Some comments on the analysis of birth weight
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MAJOR ISSUES:


(1) The choice / determination of adjustment variables.  In the first
part of the question the goal is to perform a putative confirmatory
analysis that evaluates the FirstSteps program.  

     * Include those factors that previous research has found to
       be important potential confounders.

     * Consider the alternative roles that a variable may play -- either
       confounder, precision variable, or intermediate variable.

          + The issue of what's intermediate here is tricky.  The program
            works through access to prenatal care.  What does prenatal
            care do?  Some literature review finds that prenatal care
            aims to impact:  (1) smoking; (2) nutrition; and (3) general
            health.  Thus, smoking status and weight gain are clear 
            potential intermediates.

          + One student created a table to classify as precision, confounder,
            intermediate, with justification for the choice.  Nice idea!

          + Here is where fitting more than a single model is useful.  Estimate
            the treatment comparison both without adjustment for the 
            potential intermediate variables, and then with -- and discuss the
            impact of additional adjustment on the measure.  


(2) Be sure to carefully interpret your adjusted regression coefficients.
State in clear language what this estimate contrasts, and what is "held 
constant".


(3) Since the data do not contain SES, or income the conclusions are limited.
This is an important variable as it relates to eligibility for the program.
One solution is to include as many surrogates for this as possible, but still
acknowledge the limitation.  Another approach is to limit analysis to the 
subset of data that are likely eligible -- for example, the welfare and low
education group of women.  The caveat with limiting the sample is the small 
number of cases (ie. low birth weight babies) that is left.  One approach
restricted to N=300 women, but this left only 22 low birth weight outcomes.
The use of any regression analysis will be severely limited by the number of
cases.  One "guideline" is to not use more than (number of cases)/10 predictors
in a regression model (this actually justified by predictive performance).


(4) Know how to interpret a main effect in the presence of an interaction!  
This is no longer a simple comparison of "treated" versus "control", but
rather a comparison for *a specific value of the interaction variable*!


(5) Should we use some form of statistical variable selection to simplify the
regression model?  For confirmatory regression analysis it is often preferable
to avoid using some model simplification based on statistical testing since
this will impact the real significance level of tests based on the final model
that is chosen.  Second, epidemiologists consider the simplification of a model
but look at the impact of dropping (adding) a variable in terms of the estimate
for the contrast of interest.  The goal of including potential confounders is
to remove bias, and if dropping a non-significant confounder has a modest
or large impact on the effect of interest, then bias may be present.


(6) Always stay focused on the question of interest!  Keep your analysis and
presentation anchored in the scientific question.



OTHER ISSUES:

(1) Goodness of fit for logistic regression is difficult.  Typically the use
of the residual deviance is not possible since the number of "parameters"
for this likelihood ratio comparison is increasing with sample size.  See
Hosmer and Lemeshow (2nd edition) pg 147.


(2) In the evaluation of a predictive model for logistic regression it is
often useful to consider all possible "thresholds" for a positive prediction.
An ROC curve is a useful device for showing all possible combinations of
sensitivity and specificity.  See Hosmer and Lemeshow (2nd edition) pages 156
through 164.


(3) Analysis/Presentation logic -- it often makes sense for presentation 
to consider:
     (a) crude summary measures (ie. a 2x2 table with LBW and First Steps).
     (b) commentary on the substantive issues that pertain to potential
         confounding factors.
     (c) description of the methods used for adjustment.
     (d) interpretation of the results.