Biomaterial Database

Confidence intervals for weighted proportions. 1994

J L Waller, and C L Addy, and K L Jackson, and C Z Garrison

Department of Epidemiology and Biostatistics, University of South Carolina, Columbia 29208.

We investigate methods for the construction of confidence intervals for a proportion in a stratified two-stage sampling design with few events occurring in a small number of large, unequal size strata. The critical aspect is the incorporation of the weighting scheme into the construction of a single overall confidence interval. With small numbers of events, the binomial based methods may be inadequate since the normal approximation is not valid. Computer simulations compare coverage probability and bias for five methods of obtaining confidence intervals for proportions by combining: (1) binomial variances; (2) confidence intervals based on the F-distribution approximation to the cumulative binomial; (3) the binomial variance method with exact confidence limits when a zero prevalence occurs in any stratum; (4) confidence intervals based on the F-distribution using a rescaling factor; and (5) the binomial variance method with exact confidence limits using a rescaling factor. The method that performs best in terms of coverage probability is the combination of stratum specific confidence intervals based on the F-distribution using a rescaling factor. The methods involving the binomial variance tend to be negatively biased and the methods based on the F-distribution tend to be positively biased. Application of these methods with data from a study of adolescent depression that employs a stratified two-stage sampling design is consistent with these results.

UI	MeSH Term	Description	Entries
D008297	Male		Males
D003198	Computer Simulation	Computer-based representation of physical systems and phenomena such as chemical processes.	Computational Modeling,Computational Modelling,Computer Models,In silico Modeling,In silico Models,In silico Simulation,Models, Computer,Computerized Models,Computer Model,Computer Simulations,Computerized Model,In silico Model,Model, Computer,Model, Computerized,Model, In silico,Modeling, Computational,Modeling, In silico,Modelling, Computational,Simulation, Computer,Simulation, In silico,Simulations, Computer
D003866	Depressive Disorder	An affective disorder manifested by either a dysphoric mood or loss of interest or pleasure in usual activities. The mood disturbance is prominent and relatively persistent.	Depression, Endogenous,Depression, Neurotic,Depression, Unipolar,Depressive Syndrome,Melancholia,Neurosis, Depressive,Unipolar Depression,Depressions, Endogenous,Depressions, Neurotic,Depressions, Unipolar,Depressive Disorders,Depressive Neuroses,Depressive Neurosis,Depressive Syndromes,Disorder, Depressive,Disorders, Depressive,Endogenous Depression,Endogenous Depressions,Melancholias,Neuroses, Depressive,Neurotic Depression,Neurotic Depressions,Syndrome, Depressive,Syndromes, Depressive,Unipolar Depressions
D005260	Female		Females
D006801	Humans	Members of the species Homo sapiens.	Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000293	Adolescent	A person 13 to 18 years of age.	Adolescence,Youth,Adolescents,Adolescents, Female,Adolescents, Male,Teenagers,Teens,Adolescent, Female,Adolescent, Male,Female Adolescent,Female Adolescents,Male Adolescent,Male Adolescents,Teen,Teenager,Youths
D015982	Bias	Any deviation of results or inferences from the truth, or processes leading to such deviation. Bias can result from several sources: one-sided or systematic variations in measurement from the true value (systematic error); flaws in study design; deviation of inferences, interpretations, or analyses based on flawed data or data collection; etc. There is no sense of prejudice or subjectivity implied in the assessment of bias under these conditions.	Aggregation Bias,Bias, Aggregation,Bias, Ecological,Bias, Statistical,Bias, Systematic,Ecological Bias,Outcome Measurement Errors,Statistical Bias,Systematic Bias,Bias, Epidemiologic,Biases,Biases, Ecological,Biases, Statistical,Ecological Biases,Ecological Fallacies,Ecological Fallacy,Epidemiologic Biases,Experimental Bias,Fallacies, Ecological,Fallacy, Ecological,Scientific Bias,Statistical Biases,Truncation Bias,Truncation Biases,Bias, Experimental,Bias, Scientific,Bias, Truncation,Biase, Epidemiologic,Biases, Epidemiologic,Biases, Truncation,Epidemiologic Biase,Error, Outcome Measurement,Errors, Outcome Measurement,Outcome Measurement Error
D015983	Selection Bias	The introduction of error due to systematic differences in the characteristics between those selected and those not selected for a given study. In sampling bias, error is the result of failure to ensure that all members of the reference population have a known chance of selection in the sample.	Bias, Selection,Sampling Bias,Sampling Biases,Sampling Error,Selection Biases,Bias, Sampling,Biases, Sampling,Biases, Selection,Error, Sampling,Errors, Sampling,Sampling Errors
D015995	Prevalence	The total number of cases of a given disease in a specified population at a designated time. It is differentiated from INCIDENCE, which refers to the number of new cases in the population at a given time.	Period Prevalence,Point Prevalence,Period Prevalences,Point Prevalences,Prevalence, Period,Prevalence, Point,Prevalences
D016001	Confidence Intervals	A range of values for a variable of interest, e.g., a rate, constructed so that this range has a specified probability of including the true value of the variable.	Confidence Interval,Interval, Confidence,Intervals, Confidence