Joint modeling of longitudinal and survival data has received much attention and is becoming increasingly useful. In clinical studies, longitudinal biomarkers are used to monitor disease progression and to predict survival. These longitudinal measures are often missing at failure times and may be prone to measurement errors. In previous studies these two types of data are frequently analyzed separately where a mixed effects model is used for longitudinal data and a survival model is applied to event outcomes. The argument in favor of a joint model has been the efficient use of the data as the survival information goes into modeling the longitudinal process and vice versa. In this thesis, we present joint maximum likelihood methods, a two stage approach and time dependent covariate methods that link longitudinal data to survival data. First, we use simulation studies to explore and assess the performance of these methods with bias, accuracy and coverage probabilities. Then, we focus on four time dependent methods considering models that are unadjusted and adjusted for time. Finally, we consider mediation analysis for longitudinal and survival data. Mediation analysis is introduced and applied in a research framework based on genetic variants, longitudinal measures and disease risk. We implement accelerated failure time regression using the joint maximum likelihood approach (AFT-joint) and an accelerated failure time regression model using the observed longitudinal measures as time dependent covariates (AFT-observed) to assess the mediated effect. We found that the two stage approach (TSA) performed best at estimating the link parameter. The joint maximum likelihood methods that used the predicted values of the longitudinal measures, similar to the TSA, provided larger estimates. The time dependent covariate methods that used the observed longitudinal measures in the survival analysis underestimated the true estimates. The mediation results showed that the AFT-joint and the AFT-observed underestimated the mediated effect. Comparison of the methods in Framingham Heart Study data revealed similar patterns. We recommend adjusting for time when estimating the association parameter in time dependent Cox and logistic models. Additional work is needed for estimating the mediated effect with longitudinal and survival data.

Summaries in Afrikaans and English / Text in Afrikaans / Die siviele lasterreg word gekenmerk deur verdeeldheid aangaande bewyspligtigheid. 'n Unieke situasie doen horn voor: weerlegbare regsvermoedens van onregmatigheid en animus iniuriandi word opgevolg deur verskeie regsverdigingsgronde. Bykomend hiertoe stel die Grondwet die vereiste van konstitusionele regverdiging vir beperkings op fundamentele regte. 'n Oorsig oor die regspraak in sowel die voorgrondwetlike - as na-grondwetlike bedeling, dui op 'n versuim deur die howe om behoorlik aandag te skenk aan die bewyspligtigheidsgevolge van die regverskynsels wat hulself in die lasterreg voordoen. In hierdie verhandeling word bewyspligtigheid in lastersake krities ondersoek om vas te stel of dit die reg korrek weerspieel en om 'n werkbare bewyslasformule vir lasteraksies in 'n konstitusionele litigasie te vind. Daar word voorgestel dat die probleem opgelos word deur 'n tweefase-benadering: Die eiser moet in die eerste fase die omvang van sy reg bewys en dat daarop inbreuk gemaak is. In die tweede fase moet die verweerder sy regverdigingsgronde bewys, asook dat dit konstitusioneel regverdigbaar is. / The civil law of defamation is marked by discord regarding onus of proof. A unique situation evidences itself: rebuttable presumptions of law concerning unlawfulness and animus iniuriandi are followed by various grounds of justification. In addition thereto the Constitution sets the requirement of constitutional justification for limitations on fundamental rights. An overview of case law in the pre-constitutional as well as the post-constitutional dispensation, indicates a failure by the courts to pay proper attention to the evidentiary consequences of the legal phenomena found in the law of defamation. In this dissertation onus of proof in defamation cases is critically examined to ascertain whether it reflects the law correctly and to find a workable "onus of proof" -formula for defamation cases in a constitutional dispensation. It is suggested that the problem be solved by a two stage approach: in the first phase, the plaintiff must prove the extent of his right and the encroachment thereof . In the second phase the defendant must prove his grounds of justification and show that they are constitutionally justifiable. / Constitutional, International & Indigenous Law / LL.M.

Summaries in Afrikaans and English / Text in Afrikaans / Die siviele lasterreg word gekenmerk deur verdeeldheid aangaande bewyspligtigheid. 'n Unieke situasie doen horn voor: weerlegbare regsvermoedens van onregmatigheid en animus iniuriandi word opgevolg deur verskeie regsverdigingsgronde. Bykomend hiertoe stel die Grondwet die vereiste van konstitusionele regverdiging vir beperkings op fundamentele regte. 'n Oorsig oor die regspraak in sowel die voorgrondwetlike - as na-grondwetlike bedeling, dui op 'n versuim deur die howe om behoorlik aandag te skenk aan die bewyspligtigheidsgevolge van die regverskynsels wat hulself in die lasterreg voordoen. In hierdie verhandeling word bewyspligtigheid in lastersake krities ondersoek om vas te stel of dit die reg korrek weerspieel en om 'n werkbare bewyslasformule vir lasteraksies in 'n konstitusionele litigasie te vind. Daar word voorgestel dat die probleem opgelos word deur 'n tweefase-benadering: Die eiser moet in die eerste fase die omvang van sy reg bewys en dat daarop inbreuk gemaak is. In die tweede fase moet die verweerder sy regverdigingsgronde bewys, asook dat dit konstitusioneel regverdigbaar is. / The civil law of defamation is marked by discord regarding onus of proof. A unique situation evidences itself: rebuttable presumptions of law concerning unlawfulness and animus iniuriandi are followed by various grounds of justification. In addition thereto the Constitution sets the requirement of constitutional justification for limitations on fundamental rights. An overview of case law in the pre-constitutional as well as the post-constitutional dispensation, indicates a failure by the courts to pay proper attention to the evidentiary consequences of the legal phenomena found in the law of defamation. In this dissertation onus of proof in defamation cases is critically examined to ascertain whether it reflects the law correctly and to find a workable "onus of proof" -formula for defamation cases in a constitutional dispensation. It is suggested that the problem be solved by a two stage approach: in the first phase, the plaintiff must prove the extent of his right and the encroachment thereof . In the second phase the defendant must prove his grounds of justification and show that they are constitutionally justifiable. / Constitutional, International and Indigenous Law / LL.M.

Parametric models are used to understand dynamical systems and predict its future behavior. It is difficult to estimate the model’s parametric values since there are usually many parameters and they are highly correlated. The aim of this project is to apply the method of indirect inference and the two stage approach to estimate the drift and volatility parameters of a Geometric Brownian Motion. This was first done by estimating the parameters of a known Geometric Brownian process. Then, the Coca-Cola Company’s stock was used for a five-year forecast to study the estimators’ predictive power. The two stage approach struggles when the data does not truly follow a Geometric Brownian Motion, but when it does it produces highly efficient and accurate estimates. The method of indirect inference produces better estimates, than the two stage approach,for data that deviates from a Geometric Brownian Motion.Therefore, it is preferable to use indirect inference over two stage approach for stock price forecasting. / Parametriska modeller används för attförstå dynamiska system och förutspå dess framtida beteende.Det är utmanande att skatta modellens parametriska värdeneftersom det vanligtvis finns många parametrar och de är oftastarkt korrelerade. Målet med detta projekt är att tillämpametoderna indirect inference och two stage approach för attskatta drivnings- och volatilitetsparametrarna av en geometriskBrownsk rörelse. Först skattades parametrarna av en kändGeometrisk Brownsk rörelse. Sedan användes The Coca-ColaCompanys aktie i syfte att studera estimatorernas förmåga attförutspå en femårig period. Two stage approach fungerar dåligtför data som inte helt följer en geometrisk Brownsk rörelse, mennär datan gör det är skattningarna noggranna och effektiva.Indirect inference ger bättre skattningar än two stage approachnär datan inte helt följer en geometrisk Brownsk rörelse. Därförär indirect inference att föredra för aktieprognoser. / Kandidatexjobb i elektroteknik 2022, KTH, Stockholm

Text in Afrikaans, abstract in English / Writer investigates the constitutionality of section 18(4)(d) of the Child Care Act 74 of 1983 against the backdrop of the South African common law and the common law of comparative legal systems. In the South Africa law the mother of an illegitimate child has guardianship. The natural father does not have parental power which weakens his legal position. In analysing the judgement of the Constitutional Court, writer criticises the court for stating that in the case of a newborn baby the kind of discrimination which section 18( 4 )( d) authorises against a natural father may be justifiable in the initial period after the child is born. The constitutional position of the natural father in American jurisprudence is discussed at length. Writer concludes that the natural father has to take positive steps to vest a right to be heard in an adoption application. Proposals for legal reform are also made. / Private Law / LL. M. (Law)

Text in Afrikaans, abstract in English / Writer investigates the constitutionality of section 18(4)(d) of the Child Care Act 74 of 1983 against the backdrop of the South African common law and the common law of comparative legal systems. In the South Africa law the mother of an illegitimate child has guardianship. The natural father does not have parental power which weakens his legal position. In analysing the judgement of the Constitutional Court, writer criticises the court for stating that in the case of a newborn baby the kind of discrimination which section 18( 4 )( d) authorises against a natural father may be justifiable in the initial period after the child is born. The constitutional position of the natural father in American jurisprudence is discussed at length. Writer concludes that the natural father has to take positive steps to vest a right to be heard in an adoption application. Proposals for legal reform are also made. / Private Law / LL. M. (Law)