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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