Are we missing the importance of missing values in HIV prevention Randomized clinical trials? Review and Recommendations

Abstract

Missing data in HIV prevention trials is a common complication to interpreting outcomes. Even a small proportion of missing values in randomized trials can cause bias, inefficiency and loss of power. We examined the extent of missing data and methods in which HIV prevention randomized clinical trials (RCT) have managed missing values. We used a database maintained by the HIV/AIDS Prevention Research Synthesis (PRS) Project at the Centers for Disease Control and Prevention (CDC) to identify related trials for our review. The PRS cumulative database was searched on June 15, 2010 and all citations that met the following criteria were retrieved: All RCTs which reported HIV/STD/HBV/HCV behavioral interventions with a biological outcome from 2005 to present.

Out of the 57 intervention trials identified, all had some level of missing values. We found that the average missing values per study ranged between 3% to 97%. Averaging over all studies the percent of missing values was 26%. None of the studies reported any assumptions for managing missing data in their RCTs. Under some relaxed assumptions discussed below, we expect only 12% of studies to report unbiased results. There is a need for more detailed and thoughtful consideration of the missing data problem in HIV prevention trials. In the current state of managing missing data we risk major biases in interpretations. Several viable alternatives are available for improving the internal validity of RCTs by managing missing data.

The validity of statistical inferences is at risk when analyzed data are incomplete, especially if missing data are handled incorrectly. It has been shown that even very small proportions of incomplete cases (in RCTs) can lead to substantial missing information, and misleading inferences.(1) Although the statistical tools to deal with incomplete data are available in statistics and biostatistics literature,(2-4) the degree to which HIV prevention scientists are applying them to their studies is unknown. For example, although drop-out is a common complication in longitudinal studies of health and health behavior, it is still the convention to use only the available data.(2,5,6) It has been shown repeatedly that ignoring the problems caused by missing data could lead to biased results, flawed interpretation, loss of statistical power and inefficiency.(2,5)

Many studies show that incomplete data may differ by key variables such as treatment group, gender, age, race, and education level.(7-9) Hence, we expect a higher probability of nonresponse for some subgroups compared with others. Differential missing data can lead to differences between those with complete data and those with incomplete data, causing a lack of generalizability to nonresponders. Despite this fact, one of the most commonly used missing data techniques is list-wise deletion, which makes use of complete case data to the exclusion of cases with incomplete data. When study completers differ substantively from non-completers, statistical conclusions drawn from the selected data will be particularly misleading. Although deleting cases with incomplete data is straight-forward and is the default in many statistical packages (e.g. SAS, SPSS, MINITAB), this technique may lead to important biases and loss of statistical power. Fortunately, methods have been developed to handle missing data with significant advantages over case deletion. The purpose of this commentary is to review the techniques used for managing missing data and assumptions for managing missing data for recent published HIV prevention trials.

In this review we examine the missing data assumptions, their applications, and their solutions. Our focus is on the extent of missing data in HIV prevention trials and the implications for interpreting findings. We conclude with some recommendations for managing missing data in future prevention trials.

Missing data assumptions

Prior to examining the methods used for managing missing data in HIV prevention trials, we review the underlying assumptions for managing missing data. Assumptions for managing missing values are built upon some conceptual mechanisms. These mechanisms can be thought of as the reasons for missing values. These assumptions are important to understand in order to choose the correct analysis procedures. It is also very important to report the assumptions so researchers reading manuscripts will know the exact assumptions made. The main mechanisms for missing values are: Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not at Random (MNAR).(10,3)

MCAR is what most people would think if told that data was randomly missing. Under the MCAR mechanism, the observed data are a random subset of the hypothetical, (but unobserved) complete data set, and are representative of the hypothetically complete set and population. This happens when missingness is unrelated to values in the data set, either missing or observed.(3) Consider an HIV prevention study where HIV status is missing due to a random error in data entry, this condition of “nonresponse” would be MCAR; the missingness is unrelated to the response variables. Another analogue is to think of MCAR as scenario in which a lightning strike destroyed certain parts of the data completely by chance.

MAR should be thought as conditional missingness. Under the MAR assumption, missingness can be related to an observed part of the data. For example, in the same HIV prevention trial, if HIV status is missing as a function of age and gender alone, having complete data of the variables age and gender will constitute a MAR mechanism. Also, consider a case that missing values are more prevalent in the treatment arm relative to control arm, as long as we have the treatment assignment, this will be considered MAR mechanism.

When MAR cannot be assumed, we have to assume the data are missing at some non-random mechanism, MNAR. Under this assumption missing values can be due to unobserved (missing) values, even after controlling for other variables. For example, if HIV status is more likely to be missing for individuals whose unobserved HIV status is positive, then unobserved HIV status values are MNAR. In this case, the observed data represent a subgroup of participants whose HIV status is more likely to be negative. Clearly, statistical inferences derived from the available data would be unrepresentative of non-responders.

The caveat is that the distinction between MAR and MNAR assumptions cannot be verified with unplanned missingness without follow up with non-responders, i.e. getting more information about the missing values. Obviously, following up non-respondents does not occur in prevention trials. The distinction between MAR and MNAR is important in order to define ignorable missingness.

When data are complete, researchers have to come up with a substantive model (e.g. regression model) in order to explain the data. When data are incomplete, researchers have to model not only the available data, but the missingness as well unless they are willing to assume some ignorability assumption. Ignorable Missingness refers to whether or not the mechanism accounting for the missingness must be explicitly modeled together with the substantive model.(10,3) Often, researchers mistakenly confuse the ignorability concept with the claim that the missing data can be ignored. However, when making statistical inferences the missing data should never be ignored. The difference between ignorable and non-ignorable missingness is whether a separate model for missingness must be included together with the substantive model. Under the ignorability assumption only the substantive model need to be specified (e.g. regression model), while under non-ignorable set-ups joint models for the substantive and missingness models need to be specified using either selection models,(3) pattern-mixture models (3) or shared parameter models.(3)

We can assume ignorable missingness when data are MAR and when the missingness has no bearing on the substantive model parameters.(5) When using likelihood-based or Bayesian estimation techniques MAR and MCAR can reasonably be treated as ignorable (11) which means that no additional information is required about the distribution of the nonresponse.(10) However, when using semi-parametric techniques such as generalized estimating equations (GEE),(12) only the MCAR condition is ignorable. Always, if data are MNAR, the condition is non-ignorable.

POSSIBLE SOLUTIONS TO MISSING DATA

There are several statistical procedures that deal with incomplete data. We introduce a few of them here with relative advantages and disadvantages.

Complete Case Analysis

The most common and straightforward approach to dealing with incomplete data is to omit those subjects with incomplete data from the analysis. This is often the default method of handling incomplete data by statistical procedures in commonly-used statistical software packages, such as Stata,(13) SAS,(14) and SPSS.(15) The advantage of case deletion is that it can be used for any kind of statistical analysis and no special computational methods are required, when data are MCAR this approach may yield results that are unbiased.(16,3) However the disadvantages are loss of power, inefficiency, and possible bias. Reduced sample size may impose limitations on the types of analyses that can be conducted, and may preclude the use of large-sample techniques. In particular, consider data trial with 10 variables and each variable is missing 5% of it values randomly (MCAR). Using case deletion will reduce the data to around 60%, larger data sets and larger rates of missing values can have even bigger impacts (e.g 20 variable and 10% missing values will result in 12% of the data).

Generalized estimating equation (GEE)

For correlated data, generalized estimating equation (GEE),(12) became one of the most used procedures in practice. GEE Procedures are used regularly is large studies when clustering or longitudinal structures are desired or unavoidable. Using this procedure, the researcher specifies a working correlation structure but this structure does not have to hold exactly. This constitutes as a semi-parametric procedure as the model for the data has to be evaluated but the correlations are not of main interest. Unfortunately, GEE of incomplete data is unbiased only under the MCAR assumption. However, an infrequently used extension, weighted GEE,(17) allows missing data under the MAR condition.

Maximum likelihood

Maximum likelihood is a large sample technique looking for the parameter estimates that have the greatest likelihood of producing the observed data, given a specified model. These parameters are called the maximum likelihood estimates (MLE).(18,19,16,3) Maximum likelihood estimation does not require observations to be balanced; individuals may have differing numbers of observations spaced at different intervals. All complete and partially-observed cases contribute to the maximum likelihood estimation of model parameters, and the missing data values are treated as random variables to be averaged over.(20)

Bayesian Estimation and Multiple Imputation

Bayesian estimation techniques use prior information (distribution) together with the likelihood distribution to produce a posterior distribution. The estimates drawn from the posterior distribution takes into account prior knowledge and the distribution of the data.(21,3) Usually this is being done using Markov Chain Monte Carlo (MCMC) estimation which allows the analysis of the data without dropping cases.

Multiple imputation (MI)(2) replaces missing observations with m>1 plausible values to complete multiple alternative completed data sets.(3,4,11) The complete data sets are analyzed individually, and multiple parameter estimates are combined. MI provides the advantage of allowing complete-data analytical routines while accounting for uncertainty of estimates due to imputation. In the past a small number of imputations were considered adequate for efficient parameter estimation,(5) but many more may be needed to improve efficiency.(22-24)

MISSING DATA IN HIV PREVENTION TRIALS

Our review was performed with assistance of the HIV/AIDS Prevention Research Synthesis (PRS) Project at the Centers for Disease Control and Prevention (CDC).(25) This is database of prevention studies maintained by the CDC for monitoring evidence-based HIV behavioral interventions. The review process is conducted using well-established systematic procedures for searching and reviewing the intervention research literature. Our search was based on automated strategies in 4 electronic bibliographic databases (EMBASE, MEDLINE, PsycINFO, and Sociological Abstracts) together with a manual search which involved reviewing approximately 35 journals to identify articles not yet indexed in the electronic databases. More detailed information about the CDC PRS database can be found in the CDC literature.(25)

The PRS cumulative database was searched on June 15, 2010 and all citations that met the following criteria were retrieved.

1. Reports of HIV/STD/HBV/HCV behavioral interventions: Rationale, the interpretation of biological and behavioral interventions differs along multiple dimensions. We chose to exclude biological interventions because the conditions under which data are missing vary considerably from those of behavioral interventions.

2. Based on a randomized control trial (RCT) research design. The RCT is the most rigorous design for testing clinical methods and procedures and findings can be blurred by missing data.

3. Reported a biological outcome. In particular, any sexually transmitted infection/disease endpoint, such as HIV incidence/seroconversion, STD incidence/re-infection, or Hepatitis B or C infection. Biological endpoints in HIV prevention trials avoid self report biases and represent a clinical disease outcome.

4. From 2005 to present. Studies prior to 2005 do not represent the current state of HIV prevention science and the implications for missing data are fewer for these studies.

The search resulted in (n=57) citations that met the inclusion criteria. A reviewer with background in HIV prevention assessed each study and extracted pre-specified needed information (See Table 1). A second reviewer with background in biostatistics assessed a sample of studies and arrived at 100% agreement with the first reviewer. The results of the reviewing process plus descriptive information on the studies were entered into a computer database and are summarized in Table 1.(26-82)

Table 1.

Summary of behavioral HIV prevention trials reporting biological outcomes

Author(s)	Year	Country	Target Pop	Outcome	Min Missing Values	Max Missing Values	Mean Missing Values	Mentioned Missing in Analysis	Main Analysis	Missingness Assumption
CCA
Abou-Saleh et al.(26)	2008	United Kingdom	Injection Drug Users, Users in Treatment	Hepatitis C: blood test 12 months	13.95%	44.23%	25.65%	No	Chi square	N.R.
Artz et al (27)	2005	United States	Clinic Patients, Urban/Inner City, Female	STD: test, Pregnancy: test; 6 months	16.39%	16.39%	16.39%	Yes	Mantel-Haenszel Rate Ratio	N.R.
Becker et al.(28)	2010	Tanzania	Clinic Patients, Pregnancy, Female	HIV: test 9 months	7.49%	61.32%	38.12%	No	ANOVA, f-test, chi square	N.R.
Boyer et al.(29)	2005	United States	Military, Female	STD: test, Pregnancy: test 14 months	10.96%	43.93%	24.39%	No	Multivariate logistic regression, Huber-White sandwich estimator, chi square	N.R.
Brems et al.(30)	2009	United States	Alcohol Users, Users in Treatment	HIV: self-report, STD: test 3-4 months	0%	23.08%	12.59%	No	MANOVA	N.R.
Chacko et al.(31)	2010	United States	Youth and Young Adults, Clinic Patients, HIV negative, Urban, Female, High sexual risk behaviors	STD: test 12 months	17.93%	39.06%	29.99%	No	Multiple logistic regression	N.R.
Corbett et al.(32)	2007	Zimbabwe	HIV negative	HIV: test 3 month	26.90%	69.73%	48.36%	Yes	Standardized Incidence Ratio, Wilcoxon Rank Sum, t-test	N.R.
Crosby et al.(33)	2009	United States	Heterosexual, Black/African American, Male, Young Adult, Clinic Patient, STD diagnosis	STD: chart abstraction 6 month	25.53%	26.40%	25.97%	Yes	Logistic regression, linear regression, sensitivity analysis	N.R.
DiClemente et al.(34)	2009	United States	Female, Urban, Black/ African American, Youth, Clinic Patients	STD: test 12 months	0%	16.95%	10.85%	No	Logistic regression, linear regression	N.R.
Gregson et al.(35)	2007	Zimbabwe	Commercial sex worker clients, community members	HIV: test, STI: self-report 3 years	19.18%	28.31%	23.69%	No	adjusted incidence rate ratio, t-test, coefficient of variation	N.R.
Grimley et al.(36)	2009	United States	Clinic patients, Urban, Lower income/ indigent	STD: test 6 months	24.63%	41.85%	33.24	Yes	Chi square, Fisher exact test, logistic regression	N.R.
Hoke et al.(37)	2007	Madagascar	Female, Commercial sex workers	STD: test 18 months	1.76%	9.71%	5.10%	Yes	Logistic regression	N.R.
Jemmott et al.(38)	2005	United States	Youth, Clinic Patients, Black/African American/Spanish/Hispanic/ Latino, Urban, Female, Low income/indigent	STD: test 12 months	4.26%	14.04%	8.11%	No	Chi square, ANOVA, Poission regression, t-test	N.R.
Kalichman et al.(39)	2005	United States	Clinic Patients	STD: chart abstraction 12 months	6.38%	29.08%	20.48%	Yes	ANOVA, Multinomial logistic regression	N.R.
Koblin et al.(40)	2009	United States	Crack and other substance users, HIV negative, Female, High sexual risk behavior	HIV: test 12 months	10.83%	19.48%	14.64%	No	McNemar discordant pair analysis	N.R.
Lau et al.(41)	2008	China	Males, Homosexual, other high risk sexual behavior	STD: self-report	59.00%	59.00%	59.00%	Yes	Chi square	N.R.
Lau et al.(42)	2010	China	Adult, Truck Drivers, Male, Commercial sex worker clients, other high risk sexual behaviors	STD: self-report, HIV: test 6 months	3.90%	4.55%	4.15%	No	Chi square	N.R.
Low et al.(43)	2006	United Kingdom	Clinic patients, STD diagnosis, sex partners of those with other high risk	STD: test 6 weeks	0%	30.88%	20.57%	Yes	Regression models	N.R.
Matovu et al.(44)	2007	Uganda	Uncircumcised, HIV negative, Male, High risk	STD: test 24 month	7.97%	60.55%	26.15%	No		N.R.
McNulty et al.(45)	2008	United Kingdom	Service Providers	STD: test 10 months	0%	9.52%	6.94%	Yes	Logarithmic link function,	N.R.
Metcalf et al.(46)	2005	United States	Clinic patients, HIV negative	STD: test 12 months	1.26%	29.04%	14.02%	Yes	Relative Risk	N.R.
Morisky et al.(47)	2005	Philippines	Female, Commercial sex worker	STD: chart abstraction 2 years				No	Chi square, ANOVA, regression models	N.R.
Ngugi et al.(48)	2007	Kenya	HIV negative, Female, Commercial sex worker	HIV: test, STD: test 12 months				Yes	Wilcoxon signed rank test, chi square	N.R.
Patterson et al.(49)	2008	Mexico	HIV negative, High risk residential area, commercial sex worker, other high risk sexual behavior	HIV: test, STD: test 6 months				No	Repeated measures ANCOVA, Cohen d test, chi square, Poisson regression	N.R.
Peipert et al.(50)	2008	United States	Female, Heterosexual, High Risk	STD: test, Pregnancy: test 24 month	38.97%	50.00%	44.49%	No	Logistic regression, log rank statistic	N.R.
Petersen et al.(51)	2007	United States	Clinic patients, Female, High sexual risk behavior	STD: test, Pregnancy: test 12 month	3.53%	3.53%	3.53%	Yes	McNemar's chi square	N.R.
Pronyk et al.(52)	2006	Southern African (Limpopo province)	Rural, General Population, low income/ indigent	HIV: test 2 years	.93%	42.29%	19.78%	Yes	Coefficient of variance	N.R.
Ross et al.(53)	2007	Tanzania	Youth, Rural residence	HIV: test, STD: test, Pregnancy: test 3 years	26.37%	27.64%	27.01%	Yes	Unadjusted risk ratio, ANOVA, t-statistic, logisitic and Poisson regression	N.R.
Roye et al.(54)	2006	United States	Youth, HIV negative, Black/African American/Spanish/Hispanic/ Latino, Urban, Females, High risk sexual behavior	Chlamydia: test, Other STD: self-report 12 months	27.16%	64.20%	41.14%	No	Chi square, logistic regression, t-test	N.R.
Samet et al.(55)	2008	Russia	Drug Users in Treatment	HIV: test 6 months	10.50%	20.44%	15.47%	No	Logistic regression, median regression, chi square	N.R.
Scholes et al.(56)	2007	United States	Young Adult, males	STD: test	92.18%	99.30%	97.24%	No		N.R.
Semaan et al.(57)	2009	United States	Adult, crack users, injection drug users, other substance users, clinic patients, HIV negative, heterosexuals	STD: test 12 months				No	Unadjusted odds ratio, multivariate logistic regression, multiple logistic regression	N.R.
Spielberg et al.(58)	2005	United States	Injection drug users, high risk behavior	HIV: test	77.16%	97.08%	87.76%	No	Multiple logistic regression, Wald test, univariate logistic model; chi square	N.R.
Steiner et al.(59)	2006	Jamaica	Clinic patients, male	STD: test 6 months	38.46%	41.26%	39.86%	Yes	Wilcoxon rank sum test	N.R.
Thurman et al.(60)	2008	United States	STD diagnosis, Black or African American, Spanish/Hispanic/ Latino, Female	HIV: test, STD: test 12 months	0%	15.38%	5.01%	No	Pearson's chi square, multivariate logistic regression analysis	N.R.
Trenholm et al.(61)	2008	United States	Youth, Black or African American, Spanish/Hispanic/ Latino, White, Rural, Urban, Low income/ indigent	STD: self-report, Pregnancy: self-report 42-78 months	35%	43%	39%	Yes	Weighted regression model	N.R.
Verhoeven et al.(62)	2005	Belgium	Service Providers	STD: test	20%	33.33%	26.67%	Yes	T-test, Chi square, ANOVA, Intracluster correlation coefficient (ICC)	N.R.
Wechsberg et al.(63)	2006	Southern Africa (Pretoria)	Crack users, people of color, females, commercial sex workers, other high sexual risk behaviors	STD- self-report				No	Bivariate analysis, logistic regression analysis; McNemar; t-test;	N.R.
Wechsberg et al.(64)	2008	South Africa	Alcohol users, other substance users, people of color, females, low income/indigent	STD: test 1 month				Yes	T-test, ANCOVA	N.R.
Wolitski et al.(65)	2005	United States	HIV positive, Male, Bisexual and Homosexual	STD: test 6 months	9.20%	50.92%	23.03%	Yes	Chi square, logistic regression for dichotmous data, cumulative logit models for ordinal data, odds ratio (OR),	N.R.
Wu et al.(66)	2005	China	High risk	STD: test 1 year				No	Multivariate analysis	N.R.
Wu et al.(67)	2007	China	Injection drug users	Hepatitis: test, HIV: test 12 months	87.61%	87.61%	87.61%	Yes	Chi square, t-test	N.R.
GEE
Jemmott et al.(68)	2007	United States	Clinic Patients, Black/ African American, Urban, Female	STD: test 12 months	5.65%	17.28%	13.08%	Yes	GEE, binomial-error model with logit link functions, Poisson error models with log-link functions, Wald chi square test	N.R.
Kissinger et al.(69)	2005	United States	Clinic patients, STD diagnosis, Male, Heterosexual, High risk sexual behavior	STD: test 1 month	21.19%	21.19%	21.19%	No	Bivariate GEE, Multivariate GEE	N.R.
Latkin et al.(70)	2009	United States and Thailand	Injection Drug Users, Users out of treatment, HIV negative, Urban, Living in a High Risk area, Sex partners of IDU	HIV: test 24 months	17%	18%	17.5%	No	GEE modeling methods	N.R.
Lutchers et al.(71)	2008	Kenya	Adult, clinic patients, HIV positive	STD: test 12 months	2.99%	15.38%	9.19%	No	Bivariate cross-sectional logistic regression model, GEE	N.R.
Sherman et al.(72)	2008	Thailand	Young adults, substance users, sex partners of those with other high risk	Hepatitis: test, HIV: test, STD: test 12 months	4.85%	13.48%	9.98%	No	Logistic regression, GEE, Wald test,	N.R.
Stephenson et al.(73)	2008	United Kingdom	Youth, Rural and urban, high sexual risk behavior	STD: self-report, Pregnancy: self-report 7 years	6.64%	58.09%	23.66%	Yes	GEE, logistic regression model	N.R.
Wilson et al.(74)	2009	United States	Clinic patients with STD diagnosis, People of color, living in high risk area, urban, sex partners of those with other high risk	STD: test 6 months	3.71%	13.49%	7.89%	Yes	multiple logistic regression model; GEE	N.R.
Wingood et al.(75)	2006	United States	Youth, Black or African American, Other high risk sexual behavior	STD: test 12 months	10.69%	16.44%	13.02%	Yes	T-test and chi square, logistic regression GEE, linear regression GEE	N.R.
ML
Carey et al.(76)	2010	United States	Clinic Patients, High Sexual Risk Behavior	STD: test 12 months	0%	47.60%	27.97%	Yes	Generalized multilevel models using logit link, GEE, linear mixed model	N.R.
Garfein et al.(77)	2007	United States	Young Adults, Injection Drug Users, HIV negative	Hepatitis: test, HIV: test 6 months	22.74%	39.01%	29.94%	Yes	negative binomial fit of repeated count data; zero-inflated negative binomial model; cumulative logit models for repeated ordinal data; Poisson regression	N.R.
Jeweks et al.(78)	2008	South Africa	Rural, Youth and young adults	HIV: test, STD: test, Pregnancy: self-report 24 months	21.40%	28.08%	24.16%	Yes	Fitting generalizes linear mixed models, GEE model	N.R.
Kelly et al.(79)	2006	Bulgaria	Low income/indigent, Male, Social group leaders	STD: test 12 months	0%	10.27%	3.81%	Yes	Mixed effects linear regression, logistic regression	N.R.
Kershaw et al.(80)	2009	United States	Young adults, Clinic patients, Pregnancy, Female	STD: test, Pregnancy: self-report 12 months	9.75%	28.06%	16.33%	Yes	random effects regression, post hoc analysis, generalized linear mixed models, logistic regression	N.R.
Marion et al.(81)	2009	United States	STD diagnosis, Black/ African American, High risk area, Female, Low income/ indigent	STD: test 15 months	23.53%	51.74%	38.75%	Yes	Multilevel random effects model	N.R.
Tebb et al.(82)	2005	United States	Youth, Clinic patients, Male, High sexual risk behavior	STD: test 18 months				No	Repeated measures ANCOVA, Mixed effects model analysis, ANOVA, f-test	N.R.

N.R. – None reported

CCA – Complete case analysis

GEE – Generalized estimating equations

ML – Maximum likelihood

The trials were conducted all over the world with regions/countries ranging from the United States and Mexico in North America, Jamaica in Central America, United Kingdom and Belgium in Western Europe, Russia and Bulgaria in Eastern Europe, Thailand, Philippines and China in Asia and several countries in Sub-Saharan Africa such as Tanzania, Zimbabwe, South Africa, Kenya, Uganda and Madagascar.

All of the trials had some level of missing values. Although not all studies reported them in the same manner, we found that the averaged missing values per study ranged between 3% to 97%. Averaging over all studies the percent of missing values was 26% (median 23%). In this (missing values) sample, values greater then 50% were considered outliers. We had four outliers in our sample. We extracted the information about the missing data levels from the participant flow charts reported in each trial. It is clear from the range of cell sizes that many studies varied in available data for different analyses. We speculate that the majority of missing values are due to missing outcomes, but cannot know it for certain for all studies due to the differences in reporting. However, due to the fact both types of missing values may bias the results we do not distinguish between them.

None (0%) of the studies reported any information on what missing data assumptions were used in their analyses. In most cases this implies that only analyses under the MCAR the results will be unbiased. The majority of studies (42, 74%) used complete case analysis (CCA) and reduced the sample only for those with complete data (Table 1, references 26-67). Eight studies (14%) used some variation of GEE analysis which used the whole data (observed and missing) but is potentially biased under MAR assumption (Table 1, references 68-75). There are few studies that used maximum likelihood estimation (7, 12%) and therefore their results will be unbiased under the MAR assumption (Table 1, references 76-82). Collins et al.(21) showed that if one collects enough auxiliary information, one can get close to the MAR assumption. Assuming all studies collected enough information so that the MAR assumption is reasonable, and since we know that MCAR rarely happens in practice, only 7 studies out of 57 (12%) had some of their analyses done so we can expect them to be unbiased.

The studies reviewed that used complete case analysis (n=42, 74%; references 26-67) did so for many different types of analyses. For example, parametric tests such as t-test, F-test, and chi-squared tests; non-parametric tests such as Rank tests; regression analyses such as linear regression, multiple regression, logistic regression, Poisson and binomial regressions; Analysis of variance (ANOVA) with its derivatives MANOVA and ANCOVA. All these analyses are in danger of being biased under MAR and MNAR, and have a chance of being unbiased under MCAR.

The studies using GEE in our review (n=8, 14%; references 68-75) reported conventional (unweighted) GEE, which implies possible biased results unless missing data were missing completely at random (MCAR).

Studies using maximum likelihood estimation (n=7, 12%; references 76-82) used Generalized multilevel models and linear mixed models. These procedures are also called generalized linear mixed model, mixed effect linear regression, random effect regression, and multilevel random effect model. These procedures are expected to be unbiased under both MAR and MCAR.

Bayesian and multiple imputation procedures are well equipped to deal with incomplete data. Unfortunately none of the trials we reviewed used these procedures. Both of these procedures (with adequate modeling) can be unbiased under MAR, MCAR and MNAR scenarios.

RECOMMENDATIONS

With any applied research and in particular RCTs, the best thing to do with regard to missing data is to avoid it. The second best thing is to plan for it, understand it and address it with appropriate modeling techniques. (1) Plan for missingness. Researchers should anticipate unavoidable missing data. Variables determined to relate to non-response should be identified and measured. (2) Minimize nonresponse. Incorporate procedures into the study plan to reduce missed assessments and ensure regular review of data. (3) Determine the mechanism of missingness. Researchers should test the assumption of MCAR, and carefully consider the plausibility of ignorable missingness. (4) Apply appropriate techniques. Techniques such as ML, GEE, Bayesian, and MI are effective when applied appropriately under proper assumptions, but will provide misleading results when implemented incorrectly. (5) Report missingness and techniques used. Researchers should fully describe missing data methods; the incomplete data structure, missing data assumptions, and the techniques selected to handle them. (6) Sensitivity analysis. Researchers should analyze their data under different missing data assumptions and report the differences the missing data assumptions make on conclusions.

CONCLUSIONS

In this review, we examined the past five years of behavioral HIV prevention RCTs reporting biological outcomes. We found that all the reviewed publications had varying degrees of missing data, and yet none reported assumptions regarding the management of missing data. Most studies used statistical methods which are most probably biased to most common missing data assumptions. In particular, most studies reviewed used complete case analysis (n=42, 74%; references 26-67), eight studies (14%) used some GEE type procedures,(68-75) seven studies (12%) used maximum likelihood procedures,(76-82) while none used Bayesian or multiple imputation procedures. Although we cannot comment on the direction and magnitude of the bias, the fact that approximately 88% (74%+14%) of the studies reported possibly biased results (under the MAR assumption) is alarming. We touched on some available methodology more appropriate to deal with incomplete data and gave some general recommendations of how to deal with incomplete data.

The idea that missing data can impact the results of clinical trials is not new. Researchers in many fields have shown the risk of ignoring the missing data complications.(3,5,11,16) Recently there were several reviews which examined the problem from different directions. One study, for example, reports on the use and abuse of missing data procedures in longitudinal data settings in developmental psychology,(83) while another discuss issues of noncompliance in randomized trials.(84)

We hope researchers will attend more closely to the missing data in HIV prevention trials. Methods for incomplete data are available and offer the potential for unbiased and efficient estimation. Not thinking of the missing data problem does not mean the problem goes away. Leaving the problem to the pre-specified statistical software will, in most cases, reduce the data to complete set, an unsatisfactory solution to missing data.

We entreat researchers to disclose missing data rates, missing data assumptions, and the methods used to address them in published work. We hope that this practice will promote the application of proper techniques and a greater understanding of the methodological and statistical issues involved in handling incomplete data.