*! version 1.6.0 03dec2011
help dthaz

Title

dthaz -- Discrete-time hazard and survival probability estimates

Syntax

dthaz [varlist] [if] [weight]
[, specify(numlist)
tpar(#)
truncate(#)
pretrunc(#)
cloglog
cluster(varname)
display(#)
level(#)
model
suppress
graph(#)
graph_twoway_options copyleft]

Model
specify(numlist) specify values for predicted population values

tpar(#) select alternative parameterizations of time

truncate(#) truncate the maximum time of length to event

pretrunc(#) ignore some initial time periods in the model

cloglog use a complimentary log-log link (see cloglog)

SE/Robust
cluster(varname) adjust standard errors for intragroup
correlation

Reporting
display(#) limit the maximum displayed period

level(#) set confidence level; default is level(95)

model output model estimate

suppress switch off dthaz output

Graph options
graph(#) conditional hazard, survival, or cumulative incidence curves

twoway_options graph twoway options

Miscellaneous
copyleft display license information

fweights, iweights, and pweights are allowed; see weight.

Description

dthaz estimates the hazard and survival probabilities of the population, given
the specified model by means of a logit link (default) or by a complementary
log-log link. This program requires data in person-period
format, and person-period variables may be created using prsnperd.

Typed with no varlist and with no tpar() option, dthaz estimates
baseline conditional hazard (h) and survival probabilities (S) for the sample. These estimates
correspond exactly with actuarial estimates of sample hazard and sample survival functions.
Specifying numeric predictors in varlist and the required set of associated
values with the specify() option adds them to the model following as follows (for logit hazard):

h_i = 1/(1+e^-(a_i*d_i + BX_i))

Where:

a_i is the effect of the ith time period, d_i,

B is a vector of effects for a vector of predictors X_i during the ith time period, and

S_i = (1-h_1)*(1-h_2) * ¥ ¥ ¥ * (1-h_i).

The reported conditional hazard and survival probabilities are accompanied by
standard errors approximated using a first order application of the delta method
(Dinno and Kim, 2011). The normally approximated confidence intervals
drawn using the graph() option are obtained by application of these
standard errors with the alpha specified by level().

Options

Model

specify(numlist) The user must specify
which category of population members the hazard and survival estimates are to
be calculated. Currently, if specifications are made with this option, they
must be made for each of the variables specified in varlist. Specifications
may be separated by spaces, commas or both.

tpar(#) The user may select alternative
parameterizations of time. Such time parameterizations allow a parsimonious
smoothing of the effects of time, and are as follows:

-1 Fully discrete time parameterization. This setting is the default, and
reflects unique effects of time for each period.

0 Constant time parameterization. This model constrains the effect of time to
be constant across all periods. The model includes a prespecified constant
term, is used in the following models, and permits model nesting.

N Polynomial time parameterization. This model constrains the effect of
time as a polynomial function of order N. If the representation of time is
over-specified (i.e. has more predictors than the number of periods in the dataset,
or than the number the analysis has been truncated to) then the user will be warned
and the parameterization will be reset to its maximum. Lower order models nest
within higher order ones. N > 0.

-2 Root time parameterization. This model constrains the effect of time as a
square-root function of period (plus constant plus linear terms)

truncate(#) The user may truncate the
maximum time of length to event to this number. The estimate will censor data
for time periods beyond this point. Negative values and values greater than the
maximum period value are ignored.

Note: Specifying this option for the baseline model will produce
exactly the same estimates as for the untruncated model for the given periods,
since baseline estimates are always equal to the sample hazard and sample
survival functions.

pretrunc(#) The user may discard early time periods from
the new dataset. For example, when pre-truncating with a value of 2, the period
that would be indicated by _d3 becomes _d1 instead, and the value of _period
would be decreased by 2. The dataset is preserved when using this option

Note: Specifying values of truncate greater than the one
minus the maximum value of length-to-event (or specifying negative values)
produces the same dataset as one with no value of truncate specified. Also,
truncate and pretrunc cannot be combined when their values would
result in fewer than two periods. Discrete time survival analyses conducted
upon pre-truncated datasets are, in effect analyses conducted upon separate
populations from the not pre-truncated datasets if the conditional hazard
during the pre-truncated periods is greater than zero. The author suggests
that an analyst may desire to perform a pre-truncated analysis either because
there are no events during initial periods, or because she is interested in
analyzing a surviving sub-population at a later starting period. However, in
cases where events occurred during the pre-truncated periods, a survival
analysis cannot be said to generalize to the population of the not
pre-truncated dataset. In cases where events occur in initial periods, but at
rates that are too few to provide reliable estimates for these periods, the
analyst should both employ a sensitivity analysis to describe differences
between models on pre-truncated and not pre-truncated datasets, but also
examine the characteristics of anomalous individuals--qualitative data may
particularly help illuminate how these persons differ from the majority of
individuals who remain in the pre-truncated dataset.

cloglog This option switches the estimate of the
hazard function to a complementary log-log link. This produces estimates under
an assumption of proportional hazards, rather than an assumption of proportional
odds. The general discrete time complimentary log log hazard model is:

h = 1-exp(-exp(a_i*d_i + B*X_i))

Where the parameters follow the same conventions described for the logit hazard
model above.

SE/Robust

cluster(varname) The user may adjust
the standard errors of the estimates for person-level (between person) variance
in repeated measures designs by specifying the id variable used to
construct the person-period dataset.

Reporting

display(#) The user may limit the
maximum period for hazard and survival probabilities to this number. This
option only affects which values are displayed. The estimated and values
returned in r(Hazard) remain as for the maximum period of the person-period
dataset. Negative values and values greater than the maximum period value are
ignored.

level(#); see [R] estimation options.

model This option includes the estimated model in
the output.

suppress Switches off dthaz output. Graphs still display if
selected. The estimated model is displayed if the model option is turned
on.

Graph options

graph(#) Users may opt to graph
conditional hazard probabilities (1), survival probabilities (2), both (3)
or (4) cumulative incidence probabilities (i.e. 1 - survival) against discrete
time periods. Graphing options available to grtwoway are
available. The default setting is no graph.

Note: the graph() option does not yet plot
confidence intervals in Stata 7.

Miscellaneous

copyleft dthaz is free software, licensed under the GPL. The copyleft option displays
the copying permission statement for dthaz. The full license can be obtained
by typing:

. net describe dthaz, from (http://www.doyenne.com/stata)

and clicking on the click here to get link for the ancillary file.

Examples

. dthaz

. dthaz sex region, specify(0 6) truncate(6)

. dthaz sex educate class, sp(1, 12, 0) gr(3)

. dthaz party age, sp(0 1) model cloglog

. dthaz, tp(3)

Author

Alexis Dinno
Portland State University
alexis dot dinno at pdx dot edu

Please contact me with any questions, bug reports or suggestions for improvement.

My thanks to Dr. Suzanne Graham.

References

Dinno A and Kim JS. 2011. "Approximating Confidence Intervals About Discrete-Time Survival/Cumulative Incidence Estimates Using the Delta Method." Unpublished (manuscript available on request)

Singer JD and Willett JB. 2003. Applied Longitudinal Data Analysis: Modeling Change and Event Occurence. Oxford, UK: Oxford University Press. 672 pages.

Willet JB and Singer JD. 1991. "From Whether to When: New Methods for Studying Student Dropout and Teacher Attrition." Review of Educational Research. 61: 407-450

Singer JD and Willett JB. 1991. "Modeling the Days of Our Lives: Using Survival Analysis When Designing and Analyzing Longitudinal Studies of Duration and Timing of Events." Psychological Bulletin. 110: 268-290

Saved results

In addition to the results returned by the estimation commands logistic or cloglog, dthaz saves the following in e():

Matrices

e(Hazard) Conditional hazard vector for the specified group

e(HazardSE) Standard error vector for the conditional hazards

e(Survival) Survival probability vector for the specified group

e(SurvivalSE) Standard error vector for the survival probabilities

Also See

Help: prsnperd, msdthaz