This course mainly contains survival analysis, clinical trials and accelerated life testing (ALT) model.

Objective of survival analysis is (i) to estimate survival time for a group of patients, such as time until second heart-attack for a group of patients. (ii) to compare survival time between two or more groups, such as treated vs. placebo patients in a randomized controlled trail. (iii) to access the relationship of co-variates to survival time, such as: does weight, insulin resistance, or cholesterol influence survival time of patients?

Clinical trials (also called medical research and research studies) are used (i) to determine whether new drugs or treatments are both safe and effective. (ii) to compare a new treatment to a treatment that is already available.

Now a days, modern technology produce high reliability products. For such products, under operating stress(Temperature, Voltage, Load, Cycle, etc.) level, it takes a lot of time to get a sufficient number of failures to be used to estimate lifetime distributions which is useful to determine the products quality. Therefore, a sufficient number of failures obtained under high stress levels with small duration of times. These accelerated data are analyzed under accelerated life testing(ALT) environment (i) to estimate reliability for a specified time under x0 (ii) to estimate median or other quantiles under x0.

Therefore from the above aim and objectives it is clear that, the applications of this course are to analyze the medical research data and industrial products lifetimes data.

Parametric Regression Models: Introduction. Inclusion of strata. Specifying a Distributions. Residuals. Residual analysis and other model checks. Predicted values. Fitting the Model. Exponential, Weibull, Normal, Lognormal and Gamma regression models. Interval estimation of the parameters and quantiles. Applications of parametric regression models.

Proportional Hazards Models: Introduction. Hypothesis test. Stratified and Penalized Cox models.  Residual analysis. Partial likelihood.  Applications of proportional hazards model. Estimation of hazard ratio. Comparison of two or more survival functions.

Extension of the Cox PH Model: Definition and examples of time-dependent variables, extended Cox model for time-dependent variables, hazard ratio for extended cox model, assessing time-dependent variables that do not satisfy PH assumption, extended cox likelihood. Application of the extended Cox model.

Accelerated life testing models:  Accelerating variables, different types of life-stress relationships. Constant-stress and step-stress accelerated test models. Different methods for representing and analyzing accelerated life test (ALT) data based on different sampling schemes. Application of accelerated life testing models.

Multivariate lifetime models: Multivariate lifetime distributions and their characteristics, parametric and nonparametric estimation of multivariate lifetime distribution, models with multiple failure modes.

Clinical Trials: Basic concepts of clinical trials. Controlled and uncontrolled clinical trials, historical controls, protocol, placebo, randomization, blind and double blind trials, ethical issues, protocol deviations, volunteer bias. Simple comparative trials, Cross-over trials, size of trials, meta analysis, interim analysis, multi-centre trials, combining trials.

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