Application of Current-Status Survival Analysis Methodology to Estimation of Age at First Sex: Uganda

Application of Current-Status Survival Analysis Methodology to Estimation of Age at First Sex: Uganda Leonard K. Atuhaire 1 ABSTRACT Computing quantiles of age at first sex using only recalled age at first sex can be problematic when (i) misreporting of age at first sex is substantial, and (ii) a considerable number of respondents have not become sexually active by the time of data collection. Life Table and related Survival Analysis methods that use age at the time of a survey as the censoring time for those who had not had sex by the time of the survey solves the second problem, but can give misleading results if misreporting of age at first sex exists. Methods that use only current age and current virginity status (assuming these are correctly reported) would thus be preferred. The application of such methods is investigated using data from the Uganda Demographic and Health Survey (UDHS). Results show that such methods are applicable, and in the case of the UDHS, the log-logistic distribution provides a good fit from which quantiles of age at first sex can be derived. From the fitted model, the median age at first sex is estimated as 18.33 years for males, and 17.88 years for females for the cohort aged 15-24 in 2006. Key words: Survival Analysis, Accelerated Time Models, Age at First Sex, Demographic and Health Survey. Application de la méthode d analyse de survie en l état actuel pour estimer «l âge du premier rapport sexuel» en Ouganda RÉSUMÉ Le calcul des quantiles de l âge auquel les premiers rapports sexuels ont eu lieu en se basant uniquement sur l âge remémoré des premiers rapports sexuels peut s avérer problématique quand i)il y a beaucoup de renseignements erronés sur l âge auquel le premier rapport sexuel a eu lieu, et ii)un grand nombre de personnes interrogées n avaient pas eu leurs premières relations sexuelles au moment de la collecte des données. Les méthodes d analyses de la table de survie et les méthodes d analyses de survie connexes qui s appuient sur l âge au moment de l enquête comme période de censure pour les personnes qui n avaient jamais eu de rapports sexuels au moment de l enquête, permettent de résoudre le deuxième problème. Néanmoins, elles peuvent aboutir à des résultats erronés si le premier problème 1 Institute of Statistics and Applied Economics, Makerere University, P. O. Box 7062 Kampala, Uganda, Email: latuhaire@isae.mak.ac.ug The African Statistical Journal, Volume 12, May 2011 141

Leonard K. Atuhaire persiste. Les méthodes qui utilisent uniquement l âge et l état de virginité effectifs au moment de l enquête (en supposant que ces renseignements sont exacts) seraient donc préférables. Nous étudions l application de ces méthodes en utilisant les données de l Enquête démographique et sanitaire effectuée en Ouganda (UDHS). Les résultats montrent qu il est possible d appliquer ces méthodes et, dans le cas de l UDHS, la courbe logarithmique-logistique constitue un bon modèle à partir duquel on peut déterminer les quantiles de l âge auquel le premier rapport sexuel a eu lieu. Sur la base du modèle utilisé, on estime l âge médian des premiers rapports sexuels à 18,33 ans pour les hommes et à 17,88 ans pour les femmes, pris dans une cohorte âgée de 15 à 24 ans en 2006. Mots clefs : Analyse de survie, modèles à temps accéléré, relations sexuelles, l Enquête démographique et sanitaire 1.0 INTRODUCTION Age at first sex, the onset of exposure to the risk of pregnancy, is an important variable in the study of fertility. It is also crucial in monitoring the evolution of the HIV/AIDS epidemic as an indicator of behaviour change (Zaba et al., 2004). Estimating the quantiles of age at first sex is not straightforward because of the inclusion of respondents who may not have become sexually active debut at the time of a survey. When this is the case, the recommended method (e.g., Davis and Lay Yee, 1999; Zaba et al.,2002) is non-parametric Survival Analysis using both recall and current status data. With this method, respondents who have never had sex are (right) censored at their current (survey) age. Parametric methods have also been used (Wielandt and Boldsen, 1989; Feeney and Zaba, 2001). These methods obviously require correct recall of age at first sex. However, misreporting of age at first sex in parts of sub-saharan Africa is common (Wringe et al., 2009). If this is the case, these methods can, in theory, give misleading results. When current age and current virginity status are reported truthfully, a method using only these data has an obvious advantage over methods that rely, at least in part, on recall data. This type of data, that is, when what is available is data on whether or not the event of interest has occurred, while time-to-event data are what is of interest, is known as current-status data (Shiboski, 1998). 142 Journal statistique africain, numéro 12, mai 2011

Application of Current-Status Survival Analysis Methodology to Estimation of Age at First Sex This paper explores the possibility of using current status data to estimate age at first sex, based on data from the Uganda Demographic and Health Survey (UDHS) (Uganda Bureau of Statistics (UBOS) and Macro International Inc., 2007). 2.0 METHODS The data are from the 2006 UDHS, a nationally representative survey based on a sample of 8,531 women age 15-49 and 2,503 men age 15-54 Uganda Bureau of Statistics (UBOS) and Macro International Inc., 2007). It was conducted as part of the worldwide Demographic and Health Surveys (DHS) project. The analysis in this study is restricted to the 15-24 age group (3,610 women and 979 men) to ensure homogeneity, as evidence suggests that age at first sex has been rising (Slaymaker et al., 2009). In addition to age, sex, and other socio-economic characteristics, respondents were asked at what age they had sexual intercourse for the first time. This was recorded as 0 for a respondent who had never had sexual intercourse, and 1 if otherwise. Current-status data can be used to approximate a virginity survival function by computing the proportion who have never had sex by age in single years. This method was used, for example by Asiimwe-Okiror et al (1997). This survival curve is obviously limited to the age range of the respondents and is not a true survival curve, since it is not guaranteed to be monotonic without additional manipulation (Ayer et al., 1955). The approach followed that of Araneda et al. (2008) who used parametric current-status survival analysis to predict the sensory shelf life of a product using consumer evaluation (acceptable/not acceptable) of, in each case, a single sample with an established storage time. The likelihood function used to estimate the survival function S(t) using only current-status data (e. g. Meeker and Escobar, 1998; Klein and Moeschberger, 2003) can be written as: L = (1) The African Statistical Journal, Volume 12, May 2011 143

Leonard K. Atuhaire Where S(.) and F(.) are the Survival and Distribution functions for the assumed distribution of t, and δi = (1 if the observation is right censored; (0 if the observation is left censored. This method requires software that can handle both left-censored and right-censored data. For this study we used the survreg procedure in the package R version 2.6.0 (R Development Core Team, 2007) which fits parametric survival regression models. The challenge was to fit an Accelerated Time Model (Kalbfleisch and Prentice, 2002; Klein and Moeschberger, 2003), without any covariates, i.e. the model Log T i = a + σw (2) where Ti is the age (in completed years since birth) at first sex for the ith individual; a and σ are location and scale parameters, respectively; and W is an error term. The available distributions for T include the exponential, Weibull, lognormal, and log-logistic. These were compared using the Akaike Information Criterion (AIC), the best model being the one with the smallest AIC. This was done separately for each sex. Only visual assessment of the fitted parametric model with the nonparametric estimates was carried out. The parameter estimates from the best fitting model were used to estimate the survival curve using Where S(t) = S 0 ((log(t) a)/ σ) (3) S 0 (W) = 1- F(W) (4) Where F(W) is the Distribution Function for W. 144 Journal statistique africain, numéro 12, mai 2011

Application of Current-Status Survival Analysis Methodology to Estimation of Age at First Sex The median, the most useful quantile in such studies, was estimated by solving S(tm) = 0.5. 3.0 RESULTS Table 1 shows the maximized log-likelihoods for the different models fitted. The maximized log-likelihoods clearly show the better fit of the log-logistic distribution, compared to the lognormal and the Weibull distributions, even without computing the AIC. Table 1. Maximized log-likelihoods for the fitted models Women Men Exponential -2107.8-617.9 Weibull -1601.2-519.9 Log-normal -1577.6-517.5 Log-logistic -1574.8-517.2 Table 2 gives the parameter estimates of fitted log-logistic model. The adjusted median was obtained by adding 0.5 to the unadjusted median to compensate for reporting age at last birthday rather than exact age. Table 2. Parameter estimates of the fitted log-logistic models Women Men Location (a) 2.8552 2.8811 Scale (σ) 0.0865 0.1144 Unadjusted median 17.38 17.83 Adjusted median 17.88 18.33 The parameters were used to generate the survival curves (Figures 1 and 2). To give a quick evaluation of the performance of the fitted parametric model, the plots also show the survival curves obtained using the proportion who have never had sex by age in single years (npar), and a Kaplan-Meier estimate that uses age at the time of the survey as the censoring time for those who had not had become sexually active at the time of the survey (KM). In both cases, the log-logistic estimate of the proportion still virgin is closer to the empirical proportion than is the Kaplan-Meier estimate. The African Statistical Journal, Volume 12, May 2011 145

Leonard K. Atuhaire 0.2.4.6.8 1 Fig. 1 Virginity Survival Curves for Women Aged 15-24 10 15 20 25 Age 0.2.4.6.8 1 Fig. 2 Virginity Survival Curves for Men Aged 15-24 10 15 20 25 Age npar llogistic KM 4. CONCLUSION This paper shows that it is possible to use current status data to estimate quantiles of age at first sex using parametric models. The implication is that in cases where obtaining reliable data on age at first sex is difficult, emphasis could be placed on obtaining accurate data on current age and virginity status. However, the method applied here is not applicable to data for older adults, almost all of whom would have become sexually active by the time of the survey. REFERENCES Araneda, M., Hough, G., de Penna, E. W. (2008) Current-Status Survival Analysis Methodology Applied to Estimating Sensory Shelf Life of Readyto-eat Lettuce (Lactuca Sativa). Journal of Sensory Studies, 23, 162-170. Asiimwe-Okiror, G., A. A. Opio, J. Musinguzi, E. Madraa, G. Tembo, and M. Carael. (1997) Change in sexual behavior and decline in HIV infection among young pregnant women in urban Uganda. AIDS 11: 1,757 1,763. Ayer, M., Brunk, H. D., Ewing, G. M., Reid, W. T. and Silverman, E. (1955) An Empirical Distribution Function for Sampling with Incomplete Information. Annals of Mathematical Statistics, 26, 641-647. Davis, P., and Lay Yee, R. (1999). Early sex and its behavioral consequences in New Zealand. Journal Of Sex Research 36:135-44. 146 Journal statistique africain, numéro 12, mai 2011

Application of Current-Status Survival Analysis Methodology to Estimation of Age at First Sex Feeney, G., and Zaba, B. (2001). A minimalist Model for Projecting HIV/ AIDS. Geneva: UNAIDS. Kalbfleisch, J. D. and Prentice, R. L. (2002) The Statistical Analysis of Failure Time Data, second edition. Wiley Klein, J.P., and Moeschberger, M. L. (2003). Survival Analysis: Techniques for Censored and Truncated Data. New York: Springer. Meeer, W.Q. and Eskobar, L.A. (1998) Statistical Methods for Reliability Data. New York: Wiley R Development Core Team (2007). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Shiboski, C. (1998) Generalised additive models for current status data. Lifetime Data Analysis, 4, 29-50. Slaymaker, E., Bwanika, J.B., Kasamba, I., Lutalo, T., Maher, D., Todd, J. (2009) Trends in age at first sex in Uganda: Evidence from Demographic and Health Survey data and longitudinal cohorts in Masaka and Rakai. Sex Transm Infect, 85 (Suppl. I): i12 i19 Uganda Bureau of Statistics (UBOS) and Macro International Inc. (2007). Uganda Demographic and Health Survey 2006. Calverton, Maryland, USA: UBOS and Macro International Inc. Wielandt, H., and J. Boldsen (1989). Age at first intercourse. Journal Of Biosocial Science 21:169-77. Wringe, A., Cremin, I., Todd, J. et al (2009) Comparative assessment of the quality of age at event reporting in three HIV cohort studies in sub-saharan Africa. Sex. Transm. Infect., 85 (Suppl. I): i56 i63 Zaba, B., Pisani, E., Slaymaker, E. and Boerma, J. T. (2004) Age at first sex: understanding recent trends in African demographic surveys. Sex. Transm. Infect., 80, ii28-ii35. Zaba, B., Boerma, T., Pisani, E., Baptiste, N. (2008) Estimating levels and trends in age at first sex from surveys using Survival analysis. WP051, Measure Evaluation Project, Carolina Population Centre, University of North Carolina at Chapel Hill. The African Statistical Journal, Volume 12, May 2011 147

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