Topic 4 – Before-After Studies
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Topic 4 – Before-After Studies CEE 763. BEFORE-AFTER STUDIES. Experiment Controlled environment e.g.: Physics, animal science Observational Study Cross-Section (e.g., stop vs. yield) Before-After* Ezra Hauer, “Observational Before-After Studies in Road Safety”, ISBN 0-08-043053-8.

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Topic 4 – Before-After Studies CEE 763

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Topic 4 before after studies cee 763

Topic 4 – Before-After Studies

CEE 763


Before after studies

BEFORE-AFTER STUDIES

  • Experiment

    • Controlled environment

    • e.g.: Physics, animal science

  • Observational Study

    • Cross-Section (e.g., stop vs. yield)

    • Before-After*

      Ezra Hauer, “Observational Before-After Studies in Road Safety”, ISBN 0-08-043053-8


What is the question

WHAT IS THE QUESTION

  • Treatment – a measure implemented at a site for the purpose of achieving safety improvement.

  • The effectiveness of a treatment is the change in safety performance measures purely due to the treatment.

  • It is measured by the difference between “what would have been the safety of the site in the ‘after’ period had treatment not been applied” and “what the safety of the site in the ‘after’ period was”.


An example

AN EXAMPLE

  • R.I.D.E. (Reduce Impaired Driving Everywhere) Program


Frequency or rate

FREQUENCY OR RATE?

Expected # of Accidents/ year

C

Without Rumble Strip

B

A

With Rumble Strip

AADT

  • What conclusions would you make by using rate or frequency?


Target accidents

TARGET ACCIDENTS

  • Target accidents – Those accidents the occurrence of which can be materially affected by the treatment.

  • Case 1 – R.I.D.E:

    • An enforcement program in Toronto to reduce alcohol-related injury accidents

    • Target accidents: alcohol-impaired accidents or total accidents?


Target accidents continued

TARGET ACCIDENTS (continued)

  • Case 2 – Sound-wall effect

    • The study was to look at whether the construction of sound-walls increased crashes or not.

    • Target accidents: run-off-the-road accidents or total accidents?


Target accidents continued1

TARGET ACCIDENTS (continued)

  • Case 3 – Right-turn-on-red policy

    • The study was to look at whether allowing vehicles to make right turns on red increased crashes or not.

    • Target accidents: accidents that involve at least one right-turn vehicle or total accidents?


Right turn on red case

RIGHT-TURN-ON-RED CASE

  • Case 3 – Right-turn-on-red policy

*Comparison accidents are those that do not involve any right-turn vehicles

*Other accidents are those that do not involve any right-turn vehicles


Prediction and estimation

PREDICTION AND ESTIMATION

  • Prediction – to estimate what would have been the safety of the entity in the ‘after’ period had treatment not been applied.

  • Many ways to predict.

  • Estimation – to estimate what the safety of the treated entry in the ‘after’ period was.


Prediction

PREDICTION

  • One-year before (173)

  • Three-year before average (184)

  • Regression (165)

  • Comparison group (160)


Four step process for a b a study

FOUR-STEP PROCESS FOR A B-A STUDY

  • Step 1 – Estimate λ and predict π

    • λ is the expected number of target accidents in the ‘after’ period

    • π is what the expected number of target accidents in an ‘after’ period would have been had it not been treated

  • Step 2 – Estimate VAR{λ} and VAR{π}

  • Step 3 – Estimate δ and θ

    • δ is reduction in the expected number of accidents;

    • θ is safety index of effectiveness

  • Step 4 – Estimate VAR{δ} and VAR{θ}


Equations

EQUATIONS


Example na ve before after study

EXAMPLENAÏVE BEFORE-AFTER STUDY

  • Consider a Naïve B-A study with 173 accidents in the ‘before’ year and 144 accidents in the ‘after’ year. Determine the effectiveness of the treatment.


Comparison group c g b a study

COMPARISON GROUP (C-G) B-A STUDY

  • Comparison group – a group of sites that did not receive the treatment

  • Assumptions

    • Factors affecting safety have changed from “before” to “after” in the same manner for the treatment group and the comparison group

    • These factors influence both groups in the same way

      Whatever happened to the subject group (except for the treatment itself) happened exactly the same way to the comparison group


Example

EXAMPLE

  • Where R.I.D.E. was implemented, alcohol-related crash was changed from 173 (before) to 144 (after). Where R.I.D.E. was NOT implemented, alcohol-related crash was changed from 225 (before) to 195 (after). What would be the crash in the after period had R.I.D.E. not been implemented?


C g method

C-G METHOD

Odds ratio


Equations1

EQUATIONS


Example1

EXAMPLE

  • The table shows the accident counts for the R.I.D.E. program at both treatment sites and comparison sites.


The eb method

THE EB METHOD

EB estimate of the expected number of ‘after’ accidents had the treatment not been implemented.

Y is the ratio between ‘before’ period and ‘after’ period

If not giving, use the actual counts K (‘before’ period) to estimate population mean, E{k}

s2 is sample variance for the ‘before’ period

Variance if ‘before’ has multiple years


Example2

EXAMPLE

  • Accidents recorded at 5 intersections over a two-year period are shown in the table. What is the weighting factor, α for the EB method?


Equations2

EQUATIONS


Example3

EXAMPLE

Using the EB method to conduct the B-A study based on the information in the table.


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