic period, between the months of May–June 2020 and October 2020–February 2021 for the study. Only those responses were considered who felt distressed (“yes” to item 26 of SDQ). The numbers of such responses were 772/1020 and 584/743, respectively, in the two surveys. Distress levels were treated as ordered variables and three categories of distress level, viz., “Normal”, “Borderline”, and “Abnormal” were estimated through behavioral problems using ordinal regression (OR) methods with a negative log-log link function. The fitting of OR models was tested and accepted using Cox and Snell, Nagelkerke, and McFadden test. Hyperactivity-inattention and emotional symptoms were significant contributors to estimating levels of distress among respondents in survey 1 (p < 0.05). In addition to these components, in survey 2, peer problems were also significant. OR models were good at estimating the extreme categories; however, the “Borderline” category was not estimated well. One of the reasons was the use of qualitative and complex data with the least wide “Borderline” category, both for the “Difficulty” and the “Impact” scores

Extracting relevant predictors of the severity of mental illnesses from clinical information using regularisation regression models

Mental disorders are common non-communicable diseases whose occurrence rises at epidemic rates globally. The determination of the severity of a mental illness has important clinical implications and it serves as a prognostic factor for effective intervention planning and management. This paper aims to identify the relevant predictors of the severity of mental illnesses (measured by psychiatric rating scales) from a wide range of clinical variables consisting of information on both laboratory test results and psychiatric factors . The laboratory test results collectively indicate the measurements of 23 components derived from vital signs and blood tests results for the evaluation of the complete blood count. The 8 psychiatric factors known to affect the severity of mental illnesses are considered, viz. the family history, course and onset of an illness, etc. Retrospective data of 78 patients diagnosed with mental and behavioural disorders were collected from the Lady Hardinge Medical College & Smt. S.K, Hospital in New Delhi, India. The observations missing in the data are imputed using the non-parametric random forest algorithm. The multicollinearity is detected based on the variance inflation factor. Owing to the presence of multicollinearity, regularisation techniques such as ridge regression and extensions of the least absolute shrinkage and selection operator (LASSO), viz. adaptive and group LASSO are used for fitting the regression model. Optimal tuning parameter λ is obtained through 13-fold cross-validation. It was observed that the coefficients of the quantitative predictors extracted by the adaptive LASSO and the group of predictors extracted by the group LASSO were comparable to the coefficients obtained through ridge regression

Estimation of Survival Function and Probability of Onset of Diabetic Nephropathy using Path Analysis and Analysis of Covariance

Abstract:-The objective of this paper is to estimate the probability of onset of diabetic nephropathy (DN) arising out of type 2 diabetic patients. To achieve our goal, firstly we have analyzed the association of occurrence of renal complication with the available risk factors by applying path analysis viz., is an extension of multiple regression model that helps in better prediction, since it can model the impact of each factor on an outcome variable. The results of the path analysis showed that serum creatinine (SrCr), number of successes ((NOS), i.e. SrCr ≥ 1.4mg/dl) and age at onset of diabetes are the most appropriate predictors for estimating the progression of DN. Thus, using these significant predictors we have estimated the probability of onset of DN for two different levels of age at onset of diabetes diagnosis (Age at onset of diabetes ≤ 40 years and Age at onset of diabetes &gt; 40 years) by applying ANCOVA with two covariates SrCr and NOS. The results of the analysis indicates that the probability of the onset of DN differ among the two levels of age at onset of diabetes. And SrCr and number of successes are the significant contributors for predicting probability

Identifying patients with diabetic nephropathy based on serum creatinine under zero truncated model

Diabetes mellitus is a clinical syndrome characterized by hyperglycemia due to absolute or relative insufficiency of insulin in the body. Diabetic nephropathy is a generic term referring to deleterious effect on renal structure and/or function caused by diabetes mellitus.&nbsp; In this paper, we estimate the probability of occurrence of diabetic nephropathy, taking serum creatinine as a marker for renal function/dysfunction. We adopted a Zero truncated binomial distribution (ZTBD) with parameters (ni, p), where p, the probability that serum creatinine &ge; cutoff value, was unknown. Maximum likelihood and residual bootstrapping methods were used to estimate p. Retrospective data was collected from 132 patients diagnosed as diabetic as per ADA standards. Out of the available data of 132 patients, 72 patients had no diabetic renal complications with serum&nbsp; creatinine&nbsp; mean &plusmn; s.d as 0.9774&plusmn; 0.12508 and 60 patients had certain diabetic complications with serum creatinine&nbsp; mean &plusmn; s.d. as 1.6462 &plusmn;0.28827.The mean &plusmn; s.d. for duration of disease for 60 patients came out to be 15.46667&plusmn; 5.54 (yrs) and median as 17.1 yrs. The two groups of patients were found to be significantly different with p&lt;.001. The value of p̃ came out to be 0.4555397 and 0.445545 using maximum likelihood and residual bootstrapping methods respectively. It was found that 60 patients had non -zero probability of renal disease under ZTBD. From this study, it was concluded that the duration of diabetes along with elevated levels of serum creatinine defines a high risk group for the diabetic nephropathy