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Essentials of Biostatistics

Biostatistical methods have gained importance in medical and health research because of the exactitude they provide in the results and conclusions. Many of our readers do not feel comfortable with these methods because the focus of their training is medicine, rightly so, and not research methodology. In order to help our readers with the basics of statistical methods, we are starting a series of articles. This series does not assume any prior know- ledge of statistics and starts from scratch. Subsequent articles of the series are built up on the material already presented in the previous articles. I hope that our readers will find the series useful. The authors would welcome any comments. These may be directly communicated to Prof A. Indrayan, Division of Biostatistics and Medical Informatics, University College of Medical Sciences, Dilshad Garden, Delhi 110 095, India. E-mail: indrayan@ucms.ernet.in.

H.P.S. Sachdev

Indian Pediatrics 1999; 36:476-483 

1. Medical Uncertainties


A. Indrayan
L. Satyanarayana

From the Division of Biostatistics and Medical Informatics, University College of Medical Sciences, Dilshad Garden, Delhi 110 095, India and *Institute of Cytology and Preventive Oncology, Maulana Azad Medical College Campus, New Delhi I/O 002, India.

Reprint requests: Dr. A. Indrayan, Professor of Bio- statistics, Division of Biostatistics and Medical Informatics, University College of Medical Sciences, Dilshad Garden, Delhi 110 095, India.

Health greatly differs from person to per- son and in a person from time to time. This is more prominent in children than in adults. We all know that measurements such as heart rate, hemoglobin level, birth weight and arm circumference, differ from child to child even when they are in perfect health. Variations occur not only between children but also within a child from time to time. In the face of such variations, it is not surprising that response to a stimulus such as a drug can seldom be exactly reproduced even in the same child. Uncertainties resulting from these variations are essential feature of the practice of medicine and deserve to be recognized.

Biostatistics is the science of management of uncertainties in health and medicine. As we proceed, we will demonstrate how much statistical pediatric practice is due to these un- certainties, and what can be done to delineate and minimize the role of uncertainties and thus increase the efficiency of medical decisions. Our attempt in Section 1.1 is to highlight statistical aspects of day to day clinical practice. But it is in the case of medical research that many statistical subtle- ties emerge. Some of these are described in Section 1.2. Biostatistics is many times associated with community health and epidemiology. This association is indeed strong. While epidemiological perspective will be visible throughout this series, some aspects of health planning and evaluation are specifically discussed in Section 1.3. Management of un- certainties is given in Section 104.

Our explanation of statistics would not be complete without describing two usages of the term. The meaning described in the preceding paragraph is valid when the term is used as a singular. More common use however is in the form of plural. Numerical information is called statistics. It is in this sense that the media use this term while talking of football statistics or income statistics and even health statistics.

Biostatistics these days is a highly developed science. It is not possible to include all that is known, nor even all that is important, in this series. Nonetheless, our attempt in this series is to cover most of what. is commonly used in pediatric care and research.

1.1 Uncertainties in Medical Care

The most common source of uncertainty in medicine is the natural biologic variability between and within individuals. Variations between laboratories, instruments, observers, etc., further aggravate these uncertainties. Other sources of uncertainties are incomplete information of the patient, lack of medical knowledge, etc. We first discuss the sources of variability and then the other sources of uncertainty.

Sources of Variability

Body temperature and birth weight are examples of measurements that a pediatrician uses nearly every day. These are evaluated against normals or reference values. The need to define and use normals of such measurements arise from the realization that variations exist and it is perfectly normal for variations to occur in healthy subjects. The following is a list of various sources of variability though this is perhaps restricted to only those that have profound effect.

Biological variability: Variables such as age, sex, birth order, height and weight are some of those biological factors which occur naturally in a health setup. Health parameters of children are quite different from those of adults. Anatomical, physiological, biochemical-al-most all kinds of measurements-differ from age to age. Thus, level such as hemoglobin seen in subjects of age, say, 10 years can hardly be applied to the subjects of age one month.

Environmental variability: While our anatomy and physiology are traceable mostly to hereditary factors, the pathology is mostly caused by the environment. Nutrition is probably the most dominant factor controlling body's defence mechanism. Pollution is now acquiring center stage in health scenario with predilection of grim consequences. Flies, mosquitoes and rodents carry deadly disease. Many gastrointestinal disorders are water borne.

Sampling fluctuations: Much of what is known in medicine today is accumulation of experience. This empiricism is basic to most medical research. We dilate this aspect a little later but mention at this stage that experience is always gained on a fraction of subjects and all subjects are never observed. The know- ledge that chills, fever and splenomegaly are common in malaria is based on what has been observed in cases over a period. But the cases actually observed or studied never comprise all that occur in the world. Only a fraction of these cases, called sample, are studied. The totality of all subjects or units from which a sample is selected is called population in statistical terminology. This also is the target group to which the findings would ultimately apply. We may have population of school going children, population of mentally retarded children, population of blood samples, or simply population of persons residing in an area. One feature of samples is that they tend to provide different picture in repeated sampling. This is called sampling fluctuation or sampling error. This aspect will be discussed in a future article. Our objective of mentioning all this here is that sampling fluctuations by themselves are a source of uncertainty. A clinician constantly deals with biopsies and samples of blood, urine and stool. Sampling fluctuation is one of the many reasons that repeat investigations sometimes become necessary.

Observer variability: Two pediatricians are likely to differ in asessing the severity of ill- ness in febrile children. Barring some clear- cut cases, clinicians tend to differ in their assessment of the same subject. Some clinicians are more skillful than others in extracting information from the patient and in collating pieces of information into a solid diagnostic evidence.

Variability in treatment strategies: Physician is not only an observer but more importantly a healer. Variability in treatment strategies of different physicians is very wide, and they accordingly affect the putcomes. Some emphasize on life style changes while others depend primarily on drugs. Choice of drugs and dosages too differ from physician to physician. Instrument or laboratory variability: Weight of children on beam balance and on spring balance may differ. Apart from such simple cases, laboratories too tend to differ in their results on the split of the same sample. Send two parts of the same blood sample to two different laboratories for hemogram and be pre- pared to receive different reports! The difference could be genuine due to sampling fluctuation or could be due to difference in chemicals, reagents or techniques in the two laboratories. Above all, the human element in the two laboratories could be very different. Differences occur despite standardization though, in some cases, even the standard could differ between laboratories.

Other Sources of Uncertainties

Incomplete information: Even while interviewing a child's parent, it cannot be ensured that the person is not forgetting or not intentionally suppressing part of the information. Sometimes the patient is in coma and sometimes the required investigation facility is not available in the hospital. Thus the information remains incomplete in many cases despite best efforts. Clinicians are required to take decisions on intervention based upon such incomplete information.

Imperfect tools: A clinician also uses various kinds of tools during the course of his practice. Examples are signs-symptoms syndrome, anthropometric measurements, laboratory and radiological investigations and interventions in the form of treatment or surgery. Besides his own skills in making optimum use of what is available, the efficiency of a clinician also depends on the validity and reliability of the tools used by him. Validity is the ability to correctly measure what a tool is supposed to measure, and reliability is consistency in repeated use. These are seldom perfect and add to the uncertainty spectrum.

Others: The other sources of uncertainties are inadequate medical knowledge for some .conditions, inability to recall all that is known while confronting a patient, poor compliance of regimen by the patient, etc.

The objective of describing sources of uncertainty in such a detail is to sensitize the reader about unfailing presence of these sources in practically all medical situations. Sometimes they become so profound that medicine transgresses to an art from a science. Many clinicians deal with these uncertainties in their own subjective ways and some are very successful. But most are not as skillful. To restore semblance of science, we need to find means to measure these uncertainties, to evaluate their impact and, of course, to keep this impact under control. All these aspects are primarily attributed to the domain of statistics and is the subject matter of the articles in this series. The main strategy followed by statistical methods is to separate trend from noise-like fluctuations. These trends can be safely used to give expected results in substantial portion of cases.

1.2 Uncertainties in Medical Research

Statistics is not merely measurement of uncertainties. It is concerned with their control also. Need to control them is more conspicuous in a research setup than in every day practice.

Empiricism in Medical Research

Apart from surgeries, medical research can be divided into three broad categories. The first consists of clinical trials, which are done to investigate new modes of therapy. Research on new diagnostic procedures also come under this category. An example is a trial on "surfactant" in preterm babies with respiratory distress syndrome( I). Immunogloblins in the treatment of childhood in- fections(2), zinc in diarrhea(3) and role of vitamin A in decreasing morbidity in childhood(4) are other examples of pediatric research. As stated earlier, variations between and within subjects occur due to a large number of factors and it is quite often not possible to take full care of all of them while conducting such trials. Efforts are made to conduct these trials in controlled conditions so that the influence of extraneous factors is minimized, if not ruled out. Also, these are conducted on sufficiently large number of patients so that a trend, if any, could be successfully detected.

The second kind of medical research is based on laboratory experiments. These are often done on animals and we exclude their discussion in this series.

The third type of medical research is mostly epidemiological in nature. In this kind of research, associations or cause-effect type of relationships between etiologic factors and outcomes are investigated. Research on factors causing childhood diarrhea, neonatal sepsis and other infections in some but not in others are examples of this type. This type of research also helps to understand the mechanism involved. The relationship under such investigation is influenced even more by various sources of uncertainty and thus the conclusion requires accumulation of experience on larger number of cases. Thus, empiricism is a sine-qua-non feature of this kind of research. Statistical methods again are needed to separate clear- signals from chance fluctuations.

Elements of Minimizing the Impact of

Biological variations and other sources of uncertainty would definitely occur but investigations can be designed in a manner that their influence on decisions is minimized. Details are given in Article 2 of this series. Briefly, the following steps are taken. A control group is included where needed. A comparative group with "no treatment" or "existing treatment" is called a control. The sample of subjects for an investigation is chosen such that the subjects truly represent the whole spectrum of the target "population". Among the precautions that need to be some- times taken is matching of the subjects in various groups so that the known sources of variability do not much influence the outcome. An alternative is randomization. This is achieved by random allocation of subjects to different groups. The techniques of observation and measurement are standardized and uniformly implemented to minimize the influence of different factors.

Thus the general principles to minimize the impact of uncertainties are (i) inclusion of a control group where appropriate, (ii) proper selection of subjects, (iii) matching or randomization, and (iv) use of standardized methods.

Analysis Versus Synthesis

Because of the uncertainties involved at every stage of medical investigations, the conclusions can seldom be drawn in a straight for- ward manner. It is generally necessary that the data are collated in the form of tables, charts or diagrams. Some summary measures are also chosen and computed to draw inferences. Because of the inherent variations in the data and because only a sample of the subjects is investigated rather than the entire "population", some special methods are required to draw valid conclusions. These methods are collectively called techniques of statistical inference. These techniques depend on the type of questions asked, on the design of the study, on the kinds of measurements used, on the number of groups investigated, on the number of primary focus and would be discussed in various articles of this series. All data processing activities beginning from theirexploration and ending with drawing inferences are generically called statistical analysis. The role of this analysis is to help draw valid and reliable conclusions. The term analysis probably comes from the fact that the total variability in the data is broken into its various components, thus helping to sieve clear signals or trends from the fluctuations.

While statistical analysis is an essential step in empirical research, the importance of synthesis is sometimes overlooked. This is the process of combining and reconciling varied and sometimes conflicting evidence. A major scientific activity is to synthesize these varying results and arrive at a consensus. Discussion part of most articles published in medical journals try to do such synthesis. The objective of most review articles is basically to present a holistic view after reconciling the varying results in different studies. In addition are the techniques such as meta analysis(5) which seek to combine evidence from different studies. We will not have occasion to discuss the synthesis methods in this series but we do want to emphasize that these methods too are primarily statistical in nature and are important for medical research.

1.3 Uncertainties in Health Planning and Evaluation

Most of the discussion so far is focused on clinical aspects. But medical care is just one component of the health services spectrum. "An ounce of prevention is better than a pound of cure". At individual level the prevention is in terms of steps such as immunization and improved personal hygiene. Health education is basic to all prevention and is much more efficiently done at community level than at individual level. Provision of facilities such as primary health centers, maternal and child care centers, hospitals and doctors, medicines and other supplies, on one hand; and environmental sanitation, pollution control and supply of safe water for drinking on the other; are the components of health care spectrum. All these are geared to meet the specific needs of the population. These needs greatly vary from population to population, from area to area and from time to time, depending upon the perceived need, level of infrastructure and urgency. A predominantly pediatric population with high prevalence of infectious disease re- quires entirely different services than aging population with mostly chronic ailments. These variations commandeer use of statistical methods to. the process of health planning.

Health Situation Analysis

Quality and type of health services required for a community depend definitely on the size of the community but also on its age-sex structure, extent of prevalence of various conditions of health and ill-health in different sections of the community, culture, traditions, perception, socio-economic status of the population, the existing infrastructure, etc. Thus, all these are needed to be properly assessed in order to prepare an adequate plan. This assessment is generically called health situation analysis. This analysis is the first step in planning of the services. Then a program is drawn and implemented. The next is its evaluation.

Evaluation of Health Programs

Evaluation of a health program has two distinct components. First is assessing the ex- tent to which objectives of the program have been achieved. This requires that the objectives are in measurable format If the objective is to control nutritional blindness, it is always desirable to state the magnitude existing at the time of the launch of the program and the level of reduction expected at the end of the pro- gram or in each year of its implementation. If this level is mentioned for each age, sex, urban/rural area and socio-economic group then the task of implementers and of evaluators becomes simpler. Second and more important component of evaluation is to identify the factors responsible for that kind of achievement-good or bad-and to measure relative importance of these factors. Thus, the evaluation might reveal that the objectives were unrealistic considering prevalent health situation and considering the program inputs. Supplies may be adequate but the population may lack capacity to absorb due to cultural or economic barriers. Among other factors which could contribute to partial failure are errors in identification of the target beneficiaries, inadequate or ineffective supervision and lack of expertise or motivation. Thus evaluation is the appraisal of the impact as well as of the process.

Just as any other investigation, evaluation too passes through various stages each of which contains an element of uncertainty. Because of inter- and intra-individual variations in receivers as well as in providers, some segments could be benefited more than the others despite equal allocation of resources. The tools to implement the program are never perfect. Supplies may be impeded due to 11 variety to bottle necks in the pathway such as in. storage and transport. Some officials are more motivated than others and work better despite less supplies.

1.4 Management of Uncertainties

Management in any sphere is 'a complex process, more so if it concerns with phenomenon such as uncertainties. As already stated, uncertainties in most medical set-ups are generally intrinsic -and can seldom be eliminated. But their impact on medical decisions can certainly be minimized and it can be fairly ensured that the likelihood of correct decisions is high and of wrong decision under control. In Section 1.2, we briefly describe some elementary methods to minimize the impact of uncertainties on conclusions of a research investigation. This minimization is indeed a challenge in all set-ups: clinical practice, community health care and medical research. Measurement and consequent quantification is a definite help. This can lead to mathematics, perhaps intricate calculations, but our effort in this series is to describe the methods without using calculus. Real life examples, some of which are picked up from the literature, should provide further help in appreciating the medical significance of these methods.

The process to keep a check on the impact of uncertainties on decisions begins from the stage of conceptualizing or encountering a problem. Identification of the characteristics that need to be assessed; definitions to be used; methods of observation, investigation and measurements to be adopted; methods of analysis and of interpretation; all are important. We devote many of the subsequent articles to these aspects. These include the following:

  • Designs for research investigations, so that the conclusions remain focused on the questions proposed to be investigated. Methods of sampling and tools of data collection.

  • Numerical and graphic methods to describe variation in data. These help to understand the salient features of data and to assess the magnitude of variation.

  • The nature of the reference values so commonly used in medical practice, measurement of uncertainty in terms of probability, and assessment of validity of medical tests.

  • The need and rationale of confidence intervals and tests of statistical significance (such as "t" and chi-square) in view of the sampling fluctuations. These methods as- sign probabilities to various types of right and wrong decisions based on samples and help us to draw conclusions.

  • Methods to take decisions despite the presence of. uncertainties, particularly with regard to assessing that (i) difference between samples from two or more groups is real or has arisen due to chance, and the assessment of the magnitude of difference in terms of relative risk and odds ratio; and (ii) whether or not relationships between two or more variables really exist and if yes, the nature of relationship and measurement of its magnitude.

  • Elements of more complex statistical methods such as multivariate analysis of variance, cluster analysis, and factor analysis. Only the basic features of these methods will be discussed. The objective is to describe medical situations where such methods can be advantageously used.

  • Methods to assess quality, not only of medical care but also of statistical tools and data.

  • Situations where statistical fallacies can arise. Cautions in presentation, analysis and interpretation of data are advised.

The sequence of presentation, thus, is generally the same in which medical studies are planned and carried out. No knowledge of statistics is assumed, and we start from a scratch. Only high school level algebra will be enough to understand the text.



1. Long W, Corbet A, Cotton R, Courtney S, McGuiness G, Walter D, et ai. A controlled trial of synthetic surfactant in infants weighing 1250g or more with respiratory distress syndrome. N Engl J Med 1991; 325: 1696- 1703.

2. Jenson JB, Pollck B. Meta-analyses of the effectiveness of intravenous immunoglobin for prevention and treatment of neonatal sepsis. Pediatrics 1997; 99: e2.

3. Roy SK, Tomkins AM, Akramyzzamas SM, Behrens RH, Haider R, Mahalanobis D, et at. Randomized control trial of zinc supplementation in malnourished Bangladeshi children with acute diarrhea. Arch Dis Child 1997; 77: 196-200.

4. Donnen P, Dramaix M, Brasseur D, Bitwe R, Vertanges F, Hennart P. Randomized placebo controlled clinical trial of the effect of a single high dose or daily low doses of vitamin A on the morbidity of hospitalized malnourished children. Am J Clin Nutr 1998; 68: 1254-1260.

5. Liberati A. Meta-analysis: Statistical alchemy for the 21st Century: Discussion. J Clin Epidemiol1995; 48: 81-86.


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