# SIMSTAT: Time Series and Survival Analysis

Time series lags, ACF and PACF
You provide a sample and indicate the lags required, then all posible autocorrelations and partial autocorrelations are calculated and an overall test statistic is derived to test the null hypotheses of no significant autocorrelations. The sample should be a time series at equal increments of time (or distance, etc.) with no missing values. You can also specify the order of seasonal or non-seasonal differencing and the seasonality required, after which the differenced time series, autocorrelation function or partial autocorrelation function can be plotted.

Autoregressive integrated moving average modelling (ARIMA)
This option is selected when you have measurements at equal intervals of time (or space, etc.) and you suspect a time series model might be appropriate. It is presumed that you will first investigate the autocorrelation structure of your time series data using the SIMSTAT time series option before attempting to fit an ARIMA model. Fitting ARIMA models is an iterative technique and, like all nonlinear regression procedures, gives non-unique solutions that are very dependent on choosing a sensible model and having good starting estimates. You should only use this technique if you understand the function of the autoregressive and moving average parameters and the effect of applying seasonal and non-seasonal differencing to create a differenced set for fitting. The procedure can be used to predict future values of the series with 95% confidence limits, and goodness of fit can be judged by observing the fit to the differenced series and the scatter of the differenced residuals. Try fitting the test file times.tf1 using the default settings before analysing your own data. Note that you can change the default settings at will but the defaults will be restored each time program SIMSTAT is re-started. Expert users can display a monitoring screen to observe the regression sequences and this can be toggled on or off. However, if you close down the monitoring screen during a run it cannot be reactivated until you re-start program SIMSTAT.

Survival curves
This option is selected when you have survival times but with no covariates, as survival analysis with covariates is handled by the generalized linear model routines. There are two procedures: analysis of one set of survival data, and comparison of two sets of survival data. The data must be formatted as in the survive.tf? test files, that is where column 1 has the times in nondecreasing order, column 2 holds the censoring codes (0 for failure, or 1 for right-censoring), and column 3 contains the frequencies of the failure or censoring, i.e. replicate information. If one data set is analysed, the program will construct a Kaplan-Meier product limit nonparametric survivor function, and it will also fit a Weibull distribution by maximum likelihood. If two data sets are to be compared, then a Mantel-Haenszel test, otherwise known as the log rank test, will be performed to test for proportional hazards, and various graphical procedures are available to estimate the goodness of fit of a Weibull or exponential distribution and to assess the proportional hazards assumption. Test files are survive.tf1, survive.tf2, survive.tf3, and survive.tf4.

Survival analysis by GLM
This provides a sub-section of the GLM options that are required to fit the exponential, Weibull, extreme value, and Cox proportional hazards models, to survival data with covariates. The data file format must be
x1, x2,..., xm, y, t, s
where x1 to xm are the m covariates, y is 0 for failure or 1 for right-censoring, t is the observed time, and s is the stratum indicator. Test files are cox.tf1, cox.tf2, cox.tf3, and cox.tf4.

Cox regression
This is a comprehensive procedure for fitting the proportional hazards model to survival data, followed by options to check the goodness of fit by analyzisng residuals, and allowing the construction of survivor function curves for the various strata.

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