Data Dependent Cells Chi‐Square Test With Recurrent Events

We consider a recurrent event wherein the inter‐event times are independent and identically distributed with a common absolutely continuous distribution function F. In this article, interest is in the problem of testing the null hypothesis that F belongs to some parametric family where the q‐dimensional parameter is unknown. We propose a general Chi‐squared test in which cell boundaries are data dependent. An estimator of the parameter obtained by minimizing a quadratic form resulting from a properly scaled vector of differences between Observed and Expected frequencies is used to construct the test. This estimator is known as the minimum chi‐square estimator. Large sample properties of the proposed test statistic are established using empirical processes tools. A simulation study is conducted to assess the performance of the test under parameter misspecification, and our procedures are applied to a fleet of Boeing 720 jet planes' air conditioning system failures.     

Condom use among married and cohabiting women and its implications for HIV infection in Mahikeng,South Africa

Married and cohabiting women have been neglected in the promotion of condoms as the most effective prevention method of sexually transmitted infections (STIs) and HIV. As a result, HIV prevalence is increasing in this population group in high HIV prevalence settings. The study assesses the prevalence of and identifies the predictors of consistent use of male condoms among married and cohabiting women, and examines its implications for HIV transmission. The data used were obtained from a cross-sectional survey on sexual and reproductive health conducted among women aged 18–49 years of age in Mahikeng Local Municipality in 2012 using mixed methods. A structured questionnaire and in-depth interview guide were used to collect quantitative data from 568 and qualitative data from 33 married or cohabiting women. The data were analysed using logistic regression and thematic content analysis methods. The results show that only 16.2% of the women consistently used condoms. Women having no and 1–2 surviving children, educated women, women in relationships in which most sexual decisions were jointly made with husbands/partners, women having high risk perceptions of STIs and HIV infection and women who negotiate condom use with and know the HIV status of their husbands/partners were significantly more likely to have consistently used condoms. However, women who perceived that condoms reduce sexual pleasure, feared they would be blamed for infidelity by husbands/partners, trusted that their husbands/partners were faithful and feared condoms could lead to relationship instability used condoms inconsistently. We conclude that the prevalence of consistent use of condoms by married and cohabiting women in the study is low, indicating that promotion of condoms among married or cohabiting women is neglected, which could increase the risk of HIV transmission. Based on our findings, we recommend the review of condom programmes with a view to targeting married or cohabiting couples as an important group for condom promotion and uptake.     

Optimal goodness-of-fit tests for recurrent event data

A class of tests for the hypothesis that the baseline intensity belongs to a parametric class of intensities is given in the recurrent event setting. Asymptotic properties of a weighted general class of processes that compare the non-parametric versus parametric estimators for the cumulative intensity are presented. These results are given for a sequence of Pitman alternatives. Test statistics are proposed and methods of obtaining critical values are examined. Optimal choices for the weight function are given for a class of chi-squared tests. Based on Khmaladze’s transformation we propose distributional free tests. These include the types of Kolmogorov–Smirnov and Cramér–von Mises. The tests are used to analyze two different data sets.