Correcting for natural time lag bias in non-participants in pre-post intervention evaluation studies
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1 Correcting for natural time lag bias in non-participants in pre-post intervention evaluation studies Gandhi R Bhattarai PhD, OptumInsight, Rocky Hill, CT ABSTRACT Measuring the change in outcomes between post period and pre-period across intervention and control group (difference-of-difference) has been the standard approach in program impact evaluation studies. When the intervention involves initially contacting large number of its qualified members there may be a natural time lag between the qualified date and the final confirmation of engagement by the member. This will result in an unbalanced distribution of time and duration of follow-up period. This paper presents a SAS macro to systematically adjust for the index date in non-participants so that the follow-up time and duration is comparable. INTRODUCTION Financial or clinical impact of any healthcare intervention includes the comparison of cost or health quality differences from pre-intervention period to post-intervention period between the participants and nonparticipants. This is often referred as difference-of-difference analysis in literature. The post-intervention impact starts, and, is generally measured from the date of participation (an index date) to the follow-up end date. All members are qualified from a common pool at the same time. While the members who declined participation on the first contact remain in non-participant cohort, the ultimate participants may take some time to decide or receive any services from the engagement specialist. This creates a natural time lag between identification and receiving actual services. This introduces some bias in estimating the difference-of-differences between participants and non-participants as the actual intervention date is lagged among the participants. The longer the gap among participants the bigger will be the bias. This paper presents a SAS macro to systematically adjust the index date in non-participants so that both cohorts have similar follow-up begin time. METHODOLOGY The overall approach is to make the univariate distribution of the time lag similar in both engaged and control groups. In order to achieve this, a proportionate distribution of time lag is assigned to the control group based on their available length of time. The process flow is as follows: Calculate gap days for engaged (engaged date qualified date) Calculate the proportion of each gap day and the cumulative proportion Sort by descending order of gap days and assign a sequence number Calculate the available days for control (follow-up end date qualified date) Sort the available days in descending order and divide data in the same proportion of gap days Assign gap days from the engaged to control in matching sequence SAS Code is presented as an automated macro in the appendix. The following variables are needed in the input data for this exercise: CASEID = Case ID number (member id) REFDATE = Date qualified for program (for all) ENGDATE = Date engaged in the program (for engaged only) ENDDATE = Date eligibility ends (or engagement end date for engaged) ENGAGED = Participation flag (1=engaged, 0=control) RESUTS A sample data used in this paper comes with 61 days average time lag between the first qualified date and the engagement date. The time lag ranges from 0 to 179 days. The control group does not have such time lag as the follow-up start date is same as qualified date. 1
2 Time lag (in days) in the unadjusted data engaged N Obs Mean Std Dev Minimum 1st Quartile Median 3rd Quartile Maximum Not engaged Engaged After the adjustment, the average time lag among the control is days, just one day less than the engaged. Time lag (in days) after the adjustment engaged N Obs Mean Std Dev Minimum 1st Quartile Median 3rd Quartile Maximum Not engaged Engaged Student t-test results for the equality of mean time lag Mean Difference DF t-value Pr > t The results now look statistically comparable with just one day difference in time lag. However, we may need to drop a few sample for any other adjustment, for example, we want at least 30 days available for post-period. Even after dropping some of the control sample due to this 30 days requirement in the post period, the difference will be only five days between engaged and control. CONCLUSIONS The macro has been able to reassign the new index date for the control to eliminate the natural time lag that occurred in the engaged group. Based on the adjustment, the start of follow-up period will be similar in both group and reduce any seasonal effects between these two cohorts. REFERENCES SAS 9.2 Macro Language: Reference. Cary, NC: SAS Institute Inc. SAS 9.2 Language Reference: Concepts. Cary, NC: SAS Institute Inc. ACKNOWLEDGMENTS SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. indicates USA registration. Other brand and product names are registered trademarks or trademarks of their respective companies. CONTACT INFORMATION Your comments and questions are valued and encouraged. Contact the author at: Gandhi R Bhattarai, PhD OptumInsight 400 Capital Blvd Rocky Hill, CT Phone: gandhi.bhattarai@optum.com 2
3 APENDIX: SAS CODE FOR AUTOMATED TIME LAG ADJUSTMENT %let path=yourpathhere; Libname lib &path ; /* Suppose we have a dataset with the following fields: caseid = Case ID number (member id) refdate = Date qualified for program engdate = Date engaged into the program enddate = Date disenrolled from program or end of eligibility engaged = Engagement flag (1=engaged, 0=not engaged) */ /* INPUT DATA: LIB.TLAG_RAWDAT.SAS7BDAT */; /*** Make changes only here */ * In this example, we require 60 days before referral and 30 days after index; %let minpost = 30; /* Minimum post period days (if necessary) */ %let minavail = 90; /* Minimum availability days for control */ %let lastdate = '30JUN2011'd; /* Last day an index date can be re-assigned */ data tlag_rawdat; set lib.tlag_rawdat; /* Calculate the gap from qualified date to engaged date */ if engaged=1 then do; engdtlag=engdate - refdate; else do; engdtlag=0; /* Calculate the days until final follow-up; availdays=enddate - refdate; if engaged=0 then do; if availdays<=&minavail then delete; * Drop if at least 90 days is not available (60 pre + 30 post); /* Count sample by cohorts and keep in memory */ create table counts as select engaged, count(*) as mbrcnt from tlag_rawdat group by engaged; data _null_; set counts; if engaged=1 then do; call symput ('engdcnt', mbrcnt); if engaged=0 then do; call symput ('ctrlcnt', mbrcnt); /* Check the counts */ %put engdcnt = &engdcnt; %put ctrlcnt = &ctrlcnt; /* Separate data into engaged and control */ data engd ctrl; set tlag_rawdat; if engaged=1 then output engd; else output ctrl; 3
4 %macro runlag (engdin, ctrlin, outdat); /* Gap days and overall ratio, sorted by descending lag time */ create table engd1 as select engdtlag, count(*) as gapcnt from &engdin group by engdtlag order by engdtlag desc; /* Calculate the cumulative ratio of gap days */ data engd1; set engd1; seqnum=_n_; ratio=gapcnt/&engdcnt; retain cumratio; if seqnum=1 then do; cumratio=ratio; cumratio=ratio + cumratio; seqnumt=round(&ctrlcnt * cumratio, 5.); /* Sort the control by descending available days and order the values*/ proc sort data=&ctrlin; by descending availdays; data ctrl1; set &ctrlin; seqnum0=_n_; drop engdtlag; create table &outdat as select distinct * from engd1 as l right join ctrl1 as r on r.seqnum0=l.seqnumt order by seqnum0; /* Merge all data together */ proc sort data=&outdat nodupkey; by caseid; proc sort data=&engdin nodupkey; by caseid; data &outdat; merge &outdat (in=a) &engdin (in=b); by caseid; if a or b; data lib.&outdat; set &outdat; retain assigngap ; if engdtlag^=. then assigngap=engdtlag; if assigngap=. then assigngap=0; format indexdate mmddyy10.; if engaged=1 then do; indexdate=engdate; else if engaged=0 then do; if assigngap>availdays then assigngap=availdays; indexdate=min((refdate+assigngap), &lastdate); 4
5 postdays=enddate-indexdate; if postdays<=&minpost then dropflag=1; else dropflag=0; keep caseid refdate indexdate assigngap postdays enddate engaged dropflag; ods rtf file= &path/test.rtf ; /* Final check for time lag */ proc ttest data=lib.&outdat; var assigngap; class engaged; title 'Time lag test without dropping anyone'; title; proc ttest data=lib.&outdat; var assigngap; class engaged; where dropflag=0; title 'Time lag after dropping <=30 days post period'; title; ods rtf close; %m %runlag (engd, ctrl, tlag_finaldat); **************** CODE COMPLETE ***************; * Final data is lib.tlag_finaldat.sas7bdat ; **********************************************; 5
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